TSTP Solution File: GRP424-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP424-1 : 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 : n017.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 01:18:22 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 : GRP424-1 : TPTP v8.1.2. Released v2.6.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 00:57:58 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.38 Command-line arguments: --no-flatten-goal
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Axiom 1 (single_axiom): multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Z)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z))) = Y.
% 0.19/0.40
% 0.19/0.40 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z))) = Y.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z)))
% 0.19/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.40 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.19/0.40 = { by axiom 1 (single_axiom) }
% 0.19/0.40 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.19/0.40 = { by axiom 1 (single_axiom) }
% 0.19/0.41 Y
% 0.19/0.41
% 0.19/0.41 Lemma 3: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z))) = Y.
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z)))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z)))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.19/0.41 = { by lemma 2 }
% 0.19/0.41 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z)))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 Y
% 0.19/0.41
% 0.19/0.41 Lemma 4: multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W))) = multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(W))).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W)))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W)))
% 0.19/0.41 = { by lemma 3 R->L }
% 0.19/0.41 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))
% 0.19/0.41 = { by lemma 2 R->L }
% 0.19/0.41 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.42 multiply(inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))))), multiply(S, inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))))), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))))
% 0.19/0.42 = { by axiom 1 (single_axiom) }
% 0.19/0.42 multiply(inverse(multiply(inverse(multiply(S, inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))), multiply(S, inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))))), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))))
% 0.19/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.42 multiply(inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))), multiply(V, inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))))), multiply(S, inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))))), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))))
% 0.19/0.42 = { by axiom 1 (single_axiom) }
% 0.19/0.42 multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T)), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))), multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))), multiply(V, inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))
% 0.19/0.42 = { by lemma 2 }
% 0.19/0.42 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(U, inverse(T)))), inverse(multiply(inverse(T), T)))), T))))))
% 0.19/0.42 = { by lemma 3 }
% 0.19/0.42 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(W)))
% 0.19/0.42
% 0.19/0.42 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(inverse(a1), a1)
% 0.19/0.42 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.42 multiply(inverse(a1), multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(a1), Y)))), multiply(X, inverse(Y)))), inverse(multiply(inverse(Y), Y))))
% 0.19/0.42 = { by lemma 4 }
% 0.19/0.42 multiply(inverse(multiply(Z, inverse(multiply(inverse(Y), Y)))), multiply(Z, inverse(multiply(inverse(Y), Y))))
% 0.19/0.42 = { by lemma 4 R->L }
% 0.19/0.42 multiply(inverse(b1), multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(b1), Y)))), multiply(W, inverse(Y)))), inverse(multiply(inverse(Y), Y))))
% 0.19/0.42 = { by axiom 1 (single_axiom) }
% 0.19/0.42 multiply(inverse(b1), b1)
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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