TSTP Solution File: GRP410-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP410-1 : 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 : n022.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 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP410-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % 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 : n022.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 19:48:09 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.43 Command-line arguments: --no-flatten-goal
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Axiom 1 (single_axiom): multiply(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))) = Y.
% 0.20/0.50
% 0.20/0.50 Lemma 2: multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))) = multiply(inverse(multiply(W, inverse(multiply(Y, Z)))), multiply(W, inverse(Z))).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.20/0.50 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.50 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(W, inverse(multiply(Y, Z)))), multiply(W, inverse(Z))), inverse(multiply(inverse(Z), Z)))))), multiply(X, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.20/0.50 = { by axiom 1 (single_axiom) }
% 0.20/0.50 multiply(inverse(multiply(W, inverse(multiply(Y, Z)))), multiply(W, inverse(Z)))
% 0.20/0.50
% 0.20/0.50 Lemma 3: multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z))) = Y.
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z)))
% 0.20/0.50 = { by lemma 2 R->L }
% 0.20/0.50 multiply(multiply(inverse(multiply(W, inverse(multiply(Y, inverse(multiply(inverse(Z), Z)))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.20/0.50 = { by axiom 1 (single_axiom) }
% 0.20/0.50 Y
% 0.20/0.50
% 0.20/0.50 Lemma 4: inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))) = Y.
% 0.20/0.50 Proof:
% 0.20/0.50 inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))))
% 0.20/0.50 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.50 multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.20/0.50 = { by lemma 3 }
% 0.20/0.50 multiply(multiply(inverse(multiply(W, inverse(multiply(Y, multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.20/0.50 = { by axiom 1 (single_axiom) }
% 0.20/0.50 Y
% 0.20/0.50
% 0.20/0.50 Lemma 5: multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z)) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z)).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z))
% 0.20/0.50 = { by lemma 4 R->L }
% 0.20/0.50 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.20/0.50 = { by lemma 3 R->L }
% 0.20/0.50 multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.20/0.51 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(T, inverse(multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))
% 0.20/0.51 = { by axiom 1 (single_axiom) }
% 0.20/0.51 multiply(multiply(inverse(multiply(T, inverse(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))
% 0.20/0.51 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(T, inverse(multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))))
% 0.20/0.51 = { by axiom 1 (single_axiom) }
% 0.20/0.51 multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))), multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))), multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.20/0.51 = { by lemma 3 }
% 0.20/0.51 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))))
% 0.20/0.51 = { by lemma 4 }
% 0.20/0.51 multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z))
% 0.20/0.51
% 0.20/0.51 Lemma 6: multiply(inverse(X), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W)) = multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, W)).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(inverse(X), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W))
% 0.20/0.51 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.51 multiply(inverse(multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z)))), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W))
% 0.20/0.51 = { by lemma 5 R->L }
% 0.20/0.51 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, W))
% 0.20/0.51
% 0.20/0.51 Lemma 7: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(inverse(Y), Y)
% 0.20/0.51 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.51 multiply(inverse(Y), multiply(multiply(inverse(multiply(U, inverse(multiply(Y, W)))), multiply(U, inverse(W))), inverse(multiply(inverse(W), W))))
% 0.20/0.51 = { by lemma 6 }
% 0.20/0.51 multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(multiply(inverse(W), W))))
% 0.20/0.51 = { by lemma 6 R->L }
% 0.20/0.51 multiply(inverse(X), multiply(multiply(inverse(multiply(Z, inverse(multiply(X, W)))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W))))
% 0.20/0.51 = { by axiom 1 (single_axiom) }
% 0.20/0.51 multiply(inverse(X), X)
% 0.20/0.51
% 0.20/0.51 Lemma 8: multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z))), inverse(multiply(inverse(W), W))) = inverse(Z).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z))), inverse(multiply(inverse(W), W)))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Z), Z)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 0.20/0.51 = { by axiom 1 (single_axiom) }
% 0.20/0.51 inverse(Z)
% 0.20/0.51
% 0.20/0.51 Lemma 9: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(Z), Z)))), multiply(W, inverse(multiply(inverse(Z), Z)))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.51 = { by lemma 8 }
% 0.20/0.51 inverse(multiply(inverse(Z), Z))
% 0.20/0.51
% 0.20/0.51 Lemma 10: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)) = multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), Z)).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(multiply(inverse(U), U))), inverse(multiply(inverse(U), U)))))), multiply(X, Z))
% 0.20/0.51 = { by lemma 6 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(multiply(T, inverse(multiply(multiply(inverse(W), W), inverse(multiply(inverse(U), U)))))), multiply(T, inverse(inverse(multiply(inverse(U), U))))), Z))
% 0.20/0.51 = { by lemma 9 }
% 0.20/0.51 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(multiply(T, inverse(inverse(multiply(inverse(U), U))))), multiply(T, inverse(inverse(multiply(inverse(U), U))))), Z))
% 0.20/0.51 = { by lemma 7 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), Z))
% 0.20/0.51
% 0.20/0.51 Lemma 11: multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)), inverse(multiply(inverse(W), W))) = Z.
