TSTP Solution File: GRP188-2 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP188-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:14:22 EDT 2023
% Result : Unsatisfiable 0.45s 0.71s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP188-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.04/0.14 % Command : toma --casc %s
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 19:42:05 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.45/0.71 % SZS status Unsatisfiable
% 0.45/0.71 % SZS output start Proof
% 0.45/0.71 original problem:
% 0.45/0.71 axioms:
% 0.45/0.71 multiply(identity(), X) = X
% 0.45/0.71 multiply(inverse(X), X) = identity()
% 0.45/0.71 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.45/0.71 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.45/0.71 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.45/0.71 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.45/0.71 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.45/0.71 least_upper_bound(X, X) = X
% 0.45/0.71 greatest_lower_bound(X, X) = X
% 0.45/0.71 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.45/0.71 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.45/0.71 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.45/0.71 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.45/0.71 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.45/0.71 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.45/0.71 inverse(identity()) = identity()
% 0.45/0.71 inverse(inverse(X)) = X
% 0.45/0.71 inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X))
% 0.45/0.71 goal:
% 0.45/0.71 least_upper_bound(b(), least_upper_bound(a(), b())) != least_upper_bound(a(), b())
% 0.45/0.71 To show the unsatisfiability of the original goal,
% 0.45/0.71 it suffices to show that least_upper_bound(b(), least_upper_bound(a(), b())) = least_upper_bound(a(), b()) (skolemized goal) is valid under the axioms.
% 0.45/0.71 Here is an equational proof:
% 0.45/0.71 4: least_upper_bound(X0, X1) = least_upper_bound(X1, X0).
% 0.45/0.71 Proof: Axiom.
% 0.45/0.71
% 0.45/0.71 6: least_upper_bound(X0, least_upper_bound(X1, X2)) = least_upper_bound(least_upper_bound(X0, X1), X2).
% 0.45/0.71 Proof: Axiom.
% 0.45/0.71
% 0.45/0.71 7: least_upper_bound(X0, X0) = X0.
% 0.45/0.71 Proof: Axiom.
% 0.45/0.71
% 0.45/0.71 23: least_upper_bound(X3, least_upper_bound(X3, X2)) = least_upper_bound(X3, X2).
% 0.45/0.71 Proof: A critical pair between equations 6 and 7.
% 0.45/0.71
% 0.45/0.71 33: least_upper_bound(b(), least_upper_bound(a(), b())) = least_upper_bound(a(), b()).
% 0.45/0.71 Proof: Rewrite lhs with equations [4,23]
% 0.45/0.71 rhs with equations [4].
% 0.45/0.71
% 0.45/0.71 % SZS output end Proof
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