TSTP Solution File: GRP408-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP408-1 : 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 : n008.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 0.18s 0.74s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP408-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Aug 29 01:32:17 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.18/0.74 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.18/0.74
% 0.18/0.74 % SZS status Unsatisfiable
% 0.18/0.74
% 0.18/0.84 % SZS output start Proof
% 0.18/0.85 Axiom 1 (single_axiom): multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), multiply(inverse(Y), Y))))) = Z.
% 0.18/0.85
% 0.18/0.85 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))))).
% 0.18/0.85 Proof:
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z))))
% 0.18/0.85 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.85 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)))))
% 0.18/0.85 = { by axiom 1 (single_axiom) }
% 0.18/0.85 multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.18/0.85
% 0.18/0.85 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.
% 0.18/0.85 Proof:
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), multiply(inverse(Z), multiply(inverse(Z), Z))))
% 0.18/0.85 = { by lemma 2 }
% 0.18/0.85 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.18/0.85 = { by axiom 1 (single_axiom) }
% 0.18/0.85 W
% 0.18/0.85
% 0.18/0.85 Lemma 4: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(Y), multiply(inverse(Y), Y)))) = Z.
% 0.18/0.85 Proof:
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.85 = { by lemma 3 R->L }
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), multiply(inverse(U), multiply(inverse(U), U)))), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.85 = { by lemma 3 R->L }
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), multiply(inverse(U), multiply(inverse(U), U)))), Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), multiply(inverse(U), multiply(inverse(U), U)))), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.85 = { by lemma 3 }
% 0.18/0.85 Z
% 0.18/0.85
% 0.18/0.85 Lemma 5: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y)))))) = Z.
% 0.18/0.85 Proof:
% 0.18/0.85 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.18/0.85 = { by lemma 2 R->L }
% 0.18/0.85 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z)), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.18/0.85 = { by axiom 1 (single_axiom) }
% 0.18/0.85 Z
% 0.18/0.85
% 0.18/0.85 Lemma 6: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(Y), multiply(inverse(Y), Y))) = Z.
% 0.18/0.85 Proof:
% 0.18/0.85 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(Y), multiply(inverse(Y), Y)))
% 0.18/0.85 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.85 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(Y), multiply(inverse(Y), Y)))), multiply(inverse(multiply(X, inverse(Z))), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z))))))))
% 0.18/0.85 = { by lemma 4 }
% 0.18/0.85 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(Z), multiply(inverse(multiply(X, inverse(Z))), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z))))))))
% 0.18/0.85 = { by lemma 5 }
% 0.18/0.85 Z
% 0.18/0.85
% 0.18/0.85 Lemma 7: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W)) = multiply(inverse(multiply(V, Z)), multiply(V, W)).
% 0.18/0.85 Proof:
% 0.18/0.85 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))
% 0.18/0.85 = { by lemma 5 R->L }
% 0.18/0.85 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))))))
% 0.18/0.85 = { by lemma 3 }
% 0.18/0.85 multiply(inverse(multiply(V, Z)), multiply(V, W))
% 0.18/0.85
% 0.18/0.85 Lemma 8: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 0.18/0.85 Proof:
% 0.18/0.85 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.18/0.85 = { by lemma 3 R->L }
% 0.18/0.85 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.18/0.85 = { by lemma 5 }
% 0.18/0.85 multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))
% 0.18/0.85 = { by lemma 5 R->L }
% 0.18/0.85 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.18/0.85 = { by lemma 3 }
% 0.18/0.85 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.18/0.85
% 0.18/0.85 Lemma 9: multiply(V, multiply(inverse(multiply(inverse(multiply(U, Z)), multiply(U, V))), W)) = multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))), W)).
