TSTP Solution File: GRP193-2 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP193-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n013.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 01:14:24 EDT 2023
% Result : Unsatisfiable 1.88s 2.20s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP193-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : toma --casc %s
% 0.12/0.35 % Computer : n013.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Aug 29 01:33:16 EDT 2023
% 0.12/0.35 % CPUTime :
% 1.88/2.20 % SZS status Unsatisfiable
% 1.88/2.20 % SZS output start Proof
% 1.88/2.20 original problem:
% 1.88/2.20 axioms:
% 1.88/2.20 multiply(identity(), X) = X
% 1.88/2.20 multiply(inverse(X), X) = identity()
% 1.88/2.20 multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 1.88/2.20 greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X)
% 1.88/2.20 least_upper_bound(X, Y) = least_upper_bound(Y, X)
% 1.88/2.20 greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z)
% 1.88/2.20 least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z)
% 1.88/2.20 least_upper_bound(X, X) = X
% 1.88/2.20 greatest_lower_bound(X, X) = X
% 1.88/2.20 least_upper_bound(X, greatest_lower_bound(X, Y)) = X
% 1.88/2.20 greatest_lower_bound(X, least_upper_bound(X, Y)) = X
% 1.88/2.20 multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z))
% 1.88/2.20 multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z))
% 1.88/2.20 multiply(least_upper_bound(Y, Z), X) = least_upper_bound(multiply(Y, X), multiply(Z, X))
% 1.88/2.20 multiply(greatest_lower_bound(Y, Z), X) = greatest_lower_bound(multiply(Y, X), multiply(Z, X))
% 1.88/2.20 greatest_lower_bound(identity(), a()) = identity()
% 1.88/2.20 greatest_lower_bound(identity(), b()) = identity()
% 1.88/2.20 greatest_lower_bound(identity(), c()) = identity()
% 1.88/2.20 greatest_lower_bound(a(), b()) = identity()
% 1.88/2.20 greatest_lower_bound(greatest_lower_bound(a(), multiply(b(), c())), multiply(greatest_lower_bound(a(), b()), greatest_lower_bound(a(), c()))) = greatest_lower_bound(a(), multiply(b(), c()))
% 1.88/2.20 goal:
% 1.88/2.20 greatest_lower_bound(a(), multiply(b(), c())) != greatest_lower_bound(a(), c())
% 1.88/2.20 To show the unsatisfiability of the original goal,
% 1.88/2.20 it suffices to show that greatest_lower_bound(a(), multiply(b(), c())) = greatest_lower_bound(a(), c()) (skolemized goal) is valid under the axioms.
% 1.88/2.20 Here is an equational proof:
% 1.88/2.20 0: multiply(identity(), X0) = X0.
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 3: greatest_lower_bound(X0, X1) = greatest_lower_bound(X1, X0).
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 4: least_upper_bound(X0, X1) = least_upper_bound(X1, X0).
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 5: greatest_lower_bound(X0, greatest_lower_bound(X1, X2)) = greatest_lower_bound(greatest_lower_bound(X0, X1), X2).
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 8: greatest_lower_bound(X0, X0) = X0.
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 9: least_upper_bound(X0, greatest_lower_bound(X0, X1)) = X0.
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 10: greatest_lower_bound(X0, least_upper_bound(X0, X1)) = X0.
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 14: multiply(greatest_lower_bound(X1, X2), X0) = greatest_lower_bound(multiply(X1, X0), multiply(X2, X0)).
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 18: greatest_lower_bound(a(), b()) = identity().
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 19: greatest_lower_bound(greatest_lower_bound(a(), multiply(b(), c())), multiply(greatest_lower_bound(a(), b()), greatest_lower_bound(a(), c()))) = greatest_lower_bound(a(), multiply(b(), c())).
% 1.88/2.20 Proof: Axiom.
% 1.88/2.20
% 1.88/2.20 23: greatest_lower_bound(a(), greatest_lower_bound(multiply(b(), c()), greatest_lower_bound(a(), c()))) = greatest_lower_bound(a(), multiply(b(), c())).
% 1.88/2.20 Proof: Rewrite equation 19,
% 1.88/2.20 lhs with equations [18,0,5]
% 1.88/2.20 rhs with equations [].
