TSTP Solution File: GRP444-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP444-1 : 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 : n027.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 01:18:27 EDT 2023
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP444-1 : 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 : n027.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 : Tue Aug 29 00:48:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Command-line arguments: --flatten
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.54 % SZS output start Proof
% 0.20/0.54 Axiom 1 (single_axiom): inverse(multiply(X, multiply(Y, multiply(multiply(Z, inverse(Z)), inverse(multiply(W, multiply(X, Y))))))) = W.
% 0.20/0.54
% 0.20/0.54 Lemma 2: inverse(multiply(X, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))), multiply(multiply(V, inverse(V)), Z)))) = W.
% 0.20/0.54 Proof:
% 0.20/0.54 inverse(multiply(X, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))), multiply(multiply(V, inverse(V)), Z))))
% 0.20/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.54 inverse(multiply(X, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))), multiply(multiply(V, inverse(V)), inverse(multiply(W, multiply(X, multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))))))))))
% 0.20/0.54 = { by axiom 1 (single_axiom) }
% 0.20/0.54 W
% 0.20/0.54
% 0.20/0.54 Lemma 3: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(Z, inverse(Z)), W), multiply(multiply(V, inverse(V)), U)))) = multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(W, U)))).
% 0.20/0.54 Proof:
% 0.20/0.54 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(Z, inverse(Z)), W), multiply(multiply(V, inverse(V)), U))))
% 0.20/0.54 = { by lemma 2 R->L }
% 0.20/0.54 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(U, multiply(multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(W, U)))), multiply(multiply(X, inverse(X)), Y))))), multiply(multiply(V, inverse(V)), U))))
% 0.20/0.54 = { by lemma 2 }
% 0.20/0.54 multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(W, U))))
% 0.20/0.54
% 0.20/0.54 Lemma 4: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(Y, inverse(Y))
% 0.20/0.54 = { by lemma 2 R->L }
% 0.20/0.54 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.20/0.54 = { by lemma 2 R->L }
% 0.20/0.54 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, inverse(multiply(multiply(multiply(X2, inverse(X2)), Z), multiply(multiply(multiply(Y2, inverse(Y2)), inverse(multiply(V, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, V)))), multiply(multiply(X2, inverse(X2)), Z))))), multiply(multiply(Z2, inverse(Z2)), V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.20/0.54 = { by lemma 2 }
% 0.20/0.54 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, inverse(multiply(multiply(multiply(X2, inverse(X2)), Z), multiply(multiply(multiply(Y2, inverse(Y2)), W), multiply(multiply(Z2, inverse(Z2)), V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.20/0.54 = { by lemma 2 R->L }
% 0.20/0.54 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, inverse(multiply(multiply(multiply(X2, inverse(X2)), Z), multiply(multiply(multiply(Y2, inverse(Y2)), inverse(multiply(V, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Z, multiply(W, V)))), multiply(multiply(X2, inverse(X2)), Z))))), multiply(multiply(Z2, inverse(Z2)), V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.20/0.54 = { by lemma 2 }
% 0.20/0.54 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, multiply(multiply(X, inverse(X)), inverse(multiply(Z, multiply(W, V))))))), multiply(multiply(S, inverse(S)), T))))
% 0.20/0.54 = { by lemma 2 }
% 0.20/0.54 multiply(X, inverse(X))
% 0.20/0.54
% 0.20/0.54 Lemma 5: inverse(multiply(X, multiply(inverse(X), multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W)))))))) = Z.
% 0.20/0.54 Proof:
% 0.20/0.54 inverse(multiply(X, multiply(inverse(X), multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))))))
% 0.20/0.54 = { by lemma 4 }
% 0.20/0.54 inverse(multiply(X, multiply(inverse(X), multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(X, inverse(X))))))))
% 0.20/0.54 = { by axiom 1 (single_axiom) }
% 0.20/0.54 Z
% 0.20/0.54
% 0.20/0.54 Lemma 6: multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(Y, W)))) = inverse(W).
