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Make anthem axiomatization more consistent

This commit is contained in:
Patrick Lühne 2019-11-02 05:06:55 +01:00
parent e382058c2d
commit 228b2032f7
Signed by: patrick
GPG Key ID: 05F3611E97A70ABF
1 changed files with 8 additions and 8 deletions
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16
src/tptp_preamble_anthem_axioms.tptp
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@ -1,15 +1,15 @@
tff(axiom, axiom, ![X: object]: (p__is_integer__(X) <=> (?[Y: $int]: (X = f__integer__(Y))))).
tff(axiom, axiom, ![X: object]: (p__is_symbolic__(X) <=> (?[Y: $i]: (X = f__symbolic__(Y))))).
tff(axiom, axiom, ![X: object]: (p__is_integer__(X) <=> (?[N: $int]: (X = f__integer__(N))))).
tff(axiom, axiom, ![X1: object]: (p__is_symbolic__(X1) <=> (?[X2: $i]: (X1 = f__symbolic__(X2))))).
tff(axiom, axiom, ![X: object]: ((X = c__infimum__) | p__is_integer__(X) | p__is_symbolic__(X) | (X = c__supremum__))).
tff(axiom, axiom, ![X: $int, Y: $int]: ((f__integer__(X) = f__integer__(Y)) <=> (X = Y))).
tff(axiom, axiom, ![X: $i, Y: $i]: ((f__symbolic__(X) = f__symbolic__(Y)) <=> (X = Y))).
tff(axiom, axiom, ![X1: $int, X2: $int]: (p__less_equal__(f__integer__(X1), f__integer__(X2)) <=> $lesseq(X1, X2))).
tff(axiom, axiom, ![N1: $int, N2: $int]: ((f__integer__(N1) = f__integer__(N2)) <=> (N1 = N2))).
tff(axiom, axiom, ![S1: $i, S2: $i]: ((f__symbolic__(S1) = f__symbolic__(S2)) <=> (S1 = S2))).
tff(axiom, axiom, ![N1: $int, N2: $int]: (p__less_equal__(f__integer__(N1), f__integer__(N2)) <=> $lesseq(N1, N2))).
tff(axiom, axiom, ![X1: object, X2: object]: ((p__less_equal__(X1, X2) & p__less_equal__(X2, X1)) => (X1 = X2))).
tff(axiom, axiom, ![X1: object, X2: object, X3: object]: ((p__less_equal__(X1, X2) & p__less_equal__(X2, X3)) => p__less_equal__(X1, X3))).
tff(axiom, axiom, ![X1: object, X2: object]: (p__less_equal__(X1, X2) | p__less_equal__(X2, X1))).
tff(axiom, axiom, ![X1: object, X2: object]: (p__less__(X1, X2) <=> (p__less_equal__(X1, X2) & (X1 != X2)))).
tff(axiom, axiom, ![X1: object, X2: object]: (p__greater_equal__(X1, X2) <=> p__less_equal__(X2, X1))).
tff(axiom, axiom, ![X1: object, X2: object]: (p__greater__(X1, X2) <=> (p__less_equal__(X2, X1) & (X1 != X2)))).
tff(axiom, axiom, ![X: $int]: p__less__(c__infimum__, f__integer__(X))).
tff(axiom, axiom, ![X1: $int, X2: $i]: p__less__(f__integer__(X1), f__symbolic__(X2))).
tff(axiom, axiom, ![X: $i]: p__less__(f__symbolic__(X), c__supremum__)).
tff(axiom, axiom, ![N: $int]: p__less__(c__infimum__, f__integer__(N))).
tff(axiom, axiom, ![N: $int, S: $i]: p__less__(f__integer__(N), f__symbolic__(S))).
tff(axiom, axiom, ![S: $i]: p__less__(f__symbolic__(S), c__supremum__)).