% 0.18/0.85 Proof:
% 0.18/0.85 multiply(V, multiply(inverse(multiply(inverse(multiply(U, Z)), multiply(U, V))), W))
% 0.18/0.85 = { by lemma 7 R->L }
% 0.18/0.85 multiply(V, multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 0.18/0.85 = { by lemma 3 R->L }
% 0.18/0.85 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), multiply(inverse(Z), multiply(inverse(Z), Z)))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 0.18/0.85 = { by lemma 8 R->L }
% 0.18/0.85 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), multiply(inverse(Z), multiply(inverse(Z), Z)))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 0.18/0.85 = { by lemma 3 }
% 0.18/0.85 multiply(X, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 0.18/0.85 = { by lemma 7 }
% 0.18/0.85 multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))), W))
% 0.18/0.85
% 0.18/0.85 Lemma 10: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.18/0.85 Proof:
% 0.18/0.85 multiply(inverse(Y), Y)
% 0.18/0.85 = { by lemma 6 R->L }
% 0.18/0.85 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Y)))), multiply(inverse(W), multiply(inverse(W), W))))
% 0.18/0.85 = { by lemma 9 R->L }
% 0.18/0.85 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, inverse(X)))), multiply(inverse(W), multiply(inverse(W), W))))
% 0.18/0.85 = { by lemma 6 }
% 0.18/0.85 multiply(inverse(X), X)
% 0.18/0.85
% 0.18/0.85 Lemma 11: inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), multiply(inverse(Z), Z)))) = Y.
% 0.18/0.85 Proof:
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), multiply(inverse(Z), Z))))
% 0.18/0.85 = { by lemma 10 }
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.85 = { by lemma 10 }
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.85 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.85 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), multiply(inverse(Y), multiply(inverse(Y), Y)))))), multiply(inverse(V), multiply(inverse(V), V)))))
% 0.18/0.85 = { by axiom 1 (single_axiom) }
% 0.18/0.85 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(V), multiply(inverse(V), V)))))
% 0.18/0.85 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.85 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), Y))), multiply(inverse(U), multiply(inverse(U), U)))))), multiply(inverse(V), multiply(inverse(V), V)))))
% 0.18/0.85 = { by axiom 1 (single_axiom) }
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), Y))), multiply(inverse(U), multiply(inverse(U), U))))
% 0.18/0.85 = { by lemma 3 }
% 0.18/0.85 Y
% 0.18/0.85
% 0.18/0.85 Lemma 12: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.18/0.85 Proof:
% 0.18/0.85 inverse(multiply(inverse(X), X))
% 0.18/0.85 = { by lemma 10 }
% 0.18/0.85 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y))), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y))))
% 0.18/0.85 = { by lemma 11 }
% 0.18/0.86 multiply(inverse(Y), Y)
% 0.18/0.86
% 0.18/0.86 Lemma 13: inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Y), Y)))) = Y.
% 0.18/0.86 Proof:
% 0.18/0.86 inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Y), Y))))
% 0.18/0.86 = { by lemma 8 }
% 0.18/0.86 inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.86 = { by lemma 10 }
% 0.18/0.86 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), Y)), multiply(inverse(multiply(Z, W)), Y))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.86 = { by lemma 2 }
% 0.18/0.86 multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), Y)), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.18/0.86 = { by axiom 1 (single_axiom) }
% 0.18/0.86 Y
% 0.18/0.86
% 0.18/0.86 Lemma 14: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(Z, W)), multiply(Z, multiply(inverse(Y), Y)))))) = multiply(inverse(Y), W).
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(Z, W)), multiply(Z, multiply(inverse(Y), Y))))))
% 0.18/0.86 = { by lemma 8 }
% 0.18/0.86 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(Y), W)), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.18/0.86 = { by lemma 5 }
% 0.18/0.86 multiply(inverse(Y), W)
% 0.18/0.86
% 0.18/0.86 Lemma 15: multiply(multiply(inverse(X), X), multiply(inverse(Y), Y)) = multiply(inverse(Y), Y).
