TSTP Solution File: GRP407-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP407-1 : 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 : n032.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 01:18:18 EDT 2023
% Result : Unsatisfiable 0.17s 0.41s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP407-1 : TPTP v8.1.2. Released v2.6.0.
% 0.06/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 22:21:31 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.41 Command-line arguments: --flatten
% 0.17/0.41
% 0.17/0.41 % SZS status Unsatisfiable
% 0.17/0.41
% 0.17/0.45 % SZS output start Proof
% 0.17/0.45 Axiom 1 (single_axiom): multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), multiply(inverse(Y), Y))))) = Z.
% 0.17/0.45
% 0.17/0.45 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))) = multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y))))).
% 0.17/0.45 Proof:
% 0.17/0.45 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z))))
% 0.17/0.45 = { by axiom 1 (single_axiom) R->L }
% 0.17/0.45 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))))), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.17/0.45 = { by axiom 1 (single_axiom) }
% 0.17/0.45 multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.17/0.45
% 0.17/0.45 Lemma 3: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), multiply(inverse(Z), multiply(inverse(Z), Z)))) = W.
% 0.17/0.45 Proof:
% 0.17/0.45 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), multiply(inverse(Z), multiply(inverse(Z), Z))))
% 0.17/0.45 = { by lemma 2 }
% 0.17/0.45 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.17/0.45 = { by axiom 1 (single_axiom) }
% 0.17/0.45 W
% 0.17/0.45
% 0.17/0.45 Lemma 4: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y)))))) = Z.
% 0.17/0.45 Proof:
% 0.17/0.45 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.17/0.45 = { by lemma 2 R->L }
% 0.17/0.45 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z)), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.17/0.45 = { by axiom 1 (single_axiom) }
% 0.17/0.45 Z
% 0.17/0.45
% 0.17/0.45 Lemma 5: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W)) = multiply(inverse(multiply(V, Z)), multiply(V, W)).
% 0.17/0.45 Proof:
% 0.17/0.45 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))
% 0.17/0.45 = { by lemma 4 R->L }
% 0.17/0.45 multiply(inverse(multiply(V, Z)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), multiply(inverse(Z), multiply(inverse(Z), Z))))))
% 0.17/0.45 = { by lemma 3 }
% 0.17/0.45 multiply(inverse(multiply(V, Z)), multiply(V, W))
% 0.17/0.45
% 0.17/0.45 Lemma 6: multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V))) = multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, multiply(Y, multiply(Z, W)))).
% 0.17/0.45 Proof:
% 0.17/0.45 multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))
% 0.17/0.45 = { by lemma 4 R->L }
% 0.17/0.45 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.45 = { by lemma 4 R->L }
% 0.17/0.45 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.45 = { by axiom 1 (single_axiom) R->L }
% 0.17/0.45 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.45 = { by lemma 2 R->L }
% 0.17/0.45 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), V)), Y2)), multiply(inverse(V), multiply(inverse(V), V)))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.45 = { by lemma 2 }
% 0.17/0.45 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(inverse(multiply(multiply(S, inverse(multiply(inverse(Y2), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.45 = { by lemma 2 R->L }
% 0.17/0.45 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(inverse(multiply(Z, W)), W))), Y2)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.45 = { by lemma 2 }
% 0.17/0.45 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.46 = { by axiom 1 (single_axiom) }
% 0.17/0.46 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.46 = { by lemma 4 }
% 0.17/0.46 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.46 = { by lemma 5 }
% 0.17/0.46 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), multiply(Z, W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.46 = { by lemma 5 }
% 0.17/0.46 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.46 = { by lemma 5 }
% 0.17/0.46 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), multiply(Z, W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.46 = { by lemma 5 }
% 0.17/0.46 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W)))), multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 0.17/0.46 = { by lemma 2 }
% 0.17/0.46 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W)))), multiply(inverse(W), multiply(inverse(W), W)))))))
% 0.17/0.46 = { by axiom 1 (single_axiom) }
% 0.17/0.46 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, multiply(Y, multiply(Z, W))))
% 0.17/0.46
% 0.17/0.46 Lemma 7: multiply(X, multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(X, multiply(inverse(Z), multiply(inverse(Z), Z))))))) = multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W))).
