TSTP Solution File: GRP419-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP419-1 : 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 : n026.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 01:18:21 EDT 2023
% Result : Unsatisfiable 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP419-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 23:51:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.47
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 Axiom 1 (single_axiom): inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))) = Y.
% 0.19/0.54
% 0.19/0.54 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z)) = inverse(multiply(inverse(multiply(W, inverse(multiply(Y, inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V))).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 inverse(multiply(inverse(multiply(W, inverse(multiply(Y, inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 0.19/0.54
% 0.19/0.54 Lemma 3: inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y)) = W.
% 0.19/0.54 Proof:
% 0.19/0.54 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Y), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))))
% 0.19/0.54 = { by lemma 2 R->L }
% 0.19/0.54 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 W
% 0.19/0.54
% 0.19/0.54 Lemma 4: inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))) = Y.
% 0.19/0.54 Proof:
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))))
% 0.19/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))))
% 0.19/0.54 = { by lemma 2 R->L }
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), multiply(U, T))))
% 0.19/0.54 = { by lemma 3 R->L }
% 0.19/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z)))), multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), multiply(U, T))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.54 inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), multiply(U, T))))
% 0.19/0.54 = { by axiom 1 (single_axiom) }
% 0.19/0.55 Y
% 0.19/0.55
% 0.19/0.55 Lemma 5: multiply(X, inverse(multiply(inverse(multiply(Y, inverse(multiply(X, inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(Y, Z)))) = multiply(inverse(multiply(W, V)), multiply(W, V)).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(X, inverse(multiply(inverse(multiply(Y, inverse(multiply(X, inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(Y, Z))))
% 0.19/0.55 = { by lemma 3 R->L }
% 0.19/0.55 multiply(X, inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), V)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(Y, Z))))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 multiply(X, multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), V))
% 0.19/0.55 = { by lemma 3 R->L }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), V)), multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), V))
% 0.19/0.55 = { by lemma 4 R->L }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, V)), multiply(W, V)))), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), V))
% 0.19/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.55 inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, V)), multiply(W, V)))), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), V))), inverse(multiply(X2, inverse(multiply(inverse(X2), X2)))))))), multiply(S, X2)))
% 0.19/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.55 inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(inverse(inverse(multiply(inverse(multiply(W, V)), multiply(W, V))))), inverse(multiply(Z2, inverse(multiply(inverse(Z2), Z2)))))))), multiply(Y2, Z2))), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(V)), inverse(multiply(T, inverse(multiply(inverse(T), T)))))))), inverse(multiply(inverse(X), inverse(multiply(multiply(U, T), inverse(multiply(inverse(multiply(U, T)), multiply(U, T))))))))), V))), inverse(multiply(X2, inverse(multiply(inverse(X2), X2)))))))), multiply(S, X2)))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 inverse(multiply(inverse(multiply(S, inverse(multiply(multiply(inverse(multiply(Y2, inverse(multiply(inverse(inverse(inverse(multiply(inverse(multiply(W, V)), multiply(W, V))))), inverse(multiply(Z2, inverse(multiply(inverse(Z2), Z2)))))))), multiply(Y2, Z2)), inverse(multiply(X2, inverse(multiply(inverse(X2), X2)))))))), multiply(S, X2)))
% 0.19/0.55 = { by lemma 2 }
% 0.19/0.55 inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(W2, inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, V)), multiply(W, V)))), inverse(multiply(V2, inverse(multiply(inverse(V2), V2)))))))), multiply(W2, V2))), inverse(multiply(X2, inverse(multiply(inverse(X2), X2)))))))), multiply(S, X2)))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 multiply(inverse(multiply(W2, inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, V)), multiply(W, V)))), inverse(multiply(V2, inverse(multiply(inverse(V2), V2)))))))), multiply(W2, V2))
% 0.19/0.55 = { by lemma 2 }
% 0.19/0.55 inverse(multiply(inverse(multiply(U2, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(W, V))), inverse(multiply(T2, inverse(multiply(inverse(T2), T2)))))))), multiply(U2, T2)))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 multiply(inverse(multiply(W, V)), multiply(W, V))
% 0.19/0.55