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(multiply(inverse(X), X), multiply(inverse(Y), Y))
% 0.18/0.86 = { by lemma 13 R->L }
% 0.18/0.86 multiply(multiply(inverse(X), X), multiply(inverse(Y), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(Y), Y))))))
% 0.18/0.86 = { by lemma 12 R->L }
% 0.18/0.86 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(Y), Y))))))
% 0.18/0.86 = { by lemma 14 }
% 0.18/0.86 multiply(inverse(Y), Y)
% 0.18/0.86
% 0.18/0.86 Lemma 16: multiply(multiply(inverse(X), X), Y) = Y.
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(multiply(inverse(X), X), Y)
% 0.18/0.86 = { by lemma 11 R->L }
% 0.18/0.86 inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(inverse(Y), Y))))
% 0.18/0.86 = { by axiom 1 (single_axiom) R->L }
% 0.18/0.86 inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(X), X), multiply(inverse(Z), Z))), multiply(inverse(Y), Y))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))))
% 0.18/0.86 = { by lemma 15 }
% 0.18/0.86 inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Y), Y))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))))
% 0.18/0.86 = { by lemma 10 R->L }
% 0.18/0.86 inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Y), Y))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Y), Y))))))))
% 0.18/0.86 = { by lemma 14 }
% 0.18/0.86 inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.86 = { by lemma 13 }
% 0.18/0.86 Y
% 0.18/0.86
% 0.18/0.86 Lemma 17: multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), Z) = multiply(X, Z).
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), Z)
% 0.18/0.86 = { by lemma 14 R->L }
% 0.18/0.86 multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, Z)), multiply(V, multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(X), multiply(inverse(Y), Y))))))))
% 0.18/0.86 = { by lemma 12 R->L }
% 0.18/0.86 multiply(inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, Z)), multiply(V, multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(X), multiply(inverse(Y), Y))))))))
% 0.18/0.86 = { by lemma 11 }
% 0.18/0.86 multiply(X, multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, Z)), multiply(V, multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(X), multiply(inverse(Y), Y))))))))
% 0.18/0.86 = { by lemma 10 R->L }
% 0.18/0.86 multiply(X, multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(V, Z)), multiply(V, multiply(inverse(Z), Z))))))
% 0.18/0.86 = { by lemma 13 }
% 0.18/0.86 multiply(X, multiply(multiply(inverse(W), W), Z))
% 0.18/0.86 = { by lemma 16 }
% 0.18/0.86 multiply(X, Z)
% 0.18/0.86
% 0.18/0.86 Lemma 18: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(Y, Z))), W)), multiply(inverse(multiply(Y, Z)), multiply(inverse(multiply(V, Z)), multiply(V, Z)))))) = W.
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(Y, Z))), W)), multiply(inverse(multiply(Y, Z)), multiply(inverse(multiply(V, Z)), multiply(V, Z))))))
% 0.18/0.86 = { by lemma 8 }
% 0.18/0.86 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(Y, Z))), W)), multiply(inverse(multiply(Y, Z)), multiply(inverse(multiply(Y, Z)), multiply(Y, Z))))))
% 0.18/0.86 = { by axiom 1 (single_axiom) }
% 0.18/0.86 W
% 0.18/0.86
% 0.18/0.86 Lemma 19: multiply(inverse(inverse(X)), multiply(inverse(Y), Y)) = X.
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(inverse(inverse(X)), multiply(inverse(Y), Y))
% 0.18/0.86 = { by lemma 12 R->L }
% 0.18/0.86 multiply(inverse(inverse(X)), inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))))
% 0.18/0.86 = { by lemma 15 R->L }
% 0.18/0.86 multiply(inverse(inverse(X)), inverse(multiply(inverse(multiply(inverse(X), X)), multiply(multiply(inverse(Z), Z), multiply(inverse(X), X)))))
% 0.18/0.86 = { by lemma 10 }
% 0.18/0.86 multiply(inverse(inverse(X)), inverse(multiply(inverse(multiply(inverse(X), X)), multiply(multiply(inverse(Z), Z), multiply(inverse(multiply(W, V)), multiply(W, V))))))
% 0.18/0.86 = { by lemma 12 R->L }
% 0.18/0.86 multiply(inverse(inverse(X)), inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(inverse(V), V)), multiply(inverse(multiply(W, V)), multiply(W, V))))))
% 0.18/0.86 = { by lemma 17 R->L }
% 0.18/0.86 multiply(inverse(inverse(X)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(X)), multiply(inverse(V), V))), X)), multiply(inverse(multiply(inverse(V), V)), multiply(inverse(multiply(W, V)), multiply(W, V))))))
% 0.18/0.86 = { by lemma 18 }
% 0.18/0.86 X
% 0.18/0.86
% 0.18/0.86 Lemma 20: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(X).