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)), inverse(multiply(inverse(W), W)))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(W), W)))
% 0.20/0.51 = { by lemma 8 }
% 0.20/0.51 inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))
% 0.20/0.51 = { by lemma 4 }
% 0.20/0.51 Z
% 0.20/0.51
% 0.20/0.51 Lemma 12: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 multiply(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(V), V)))), multiply(W, inverse(multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.51 = { by lemma 10 }
% 0.20/0.51 multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(multiply(inverse(U), U), inverse(multiply(inverse(V), V))))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.51 = { by lemma 9 }
% 0.20/0.51 multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(T), T)))), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.51 = { by lemma 11 }
% 0.20/0.51 multiply(inverse(Z), Z)
% 0.20/0.51
% 0.20/0.51 Lemma 13: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.20/0.51 Proof:
% 0.20/0.51 inverse(multiply(inverse(X), X))
% 0.20/0.51 = { by lemma 9 R->L }
% 0.20/0.51 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(W), W)))
% 0.20/0.51 = { by lemma 12 }
% 0.20/0.51 multiply(inverse(Y), Y)
% 0.20/0.51
% 0.20/0.51 Lemma 14: inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))), W)))) = inverse(multiply(X, inverse(W))).
% 0.20/0.51 Proof:
% 0.20/0.51 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))), W))))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(W), W))), W))))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(W))), multiply(X, inverse(W))), inverse(multiply(inverse(W), W))), W))))
% 0.20/0.51 = { by lemma 4 }
% 0.20/0.51 inverse(multiply(X, inverse(W)))
% 0.20/0.51
% 0.20/0.51 Lemma 15: inverse(multiply(X, inverse(multiply(multiply(inverse(Y), Y), Z)))) = inverse(multiply(X, inverse(Z))).
% 0.20/0.51 Proof:
% 0.20/0.51 inverse(multiply(X, inverse(multiply(multiply(inverse(Y), Y), Z))))
% 0.20/0.51 = { by lemma 12 R->L }
% 0.20/0.51 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))))
% 0.20/0.51 = { by lemma 14 }
% 0.20/0.51 inverse(multiply(X, inverse(Z)))
% 0.20/0.51
% 0.20/0.51 Lemma 16: multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), multiply(inverse(W), W)) = Y.
