TSTP Solution File: GRP168-2 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP168-2 : 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 01:14:15 EDT 2023
% Result : Unsatisfiable 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP168-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.03/0.12 % Command : toma --casc %s
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 22:26:50 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.46 % SZS status Unsatisfiable
% 0.16/0.46 % SZS output start Proof
% 0.16/0.46 original problem:
% 0.16/0.46 axioms:
% 0.16/0.46 multiply(identity(), X) = X
% 0.16/0.46 multiply(inverse(X), X) = identity()
% 0.16/0.46 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.16/0.46 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.16/0.46 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.16/0.46 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.16/0.46 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.16/0.46 least_upper_bound(X, X) = X
% 0.16/0.46 greatest_lower_bound(X, X) = X
% 0.16/0.46 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.16/0.46 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.16/0.46 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.16/0.46 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.16/0.46 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.16/0.46 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.16/0.46 greatest_lower_bound(a(), b()) = a()
% 0.16/0.46 goal:
% 0.16/0.46 greatest_lower_bound(multiply(inverse(c()), multiply(a(), c())), multiply(inverse(c()), multiply(b(), c()))) != multiply(inverse(c()), multiply(a(), c()))
% 0.16/0.46 To show the unsatisfiability of the original goal,
% 0.16/0.46 it suffices to show that greatest_lower_bound(multiply(inverse(c()), multiply(a(), c())), multiply(inverse(c()), multiply(b(), c()))) = multiply(inverse(c()), multiply(a(), c())) (skolemized goal) is valid under the axioms.
% 0.16/0.46 Here is an equational proof:
% 0.16/0.46 3: greatest_lower_bound(X0, X1) = greatest_lower_bound(X1, X0).
% 0.16/0.46 Proof: Axiom.
% 0.16/0.46
% 0.16/0.46 12: multiply(X0, greatest_lower_bound(X1, X2)) = greatest_lower_bound(multiply(X0, X1), multiply(X0, X2)).
% 0.16/0.46 Proof: Axiom.
% 0.16/0.46
% 0.16/0.46 14: multiply(greatest_lower_bound(X1, X2), X0) = greatest_lower_bound(multiply(X1, X0), multiply(X2, X0)).
% 0.16/0.46 Proof: Axiom.
% 0.16/0.46
% 0.16/0.46 15: greatest_lower_bound(a(), b()) = a().
% 0.16/0.46 Proof: Axiom.
% 0.16/0.46
% 0.16/0.46 16: greatest_lower_bound(b(), a()) = a().
% 0.16/0.46 Proof: Rewrite equation 15,
% 0.16/0.46 lhs with equations [3]
% 0.16/0.46 rhs with equations [].
% 0.16/0.46
% 0.16/0.46 17: greatest_lower_bound(multiply(inverse(c()), multiply(a(), c())), multiply(inverse(c()), multiply(b(), c()))) = multiply(inverse(c()), multiply(a(), c())).
% 0.16/0.46 Proof: Rewrite lhs with equations [12,14,3,16]
% 0.16/0.46 rhs with equations [].
% 0.16/0.46
% 0.16/0.46 % SZS output end Proof
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