TSTP Solution File: GRP014-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP014-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n010.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 01:16:35 EDT 2023
% Result : Unsatisfiable 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP014-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 23:27:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.56 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.56
% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 Axiom 1 (group_axiom): multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(inverse(X), Z))), W), inverse(multiply(Y, W))))) = Z.
% 0.20/0.63
% 0.20/0.63 Lemma 2: inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W)))) = multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(V), Z)), U), inverse(multiply(V, U))))).
% 0.20/0.63 Proof:
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W))))
% 0.20/0.63 = { by axiom 1 (group_axiom) R->L }
% 0.20/0.63 multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(Y), inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(Y)), Z))), W), inverse(multiply(X, W))))))), U), inverse(multiply(V, U)))))
% 0.20/0.63 = { by axiom 1 (group_axiom) }
% 0.20/0.63 multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(V), Z)), U), inverse(multiply(V, U)))))
% 0.20/0.63
% 0.20/0.63 Lemma 3: multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), Z)), W), inverse(multiply(Y, W)))))) = Z.
% 0.20/0.63 Proof:
% 0.20/0.63 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), Z)), W), inverse(multiply(Y, W))))))
% 0.20/0.63 = { by lemma 2 R->L }
% 0.20/0.63 multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(inverse(X)), Z))), U), inverse(multiply(V, U)))))
% 0.20/0.63 = { by axiom 1 (group_axiom) }
% 0.20/0.63 Z
% 0.20/0.63
% 0.20/0.63 Lemma 4: multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(W, Z)))))) = multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), Y)), U), inverse(multiply(V, U))))).
% 0.20/0.63 Proof:
% 0.20/0.63 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(W, Z))))))
% 0.20/0.63 = { by lemma 3 R->L }
% 0.20/0.63 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), Y)), U), inverse(multiply(V, U))))))), Z), inverse(multiply(W, Z))))))
% 0.20/0.63 = { by lemma 3 }
% 0.20/0.63 multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), Y)), U), inverse(multiply(V, U)))))
% 0.20/0.63
% 0.20/0.63 Lemma 5: multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(X), Z))))) = inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V)))).
% 0.20/0.63 Proof:
% 0.20/0.63 multiply(X, inverse(multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(X), Z)))))
% 0.20/0.63 = { by lemma 3 R->L }
% 0.20/0.63 multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(inverse(X)), multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))))), Z), inverse(multiply(inverse(X), Z)))))
% 0.20/0.63 = { by axiom 1 (group_axiom) }
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))
% 0.20/0.63
% 0.20/0.63 Lemma 6: multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(Z), W)), V), inverse(multiply(Z, V))))))) = multiply(inverse(inverse(Y)), W).
% 0.20/0.63 Proof:
% 0.20/0.63 multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(Z), W)), V), inverse(multiply(Z, V)))))))
% 0.20/0.63 = { by lemma 2 R->L }
% 0.20/0.63 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(U), multiply(inverse(inverse(Y)), W))), T), inverse(multiply(U, T))))))
% 0.20/0.63 = { by lemma 3 }
% 0.20/0.63 multiply(inverse(inverse(Y)), W)
% 0.20/0.63
% 0.20/0.63 Lemma 7: multiply(inverse(Z), multiply(Z, Y)) = multiply(inverse(X), multiply(X, Y)).
% 0.20/0.63 Proof:
% 0.20/0.63 multiply(inverse(Z), multiply(Z, Y))
% 0.20/0.63 = { by axiom 1 (group_axiom) R->L }
% 0.20/0.63 multiply(inverse(Z), multiply(Z, multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(W), Y))), S), inverse(multiply(T, S)))))))
% 0.20/0.63 = { by lemma 6 }
% 0.20/0.63 multiply(inverse(inverse(W)), multiply(inverse(W), Y))
% 0.20/0.63 = { by lemma 6 R->L }
% 0.20/0.63 multiply(inverse(X), multiply(X, multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(W), Y))), U), inverse(multiply(V, U)))))))
% 0.20/0.63 = { by axiom 1 (group_axiom) }
% 0.20/0.63 multiply(inverse(X), multiply(X, Y))
% 0.20/0.63
% 0.20/0.63 Lemma 8: inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), multiply(Y, Z)))), W), inverse(multiply(X, W)))) = Z.
