TSTP Solution File: GRP440-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP440-1 : 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 : n007.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 01:18:26 EDT 2023
% Result : Unsatisfiable 0.19s 0.56s
% Output : Proof 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP440-1 : TPTP v8.1.2. Released v2.6.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 20:46:58 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.56
% 0.19/0.56 % SZS status Unsatisfiable
% 0.19/0.56
% 1.96/0.62 % SZS output start Proof
% 1.96/0.62 Axiom 1 (single_axiom): inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(W, multiply(X, Z))))))) = W.
% 1.96/0.62
% 1.96/0.62 Lemma 2: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W)))) = V.
% 1.96/0.62 Proof:
% 1.96/0.62 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), W))))
% 1.96/0.62 = { by axiom 1 (single_axiom) R->L }
% 1.96/0.62 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z))))), inverse(multiply(V, multiply(X, multiply(multiply(inverse(X), Z), inverse(multiply(W, multiply(V, Z)))))))))))
% 1.96/0.62 = { by axiom 1 (single_axiom) }
% 1.96/0.62 V
% 1.96/0.62
% 1.96/0.62 Lemma 3: multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))) = W.
% 1.96/0.62 Proof:
% 1.96/0.62 multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z))))))
% 1.96/0.62 = { by lemma 2 R->L }
% 1.96/0.62 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 1.96/0.62 = { by axiom 1 (single_axiom) R->L }
% 1.96/0.62 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z)))))), multiply(multiply(inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), Z), inverse(multiply(inverse(W), multiply(X, Z))))))), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 1.96/0.62 = { by axiom 1 (single_axiom) }
% 1.96/0.62 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), S)), X2))))
% 1.96/0.62 = { by axiom 1 (single_axiom) R->L }
% 1.96/0.62 inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(multiply(inverse(V), multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))), inverse(multiply(X2, multiply(W, multiply(multiply(inverse(W), T), inverse(multiply(S, multiply(X2, T))))))))), X2))))
% 1.96/0.62 = { by lemma 2 }
% 1.96/0.62 W
% 1.96/0.62
% 1.96/0.62 Lemma 4: inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y)))))) = Z.
% 1.96/0.62 Proof:
% 1.96/0.62 inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, Y))))))
% 1.96/0.62 = { by lemma 3 R->L }
% 1.96/0.62 inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(Z, multiply(inverse(X), multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(inverse(Y), multiply(inverse(X), V))))))))))))
% 1.96/0.62 = { by lemma 3 R->L }
% 1.96/0.62 inverse(multiply(inverse(X), multiply(X, multiply(multiply(inverse(X), multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(inverse(Y), multiply(inverse(X), V)))))), inverse(multiply(Z, multiply(inverse(X), multiply(W, multiply(multiply(inverse(W), V), inverse(multiply(inverse(Y), multiply(inverse(X), V))))))))))))
% 1.96/0.62 = { by axiom 1 (single_axiom) }
% 1.96/0.62 Z
% 1.96/0.62
% 1.96/0.62 Lemma 5: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W)))) = inverse(X).
% 1.96/0.62 Proof:
% 1.96/0.62 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W))))
% 1.96/0.62 = { by lemma 4 R->L }
% 1.96/0.62 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), inverse(multiply(inverse(X), multiply(X, multiply(Z, inverse(multiply(W, Z))))))))))
% 1.96/0.62 = { by axiom 1 (single_axiom) }
% 1.96/0.62 inverse(X)
% 1.96/0.62
% 1.96/0.62 Lemma 6: multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y))))) = Z.