% 0.17/0.46 Proof:
% 0.17/0.46 multiply(X, multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(X, multiply(inverse(Z), multiply(inverse(Z), Z)))))))
% 0.17/0.46 = { by lemma 3 R->L }
% 0.17/0.46 multiply(X, multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), X))), multiply(inverse(T), multiply(inverse(T), T)))), multiply(inverse(Z), multiply(inverse(Z), Z)))))))
% 0.17/0.46 = { by lemma 4 }
% 0.17/0.46 multiply(X, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), X))), multiply(inverse(T), multiply(inverse(T), T))))
% 0.17/0.46 = { by lemma 3 R->L }
% 0.17/0.46 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), X))), multiply(inverse(T), multiply(inverse(T), T)))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), X))), multiply(inverse(T), multiply(inverse(T), T))))
% 0.17/0.46 = { by lemma 6 R->L }
% 0.17/0.46 multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W)))
% 0.17/0.46
% 0.17/0.46 Lemma 8: multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), multiply(inverse(X), X))) = multiply(inverse(Y), Y).
% 0.17/0.46 Proof:
% 0.17/0.46 multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), multiply(inverse(X), X)))
% 0.17/0.46 = { by lemma 7 R->L }
% 0.17/0.46 multiply(inverse(Y), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(Y), multiply(inverse(W), multiply(inverse(W), W)))))))
% 0.17/0.46 = { by lemma 4 }
% 0.17/0.46 multiply(inverse(Y), Y)
% 0.17/0.46
% 0.17/0.46 Lemma 9: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.17/0.46 Proof:
% 0.17/0.46 multiply(inverse(Y), Y)
% 0.17/0.46 = { by lemma 8 R->L }
% 0.17/0.46 multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))
% 0.17/0.46 = { by lemma 7 R->L }
% 0.17/0.46 multiply(inverse(X), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(X), multiply(inverse(W), multiply(inverse(W), W)))))))
% 0.17/0.46 = { by lemma 4 }
% 0.17/0.46 multiply(inverse(X), X)
% 0.17/0.46
% 0.17/0.46 Lemma 10: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y)) = multiply(inverse(Z), Z).
% 0.17/0.46 Proof:
% 0.17/0.46 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y))
% 0.17/0.46 = { by lemma 8 R->L }
% 0.17/0.46 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W))))
% 0.17/0.46 = { by lemma 8 R->L }
% 0.17/0.46 multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W)))), multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W))))
% 0.17/0.46 = { by lemma 6 R->L }
% 0.17/0.46 multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))
% 0.17/0.46 = { by lemma 8 }
% 0.17/0.46 multiply(inverse(Z), Z)
% 0.17/0.46
% 0.17/0.46 Lemma 11: inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), multiply(inverse(Z), Z)))) = Y.
% 0.17/0.46 Proof:
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), multiply(inverse(Z), Z))))
% 0.17/0.46 = { by lemma 9 }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.17/0.46 = { by lemma 9 }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.17/0.46 = { by lemma 2 }
% 0.17/0.46 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(V), multiply(inverse(V), V)))))
% 0.17/0.46 = { by axiom 1 (single_axiom) }
% 0.17/0.46 Y
% 0.17/0.46
% 0.17/0.46 Lemma 12: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.17/0.46 Proof:
% 0.17/0.46 inverse(multiply(inverse(X), X))
% 0.17/0.46 = { by lemma 10 R->L }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(W), W)))
% 0.17/0.46 = { by lemma 10 R->L }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(V), V))))
% 0.17/0.46 = { by lemma 11 }
% 0.17/0.46 multiply(inverse(Y), Y)
% 0.17/0.46
% 0.17/0.46 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.17/0.46 Proof:
% 0.17/0.46 multiply(multiply(inverse(b2), b2), a2)
% 0.17/0.46 = { by lemma 11 R->L }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(inverse(multiply(Y, multiply(inverse(Z), Z))), multiply(Y, multiply(inverse(Z), Z))))))
% 0.17/0.46 = { by lemma 12 R->L }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(inverse(multiply(Y, multiply(inverse(Z), Z))), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))))))
% 0.17/0.46 = { by lemma 4 }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))
% 0.17/0.46 = { by lemma 12 }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))
% 0.17/0.46 = { by lemma 12 R->L }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(inverse(b2), b2), inverse(multiply(inverse(multiply(inverse(a2), multiply(inverse(a2), a2))), multiply(inverse(a2), multiply(inverse(a2), a2))))))))
% 0.17/0.46 = { by lemma 4 }
% 0.17/0.46 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(a2), multiply(inverse(a2), a2))))
% 0.17/0.46 = { by lemma 11 }
% 0.17/0.46 a2
% 0.17/0.46 % SZS output end Proof
% 0.17/0.46
% 0.17/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------