% 0.20/0.63 Proof:
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), multiply(Y, Z)))), W), inverse(multiply(X, W))))
% 0.20/0.63 = { by lemma 5 R->L }
% 0.20/0.63 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(Y, Z))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.63 = { by lemma 7 }
% 0.20/0.63 multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(inverse(V)), multiply(inverse(V), Z))), U), inverse(multiply(inverse(V), U)))))
% 0.20/0.63 = { by axiom 1 (group_axiom) }
% 0.20/0.63 Z
% 0.20/0.63
% 0.20/0.63 Lemma 9: multiply(inverse(X), multiply(inverse(Y), multiply(Y, inverse(multiply(multiply(inverse(Z), W), inverse(multiply(X, W))))))) = Z.
% 0.20/0.63 Proof:
% 0.20/0.63 multiply(inverse(X), multiply(inverse(Y), multiply(Y, inverse(multiply(multiply(inverse(Z), W), inverse(multiply(X, W)))))))
% 0.20/0.63 = { by axiom 1 (group_axiom) R->L }
% 0.20/0.63 multiply(inverse(X), multiply(inverse(Y), multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(inverse(X)), Z))), U), inverse(multiply(V, U)))))), W), inverse(multiply(X, W)))))))
% 0.20/0.63 = { by lemma 3 }
% 0.20/0.63 multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(inverse(X)), Z))), U), inverse(multiply(V, U)))))
% 0.20/0.63 = { by axiom 1 (group_axiom) }
% 0.20/0.63 Z
% 0.20/0.63
% 0.20/0.63 Lemma 10: inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V)))) = inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z)))).
% 0.20/0.63 Proof:
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(W), Y)), V), inverse(multiply(W, V))))
% 0.20/0.63 = { by axiom 1 (group_axiom) R->L }
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(inverse(U)), inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(inverse(inverse(U))), Y))), S), inverse(multiply(T, S))))))), V), inverse(multiply(W, V))))
% 0.20/0.63 = { by lemma 2 }
% 0.20/0.63 multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(X2), inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(inverse(inverse(U))), Y))), S), inverse(multiply(T, S)))))), Y2), inverse(multiply(X2, Y2)))))
% 0.20/0.63 = { by lemma 2 R->L }
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(U)), inverse(multiply(multiply(inverse(multiply(inverse(T), multiply(inverse(inverse(inverse(U))), Y))), S), inverse(multiply(T, S))))))), Z), inverse(multiply(X, Z))))
% 0.20/0.63 = { by axiom 1 (group_axiom) }
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z))))
% 0.20/0.63
% 0.20/0.63 Lemma 11: inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(X, multiply(Y, Z)))), W), inverse(multiply(inverse(Y), W)))) = Z.