% 1.96/0.62 Proof:
% 1.96/0.62 multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y)))))
% 1.96/0.62 = { by lemma 2 R->L }
% 1.96/0.62 inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), multiply(U, inverse(multiply(T, U)))), inverse(multiply(inverse(Z), multiply(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y))))), multiply(U, inverse(multiply(T, U)))))))), inverse(Z)))))
% 1.96/0.62 = { by lemma 4 R->L }
% 1.96/0.62 inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), multiply(U, inverse(multiply(T, U)))), inverse(multiply(inverse(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y)))))), multiply(multiply(inverse(X), multiply(X, multiply(Y, inverse(multiply(inverse(Z), Y))))), multiply(U, inverse(multiply(T, U)))))))), inverse(Z)))))
% 1.96/0.62 = { by lemma 4 }
% 1.96/0.62 inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), multiply(U, inverse(multiply(T, U)))), T)), inverse(Z)))))
% 1.96/0.62 = { by lemma 4 R->L }
% 1.96/0.62 inverse(multiply(W, multiply(V, multiply(multiply(inverse(V), multiply(multiply(inverse(W), multiply(U, inverse(multiply(T, U)))), inverse(multiply(inverse(Z), multiply(Z, multiply(U, inverse(multiply(T, U)))))))), inverse(Z)))))
% 1.96/0.62 = { by lemma 2 }
% 1.96/0.62 Z
% 1.96/0.62
% 1.96/0.62 Lemma 7: inverse(multiply(X, multiply(multiply(inverse(X), multiply(Y, inverse(multiply(multiply(Z, inverse(multiply(inverse(W), Z))), Y)))), multiply(W, inverse(V))))) = V.
% 1.96/0.62 Proof:
% 1.96/0.62 inverse(multiply(X, multiply(multiply(inverse(X), multiply(Y, inverse(multiply(multiply(Z, inverse(multiply(inverse(W), Z))), Y)))), multiply(W, inverse(V)))))
% 1.96/0.62 = { by lemma 5 R->L }
% 1.96/0.62 inverse(multiply(X, multiply(multiply(inverse(X), multiply(Y, inverse(multiply(multiply(Z, inverse(multiply(inverse(W), Z))), Y)))), multiply(W, inverse(multiply(V, multiply(X, multiply(multiply(inverse(X), multiply(Y, inverse(multiply(multiply(Z, inverse(multiply(inverse(W), Z))), Y)))), multiply(Z, inverse(multiply(inverse(W), Z)))))))))))
% 1.96/0.62 = { by lemma 6 R->L }
% 1.96/0.62 inverse(multiply(X, multiply(multiply(inverse(X), multiply(Y, inverse(multiply(multiply(Z, inverse(multiply(inverse(W), Z))), Y)))), multiply(multiply(inverse(multiply(inverse(X), multiply(Y, inverse(multiply(multiply(Z, inverse(multiply(inverse(W), Z))), Y))))), multiply(multiply(inverse(X), multiply(Y, inverse(multiply(multiply(Z, inverse(multiply(inverse(W), Z))), Y)))), multiply(Z, inverse(multiply(inverse(W), Z))))), inverse(multiply(V, multiply(X, multiply(multiply(inverse(X), multiply(Y, inverse(multiply(multiply(Z, inverse(multiply(inverse(W), Z))), Y)))), multiply(Z, inverse(multiply(inverse(W), Z)))))))))))
% 1.96/0.62 = { by axiom 1 (single_axiom) }
% 1.96/0.62 V
% 1.96/0.62
% 1.96/0.62 Lemma 8: multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W))) = X.
% 1.96/0.62 Proof:
% 1.96/0.62 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W)))
% 1.96/0.62 = { by lemma 7 R->L }
% 1.96/0.62 inverse(multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(multiply(T, inverse(multiply(inverse(S), T))), U)))), multiply(S, inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(Z, inverse(multiply(W, Z)))), W))))))))
% 1.96/0.62 = { by lemma 5 }
% 1.96/0.62 inverse(multiply(V, multiply(multiply(inverse(V), multiply(U, inverse(multiply(multiply(T, inverse(multiply(inverse(S), T))), U)))), multiply(S, inverse(X)))))
% 1.96/0.62 = { by lemma 7 }
% 1.96/0.62 X
% 1.96/0.62
% 1.96/0.62 Lemma 9: inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X)))))) = Z.