% 0.19/0.55 Lemma 6: multiply(inverse(multiply(X, Y)), multiply(X, Y)) = multiply(inverse(Z), Z).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(inverse(multiply(X, Y)), multiply(X, Y))
% 0.19/0.55 = { by lemma 5 R->L }
% 0.19/0.55 multiply(inverse(Z), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Z), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V))))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 multiply(inverse(Z), Z)
% 0.19/0.55
% 0.19/0.55 Lemma 7: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(inverse(Y), Y)
% 0.19/0.55 = { by lemma 6 R->L }
% 0.19/0.55 multiply(inverse(multiply(V, U)), multiply(V, U))
% 0.19/0.55 = { by lemma 5 R->L }
% 0.19/0.55 multiply(inverse(X), inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W))))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 multiply(inverse(X), X)
% 0.19/0.55
% 0.19/0.55 Lemma 8: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)) = multiply(Z, inverse(multiply(inverse(W), W))).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z))
% 0.19/0.55 = { by lemma 7 }
% 0.19/0.55 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))
% 0.19/0.55 = { by lemma 2 }
% 0.19/0.55 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 multiply(Z, inverse(multiply(inverse(Z), Z)))
% 0.19/0.55 = { by lemma 7 R->L }
% 0.19/0.55 multiply(Z, inverse(multiply(inverse(W), W)))
% 0.19/0.55
% 0.19/0.55 Lemma 9: multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y)))
% 0.19/0.55 = { by lemma 8 R->L }
% 0.19/0.55 multiply(inverse(multiply(W, inverse(multiply(inverse(X), X)))), multiply(W, inverse(multiply(inverse(X), X))))
% 0.19/0.55 = { by lemma 7 R->L }
% 0.19/0.55 multiply(inverse(Z), Z)
% 0.19/0.55
% 0.19/0.55 Lemma 10: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.19/0.55 = { by lemma 8 R->L }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(W), W)))), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))
% 0.19/0.55 = { by lemma 9 }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))
% 0.19/0.55 = { by lemma 6 }
% 0.19/0.55 multiply(inverse(Z), Z)
% 0.19/0.55
% 0.19/0.55 Lemma 11: inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))), multiply(inverse(W), W))) = Y.
% 0.19/0.55 Proof:
% 0.19/0.55 inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))), multiply(inverse(W), W)))
% 0.19/0.55 = { by lemma 9 R->L }
% 0.19/0.55 inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))))))), multiply(inverse(W), W)))
% 0.19/0.55 = { by lemma 10 R->L }
% 0.19/0.55 inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))))))), multiply(multiply(inverse(X), X), inverse(multiply(inverse(V), V)))))
% 0.19/0.55 = { by axiom 1 (single_axiom) }
% 0.19/0.55 Y
% 0.19/0.55
% 0.19/0.55 Lemma 12: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.19/0.55 Proof:
% 0.19/0.55 inverse(multiply(inverse(X), X))
% 0.19/0.55 = { by lemma 6 R->L }
% 0.19/0.55 inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))
% 0.19/0.55 = { by lemma 10 R->L }
% 0.19/0.55 inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V)))), multiply(inverse(Z), Z)))
% 0.19/0.55 = { by lemma 9 R->L }
% 0.19/0.55 inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(U), U)))))), multiply(inverse(Z), Z)))
% 0.19/0.55 = { by lemma 11 }
% 0.19/0.55 multiply(inverse(Y), Y)
% 0.19/0.55
% 0.19/0.55 Lemma 13: multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(Y), Y)))), multiply(inverse(Z), Z)) = multiply(X, inverse(multiply(inverse(W), W))).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(Y), Y)))), multiply(inverse(Z), Z))
% 0.19/0.55 = { by lemma 7 }
% 0.19/0.55 multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(Y), Y)))), multiply(inverse(X), X))
% 0.19/0.55 = { by lemma 8 }
% 0.19/0.55 multiply(X, inverse(multiply(inverse(W), W)))
% 0.19/0.55
% 0.19/0.55 Lemma 14: multiply(multiply(multiply(inverse(X), X), Y), multiply(inverse(Z), Z)) = multiply(multiply(inverse(W), W), multiply(Y, multiply(inverse(V), V))).
% 0.19/0.55 Proof:
% 0.19/0.55 multiply(multiply(multiply(inverse(X), X), Y), multiply(inverse(Z), Z))
% 0.19/0.55 = { by lemma 12 R->L }
% 0.19/0.55 multiply(multiply(multiply(inverse(X), X), Y), inverse(multiply(inverse(U), U)))
% 0.19/0.55 = { by lemma 8 R->L }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(inverse(T), T)), inverse(multiply(inverse(S), S)))), multiply(inverse(multiply(inverse(T), T)), multiply(multiply(inverse(X), X), Y)))
% 0.19/0.55 = { by lemma 10 R->L }
% 0.19/0.55 multiply(inverse(multiply(inverse(multiply(inverse(T), T)), inverse(multiply(inverse(S), S)))), multiply(inverse(multiply(multiply(inverse(X), X), inverse(multiply(inverse(X2), X2)))), multiply(multiply(inverse(X), X), Y)))
% 0.19/0.55 = { by lemma 8 }
% 0.19/0.56 multiply(inverse(multiply(inverse(multiply(inverse(T), T)), inverse(multiply(inverse(S), S)))), multiply(Y, inverse(multiply(inverse(Y2), Y2))))
% 0.19/0.56 = { by lemma 9 }
% 0.19/0.56 multiply(inverse(multiply(inverse(Z2), Z2)), multiply(Y, inverse(multiply(inverse(Y2), Y2))))
% 0.19/0.56 = { by lemma 12 }
% 0.19/0.56 multiply(multiply(inverse(W), W), multiply(Y, inverse(multiply(inverse(Y2), Y2))))
% 0.19/0.56 = { by lemma 12 }
% 0.19/0.56 multiply(multiply(inverse(W), W), multiply(Y, multiply(inverse(V), V)))
% 0.19/0.56
% 0.19/0.56 Lemma 15: multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(Z), Z)) = multiply(X, multiply(inverse(W), W)).
