TSTP Solution File: GRP186-3 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP186-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n029.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 0.53s 0.93s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP186-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.14 % Command : toma --casc %s
% 0.12/0.37 % Computer : n029.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8042.1875MB
% 0.12/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Aug 28 19:55:56 EDT 2023
% 0.12/0.37 % CPUTime :
% 0.53/0.93 % SZS status Unsatisfiable
% 0.53/0.93 % SZS output start Proof
% 0.53/0.93 original problem:
% 0.53/0.93 axioms:
% 0.53/0.93 multiply(identity(), X) = X
% 0.53/0.93 multiply(inverse(X), X) = identity()
% 0.53/0.93 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.53/0.93 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 0.53/0.93 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 0.53/0.93 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 0.53/0.93 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 0.53/0.93 least_upper_bound(X, X) = X
% 0.53/0.93 greatest_lower_bound(X, X) = X
% 0.53/0.93 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 0.53/0.93 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 0.53/0.93 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 0.53/0.93 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 0.53/0.93 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 0.53/0.93 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 0.53/0.93 goal:
% 0.53/0.93 least_upper_bound(multiply(a(), b()), identity()) != multiply(a(), least_upper_bound(inverse(a()), b()))
% 0.53/0.93 To show the unsatisfiability of the original goal,
% 0.53/0.93 it suffices to show that least_upper_bound(multiply(a(), b()), identity()) = multiply(a(), least_upper_bound(inverse(a()), b())) (skolemized goal) is valid under the axioms.
% 0.53/0.93 Here is an equational proof:
% 0.53/0.93 0: multiply(identity(), X0) = X0.
% 0.53/0.93 Proof: Axiom.
% 0.53/0.93
% 0.53/0.93 1: multiply(inverse(X0), X0) = identity().
% 0.53/0.93 Proof: Axiom.
% 0.53/0.93
% 0.53/0.93 2: multiply(multiply(X0, X1), X2) = multiply(X0, multiply(X1, X2)).
% 0.53/0.93 Proof: Axiom.
% 0.53/0.93
% 0.53/0.93 4: least_upper_bound(X0, X1) = least_upper_bound(X1, X0).
% 0.53/0.93 Proof: Axiom.
% 0.53/0.93
% 0.53/0.93 6: least_upper_bound(X0, least_upper_bound(X1, X2)) = least_upper_bound(least_upper_bound(X0, X1), X2).
% 0.53/0.93 Proof: Axiom.
% 0.53/0.93
% 0.53/0.93 7: least_upper_bound(X0, X0) = X0.
% 0.53/0.93 Proof: Axiom.
% 0.53/0.93
% 0.53/0.93 11: multiply(X0, least_upper_bound(X1, X2)) = least_upper_bound(multiply(X0, X1), multiply(X0, X2)).
% 0.53/0.93 Proof: Axiom.
% 0.53/0.93
% 0.53/0.93 18: least_upper_bound(X3, least_upper_bound(X3, X2)) = least_upper_bound(X3, X2).
% 0.53/0.93 Proof: A critical pair between equations 6 and 7.
% 0.53/0.93
% 0.53/0.93 19: multiply(inverse(X3), multiply(X3, X2)) = multiply(identity(), X2).
% 0.53/0.93 Proof: A critical pair between equations 2 and 1.
% 0.53/0.93
% 0.53/0.93 21: least_upper_bound(X5, least_upper_bound(X3, X4)) = least_upper_bound(X3, least_upper_bound(X4, X5)).
% 0.53/0.93 Proof: A critical pair between equations 4 and 6.
% 0.53/0.93
% 0.53/0.93 25: least_upper_bound(X3, least_upper_bound(X4, X2)) = least_upper_bound(least_upper_bound(X4, X3), X2).
% 0.53/0.93 Proof: A critical pair between equations 6 and 4.
% 0.53/0.93
% 0.53/0.93 27: least_upper_bound(X3, least_upper_bound(X4, X2)) = least_upper_bound(X4, least_upper_bound(X3, X2)).
% 0.53/0.93 Proof: Rewrite equation 25,
% 0.53/0.93 lhs with equations []
% 0.53/0.93 rhs with equations [6].
% 0.53/0.93
% 0.53/0.93 29: multiply(inverse(X3), multiply(X3, X2)) = X2.
% 0.53/0.93 Proof: Rewrite equation 19,
% 0.53/0.93 lhs with equations []
% 0.53/0.93 rhs with equations [0].
% 0.53/0.93
% 0.53/0.93 32: least_upper_bound(X5, least_upper_bound(X4, X5)) = least_upper_bound(X4, X5).
% 0.53/0.93 Proof: A critical pair between equations 27 and 7.
% 0.53/0.93
% 0.53/0.93 35: least_upper_bound(X6, least_upper_bound(X7, X6)) = least_upper_bound(X6, X7).
% 0.53/0.93 Proof: A critical pair between equations 21 and 18.
% 0.53/0.93
% 0.53/0.93 40: multiply(X4, X5) = multiply(inverse(inverse(X4)), X5).
% 0.53/0.93 Proof: A critical pair between equations 29 and 29.
% 0.53/0.93
% 0.53/0.93 43: least_upper_bound(X7, X6) = least_upper_bound(X6, X7).
% 0.53/0.93 Proof: Rewrite equation 35,
% 0.53/0.93 lhs with equations [32]
% 0.53/0.93 rhs with equations [].
% 0.53/0.93
% 0.53/0.93 50: multiply(X4, inverse(X4)) = identity().
% 0.53/0.93 Proof: A critical pair between equations 40 and 1.
% 0.53/0.93
% 0.53/0.93 68: least_upper_bound(multiply(a(), b()), identity()) = multiply(a(), least_upper_bound(inverse(a()), b())).
% 0.53/0.93 Proof: Rewrite lhs with equations [43]
% 0.53/0.93 rhs with equations [11,50].
% 0.53/0.93
% 0.53/0.93 % SZS output end Proof
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