TSTP Solution File: GRP141-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP141-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n020.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 01:14:07 EDT 2023
% Result : Unsatisfiable 0.43s 0.68s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP141-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:06:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.43/0.68 % SZS status Unsatisfiable
% 0.43/0.68 % SZS output start Proof
% 0.43/0.68 original problem:
% 0.43/0.68 axioms:
% 0.43/0.68 multiply(identity(), X) = X
% 0.43/0.68 multiply(inverse(X), X) = identity()
% 0.43/0.68 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.43/0.68 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.43/0.68 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.43/0.68 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.43/0.68 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.43/0.68 least_upper_bound(X, X) = X
% 0.43/0.68 greatest_lower_bound(X, X) = X
% 0.43/0.68 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.43/0.68 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.43/0.68 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.43/0.68 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.43/0.68 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.43/0.68 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.43/0.68 least_upper_bound(a(), c()) = a()
% 0.43/0.68 least_upper_bound(b(), c()) = b()
% 0.43/0.68 goal:
% 0.43/0.68 greatest_lower_bound(greatest_lower_bound(a(), b()), c()) != c()
% 0.43/0.68 To show the unsatisfiability of the original goal,
% 0.43/0.68 it suffices to show that greatest_lower_bound(greatest_lower_bound(a(), b()), c()) = c() (skolemized goal) is valid under the axioms.
% 0.43/0.68 Here is an equational proof:
% 0.43/0.68 3: greatest_lower_bound(X0, X1) = greatest_lower_bound(X1, X0).
% 0.43/0.68 Proof: Axiom.
% 0.43/0.68
% 0.43/0.68 4: least_upper_bound(X0, X1) = least_upper_bound(X1, X0).
% 0.43/0.68 Proof: Axiom.
% 0.43/0.68
% 0.43/0.68 5: greatest_lower_bound(X0, greatest_lower_bound(X1, X2)) = greatest_lower_bound(greatest_lower_bound(X0, X1), X2).
% 0.43/0.68 Proof: Axiom.
% 0.43/0.68
% 0.43/0.68 10: greatest_lower_bound(X0, least_upper_bound(X0, X1)) = X0.
% 0.43/0.68 Proof: Axiom.
% 0.43/0.68
% 0.43/0.68 15: least_upper_bound(a(), c()) = a().
% 0.43/0.68 Proof: Axiom.
% 0.43/0.68
% 0.43/0.68 16: least_upper_bound(b(), c()) = b().
% 0.43/0.68 Proof: Axiom.
% 0.43/0.68
% 0.43/0.68 17: least_upper_bound(c(), a()) = a().
% 0.43/0.68 Proof: Rewrite equation 15,
% 0.43/0.68 lhs with equations [4]
% 0.43/0.68 rhs with equations [].
% 0.43/0.68
% 0.43/0.68 18: least_upper_bound(c(), b()) = b().
% 0.43/0.68 Proof: Rewrite equation 16,
% 0.43/0.68 lhs with equations [4]
% 0.43/0.68 rhs with equations [].
% 0.43/0.68
% 0.43/0.68 19: c() = greatest_lower_bound(c(), a()).
% 0.43/0.68 Proof: A critical pair between equations 10 and 17.
% 0.43/0.68
% 0.43/0.68 20: c() = greatest_lower_bound(c(), b()).
% 0.43/0.68 Proof: A critical pair between equations 10 and 18.
% 0.43/0.68
% 0.43/0.68 33: greatest_lower_bound(greatest_lower_bound(a(), b()), c()) = c().
% 0.43/0.68 Proof: Rewrite lhs with equations [3,5,3,19,3,20]
% 0.43/0.68 rhs with equations [].
% 0.43/0.68
% 0.43/0.68 % SZS output end Proof
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