% 0.19/0.56 Proof:
% 0.19/0.56 multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 0.19/0.56 = { by lemma 12 R->L }
% 0.19/0.56 multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))), multiply(inverse(Z), Z))
% 0.19/0.56 = { by lemma 13 }
% 0.19/0.56 multiply(X, inverse(multiply(inverse(U), U)))
% 0.19/0.56 = { by lemma 12 }
% 0.19/0.56 multiply(X, multiply(inverse(W), W))
% 0.19/0.56
% 0.19/0.56 Lemma 16: multiply(multiply(inverse(X), X), multiply(Y, multiply(inverse(Z), Z))) = multiply(Y, multiply(inverse(W), W)).
% 0.19/0.56 Proof:
% 0.19/0.56 multiply(multiply(inverse(X), X), multiply(Y, multiply(inverse(Z), Z)))
% 0.19/0.56 = { by lemma 12 R->L }
% 0.19/0.56 multiply(multiply(inverse(X), X), multiply(Y, inverse(multiply(inverse(V), V))))
% 0.19/0.56 = { by lemma 13 R->L }
% 0.19/0.56 multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(U), U)))), multiply(inverse(T), T)))
% 0.19/0.56 = { by lemma 10 R->L }
% 0.19/0.56 multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(S), S)), multiply(inverse(S), S))))))), multiply(inverse(T), T)))
% 0.19/0.56 = { by lemma 12 }
% 0.19/0.56 multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(S), S), inverse(multiply(multiply(inverse(X2), X2), multiply(inverse(S), S))))))), multiply(inverse(T), T)))
% 0.19/0.56 = { by lemma 14 R->L }
% 0.19/0.56 multiply(multiply(multiply(inverse(Y2), Y2), inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(S), S), inverse(multiply(multiply(inverse(X2), X2), multiply(inverse(S), S)))))))), multiply(inverse(Z2), Z2))
% 0.19/0.56 = { by lemma 12 R->L }
% 0.19/0.56 multiply(multiply(inverse(multiply(inverse(S), S)), inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(S), S), inverse(multiply(multiply(inverse(X2), X2), multiply(inverse(S), S)))))))), multiply(inverse(Z2), Z2))
% 0.19/0.56 = { by lemma 12 R->L }
% 0.19/0.56 multiply(multiply(inverse(multiply(inverse(S), S)), inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(S), S)), multiply(inverse(S), S)))))))), multiply(inverse(Z2), Z2))
% 0.19/0.56 = { by lemma 4 R->L }
% 0.19/0.56 multiply(multiply(inverse(multiply(inverse(S), inverse(multiply(inverse(inverse(multiply(inverse(multiply(W2, S)), multiply(W2, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(S), S)), multiply(inverse(S), S)))))))), multiply(inverse(Z2), Z2))
% 0.19/0.56 = { by lemma 15 R->L }
% 0.19/0.56 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(S), inverse(multiply(inverse(inverse(multiply(inverse(multiply(W2, S)), multiply(W2, S)))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(S), S)), multiply(inverse(S), S))))))))), multiply(inverse(multiply(W2, S)), multiply(W2, S)))), multiply(inverse(W), W))
% 0.19/0.56 = { by lemma 3 }
% 0.19/0.56 multiply(Y, multiply(inverse(W), W))
% 0.19/0.56
% 0.19/0.56 Lemma 17: multiply(multiply(X, multiply(inverse(Y), Y)), multiply(inverse(Z), Z)) = multiply(X, multiply(inverse(W), W)).