% 0.20/0.63 Proof:
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(X, multiply(Y, Z)))), W), inverse(multiply(inverse(Y), W))))
% 0.20/0.63 = { by lemma 7 }
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(inverse(Y)), multiply(inverse(Y), multiply(Y, Z)))), W), inverse(multiply(inverse(Y), W))))
% 0.20/0.63 = { by lemma 7 R->L }
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(inverse(Y)), multiply(inverse(V), multiply(V, Z)))), W), inverse(multiply(inverse(Y), W))))
% 0.20/0.63 = { by lemma 10 R->L }
% 0.20/0.63 inverse(multiply(multiply(inverse(multiply(inverse(U), multiply(inverse(V), multiply(V, Z)))), T), inverse(multiply(U, T))))
% 0.20/0.63 = { by lemma 8 }
% 0.20/0.64 Z
% 0.20/0.64
% 0.20/0.64 Lemma 12: multiply(multiply(X, W), inverse(multiply(inverse(Z), W))) = multiply(multiply(X, Y), inverse(multiply(inverse(Z), Y))).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(multiply(X, W), inverse(multiply(inverse(Z), W)))
% 0.20/0.64 = { by lemma 8 R->L }
% 0.20/0.64 multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, X)))), T), inverse(multiply(V, T)))), W), inverse(multiply(inverse(Z), W)))
% 0.20/0.64 = { by lemma 9 R->L }
% 0.20/0.64 multiply(inverse(S), multiply(inverse(X2), multiply(X2, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, X)))), T), inverse(multiply(V, T)))), W), inverse(multiply(inverse(Z), W)))), Y2), inverse(multiply(S, Y2)))))))
% 0.20/0.64 = { by lemma 11 R->L }
% 0.20/0.64 multiply(inverse(S), multiply(inverse(X2), multiply(X2, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), multiply(Z2, multiply(Z, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, X)))), T), inverse(multiply(V, T)))), W), inverse(multiply(inverse(Z), W)))))))), W2), inverse(multiply(inverse(Z), W2)))), Y2), inverse(multiply(S, Y2)))))))
% 0.20/0.64 = { by lemma 5 }
% 0.20/0.64 multiply(inverse(S), multiply(inverse(X2), multiply(X2, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), multiply(Z2, inverse(multiply(multiply(inverse(multiply(inverse(V2), multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, X)))), T), inverse(multiply(V, T))))), U2), inverse(multiply(V2, U2))))))), W2), inverse(multiply(inverse(Z), W2)))), Y2), inverse(multiply(S, Y2)))))))
% 0.20/0.64 = { by lemma 5 R->L }
% 0.20/0.64 multiply(inverse(S), multiply(inverse(X2), multiply(X2, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), multiply(Z2, multiply(Z, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, X)))), T), inverse(multiply(V, T)))), Y), inverse(multiply(inverse(Z), Y)))))))), W2), inverse(multiply(inverse(Z), W2)))), Y2), inverse(multiply(S, Y2)))))))
% 0.20/0.64 = { by lemma 11 }
% 0.20/0.64 multiply(inverse(S), multiply(inverse(X2), multiply(X2, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, X)))), T), inverse(multiply(V, T)))), Y), inverse(multiply(inverse(Z), Y)))), Y2), inverse(multiply(S, Y2)))))))
% 0.20/0.64 = { by lemma 9 }
% 0.20/0.64 multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, X)))), T), inverse(multiply(V, T)))), Y), inverse(multiply(inverse(Z), Y)))
% 0.20/0.64 = { by lemma 8 }
% 0.20/0.64 multiply(multiply(X, Y), inverse(multiply(inverse(Z), Y)))
% 0.20/0.64
% 0.20/0.64 Lemma 13: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(Y, inverse(Y))
% 0.20/0.64 = { by axiom 1 (group_axiom) R->L }
% 0.20/0.64 multiply(Y, inverse(multiply(S, inverse(multiply(multiply(inverse(multiply(inverse(Y2), multiply(inverse(S), Y))), Z2), inverse(multiply(Y2, Z2)))))))
% 0.20/0.64 = { by lemma 4 R->L }
% 0.20/0.64 multiply(Y, inverse(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), Y)), X2), inverse(multiply(S, X2))))))))
% 0.20/0.64 = { by lemma 3 R->L }
% 0.20/0.64 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), Y)), X2), inverse(multiply(S, X2)))))), inverse(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), Y)), X2), inverse(multiply(S, X2))))))))
% 0.20/0.64 = { by lemma 12 R->L }
% 0.20/0.64 multiply(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Z), X)), T), inverse(multiply(Z, T)))))), inverse(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Z), X)), T), inverse(multiply(Z, T))))))))
% 0.20/0.64 = { by lemma 3 }
% 0.20/0.64 multiply(X, inverse(multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Z), X)), T), inverse(multiply(Z, T))))))))
% 0.20/0.64 = { by lemma 4 }
% 0.20/0.64 multiply(X, inverse(multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(Z), X))), V), inverse(multiply(W, V)))))))
% 0.20/0.64 = { by axiom 1 (group_axiom) }
% 0.20/0.64 multiply(X, inverse(X))
% 0.20/0.64
% 0.20/0.64 Lemma 14: inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z)))) = multiply(Y, inverse(multiply(W, inverse(W)))).