% 1.96/0.62 Proof:
% 1.96/0.62 inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, X))))))
% 1.96/0.62 = { by lemma 8 R->L }
% 1.96/0.62 inverse(multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U)))))))))
% 1.96/0.62 = { by lemma 8 R->L }
% 1.96/0.62 inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U))), inverse(multiply(Z, multiply(X, multiply(W, multiply(multiply(inverse(W), multiply(V, inverse(multiply(U, V)))), U)))))))))
% 1.96/0.62 = { by axiom 1 (single_axiom) }
% 1.96/0.62 Z
% 1.96/0.62
% 1.96/0.62 Lemma 10: inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(Y, Z)))), multiply(W, multiply(inverse(W), Y)))) = Z.
% 1.96/0.62 Proof:
% 1.96/0.62 inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(Y, Z)))), multiply(W, multiply(inverse(W), Y))))
% 1.96/0.62 = { by lemma 9 R->L }
% 1.96/0.62 inverse(multiply(multiply(X, multiply(inverse(X), inverse(multiply(Y, Z)))), multiply(W, multiply(inverse(W), inverse(multiply(Z, multiply(X, multiply(inverse(X), inverse(multiply(Y, Z))))))))))
% 1.96/0.62 = { by lemma 9 }
% 1.96/0.62 Z
% 1.96/0.62
% 1.96/0.62 Lemma 11: inverse(multiply(multiply(X, multiply(inverse(X), Y)), multiply(Z, multiply(inverse(Z), W)))) = multiply(V, multiply(inverse(V), inverse(multiply(Y, W)))).
% 1.96/0.62 Proof:
% 1.96/0.62 inverse(multiply(multiply(X, multiply(inverse(X), Y)), multiply(Z, multiply(inverse(Z), W))))
% 1.96/0.62 = { by lemma 10 R->L }
% 1.96/0.62 inverse(multiply(multiply(X, multiply(inverse(X), Y)), multiply(Z, multiply(inverse(Z), inverse(multiply(multiply(V, multiply(inverse(V), inverse(multiply(Y, W)))), multiply(X, multiply(inverse(X), Y))))))))
% 1.96/0.62 = { by lemma 9 }
% 1.96/0.62 multiply(V, multiply(inverse(V), inverse(multiply(Y, W))))
% 1.96/0.62
% 1.96/0.62 Lemma 12: multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(Y, Z)), Y)))) = Z.
% 1.96/0.62 Proof:
% 1.96/0.62 multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(Y, Z)), Y))))
% 1.96/0.62 = { by lemma 11 R->L }
% 1.96/0.62 inverse(multiply(multiply(W, multiply(inverse(W), inverse(multiply(Y, Z)))), multiply(V, multiply(inverse(V), Y))))
% 1.96/0.62 = { by lemma 10 }
% 2.14/0.62 Z
% 2.14/0.62
% 2.14/0.62 Lemma 13: multiply(inverse(X), inverse(multiply(inverse(multiply(Y, Z)), Y))) = multiply(W, multiply(inverse(W), inverse(multiply(inverse(Z), X)))).
% 2.14/0.62 Proof:
% 2.14/0.62 multiply(inverse(X), inverse(multiply(inverse(multiply(Y, Z)), Y)))
% 2.14/0.62 = { by lemma 10 R->L }
% 2.14/0.62 inverse(multiply(multiply(V, multiply(inverse(V), inverse(multiply(X, multiply(inverse(X), inverse(multiply(inverse(multiply(Y, Z)), Y))))))), multiply(U, multiply(inverse(U), X))))
% 2.14/0.62 = { by lemma 12 }
% 2.14/0.62 inverse(multiply(multiply(V, multiply(inverse(V), inverse(Z))), multiply(U, multiply(inverse(U), X))))
% 2.14/0.62 = { by lemma 11 }
% 2.14/0.63 multiply(W, multiply(inverse(W), inverse(multiply(inverse(Z), X))))
% 2.14/0.63
% 2.14/0.63 Lemma 14: multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(Z), Z))))) = X.