% 0.20/0.54 Proof:
% 0.20/0.54 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(Y, W))))
% 0.20/0.54 = { by lemma 3 R->L }
% 0.20/0.54 inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(Y, multiply(Z, inverse(Z))))), multiply(multiply(multiply(U, inverse(U)), Y), multiply(multiply(T, inverse(T)), W))))
% 0.20/0.54 = { by lemma 5 R->L }
% 0.20/0.54 inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(Y, multiply(Z, inverse(Z))))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(W, multiply(inverse(W), multiply(multiply(V, inverse(V)), inverse(multiply(Y, multiply(Z, inverse(Z))))))))), multiply(multiply(T, inverse(T)), W))))
% 0.20/0.54 = { by lemma 2 }
% 0.20/0.55 inverse(W)
% 0.20/0.55
% 0.20/0.55 Lemma 7: multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(W, inverse(W))))) = inverse(inverse(Y)).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(W, inverse(W)))))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(Y, inverse(Y)))))
% 0.20/0.55 = { by lemma 6 }
% 0.20/0.55 inverse(inverse(Y))
% 0.20/0.55
% 0.20/0.55 Lemma 8: multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(Y))), multiply(Z, inverse(Z))))) = inverse(multiply(W, inverse(W))).
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(Y))), multiply(Z, inverse(Z)))))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(multiply(V, multiply(U, multiply(multiply(T, inverse(T)), inverse(multiply(multiply(W, inverse(W)), multiply(V, U)))))), inverse(multiply(V, multiply(U, multiply(multiply(T, inverse(T)), inverse(multiply(multiply(W, inverse(W)), multiply(V, U))))))))), multiply(Z, inverse(Z)))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(multiply(V, multiply(U, multiply(multiply(T, inverse(T)), inverse(multiply(multiply(W, inverse(W)), multiply(V, U)))))), multiply(W, inverse(W)))), multiply(Z, inverse(Z)))))
% 0.20/0.55 = { by lemma 7 }
% 0.20/0.55 inverse(inverse(multiply(V, multiply(U, multiply(multiply(T, inverse(T)), inverse(multiply(multiply(W, inverse(W)), multiply(V, U))))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 inverse(multiply(W, inverse(W)))
% 0.20/0.55
% 0.20/0.55 Lemma 9: inverse(multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(Y)))))) = inverse(multiply(Z, inverse(Z))).
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(Y))))))
% 0.20/0.55 = { by lemma 8 R->L }
% 0.20/0.55 inverse(multiply(X, multiply(inverse(X), multiply(multiply(W, inverse(W)), inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(V, inverse(V))))))))
% 0.20/0.55 = { by lemma 5 }
% 0.20/0.55 inverse(multiply(Z, inverse(Z)))
% 0.20/0.55
% 0.20/0.55 Lemma 10: inverse(multiply(inverse(X), multiply(inverse(multiply(Y, inverse(Y))), multiply(Z, inverse(Z))))) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(multiply(inverse(X), multiply(inverse(multiply(Y, inverse(Y))), multiply(Z, inverse(Z)))))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 inverse(multiply(inverse(X), multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))))))
% 0.20/0.55 = { by lemma 9 R->L }
% 0.20/0.55 inverse(multiply(inverse(X), multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(W, inverse(W)), inverse(multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(Y))))))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 11: inverse(multiply(X, inverse(multiply(Y, inverse(Y))))) = inverse(X).
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(multiply(X, inverse(multiply(Y, inverse(Y)))))
% 0.20/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.55 inverse(multiply(inverse(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W))))))), inverse(multiply(Y, inverse(Y)))))
% 0.20/0.55 = { by lemma 6 R->L }
% 0.20/0.55 multiply(multiply(U, inverse(U)), inverse(multiply(inverse(multiply(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W)))))), multiply(T, inverse(T)))), multiply(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W)))))), multiply(inverse(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W))))))), inverse(multiply(Y, inverse(Y))))))))
% 0.20/0.55 = { by lemma 10 R->L }
% 0.20/0.55 multiply(multiply(U, inverse(U)), inverse(multiply(inverse(multiply(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W)))))), multiply(T, inverse(T)))), inverse(multiply(inverse(multiply(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W)))))), multiply(inverse(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W))))))), inverse(multiply(Y, inverse(Y)))))), multiply(inverse(multiply(S, inverse(S))), multiply(X2, inverse(X2))))))))
% 0.20/0.55 = { by lemma 9 }
% 0.20/0.55 multiply(multiply(U, inverse(U)), inverse(multiply(inverse(multiply(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W)))))), multiply(T, inverse(T)))), inverse(multiply(inverse(multiply(Y2, inverse(Y2))), multiply(inverse(multiply(S, inverse(S))), multiply(X2, inverse(X2))))))))
% 0.20/0.55 = { by lemma 10 }
% 0.20/0.55 multiply(multiply(U, inverse(U)), inverse(multiply(inverse(multiply(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W)))))), multiply(T, inverse(T)))), multiply(Y2, inverse(Y2)))))
% 0.20/0.55 = { by lemma 7 }
% 0.20/0.55 inverse(inverse(multiply(Z, multiply(W, multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(Z, W))))))))
% 0.20/0.55 = { by axiom 1 (single_axiom) }
% 0.20/0.55 inverse(X)
% 0.20/0.55
% 0.20/0.55 Lemma 12: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 0.20/0.55 Proof:
% 0.20/0.55 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.20/0.55 = { by lemma 10 R->L }
% 0.20/0.55 inverse(multiply(inverse(multiply(X, inverse(multiply(Y, inverse(Y))))), multiply(inverse(multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.20/0.55 = { by lemma 11 }
% 0.20/0.55 inverse(multiply(inverse(X), multiply(inverse(multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.20/0.55 = { by lemma 10 }
% 0.20/0.55 X
% 0.20/0.55
% 0.20/0.55 Lemma 13: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(Z, inverse(Z)), multiply(multiply(W, inverse(W)), V)))) = multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(inverse(multiply(T, inverse(T))), V)))).