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(inverse(X), multiply(inverse(Y), Y))
% 0.18/0.86 = { by lemma 10 }
% 0.18/0.86 multiply(inverse(X), multiply(inverse(inverse(X)), inverse(X)))
% 0.18/0.86 = { by lemma 19 R->L }
% 0.18/0.86 multiply(inverse(X), multiply(inverse(inverse(X)), inverse(multiply(inverse(inverse(X)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))
% 0.18/0.86 = { by lemma 15 R->L }
% 0.18/0.86 multiply(inverse(X), multiply(inverse(inverse(X)), inverse(multiply(inverse(inverse(X)), multiply(multiply(inverse(W), W), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))
% 0.18/0.86 = { by lemma 12 R->L }
% 0.18/0.86 multiply(inverse(X), multiply(inverse(inverse(X)), inverse(multiply(inverse(inverse(X)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))
% 0.18/0.86 = { by lemma 19 R->L }
% 0.18/0.86 multiply(inverse(multiply(inverse(inverse(X)), multiply(inverse(Z), Z))), multiply(inverse(inverse(X)), inverse(multiply(inverse(inverse(X)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))
% 0.18/0.86 = { by lemma 5 }
% 0.18/0.86 inverse(X)
% 0.18/0.86
% 0.18/0.86 Lemma 21: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(inverse(X), X)
% 0.18/0.86 = { by lemma 6 R->L }
% 0.18/0.86 multiply(inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(multiply(inverse(X), X))))), multiply(inverse(Y), multiply(inverse(Y), Y)))
% 0.18/0.86 = { by lemma 12 }
% 0.18/0.86 multiply(inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(Y), Y)))), multiply(inverse(Y), multiply(inverse(Y), Y)))
% 0.18/0.86 = { by lemma 13 }
% 0.18/0.86 multiply(Y, multiply(inverse(Y), multiply(inverse(Y), Y)))
% 0.18/0.86 = { by lemma 20 }
% 0.18/0.86 multiply(Y, inverse(Y))
% 0.18/0.86
% 0.18/0.86 Lemma 22: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(inverse(inverse(X)), Y)
% 0.18/0.86 = { by lemma 20 R->L }
% 0.18/0.86 multiply(inverse(multiply(inverse(X), multiply(inverse(Z), Z))), Y)
% 0.18/0.86 = { by lemma 17 }
% 0.18/0.86 multiply(X, Y)
% 0.18/0.86
% 0.18/0.86 Lemma 23: multiply(inverse(X), multiply(inverse(inverse(X)), Y)) = Y.