% 2.14/0.63 Proof:
% 2.14/0.63 multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))
% 2.14/0.63 = { by lemma 5 R->L }
% 2.14/0.63 multiply(X, multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(multiply(Z, multiply(Y, multiply(multiply(inverse(Y), multiply(W, inverse(multiply(V, W)))), V)))), Z)))))
% 2.14/0.63 = { by lemma 13 }
% 2.14/0.63 multiply(X, multiply(Y, multiply(U, multiply(inverse(U), inverse(multiply(inverse(multiply(Y, multiply(multiply(inverse(Y), multiply(W, inverse(multiply(V, W)))), V))), Y))))))
% 2.14/0.63 = { by lemma 12 }
% 2.14/0.63 multiply(X, multiply(Y, multiply(multiply(inverse(Y), multiply(W, inverse(multiply(V, W)))), V)))
% 2.14/0.63 = { by lemma 8 }
% 2.14/0.63 X
% 2.14/0.63
% 2.14/0.63 Lemma 15: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 2.14/0.63 Proof:
% 2.14/0.63 multiply(inverse(Y), Y)
% 2.14/0.63 = { by lemma 7 R->L }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(Y), Y))))))
% 2.14/0.63 = { by lemma 4 R->L }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(X), multiply(X, multiply(T, inverse(multiply(inverse(multiply(inverse(Y), Y)), T))))))))))
% 2.14/0.63 = { by lemma 12 R->L }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(X), multiply(X, multiply(T, multiply(U2, multiply(inverse(U2), inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(Y), Y)), T)))), T))))))))))))
% 2.14/0.63 = { by lemma 13 R->L }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(X), multiply(X, multiply(T, multiply(inverse(T), inverse(multiply(inverse(multiply(S, multiply(T, inverse(multiply(inverse(multiply(inverse(Y), Y)), T))))), S)))))))))))
% 2.14/0.63 = { by lemma 14 R->L }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(X), multiply(X, multiply(T, multiply(inverse(T), inverse(multiply(inverse(multiply(multiply(S, multiply(T, inverse(multiply(inverse(multiply(inverse(Y), Y)), T)))), multiply(V2, multiply(inverse(V2), inverse(multiply(inverse(Y), Y)))))), S)))))))))))
% 2.14/0.63 = { by lemma 7 R->L }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(X), multiply(X, multiply(T, multiply(inverse(T), inverse(multiply(inverse(inverse(multiply(X2, multiply(multiply(inverse(X2), multiply(Y2, inverse(multiply(multiply(Z2, inverse(multiply(inverse(W2), Z2))), Y2)))), multiply(W2, inverse(multiply(multiply(S, multiply(T, inverse(multiply(inverse(multiply(inverse(Y), Y)), T)))), multiply(V2, multiply(inverse(V2), inverse(multiply(inverse(Y), Y))))))))))), S)))))))))))
% 2.14/0.63 = { by lemma 4 R->L }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(X), multiply(X, multiply(T, multiply(inverse(T), inverse(multiply(inverse(inverse(multiply(X2, multiply(multiply(inverse(X2), multiply(Y2, inverse(multiply(multiply(Z2, inverse(multiply(inverse(W2), Z2))), Y2)))), multiply(W2, inverse(multiply(multiply(S, multiply(T, inverse(multiply(inverse(multiply(inverse(Y), Y)), T)))), multiply(V2, multiply(inverse(V2), inverse(multiply(inverse(S), multiply(S, multiply(T, inverse(multiply(inverse(multiply(inverse(Y), Y)), T))))))))))))))), S)))))))))))
% 2.14/0.63 = { by lemma 9 }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(X), multiply(X, multiply(T, multiply(inverse(T), inverse(multiply(inverse(inverse(multiply(X2, multiply(multiply(inverse(X2), multiply(Y2, inverse(multiply(multiply(Z2, inverse(multiply(inverse(W2), Z2))), Y2)))), multiply(W2, inverse(S)))))), S)))))))))))
% 2.14/0.63 = { by lemma 7 }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(X), multiply(X, multiply(T, multiply(inverse(T), inverse(multiply(inverse(S), S)))))))))))
% 2.14/0.63 = { by lemma 14 }
% 2.14/0.63 inverse(multiply(Z, multiply(multiply(inverse(Z), multiply(W, inverse(multiply(multiply(V, inverse(multiply(inverse(U), V))), W)))), multiply(U, inverse(multiply(inverse(X), X))))))
% 2.14/0.63 = { by lemma 7 }
% 2.14/0.63 multiply(inverse(X), X)
% 2.14/0.63
% 2.14/0.63 Lemma 16: multiply(X, multiply(inverse(Y), Y)) = X.
