TSTP Solution File: GRP514-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP514-1 : 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 : n031.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 01:18:44 EDT 2023
% Result : Unsatisfiable 0.11s 0.41s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14 % Problem : GRP514-1 : TPTP v8.1.2. Released v2.6.0.
% 0.06/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.36 % Computer : n031.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8042.1875MB
% 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Aug 28 21:56:25 EDT 2023
% 0.11/0.36 % CPUTime :
% 0.11/0.41 Command-line arguments: --no-flatten-goal
% 0.11/0.41
% 0.11/0.41 % SZS status Unsatisfiable
% 0.11/0.41
% 0.17/0.42 % SZS output start Proof
% 0.17/0.42 Axiom 1 (single_axiom): multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))) = Y.
% 0.17/0.42
% 0.17/0.42 Lemma 2: multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z))))))) = W.
% 0.17/0.42 Proof:
% 0.17/0.42 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.17/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.17/0.42 multiply(X, multiply(multiply(W, multiply(multiply(Y, Z), inverse(multiply(W, Z)))), inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.17/0.42 = { by axiom 1 (single_axiom) }
% 0.17/0.42 W
% 0.17/0.42
% 0.17/0.42 Lemma 3: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.17/0.42 Proof:
% 0.17/0.42 multiply(X, multiply(Y, inverse(Y)))
% 0.17/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.17/0.42 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))))))
% 0.17/0.42 = { by lemma 2 }
% 0.17/0.42 X
% 0.17/0.42
% 0.17/0.42 Lemma 4: multiply(X, multiply(Y, inverse(X))) = Y.
% 0.17/0.42 Proof:
% 0.17/0.42 multiply(X, multiply(Y, inverse(X)))
% 0.17/0.42 = { by lemma 3 R->L }
% 0.17/0.42 multiply(X, multiply(Y, inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.17/0.42 = { by lemma 3 R->L }
% 0.17/0.42 multiply(X, multiply(multiply(Y, multiply(Z, inverse(Z))), inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.17/0.42 = { by axiom 1 (single_axiom) }
% 0.17/0.42 Y
% 0.17/0.42
% 0.17/0.42 Lemma 5: multiply(multiply(X, Y), multiply(Z, inverse(X))) = multiply(Z, Y).
% 0.17/0.42 Proof:
% 0.17/0.42 multiply(multiply(X, Y), multiply(Z, inverse(X)))
% 0.17/0.42 = { by lemma 2 R->L }
% 0.17/0.42 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(X, Y), multiply(multiply(multiply(Z, Y), Y), inverse(multiply(X, Y))))))))))
% 0.17/0.42 = { by lemma 4 }
% 0.17/0.42 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(Z, Y), Y)))))))
% 0.17/0.42 = { by lemma 2 }
% 0.17/0.42 multiply(Z, Y)
% 0.17/0.42
% 0.17/0.42 Lemma 6: multiply(X, multiply(Y, inverse(Z))) = multiply(Y, multiply(X, inverse(Z))).
% 0.17/0.42 Proof:
% 0.17/0.42 multiply(X, multiply(Y, inverse(Z)))
% 0.17/0.42 = { by lemma 5 R->L }
% 0.17/0.42 multiply(multiply(Z, multiply(Y, inverse(Z))), multiply(X, inverse(Z)))
% 0.17/0.42 = { by lemma 4 }
% 0.17/0.42 multiply(Y, multiply(X, inverse(Z)))
% 0.17/0.42
% 0.17/0.42 Lemma 7: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 0.17/0.42 Proof:
% 0.17/0.42 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.17/0.42 = { by lemma 4 R->L }
% 0.17/0.42 multiply(Y, multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(Y)))
% 0.17/0.42 = { by lemma 5 R->L }
% 0.17/0.42 multiply(Y, multiply(multiply(X, inverse(Y)), multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), inverse(X))))
% 0.17/0.42 = { by lemma 6 R->L }
% 0.17/0.42 multiply(Y, multiply(multiply(X, inverse(multiply(Y, inverse(Y)))), multiply(multiply(X, inverse(Y)), inverse(X))))
% 0.17/0.42 = { by lemma 5 }
% 0.17/0.42 multiply(Y, multiply(multiply(X, inverse(Y)), inverse(multiply(Y, inverse(Y)))))
% 0.17/0.42 = { by axiom 1 (single_axiom) }
% 0.17/0.42 X
% 0.17/0.42
% 0.17/0.42 Lemma 8: multiply(Y, X) = multiply(X, Y).
% 0.17/0.42 Proof:
% 0.17/0.42 multiply(Y, X)
% 0.17/0.42 = { by lemma 7 R->L }
% 0.17/0.42 multiply(Y, multiply(X, inverse(multiply(Z, inverse(Z)))))
% 0.17/0.42 = { by lemma 6 }
% 0.17/0.42 multiply(X, multiply(Y, inverse(multiply(Z, inverse(Z)))))
% 0.17/0.42 = { by lemma 7 }
% 0.17/0.42 multiply(X, Y)
% 0.17/0.42
% 0.17/0.42 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.17/0.42 Proof:
% 0.17/0.42 multiply(multiply(inverse(b2), b2), a2)
% 0.17/0.42 = { by lemma 8 R->L }
% 0.17/0.42 multiply(a2, multiply(inverse(b2), b2))
% 0.17/0.42 = { by lemma 8 R->L }
% 0.17/0.42 multiply(a2, multiply(b2, inverse(b2)))
% 0.17/0.42 = { by lemma 3 }
% 0.17/0.42 a2
% 0.17/0.42 % SZS output end Proof
% 0.17/0.42
% 0.17/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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