% 0.18/0.86 Proof:
% 0.18/0.86 multiply(inverse(X), multiply(inverse(inverse(X)), Y))
% 0.18/0.86 = { by lemma 13 R->L }
% 0.18/0.86 multiply(inverse(X), multiply(inverse(inverse(X)), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(Y), Y))))))
% 0.18/0.86 = { by lemma 10 }
% 0.18/0.86 multiply(inverse(X), multiply(inverse(inverse(X)), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)))))))
% 0.18/0.86 = { by lemma 19 R->L }
% 0.18/0.86 multiply(inverse(multiply(inverse(inverse(X)), multiply(inverse(W), W))), multiply(inverse(inverse(X)), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)))))))
% 0.18/0.86 = { by lemma 14 }
% 0.18/0.86 multiply(inverse(multiply(inverse(W), W)), Y)
% 0.18/0.86 = { by lemma 12 }
% 0.18/0.86 multiply(multiply(inverse(V), V), Y)
% 0.18/0.86 = { by lemma 16 }
% 0.18/0.87 Y
% 0.18/0.87
% 0.18/0.87 Lemma 24: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.18/0.87 Proof:
% 0.18/0.87 multiply(X, multiply(Y, inverse(Y)))
% 0.18/0.87 = { by lemma 21 R->L }
% 0.18/0.87 multiply(X, multiply(inverse(Z), Z))
% 0.18/0.87 = { by lemma 12 R->L }
% 0.18/0.87 multiply(X, inverse(multiply(inverse(inverse(W)), inverse(W))))
% 0.18/0.87 = { by lemma 20 R->L }
% 0.18/0.87 multiply(X, inverse(multiply(inverse(inverse(W)), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.18/0.87 = { by lemma 20 R->L }
% 0.18/0.87 multiply(X, inverse(multiply(inverse(multiply(inverse(W), multiply(inverse(X), X))), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.18/0.87 = { by lemma 13 R->L }
% 0.18/0.87 multiply(X, inverse(multiply(inverse(multiply(inverse(W), multiply(inverse(X), inverse(multiply(inverse(multiply(V, X)), multiply(V, multiply(inverse(X), X))))))), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.18/0.87 = { by lemma 10 }
% 0.18/0.87 multiply(X, inverse(multiply(inverse(multiply(inverse(W), multiply(inverse(X), inverse(multiply(inverse(multiply(V, X)), multiply(V, multiply(inverse(multiply(inverse(inverse(X)), W)), multiply(inverse(inverse(X)), W)))))))), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.18/0.87 = { by lemma 23 R->L }
% 0.18/0.87 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(inverse(X)), W))), multiply(inverse(X), inverse(multiply(inverse(multiply(V, X)), multiply(V, multiply(inverse(multiply(inverse(inverse(X)), W)), multiply(inverse(inverse(X)), W)))))))), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.18/0.87 = { by lemma 14 }
% 0.18/0.87 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(X)), W)), X)), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.18/0.87 = { by lemma 22 }
% 0.18/0.87 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, W)), X)), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.18/0.87 = { by axiom 1 (single_axiom) }
% 0.18/0.87 X
% 0.18/0.87
% 0.18/0.87 Lemma 25: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.18/0.87 Proof:
% 0.18/0.87 multiply(multiply(X, inverse(X)), Y)
% 0.18/0.87 = { by lemma 21 R->L }
% 0.18/0.87 multiply(multiply(inverse(Z), Z), Y)
% 0.18/0.87 = { by lemma 16 }
% 0.18/0.87 Y
% 0.18/0.87
% 0.18/0.87 Lemma 26: inverse(multiply(inverse(X), inverse(Y))) = multiply(Y, X).
% 0.18/0.87 Proof:
% 0.18/0.87 inverse(multiply(inverse(X), inverse(Y)))
% 0.18/0.87 = { by lemma 20 R->L }
% 0.18/0.87 inverse(multiply(inverse(X), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.87 = { by lemma 16 R->L }
% 0.18/0.87 inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), X)), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.87 = { by lemma 12 R->L }
% 0.18/0.87 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), X)), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.87 = { by lemma 23 R->L }
% 0.18/0.87 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), multiply(inverse(inverse(Y)), X)))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.87 = { by lemma 22 }
% 0.18/0.87 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), multiply(Y, X)))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.18/0.87 = { by lemma 4 }
% 0.18/0.87 multiply(Y, X)
% 0.18/0.87
% 0.18/0.87 Lemma 27: multiply(inverse(X), multiply(Y, inverse(Y))) = multiply(inverse(multiply(Z, X)), Z).