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(Z, inverse(Z)), multiply(multiply(W, inverse(W)), V))))
% 0.20/0.55 = { by lemma 4 }
% 0.20/0.55 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(T, inverse(T)), inverse(multiply(T, inverse(T)))), multiply(multiply(W, inverse(W)), V))))
% 0.20/0.55 = { by lemma 3 }
% 0.20/0.55 multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(inverse(multiply(T, inverse(T))), V))))
% 0.20/0.55
% 0.20/0.55 Lemma 14: inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))) = inverse(multiply(Z, inverse(Z))).
% 0.20/0.55 Proof:
% 0.20/0.55 inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))))
% 0.20/0.55 = { by lemma 12 R->L }
% 0.20/0.55 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), inverse(multiply(W, inverse(W))))))
% 0.20/0.55 = { by lemma 6 R->L }
% 0.20/0.55 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))), multiply(inverse(multiply(U, inverse(U))), multiply(W, inverse(W)))))))))
% 0.20/0.55 = { by lemma 10 }
% 0.20/0.55 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), multiply(multiply(V, inverse(V)), multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))
% 0.20/0.55 = { by lemma 12 R->L }
% 0.20/0.55 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))), inverse(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))))))), multiply(multiply(V, inverse(V)), multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))
% 0.20/0.55 = { by lemma 10 R->L }
% 0.20/0.55 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))))), multiply(inverse(multiply(S, inverse(S))), multiply(X2, inverse(X2)))))))), multiply(multiply(V, inverse(V)), multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))
% 0.20/0.55 = { by lemma 6 R->L }
% 0.20/0.55 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))), inverse(multiply(multiply(multiply(Y2, inverse(Y2)), inverse(multiply(inverse(multiply(inverse(multiply(Z2, inverse(Z2))), multiply(W2, inverse(W2)))), multiply(inverse(multiply(Z2, inverse(Z2))), inverse(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))), multiply(inverse(multiply(S, inverse(S))), multiply(X2, inverse(X2)))))))), multiply(multiply(V, inverse(V)), multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))
% 0.20/0.56 = { by lemma 13 R->L }
% 0.20/0.56 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))), inverse(multiply(inverse(multiply(multiply(multiply(V2, inverse(V2)), inverse(multiply(inverse(multiply(Z2, inverse(Z2))), multiply(W2, inverse(W2))))), multiply(multiply(X, inverse(X)), multiply(multiply(U2, inverse(U2)), inverse(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))), multiply(inverse(multiply(S, inverse(S))), multiply(X2, inverse(X2)))))))), multiply(multiply(V, inverse(V)), multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))
% 0.20/0.56 = { by lemma 8 }
% 0.20/0.56 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))), inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(multiply(X, inverse(X)), multiply(multiply(U2, inverse(U2)), inverse(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))), multiply(inverse(multiply(S, inverse(S))), multiply(X2, inverse(X2)))))))), multiply(multiply(V, inverse(V)), multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))
% 0.20/0.56 = { by lemma 8 }
% 0.20/0.56 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))), inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(multiply(X, inverse(X)), inverse(multiply(T2, inverse(T2)))))), multiply(inverse(multiply(S, inverse(S))), multiply(X2, inverse(X2)))))))), multiply(multiply(V, inverse(V)), multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))
% 0.20/0.56 = { by lemma 12 }
% 0.20/0.56 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))), inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(X, inverse(X)))), multiply(inverse(multiply(S, inverse(S))), multiply(X2, inverse(X2)))))))), multiply(multiply(V, inverse(V)), multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))