% 0.19/0.56 Proof:
% 0.19/0.56 multiply(multiply(X, multiply(inverse(Y), Y)), multiply(inverse(Z), Z))
% 0.19/0.56 = { by lemma 12 R->L }
% 0.19/0.56 multiply(multiply(X, multiply(inverse(Y), Y)), inverse(multiply(inverse(V), V)))
% 0.19/0.56 = { by lemma 8 R->L }
% 0.19/0.56 multiply(inverse(multiply(multiply(inverse(U), U), inverse(multiply(inverse(T), T)))), multiply(multiply(inverse(U), U), multiply(X, multiply(inverse(Y), Y))))
% 0.19/0.56 = { by lemma 16 }
% 0.19/0.56 multiply(inverse(multiply(multiply(inverse(U), U), inverse(multiply(inverse(T), T)))), multiply(X, multiply(inverse(S), S)))
% 0.19/0.56 = { by lemma 10 }
% 0.19/0.56 multiply(inverse(multiply(inverse(X2), X2)), multiply(X, multiply(inverse(S), S)))
% 0.19/0.56 = { by lemma 12 }
% 0.19/0.56 multiply(multiply(inverse(Y2), Y2), multiply(X, multiply(inverse(S), S)))
% 0.19/0.56 = { by lemma 16 }
% 0.19/0.56 multiply(X, multiply(inverse(W), W))
% 0.19/0.56
% 0.19/0.56 Lemma 18: multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(inverse(Z), Z)) = multiply(inverse(X), multiply(inverse(W), W)).
% 0.19/0.56 Proof:
% 0.19/0.56 multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 0.19/0.56 = { by lemma 12 R->L }
% 0.19/0.56 multiply(inverse(multiply(X, inverse(multiply(inverse(V), V)))), multiply(inverse(Z), Z))
% 0.19/0.56 = { by lemma 13 R->L }
% 0.19/0.56 multiply(inverse(multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(U), U)))), multiply(inverse(T), T))), multiply(inverse(Z), Z))
% 0.19/0.56 = { by lemma 15 }
% 0.19/0.56 multiply(multiply(inverse(X), inverse(multiply(inverse(U), U))), multiply(inverse(S), S))
% 0.19/0.56 = { by lemma 12 }
% 0.19/0.56 multiply(multiply(inverse(X), multiply(inverse(X2), X2)), multiply(inverse(S), S))
% 0.19/0.56 = { by lemma 17 }
% 0.19/0.56 multiply(inverse(X), multiply(inverse(W), W))
% 0.19/0.56
% 0.19/0.56 Lemma 19: multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(inverse(Z), Z)) = multiply(inverse(Y), multiply(inverse(W), W)).
% 0.19/0.56 Proof:
% 0.19/0.56 multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(inverse(Z), Z))
% 0.19/0.56 = { by lemma 18 R->L }
% 0.19/0.56 multiply(inverse(multiply(multiply(multiply(inverse(X), X), Y), multiply(inverse(V), V))), multiply(inverse(U), U))
% 0.19/0.56 = { by lemma 14 }
% 0.19/0.56 multiply(inverse(multiply(multiply(inverse(T), T), multiply(Y, multiply(inverse(S), S)))), multiply(inverse(U), U))
% 0.19/0.56 = { by lemma 16 }
% 0.19/0.56 multiply(inverse(multiply(Y, multiply(inverse(X2), X2))), multiply(inverse(U), U))
% 0.19/0.56 = { by lemma 18 }
% 0.19/0.56 multiply(inverse(Y), multiply(inverse(W), W))
% 0.19/0.56
% 0.19/0.56 Lemma 20: inverse(multiply(inverse(X), multiply(inverse(Y), Y))) = X.
% 0.19/0.56 Proof:
% 0.19/0.56 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 0.19/0.56 = { by lemma 17 R->L }
% 0.19/0.56 inverse(multiply(multiply(inverse(X), multiply(inverse(Z), Z)), multiply(inverse(W), W)))
% 0.19/0.56 = { by lemma 12 R->L }
% 0.19/0.56 inverse(multiply(multiply(inverse(X), inverse(multiply(inverse(V), V))), multiply(inverse(W), W)))
% 0.19/0.56 = { by lemma 15 R->L }
% 0.19/0.56 inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))), multiply(inverse(U), U))), multiply(inverse(T), T)))
% 0.19/0.56 = { by lemma 18 }
% 0.19/0.56 inverse(multiply(inverse(inverse(multiply(inverse(X), inverse(multiply(inverse(V), V))))), multiply(inverse(S), S)))
% 0.19/0.56 = { by lemma 19 R->L }
% 0.19/0.56 inverse(multiply(inverse(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))))), multiply(inverse(Y2), Y2)))
% 0.19/0.56 = { by lemma 11 }
% 0.19/0.56 X
% 0.19/0.56
% 0.19/0.56 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.19/0.56 Proof:
% 0.19/0.56 multiply(multiply(inverse(b2), b2), a2)
% 0.19/0.56 = { by lemma 20 R->L }
% 0.19/0.56 inverse(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(inverse(X), X)))
% 0.19/0.56 = { by lemma 19 }
% 0.19/0.56 inverse(multiply(inverse(a2), multiply(inverse(Y), Y)))
% 0.19/0.56 = { by lemma 20 }
% 0.19/0.56 a2
% 0.19/0.56 % SZS output end Proof
% 0.19/0.56
% 0.19/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------