% 0.18/0.87 Proof:
% 0.18/0.87 multiply(inverse(X), multiply(Y, inverse(Y)))
% 0.18/0.87 = { by lemma 14 R->L }
% 0.18/0.87 multiply(inverse(multiply(Z, X)), multiply(Z, inverse(multiply(inverse(multiply(W, multiply(Y, inverse(Y)))), multiply(W, multiply(inverse(X), X))))))
% 0.18/0.87 = { by lemma 24 }
% 0.18/0.87 multiply(inverse(multiply(Z, X)), multiply(Z, inverse(multiply(inverse(W), multiply(W, multiply(inverse(X), X))))))
% 0.18/0.87 = { by lemma 10 R->L }
% 0.18/0.87 multiply(inverse(multiply(Z, X)), multiply(Z, inverse(multiply(inverse(W), multiply(W, multiply(inverse(V), V))))))
% 0.18/0.87 = { by lemma 21 }
% 0.18/0.87 multiply(inverse(multiply(Z, X)), multiply(Z, inverse(multiply(inverse(W), multiply(W, multiply(U, inverse(U)))))))
% 0.18/0.87 = { by lemma 24 }
% 0.18/0.87 multiply(inverse(multiply(Z, X)), multiply(Z, inverse(multiply(inverse(W), W))))
% 0.18/0.87 = { by lemma 12 }
% 0.18/0.87 multiply(inverse(multiply(Z, X)), multiply(Z, multiply(inverse(T), T)))
% 0.18/0.87 = { by lemma 21 }
% 0.18/0.87 multiply(inverse(multiply(Z, X)), multiply(Z, multiply(S, inverse(S))))
% 0.18/0.87 = { by lemma 24 }
% 0.18/0.87 multiply(inverse(multiply(Z, X)), Z)
% 0.18/0.87
% 0.18/0.87 Lemma 28: multiply(inverse(multiply(inverse(multiply(X, Y)), X)), multiply(inverse(Y), Z)) = Z.
% 0.18/0.87 Proof:
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(X, Y)), X)), multiply(inverse(Y), Z))
% 0.18/0.87 = { by lemma 13 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(X, Y)), X)), multiply(inverse(Y), inverse(multiply(inverse(multiply(W, Z)), multiply(W, multiply(inverse(Z), Z))))))
% 0.18/0.87 = { by lemma 24 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(X, Y)), X)), multiply(inverse(Y), inverse(multiply(inverse(multiply(W, Z)), multiply(W, multiply(inverse(multiply(Z, multiply(V, inverse(V)))), Z))))))
% 0.18/0.87 = { by lemma 27 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(X, Y)), X)), multiply(inverse(Y), inverse(multiply(inverse(multiply(W, Z)), multiply(W, multiply(inverse(multiply(V, inverse(V))), multiply(V, inverse(V))))))))
% 0.18/0.87 = { by lemma 27 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(Y), multiply(V, inverse(V)))), multiply(inverse(Y), inverse(multiply(inverse(multiply(W, Z)), multiply(W, multiply(inverse(multiply(V, inverse(V))), multiply(V, inverse(V))))))))
% 0.18/0.87 = { by lemma 14 }
% 0.18/0.87 multiply(inverse(multiply(V, inverse(V))), Z)
% 0.18/0.87 = { by lemma 20 R->L }
% 0.18/0.87 multiply(inverse(multiply(V, multiply(inverse(V), multiply(inverse(V), V)))), Z)
% 0.18/0.87 = { by lemma 13 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, multiply(inverse(V), V)))), multiply(inverse(V), multiply(inverse(V), V)))), Z)
% 0.18/0.87 = { by lemma 4 }
% 0.18/0.87 multiply(multiply(inverse(V), V), Z)
% 0.18/0.87 = { by lemma 21 }
% 0.18/0.87 multiply(multiply(T, inverse(T)), Z)
% 0.18/0.87 = { by lemma 25 }
% 0.18/0.87 Z
% 0.18/0.87
% 0.18/0.87 Lemma 29: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(inverse(Y), Z).