% 0.20/0.64 Proof:
% 0.20/0.64 inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z))))
% 0.20/0.64 = { by lemma 5 R->L }
% 0.20/0.64 multiply(Y, inverse(multiply(multiply(inverse(Y), V), inverse(multiply(inverse(Y), V)))))
% 0.20/0.64 = { by lemma 13 R->L }
% 0.20/0.64 multiply(Y, inverse(multiply(W, inverse(W))))
% 0.20/0.64
% 0.20/0.64 Lemma 15: multiply(X, multiply(multiply(inverse(X), Y), inverse(multiply(Z, inverse(Z))))) = Y.
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(X, multiply(multiply(inverse(X), Y), inverse(multiply(Z, inverse(Z)))))
% 0.20/0.64 = { by lemma 14 R->L }
% 0.20/0.64 multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), Y))), V), inverse(multiply(W, V)))))
% 0.20/0.64 = { by axiom 1 (group_axiom) }
% 0.20/0.64 Y
% 0.20/0.64
% 0.20/0.64 Lemma 16: multiply(X, multiply(Y, inverse(Y))) = inverse(inverse(X)).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(X, multiply(Y, inverse(Y)))
% 0.20/0.64 = { by lemma 13 }
% 0.20/0.64 multiply(X, multiply(multiply(inverse(X), inverse(inverse(X))), inverse(multiply(inverse(X), inverse(inverse(X))))))
% 0.20/0.64 = { by lemma 15 }
% 0.20/0.64 inverse(inverse(X))
% 0.20/0.64
% 0.20/0.64 Lemma 17: multiply(inverse(X), multiply(X, Y)) = multiply(Y, multiply(Z, inverse(Z))).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(inverse(X), multiply(X, Y))
% 0.20/0.64 = { by axiom 1 (group_axiom) R->L }
% 0.20/0.64 multiply(W, inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(W), multiply(inverse(X), multiply(X, Y))))), U), inverse(multiply(V, U)))))
% 0.20/0.64 = { by lemma 4 R->L }
% 0.20/0.64 multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), multiply(X, Y)))), T), inverse(multiply(W, T)))), multiply(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), multiply(X, Y)))), T), inverse(multiply(W, T))), inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), multiply(X, Y)))), T), inverse(multiply(W, T))))))
% 0.20/0.64 = { by lemma 13 R->L }
% 0.20/0.64 multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), multiply(inverse(X), multiply(X, Y)))), T), inverse(multiply(W, T)))), multiply(Z, inverse(Z)))
% 0.20/0.64 = { by lemma 8 }
% 0.20/0.64 multiply(Y, multiply(Z, inverse(Z)))
% 0.20/0.64
% 0.20/0.64 Lemma 18: multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(Y, Z))), W), inverse(multiply(V, W)))))) = multiply(V, Z).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(Y, Z))), W), inverse(multiply(V, W))))))
% 0.20/0.64 = { by lemma 7 }
% 0.20/0.64 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(V, Z))), W), inverse(multiply(V, W))))))
% 0.20/0.64 = { by lemma 9 R->L }
% 0.20/0.64 multiply(inverse(X), multiply(X, inverse(multiply(inverse(U), multiply(inverse(T), multiply(T, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(V, Z))), W), inverse(multiply(V, W)))), S), inverse(multiply(U, S))))))))))
% 0.20/0.64 = { by lemma 10 R->L }
% 0.20/0.64 multiply(inverse(X), multiply(X, inverse(multiply(inverse(U), multiply(inverse(T), multiply(T, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(X2), multiply(V, Z))), Y2), inverse(multiply(X2, Y2)))), S), inverse(multiply(U, S))))))))))
% 0.20/0.64 = { by lemma 9 }
% 0.20/0.64 multiply(inverse(X), multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(X2), multiply(V, Z))), Y2), inverse(multiply(X2, Y2))))))
% 0.20/0.64 = { by lemma 3 }
% 0.20/0.64 multiply(V, Z)
% 0.20/0.64