% 0.20/0.56 = { by lemma 10 }
% 0.20/0.56 inverse(multiply(multiply(X, inverse(X)), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T))), multiply(inverse(multiply(Z, inverse(Z))), multiply(X, inverse(X)))))), multiply(multiply(V, inverse(V)), multiply(inverse(multiply(U, inverse(U))), multiply(T, inverse(T)))))))
% 0.20/0.56 = { by lemma 2 }
% 0.20/0.56 inverse(multiply(Z, inverse(Z)))
% 0.20/0.56
% 0.20/0.56 Lemma 15: multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))) = multiply(Z, inverse(Z)).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))
% 0.20/0.56 = { by lemma 12 R->L }
% 0.20/0.56 multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), inverse(multiply(W, inverse(W))))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by lemma 4 R->L }
% 0.20/0.56 multiply(Z, inverse(Z))
% 0.20/0.56
% 0.20/0.56 Lemma 16: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 0.20/0.56 Proof:
% 0.20/0.56 inverse(multiply(X, inverse(X)))
% 0.20/0.56 = { by lemma 14 R->L }
% 0.20/0.56 inverse(multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W))))
% 0.20/0.56 = { by lemma 15 R->L }
% 0.20/0.56 inverse(multiply(multiply(Z, inverse(Z)), multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))
% 0.20/0.56 = { by lemma 15 R->L }
% 0.20/0.56 inverse(multiply(multiply(multiply(T, inverse(T)), multiply(S, inverse(S))), multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(U, inverse(U)))))))
% 0.20/0.56 = { by lemma 13 }
% 0.20/0.56 multiply(multiply(X2, inverse(X2)), inverse(multiply(multiply(S, inverse(S)), multiply(inverse(multiply(S, inverse(S))), inverse(multiply(U, inverse(U)))))))
% 0.20/0.56 = { by lemma 9 }
% 0.20/0.56 multiply(multiply(X2, inverse(X2)), inverse(multiply(X2, inverse(X2))))
% 0.20/0.56 = { by lemma 4 R->L }
% 0.20/0.56 multiply(Y, inverse(Y))
% 0.20/0.56
% 0.20/0.56 Lemma 17: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(X, multiply(Y, inverse(Y)))
% 0.20/0.56 = { by lemma 16 R->L }
% 0.20/0.56 multiply(X, inverse(multiply(Z, inverse(Z))))
% 0.20/0.56 = { by lemma 12 }
% 0.20/0.56 X
% 0.20/0.56
% 0.20/0.56 Lemma 18: inverse(inverse(X)) = X.
% 0.20/0.56 Proof:
% 0.20/0.56 inverse(inverse(X))
% 0.20/0.56 = { by lemma 11 R->L }
% 0.20/0.56 inverse(multiply(inverse(X), inverse(multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by lemma 17 R->L }
% 0.20/0.56 inverse(multiply(inverse(X), multiply(inverse(multiply(Y, inverse(Y))), multiply(Z, inverse(Z)))))
% 0.20/0.56 = { by lemma 10 }
% 0.20/0.56 X
% 0.20/0.56
% 0.20/0.56 Lemma 19: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(inverse(X), multiply(X, Y))
% 0.20/0.56 = { by lemma 18 R->L }
% 0.20/0.56 multiply(inverse(X), multiply(X, inverse(inverse(Y))))
% 0.20/0.56 = { by lemma 18 R->L }
% 0.20/0.56 multiply(inverse(X), multiply(inverse(inverse(X)), inverse(inverse(Y))))
% 0.20/0.56 = { by lemma 10 R->L }
% 0.20/0.56 inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(X)), inverse(inverse(Y))))), multiply(inverse(multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.20/0.56 = { by lemma 7 R->L }
% 0.20/0.56 inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(X)), multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(Y, multiply(U, inverse(U)))), multiply(T, inverse(T)))))))), multiply(inverse(multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.20/0.56 = { by lemma 5 }
% 0.20/0.56 inverse(multiply(inverse(multiply(Y, multiply(U, inverse(U)))), multiply(inverse(multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.20/0.56 = { by lemma 10 }
% 0.20/0.56 multiply(Y, multiply(U, inverse(U)))
% 0.20/0.56 = { by lemma 17 }
% 0.20/0.56 Y
% 0.20/0.56
% 0.20/0.56 Lemma 20: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(X, inverse(X)), Y)
