TSTP Solution File: GRP509-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP509-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n014.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 01:18:42 EDT 2023
% Result : Unsatisfiable 0.15s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP509-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 01:19:45 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.40 Command-line arguments: --no-flatten-goal
% 0.15/0.40
% 0.15/0.40 % SZS status Unsatisfiable
% 0.15/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Axiom 1 (single_axiom): multiply(multiply(multiply(X, Y), Z), inverse(multiply(X, Z))) = Y.
% 0.21/0.41
% 0.21/0.41 Lemma 2: multiply(X, inverse(multiply(multiply(Y, X), inverse(multiply(Y, Z))))) = Z.
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(X, inverse(multiply(multiply(Y, X), inverse(multiply(Y, Z)))))
% 0.21/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.41 multiply(multiply(multiply(multiply(Y, X), Z), inverse(multiply(Y, Z))), inverse(multiply(multiply(Y, X), inverse(multiply(Y, Z)))))
% 0.21/0.41 = { by axiom 1 (single_axiom) }
% 0.21/0.41 Z
% 0.21/0.41
% 0.21/0.41 Lemma 3: multiply(X, multiply(multiply(Y, Z), inverse(multiply(Y, Z)))) = X.
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(X, multiply(multiply(Y, Z), inverse(multiply(Y, Z))))
% 0.21/0.41 = { by lemma 2 R->L }
% 0.21/0.41 multiply(X, multiply(multiply(multiply(Y, inverse(multiply(multiply(W, Y), inverse(multiply(W, Y))))), Z), inverse(multiply(Y, Z))))
% 0.21/0.41 = { by axiom 1 (single_axiom) }
% 0.21/0.41 multiply(X, inverse(multiply(multiply(W, Y), inverse(multiply(W, Y)))))
% 0.21/0.41 = { by lemma 2 R->L }
% 0.21/0.41 multiply(X, inverse(multiply(multiply(multiply(W, inverse(multiply(multiply(V, W), inverse(multiply(V, W))))), Y), inverse(multiply(W, Y)))))
% 0.21/0.41 = { by axiom 1 (single_axiom) }
% 0.21/0.41 multiply(X, inverse(inverse(multiply(multiply(V, W), inverse(multiply(V, W))))))
% 0.21/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.41 multiply(X, inverse(multiply(multiply(multiply(W, inverse(multiply(multiply(V, W), inverse(multiply(V, W))))), X), inverse(multiply(W, X)))))
% 0.21/0.41 = { by lemma 2 }
% 0.21/0.41 multiply(X, inverse(multiply(multiply(W, X), inverse(multiply(W, X)))))
% 0.21/0.41 = { by lemma 2 }
% 0.21/0.41 X
% 0.21/0.41
% 0.21/0.41 Lemma 4: multiply(multiply(X, Y), inverse(X)) = Y.
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(multiply(X, Y), inverse(X))
% 0.21/0.41 = { by lemma 3 R->L }
% 0.21/0.41 multiply(multiply(X, Y), inverse(multiply(X, multiply(multiply(Z, W), inverse(multiply(Z, W))))))
% 0.21/0.41 = { by lemma 3 R->L }
% 0.21/0.41 multiply(multiply(multiply(X, Y), multiply(multiply(Z, W), inverse(multiply(Z, W)))), inverse(multiply(X, multiply(multiply(Z, W), inverse(multiply(Z, W))))))
% 0.21/0.41 = { by axiom 1 (single_axiom) }
% 0.21/0.41 Y
% 0.21/0.41
% 0.21/0.41 Lemma 5: multiply(inverse(X), Y) = multiply(Y, inverse(X)).
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(inverse(X), Y)
% 0.21/0.41 = { by lemma 4 R->L }
% 0.21/0.41 multiply(multiply(X, multiply(inverse(X), Y)), inverse(X))
% 0.21/0.41 = { by lemma 2 R->L }
% 0.21/0.41 multiply(multiply(multiply(inverse(X), Y), inverse(multiply(multiply(X, multiply(inverse(X), Y)), inverse(multiply(X, multiply(X, multiply(inverse(X), Y))))))), inverse(X))
% 0.21/0.41 = { by lemma 4 R->L }
% 0.21/0.41 multiply(multiply(multiply(inverse(X), Y), inverse(multiply(multiply(multiply(X, multiply(X, multiply(inverse(X), Y))), inverse(X)), inverse(multiply(X, multiply(X, multiply(inverse(X), Y))))))), inverse(X))
% 0.21/0.41 = { by lemma 4 }
% 0.21/0.41 multiply(multiply(multiply(inverse(X), Y), inverse(inverse(X))), inverse(X))
% 0.21/0.41 = { by lemma 4 }
% 0.21/0.41 multiply(Y, inverse(X))
% 0.21/0.41
% 0.21/0.41 Lemma 6: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.21/0.41 = { by lemma 4 R->L }
% 0.21/0.41 multiply(multiply(multiply(Y, X), inverse(Y)), inverse(multiply(Y, inverse(Y))))
% 0.21/0.41 = { by axiom 1 (single_axiom) }
% 0.21/0.41 X
% 0.21/0.41
% 0.21/0.41 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(inverse(a1), a1)
% 0.21/0.41 = { by lemma 5 }
% 0.21/0.41 multiply(a1, inverse(a1))
% 0.21/0.41 = { by lemma 4 R->L }
% 0.21/0.41 multiply(a1, inverse(multiply(multiply(X, a1), inverse(X))))
% 0.21/0.41 = { by lemma 6 R->L }
% 0.21/0.41 multiply(a1, inverse(multiply(multiply(X, a1), inverse(multiply(X, inverse(multiply(Y, inverse(Y))))))))
% 0.21/0.41 = { by lemma 2 }
% 0.21/0.41 inverse(multiply(Y, inverse(Y)))
% 0.21/0.41 = { by lemma 2 R->L }
% 0.21/0.41 multiply(b1, inverse(multiply(multiply(Z, b1), inverse(multiply(Z, inverse(multiply(Y, inverse(Y))))))))
% 0.21/0.41 = { by lemma 6 }
% 0.21/0.41 multiply(b1, inverse(multiply(multiply(Z, b1), inverse(Z))))
% 0.21/0.41 = { by lemma 4 }
% 0.21/0.41 multiply(b1, inverse(b1))
% 0.21/0.41 = { by lemma 5 R->L }
% 0.21/0.41 multiply(inverse(b1), b1)
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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