% 0.20/0.64 Lemma 19: multiply(inverse(multiply(Z, multiply(W, inverse(W)))), Z) = multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), X).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(inverse(multiply(Z, multiply(W, inverse(W)))), Z)
% 0.20/0.64 = { by lemma 17 R->L }
% 0.20/0.64 multiply(inverse(multiply(inverse(S), multiply(S, Z))), Z)
% 0.20/0.64 = { by lemma 18 R->L }
% 0.20/0.64 multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), multiply(S, Z))), X2), inverse(multiply(inverse(multiply(inverse(S), multiply(S, Z))), X2))))))
% 0.20/0.64 = { by lemma 13 R->L }
% 0.20/0.64 multiply(inverse(U), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(V, X))), T), inverse(multiply(inverse(multiply(inverse(V), multiply(V, X))), T))))))
% 0.20/0.64 = { by lemma 18 }
% 0.20/0.64 multiply(inverse(multiply(inverse(V), multiply(V, X))), X)
% 0.20/0.64 = { by lemma 17 }
% 0.20/0.64 multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), X)
% 0.20/0.64
% 0.20/0.64 Lemma 20: multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(Z, inverse(Z)))) = X.
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(Z, inverse(Z))))
% 0.20/0.64 = { by lemma 13 }
% 0.20/0.64 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(multiply(inverse(W), V), inverse(multiply(inverse(W), V)))))
% 0.20/0.64 = { by lemma 3 R->L }
% 0.20/0.64 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T)))), multiply(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T))), inverse(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T)))))))), multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T)))), multiply(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T))), inverse(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T))))))), inverse(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T))))))), V), inverse(multiply(inverse(W), V)))))
% 0.20/0.64 = { by lemma 19 R->L }
% 0.20/0.64 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T)))), multiply(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T))), inverse(multiply(multiply(inverse(multiply(inverse(U), W)), T), inverse(multiply(U, T)))))))), multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), X))), V), inverse(multiply(inverse(W), V)))))
% 0.20/0.64 = { by lemma 4 }
% 0.20/0.64 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(multiply(inverse(multiply(inverse(inverse(multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(S), multiply(inverse(U), W))), X2), inverse(multiply(S, X2))))))), multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), X))), V), inverse(multiply(inverse(W), V)))))
% 0.20/0.64 = { by axiom 1 (group_axiom) }
% 0.20/0.64 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(multiply(inverse(multiply(inverse(inverse(W)), multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), X))), V), inverse(multiply(inverse(W), V)))))
% 0.20/0.64 = { by axiom 1 (group_axiom) }
% 0.20/0.64 X
% 0.20/0.64
% 0.20/0.64 Lemma 21: multiply(inverse(multiply(X, inverse(X))), inverse(multiply(Y, inverse(Y)))) = inverse(multiply(Z, inverse(Z))).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(inverse(multiply(X, inverse(X))), inverse(multiply(Y, inverse(Y))))
% 0.20/0.64 = { by lemma 14 R->L }
% 0.20/0.64 inverse(multiply(multiply(inverse(multiply(inverse(inverse(W)), inverse(multiply(X, inverse(X))))), V), inverse(multiply(inverse(W), V))))
% 0.20/0.64 = { by lemma 16 R->L }
% 0.20/0.64 inverse(multiply(multiply(inverse(multiply(multiply(W, multiply(U, inverse(U))), inverse(multiply(X, inverse(X))))), V), inverse(multiply(inverse(W), V))))