% 2.14/0.63 Proof:
% 2.14/0.63 multiply(X, multiply(inverse(Y), Y))
% 2.14/0.63 = { by lemma 15 }
% 2.14/0.63 multiply(X, multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))
% 2.14/0.63 = { by lemma 15 }
% 2.14/0.63 multiply(X, multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 2.14/0.63 = { by lemma 14 }
% 2.14/0.63 X
% 2.14/0.63
% 2.14/0.63 Lemma 17: inverse(multiply(X, inverse(multiply(Y, X)))) = Y.
% 2.14/0.63 Proof:
% 2.14/0.63 inverse(multiply(X, inverse(multiply(Y, X))))
% 2.14/0.63 = { by lemma 16 R->L }
% 2.14/0.63 inverse(multiply(X, multiply(inverse(multiply(Y, X)), multiply(inverse(inverse(multiply(Y, X))), inverse(multiply(Y, X))))))
% 2.14/0.63 = { by lemma 9 }
% 2.14/0.63 Y
% 2.14/0.63
% 2.14/0.63 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 2.14/0.63 Proof:
% 2.14/0.63 multiply(multiply(inverse(b2), b2), a2)
% 2.14/0.63 = { by lemma 9 R->L }
% 2.14/0.63 inverse(multiply(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2)), multiply(X, multiply(inverse(X), inverse(multiply(multiply(multiply(inverse(b2), b2), a2), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2))))))))
% 2.14/0.63 = { by lemma 16 }
% 2.14/0.63 inverse(multiply(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2)), multiply(X, multiply(inverse(X), inverse(multiply(multiply(inverse(b2), b2), a2))))))
% 2.14/0.63 = { by lemma 6 R->L }
% 2.14/0.63 inverse(multiply(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2)), multiply(X, multiply(inverse(X), inverse(multiply(inverse(inverse(multiply(multiply(inverse(b2), b2), a2))), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(multiply(inverse(b2), b2), a2), inverse(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2)))))))))))
% 2.14/0.63 = { by lemma 16 R->L }
% 2.14/0.63 inverse(multiply(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2)), multiply(X, multiply(inverse(X), inverse(multiply(inverse(inverse(multiply(multiply(inverse(b2), b2), a2))), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(multiply(inverse(b2), b2), a2), multiply(inverse(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2))), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2)))))))))))
% 2.14/0.63 = { by lemma 16 }
% 2.14/0.63 inverse(multiply(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2)), multiply(X, multiply(inverse(X), inverse(multiply(inverse(inverse(multiply(multiply(inverse(b2), b2), a2))), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), a2))))))))
% 2.14/0.63 = { by lemma 9 }
% 2.14/0.63 inverse(inverse(multiply(multiply(inverse(b2), b2), a2)))
% 2.14/0.63 = { by lemma 16 R->L }
% 2.14/0.63 inverse(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(inverse(b2), b2)))
% 2.14/0.63 = { by lemma 17 R->L }
% 2.14/0.63 inverse(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), inverse(multiply(a2, inverse(multiply(multiply(inverse(b2), b2), a2))))))
% 2.14/0.63 = { by lemma 17 }
% 2.14/0.63 a2
% 2.14/0.63 % SZS output end Proof
% 2.14/0.63
% 2.14/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
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