% 0.20/0.56 = { by lemma 18 R->L }
% 0.20/0.56 multiply(multiply(X, inverse(X)), inverse(inverse(Y)))
% 0.20/0.56 = { by lemma 16 R->L }
% 0.20/0.56 multiply(inverse(multiply(Z, inverse(Z))), inverse(inverse(Y)))
% 0.20/0.56 = { by lemma 7 R->L }
% 0.20/0.56 multiply(inverse(multiply(Z, inverse(Z))), multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(multiply(Y, multiply(W, inverse(W)))), multiply(V, inverse(V))))))
% 0.20/0.56 = { by lemma 19 }
% 0.20/0.56 inverse(multiply(inverse(multiply(Y, multiply(W, inverse(W)))), multiply(V, inverse(V))))
% 0.20/0.56 = { by lemma 17 }
% 0.20/0.56 inverse(inverse(multiply(Y, multiply(W, inverse(W)))))
% 0.20/0.56 = { by lemma 18 }
% 0.20/0.56 multiply(Y, multiply(W, inverse(W)))
% 0.20/0.56 = { by lemma 17 }
% 0.20/0.56 Y
% 0.20/0.56
% 0.20/0.56 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.56 Proof:
% 0.20/0.56 multiply(multiply(a3, b3), c3)
% 0.20/0.56 = { by lemma 10 R->L }
% 0.20/0.56 inverse(multiply(inverse(multiply(multiply(a3, b3), c3)), multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by lemma 20 R->L }
% 0.20/0.56 inverse(multiply(inverse(multiply(multiply(a3, multiply(multiply(Z, inverse(Z)), b3)), c3)), multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by lemma 20 R->L }
% 0.20/0.56 inverse(multiply(inverse(multiply(multiply(multiply(multiply(W, inverse(W)), a3), multiply(multiply(Z, inverse(Z)), b3)), c3)), multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by lemma 2 R->L }
% 0.20/0.56 inverse(multiply(inverse(multiply(multiply(multiply(multiply(W, inverse(W)), a3), multiply(multiply(Z, inverse(Z)), b3)), inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(a3, multiply(b3, c3)))), multiply(multiply(multiply(W, inverse(W)), inverse(multiply(b3, multiply(c3, multiply(multiply(V, inverse(V)), inverse(multiply(a3, multiply(b3, c3)))))))), multiply(multiply(Z, inverse(Z)), b3)))))), multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by axiom 1 (single_axiom) }
% 0.20/0.56 inverse(multiply(inverse(multiply(multiply(multiply(multiply(W, inverse(W)), a3), multiply(multiply(Z, inverse(Z)), b3)), inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(a3, multiply(b3, c3)))), multiply(multiply(multiply(W, inverse(W)), a3), multiply(multiply(Z, inverse(Z)), b3)))))), multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by lemma 12 R->L }
% 0.20/0.56 inverse(multiply(inverse(multiply(multiply(multiply(multiply(W, inverse(W)), a3), multiply(multiply(Z, inverse(Z)), b3)), inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(a3, multiply(b3, c3)))), multiply(multiply(multiply(multiply(W, inverse(W)), a3), multiply(multiply(Z, inverse(Z)), b3)), inverse(multiply(U, inverse(U)))))))), multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by lemma 19 R->L }
% 0.20/0.56 inverse(multiply(inverse(multiply(multiply(multiply(multiply(W, inverse(W)), a3), multiply(multiply(Z, inverse(Z)), b3)), multiply(inverse(multiply(U, inverse(U))), multiply(multiply(U, inverse(U)), inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(a3, multiply(b3, c3)))), multiply(multiply(multiply(multiply(W, inverse(W)), a3), multiply(multiply(Z, inverse(Z)), b3)), inverse(multiply(U, inverse(U)))))))))), multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by axiom 1 (single_axiom) }
% 0.20/0.56 inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(a3, multiply(b3, c3)))), multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by lemma 20 }
% 0.20/0.56 inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), multiply(inverse(multiply(X, inverse(X))), multiply(Y, inverse(Y)))))
% 0.20/0.56 = { by lemma 10 }
% 0.20/0.56 multiply(a3, multiply(b3, c3))
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56
% 0.20/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------