% 0.20/0.64 = { by lemma 20 }
% 0.20/0.64 inverse(multiply(multiply(inverse(W), V), inverse(multiply(inverse(W), V))))
% 0.20/0.64 = { by lemma 13 R->L }
% 0.20/0.64 inverse(multiply(Z, inverse(Z)))
% 0.20/0.64
% 0.20/0.64 Lemma 22: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 0.20/0.64 Proof:
% 0.20/0.64 inverse(multiply(X, inverse(X)))
% 0.20/0.64 = { by lemma 15 R->L }
% 0.20/0.64 multiply(multiply(Z, inverse(Z)), multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(multiply(X, inverse(X)))), inverse(multiply(W, inverse(W)))))
% 0.20/0.64 = { by lemma 21 }
% 0.20/0.64 multiply(multiply(Z, inverse(Z)), multiply(inverse(multiply(V, inverse(V))), inverse(multiply(W, inverse(W)))))
% 0.20/0.64 = { by lemma 21 }
% 0.20/0.64 multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z))))
% 0.20/0.64 = { by lemma 13 R->L }
% 0.20/0.64 multiply(Y, inverse(Y))
% 0.20/0.64
% 0.20/0.64 Lemma 23: inverse(inverse(inverse(inverse(X)))) = X.
% 0.20/0.64 Proof:
% 0.20/0.64 inverse(inverse(inverse(inverse(X))))
% 0.20/0.64 = { by lemma 16 R->L }
% 0.20/0.64 multiply(inverse(inverse(X)), multiply(Y, inverse(Y)))
% 0.20/0.64 = { by lemma 22 R->L }
% 0.20/0.64 multiply(inverse(inverse(X)), inverse(multiply(Z, inverse(Z))))
% 0.20/0.64 = { by lemma 16 R->L }
% 0.20/0.64 multiply(multiply(X, multiply(W, inverse(W))), inverse(multiply(Z, inverse(Z))))
% 0.20/0.64 = { by lemma 20 }
% 0.20/0.64 X
% 0.20/0.64
% 0.20/0.64 Lemma 24: multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z))) = inverse(Y).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z)))
% 0.20/0.64 = { by lemma 23 R->L }
% 0.20/0.64 inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z)))))))
% 0.20/0.64 = { by lemma 14 }
% 0.20/0.64 inverse(inverse(inverse(multiply(Y, inverse(multiply(W, inverse(W)))))))
% 0.20/0.64 = { by lemma 22 }
% 0.20/0.64 inverse(inverse(inverse(multiply(Y, multiply(V, inverse(V))))))
% 0.20/0.64 = { by lemma 16 }
% 0.20/0.64 inverse(inverse(inverse(inverse(inverse(Y)))))
% 0.20/0.64 = { by lemma 23 }
% 0.20/0.64 inverse(Y)
% 0.20/0.64
% 0.20/0.64 Lemma 25: multiply(multiply(X, W), inverse(multiply(Z, W))) = multiply(multiply(X, Y), inverse(multiply(Z, Y))).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(multiply(X, W), inverse(multiply(Z, W)))
% 0.20/0.64 = { by lemma 8 R->L }
% 0.20/0.64 multiply(multiply(X, W), inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, Z)))), T), inverse(multiply(V, T)))), W)))
% 0.20/0.64 = { by lemma 12 }
% 0.20/0.64 multiply(multiply(X, Y), inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(V), multiply(inverse(U), multiply(U, Z)))), T), inverse(multiply(V, T)))), Y)))
% 0.20/0.64 = { by lemma 8 }
% 0.20/0.64 multiply(multiply(X, Y), inverse(multiply(Z, Y)))
% 0.20/0.64
% 0.20/0.64 Lemma 26: multiply(X, multiply(multiply(inverse(X), Y), inverse(multiply(Z, Y)))) = inverse(Z).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(X, multiply(multiply(inverse(X), Y), inverse(multiply(Z, Y))))
% 0.20/0.64 = { by lemma 25 }
% 0.20/0.64 multiply(X, multiply(multiply(inverse(X), inverse(Z)), inverse(multiply(Z, inverse(Z)))))
% 0.20/0.64 = { by lemma 13 R->L }
% 0.20/0.64 multiply(X, multiply(multiply(inverse(X), inverse(Z)), inverse(multiply(W, inverse(W)))))
% 0.20/0.64 = { by lemma 15 }
% 0.20/0.64 inverse(Z)
% 0.20/0.64
% 0.20/0.64 Lemma 27: multiply(multiply(inverse(X), Y), inverse(Y)) = inverse(X).
