TSTP Solution File: GRP520-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP520-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n011.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 01:18:45 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP520-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 02:32:26 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Axiom 1 (single_axiom): multiply(X, multiply(multiply(inverse(multiply(X, Y)), Z), Y)) = Z.
% 0.19/0.39
% 0.19/0.39 Lemma 2: multiply(inverse(multiply(X, Y)), multiply(X, multiply(Z, Y))) = Z.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(inverse(multiply(X, Y)), multiply(X, multiply(Z, Y)))
% 0.19/0.39 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.39 multiply(inverse(multiply(X, Y)), multiply(X, multiply(multiply(inverse(multiply(X, Y)), multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z), W)), Y)))
% 0.19/0.39 = { by axiom 1 (single_axiom) }
% 0.19/0.39 multiply(inverse(multiply(X, Y)), multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z), W))
% 0.19/0.39 = { by axiom 1 (single_axiom) }
% 0.19/0.39 Z
% 0.19/0.39
% 0.19/0.39 Lemma 3: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Z, Y))), Z) = X.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Z, Y))), Z)
% 0.19/0.39 = { by lemma 2 R->L }
% 0.19/0.39 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Z, Y))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(Z, Y))))
% 0.19/0.39 = { by lemma 2 }
% 0.19/0.39 X
% 0.19/0.39
% 0.19/0.39 Lemma 4: multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, Z)), Z)), X)) = Y.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, Z)), Z)), X))
% 0.19/0.39 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.39 multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(multiply(inverse(multiply(inverse(multiply(Y, Z)), Z)), X), Z))), multiply(inverse(multiply(inverse(multiply(Y, Z)), Z)), X))
% 0.19/0.39 = { by lemma 3 }
% 0.19/0.39 Y
% 0.19/0.39
% 0.19/0.39 Lemma 5: inverse(multiply(inverse(multiply(X, Y)), Y)) = X.
% 0.19/0.39 Proof:
% 0.19/0.39 inverse(multiply(inverse(multiply(X, Y)), Y))
% 0.19/0.39 = { by lemma 2 R->L }
% 0.19/0.39 multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Y)), Z)), multiply(inverse(multiply(inverse(multiply(X, Y)), Y)), multiply(inverse(multiply(inverse(multiply(X, Y)), Y)), Z)))
% 0.19/0.39 = { by lemma 4 }
% 0.19/0.39 X
% 0.19/0.39
% 0.19/0.39 Lemma 6: multiply(inverse(X), multiply(Y, X)) = Y.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(inverse(X), multiply(Y, X))
% 0.19/0.39 = { by lemma 5 R->L }
% 0.19/0.39 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, Z)), Z)), X))
% 0.19/0.39 = { by lemma 4 }
% 0.19/0.39 Y
% 0.19/0.39
% 0.19/0.39 Lemma 7: multiply(X, inverse(multiply(inverse(Y), Y))) = X.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(X, inverse(multiply(inverse(Y), Y)))
% 0.19/0.39 = { by lemma 5 R->L }
% 0.19/0.39 multiply(inverse(multiply(inverse(multiply(X, Z)), Z)), inverse(multiply(inverse(Y), Y)))
% 0.19/0.39 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.39 multiply(inverse(multiply(inverse(multiply(X, Z)), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(Y), Y)), Z), Y)))), inverse(multiply(inverse(Y), Y)))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 multiply(inverse(multiply(inverse(multiply(X, Z)), multiply(inverse(multiply(inverse(Y), Y)), Z))), inverse(multiply(inverse(Y), Y)))
% 0.19/0.39 = { by lemma 3 }
% 0.19/0.39 X
% 0.19/0.39
% 0.19/0.39 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(a, b)
% 0.19/0.39 = { by lemma 7 R->L }
% 0.19/0.39 multiply(a, multiply(b, inverse(multiply(inverse(X), X))))
% 0.19/0.39 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.39 multiply(b, multiply(multiply(inverse(multiply(b, inverse(multiply(inverse(X), X)))), multiply(a, multiply(b, inverse(multiply(inverse(X), X))))), inverse(multiply(inverse(X), X))))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 multiply(b, multiply(a, inverse(multiply(inverse(X), X))))
% 0.19/0.39 = { by lemma 7 }
% 0.19/0.39 multiply(b, a)
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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