% 1.88/2.20
% 1.88/2.20 27: X2 = least_upper_bound(X2, greatest_lower_bound(X3, X2)).
% 1.88/2.20 Proof: A critical pair between equations 9 and 3.
% 1.88/2.20
% 1.88/2.20 29: greatest_lower_bound(X3, greatest_lower_bound(X3, X2)) = greatest_lower_bound(X3, X2).
% 1.88/2.20 Proof: A critical pair between equations 5 and 8.
% 1.88/2.20
% 1.88/2.20 40: greatest_lower_bound(a(), greatest_lower_bound(c(), multiply(b(), c()))) = greatest_lower_bound(a(), multiply(b(), c())).
% 1.88/2.20 Proof: Rewrite equation 23,
% 1.88/2.20 lhs with equations [3,5,29]
% 1.88/2.20 rhs with equations [].
% 1.88/2.20
% 1.88/2.20 41: greatest_lower_bound(b(), a()) = identity().
% 1.88/2.20 Proof: Rewrite equation 18,
% 1.88/2.20 lhs with equations [3]
% 1.88/2.20 rhs with equations [].
% 1.88/2.20
% 1.88/2.20 60: multiply(greatest_lower_bound(a(), b()), X0) = X0.
% 1.88/2.20 Proof: Rewrite equation 0,
% 1.88/2.20 lhs with equations [41,3]
% 1.88/2.20 rhs with equations [].
% 1.88/2.20
% 1.88/2.20 63: greatest_lower_bound(a(), b()) = identity().
% 1.88/2.20 Proof: Rewrite equation 41,
% 1.88/2.20 lhs with equations [3]
% 1.88/2.20 rhs with equations [].
% 1.88/2.20
% 1.88/2.20 86: multiply(identity(), X0) = X0.
% 1.88/2.20 Proof: Rewrite equation 60,
% 1.88/2.20 lhs with equations [63]
% 1.88/2.20 rhs with equations [].
% 1.88/2.20
% 1.88/2.20 111: greatest_lower_bound(multiply(a(), X0), multiply(b(), X0)) = X0.
% 1.88/2.20 Proof: Rewrite equation 86,
% 1.88/2.20 lhs with equations [63,14]
% 1.88/2.20 rhs with equations [].
% 1.88/2.20
% 1.88/2.20 124: multiply(b(), X4) = least_upper_bound(multiply(b(), X4), X4).
% 1.88/2.20 Proof: A critical pair between equations 27 and 111.
% 1.88/2.20
% 1.88/2.20 129: greatest_lower_bound(X5, greatest_lower_bound(X3, X4)) = greatest_lower_bound(X3, greatest_lower_bound(X4, X5)).
% 1.88/2.20 Proof: A critical pair between equations 3 and 5.
% 1.88/2.20
% 1.88/2.20 131: multiply(b(), X4) = least_upper_bound(X4, multiply(b(), X4)).
% 1.88/2.20 Proof: Rewrite equation 124,
% 1.88/2.20 lhs with equations []
% 1.88/2.20 rhs with equations [4].
% 1.88/2.20
% 1.88/2.20 185: X5 = greatest_lower_bound(X5, multiply(b(), X5)).
% 1.88/2.20 Proof: A critical pair between equations 10 and 131.
% 1.88/2.20
% 1.88/2.20 188: greatest_lower_bound(X6, greatest_lower_bound(X6, X5)) = greatest_lower_bound(X5, X6).
% 1.88/2.20 Proof: A critical pair between equations 129 and 8.
% 1.88/2.20
% 1.88/2.20 201: greatest_lower_bound(c(), a()) = greatest_lower_bound(a(), multiply(b(), c())).
% 1.88/2.20 Proof: Rewrite equation 40,
% 1.88/2.20 lhs with equations [185,188,29]
% 1.88/2.20 rhs with equations [].
% 1.88/2.20
% 1.88/2.20 216: greatest_lower_bound(a(), multiply(b(), c())) = greatest_lower_bound(a(), c()).
% 1.88/2.20 Proof: Rewrite lhs with equations [201]
% 1.88/2.20 rhs with equations [3].
% 1.88/2.20
% 1.88/2.20 % SZS output end Proof
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