% 0.20/0.64 Proof:
% 0.20/0.64 multiply(multiply(inverse(X), Y), inverse(Y))
% 0.20/0.64 = { by lemma 24 R->L }
% 0.20/0.64 multiply(multiply(inverse(X), Y), multiply(multiply(inverse(multiply(inverse(X), Y)), Z), inverse(multiply(X, Z))))
% 0.20/0.64 = { by lemma 26 }
% 0.20/0.64 inverse(X)
% 0.20/0.64
% 0.20/0.65 Lemma 28: multiply(multiply(X, Y), inverse(Y)) = X.
% 0.20/0.65 Proof:
% 0.20/0.65 multiply(multiply(X, Y), inverse(Y))
% 0.20/0.65 = { by lemma 8 R->L }
% 0.20/0.65 multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(W), multiply(W, X)))), V), inverse(multiply(Z, V)))), Y), inverse(Y))
% 0.20/0.65 = { by lemma 27 }
% 0.20/0.65 inverse(multiply(multiply(inverse(multiply(inverse(Z), multiply(inverse(W), multiply(W, X)))), V), inverse(multiply(Z, V))))
% 0.20/0.65 = { by lemma 8 }
% 0.20/0.65 X
% 0.20/0.65
% 0.20/0.65 Lemma 29: multiply(inverse(multiply(X, inverse(Y))), X) = Y.
% 0.20/0.65 Proof:
% 0.20/0.65 multiply(inverse(multiply(X, inverse(Y))), X)
% 0.20/0.65 = { by lemma 24 R->L }
% 0.20/0.65 multiply(inverse(multiply(X, multiply(multiply(inverse(multiply(inverse(Z), Y)), W), inverse(multiply(Z, W))))), X)
% 0.20/0.65 = { by lemma 28 R->L }
% 0.20/0.65 multiply(inverse(multiply(X, multiply(multiply(inverse(multiply(inverse(Z), Y)), W), inverse(multiply(Z, W))))), multiply(multiply(X, multiply(multiply(inverse(multiply(inverse(Z), Y)), W), inverse(multiply(Z, W)))), inverse(multiply(multiply(inverse(multiply(inverse(Z), Y)), W), inverse(multiply(Z, W))))))
% 0.20/0.65 = { by lemma 3 }
% 0.20/0.65 Y
% 0.20/0.65
% 0.20/0.65 Lemma 30: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.20/0.65 Proof:
% 0.20/0.65 multiply(multiply(X, inverse(X)), Y)
% 0.20/0.65 = { by lemma 22 R->L }
% 0.20/0.65 multiply(inverse(multiply(Y, inverse(Y))), Y)
% 0.20/0.65 = { by lemma 29 }
% 0.20/0.65 Y
% 0.20/0.65
% 0.20/0.65 Goal 1 (prove_associativity): multiply(a, multiply(b, c)) = multiply(multiply(a, b), c).