% 0.18/0.87 Proof:
% 0.18/0.87 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.18/0.87 = { by lemma 26 R->L }
% 0.18/0.87 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(Z), inverse(X))))
% 0.18/0.87 = { by lemma 20 R->L }
% 0.18/0.87 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(Z), multiply(inverse(X), multiply(inverse(X), X)))))
% 0.18/0.87 = { by lemma 28 R->L }
% 0.18/0.87 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), X)), multiply(inverse(Y), Z))), multiply(inverse(X), multiply(inverse(X), X)))))
% 0.18/0.87 = { by axiom 1 (single_axiom) }
% 0.18/0.87 multiply(inverse(Y), Z)
% 0.18/0.87
% 0.18/0.87 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.18/0.87 Proof:
% 0.18/0.87 multiply(multiply(a3, b3), c3)
% 0.18/0.87 = { by lemma 26 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(b3), inverse(a3))), c3)
% 0.18/0.87 = { by lemma 29 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(X, b3)), multiply(X, inverse(a3)))), c3)
% 0.18/0.87 = { by lemma 28 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), a3)), inverse(multiply(Y, Z)))), multiply(inverse(a3), multiply(inverse(multiply(inverse(multiply(X, b3)), multiply(X, inverse(a3)))), c3)))
% 0.18/0.87 = { by lemma 24 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), a3)), multiply(inverse(multiply(Y, Z)), multiply(W, inverse(W))))), multiply(inverse(a3), multiply(inverse(multiply(inverse(multiply(X, b3)), multiply(X, inverse(a3)))), c3)))
% 0.18/0.87 = { by lemma 21 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), a3)), multiply(inverse(multiply(Y, Z)), multiply(inverse(Z), Z)))), multiply(inverse(a3), multiply(inverse(multiply(inverse(multiply(X, b3)), multiply(X, inverse(a3)))), c3)))
% 0.18/0.87 = { by lemma 29 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), a3)), multiply(inverse(multiply(Y, Z)), multiply(inverse(multiply(V, Z)), multiply(V, Z))))), multiply(inverse(a3), multiply(inverse(multiply(inverse(multiply(X, b3)), multiply(X, inverse(a3)))), c3)))
% 0.18/0.87 = { by lemma 25 R->L }
% 0.18/0.87 multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(U, inverse(U)), multiply(Y, Z))), a3)), multiply(inverse(multiply(Y, Z)), multiply(inverse(multiply(V, Z)), multiply(V, Z))))), multiply(inverse(a3), multiply(inverse(multiply(inverse(multiply(X, b3)), multiply(X, inverse(a3)))), c3)))
% 0.18/0.87 = { by lemma 25 R->L }
% 0.18/0.87 multiply(multiply(multiply(U, inverse(U)), inverse(multiply(inverse(multiply(inverse(multiply(multiply(U, inverse(U)), multiply(Y, Z))), a3)), multiply(inverse(multiply(Y, Z)), multiply(inverse(multiply(V, Z)), multiply(V, Z)))))), multiply(inverse(a3), multiply(inverse(multiply(inverse(multiply(X, b3)), multiply(X, inverse(a3)))), c3)))
% 0.18/0.87 = { by lemma 18 }
% 0.18/0.87 multiply(a3, multiply(inverse(a3), multiply(inverse(multiply(inverse(multiply(X, b3)), multiply(X, inverse(a3)))), c3)))
% 0.18/0.87 = { by lemma 9 R->L }
% 0.18/0.87 multiply(a3, multiply(b3, multiply(inverse(multiply(inverse(multiply(T, b3)), multiply(T, b3))), c3)))
% 0.18/0.87 = { by lemma 29 }
% 0.18/0.88 multiply(a3, multiply(b3, multiply(inverse(multiply(inverse(b3), b3)), c3)))
% 0.18/0.88 = { by lemma 12 }
% 0.18/0.88 multiply(a3, multiply(b3, multiply(multiply(inverse(S), S), c3)))
% 0.18/0.88 = { by lemma 21 }
% 0.18/0.88 multiply(a3, multiply(b3, multiply(multiply(X2, inverse(X2)), c3)))
% 0.18/0.88 = { by lemma 25 }
% 0.18/0.88 multiply(a3, multiply(b3, c3))
% 0.18/0.88 % SZS output end Proof
% 0.18/0.88
% 0.18/0.88 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------