% 0.20/0.65 Proof:
% 0.20/0.65 multiply(a, multiply(b, c))
% 0.20/0.65 = { by lemma 28 R->L }
% 0.20/0.65 multiply(multiply(multiply(a, b), inverse(b)), multiply(b, c))
% 0.20/0.65 = { by lemma 29 R->L }
% 0.20/0.65 multiply(multiply(multiply(a, b), inverse(b)), multiply(inverse(multiply(X, inverse(multiply(b, c)))), X))
% 0.20/0.65 = { by lemma 30 R->L }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), inverse(multiply(a, b))), multiply(multiply(a, b), inverse(b))), multiply(inverse(multiply(X, inverse(multiply(b, c)))), X))
% 0.20/0.65 = { by lemma 29 R->L }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), inverse(multiply(a, b))), multiply(multiply(inverse(multiply(b, inverse(multiply(a, b)))), b), inverse(b))), multiply(inverse(multiply(X, inverse(multiply(b, c)))), X))
% 0.20/0.65 = { by lemma 27 }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), inverse(multiply(a, b))), inverse(multiply(b, inverse(multiply(a, b))))), multiply(inverse(multiply(X, inverse(multiply(b, c)))), X))
% 0.20/0.65 = { by lemma 25 R->L }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(inverse(multiply(X, inverse(multiply(b, c)))), X))
% 0.20/0.65 = { by lemma 20 R->L }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(inverse(multiply(X, multiply(multiply(inverse(multiply(b, c)), multiply(Y, inverse(Y))), inverse(multiply(Z, inverse(Z)))))), X))
% 0.20/0.65 = { by lemma 14 R->L }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(inverse(inverse(multiply(b, c))), multiply(inverse(multiply(b, c)), multiply(Y, inverse(Y))))), W), inverse(multiply(inverse(multiply(b, c)), W)))))), X))
% 0.20/0.65 = { by lemma 17 }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), W), inverse(multiply(inverse(multiply(b, c)), W)))))), X))
% 0.20/0.65 = { by lemma 11 R->L }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(U), multiply(U, multiply(T, inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))))))), multiply(T, inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))))), inverse(multiply(inverse(T), multiply(T, inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V))))))))), W), inverse(multiply(inverse(multiply(b, c)), W)))))), X))
% 0.20/0.65 = { by lemma 17 }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(multiply(T, inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V))))), multiply(S, inverse(S)))), multiply(T, inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))))), inverse(multiply(inverse(T), multiply(T, inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V))))))))), W), inverse(multiply(inverse(multiply(b, c)), W)))))), X))
% 0.20/0.65 = { by lemma 19 R->L }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), multiply(Y, inverse(Y))), inverse(multiply(inverse(T), multiply(T, inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V))))))))), W), inverse(multiply(inverse(multiply(b, c)), W)))))), X))
% 0.20/0.65 = { by lemma 17 }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), multiply(Y, inverse(Y))), inverse(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), multiply(Y, inverse(Y)))))), W), inverse(multiply(inverse(multiply(b, c)), W)))))), X))
% 0.20/0.65 = { by lemma 29 }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(multiply(inverse(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), multiply(Y, inverse(Y))), inverse(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), multiply(Y, inverse(Y)))))), W), inverse(multiply(inverse(multiply(b, c)), W))))
% 0.20/0.65 = { by lemma 30 R->L }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), multiply(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), multiply(Y, inverse(Y))), inverse(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), multiply(Y, inverse(Y))))), multiply(multiply(inverse(multiply(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), multiply(Y, inverse(Y))), inverse(multiply(inverse(multiply(multiply(Y, inverse(Y)), multiply(V, inverse(V)))), multiply(Y, inverse(Y)))))), W), inverse(multiply(inverse(multiply(b, c)), W)))))
% 0.20/0.65 = { by lemma 26 }
% 0.20/0.65 multiply(multiply(multiply(multiply(a, b), c), inverse(multiply(b, c))), inverse(inverse(multiply(b, c))))
% 0.20/0.65 = { by lemma 28 }
% 0.20/0.65 multiply(multiply(a, b), c)
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65
% 0.20/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------