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), multiply(inverse(W), W))
% 0.20/0.51 = { by lemma 13 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, multiply(inverse(U), U))), multiply(V, multiply(inverse(U), U)))))
% 0.20/0.51 = { by lemma 13 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, multiply(inverse(U), U))), multiply(V, inverse(multiply(inverse(T), T))))))
% 0.20/0.51 = { by lemma 13 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, multiply(inverse(U), U))), multiply(V, inverse(inverse(multiply(inverse(S), S)))))))
% 0.20/0.51 = { by lemma 13 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(X2), X2)))), multiply(V, inverse(inverse(multiply(inverse(S), S)))))))
% 0.20/0.51 = { by lemma 10 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(Y2), Y2)), multiply(multiply(inverse(Z2), Z2), inverse(inverse(multiply(inverse(S), S)))))))
% 0.20/0.51 = { by lemma 13 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(multiply(inverse(Z2), Z2), inverse(inverse(multiply(inverse(S), S)))))))
% 0.20/0.51 = { by lemma 13 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(multiply(inverse(Z2), Z2), inverse(multiply(inverse(V2), V2))))))
% 0.20/0.51 = { by lemma 12 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 3 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(T2, inverse(multiply(multiply(Y, inverse(multiply(inverse(S2), S2))), S2)))), multiply(T2, inverse(S2)))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 2 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(X3, inverse(multiply(Y, inverse(multiply(inverse(S2), S2)))))), multiply(X3, inverse(inverse(multiply(inverse(S2), S2))))), inverse(multiply(inverse(inverse(multiply(inverse(S2), S2))), inverse(multiply(inverse(S2), S2)))))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 11 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(multiply(X3, inverse(multiply(multiply(inverse(multiply(Y3, inverse(multiply(inverse(Z3), Z3)))), multiply(Y3, multiply(Y, inverse(multiply(inverse(S2), S2))))), inverse(multiply(inverse(S2), S2)))))), multiply(X3, inverse(inverse(multiply(inverse(S2), S2))))), inverse(multiply(inverse(inverse(multiply(inverse(S2), S2))), inverse(multiply(inverse(S2), S2)))))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by axiom 1 (single_axiom) }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(Y3, inverse(multiply(inverse(Z3), Z3)))), multiply(Y3, multiply(Y, inverse(multiply(inverse(S2), S2)))))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 10 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(W3), W3)), multiply(multiply(inverse(V3), V3), multiply(Y, inverse(multiply(inverse(S2), S2)))))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 13 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(U3), U3), multiply(multiply(inverse(V3), V3), multiply(Y, inverse(multiply(inverse(S2), S2)))))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 13 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(U3), U3), multiply(multiply(inverse(V3), V3), multiply(Y, multiply(inverse(U2), U2))))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 15 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(inverse(V3), V3), multiply(Y, multiply(inverse(U2), U2)))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 15 }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(X, multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 13 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(X, inverse(multiply(inverse(T3), T3)))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(X, inverse(multiply(S3, inverse(multiply(multiply(multiply(inverse(multiply(Y, multiply(inverse(U2), U2))), multiply(S3, inverse(X4))), inverse(multiply(inverse(X4), X4))), X4)))))), multiply(X, inverse(multiply(inverse(T3), T3)))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 5 }
% 0.20/0.51 multiply(multiply(inverse(multiply(multiply(inverse(Y4), Y4), inverse(multiply(S3, inverse(multiply(multiply(multiply(inverse(multiply(Y, multiply(inverse(U2), U2))), multiply(S3, inverse(X4))), inverse(multiply(inverse(X4), X4))), X4)))))), multiply(multiply(inverse(Y4), Y4), inverse(multiply(inverse(T3), T3)))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 4 }
% 0.20/0.51 multiply(multiply(inverse(multiply(multiply(inverse(Y4), Y4), inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(multiply(inverse(Y4), Y4), inverse(multiply(inverse(T3), T3)))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 9 }
% 0.20/0.51 multiply(multiply(inverse(multiply(multiply(inverse(Y4), Y4), inverse(multiply(Y, multiply(inverse(U2), U2))))), inverse(multiply(inverse(Z4), Z4))), inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 13 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(multiply(inverse(Y4), Y4), inverse(multiply(Y, multiply(inverse(U2), U2))))), inverse(multiply(inverse(Z4), Z4))), inverse(multiply(inverse(multiply(inverse(U2), U2)), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by lemma 9 R->L }
% 0.20/0.51 multiply(multiply(inverse(multiply(multiply(inverse(Y4), Y4), inverse(multiply(Y, multiply(inverse(U2), U2))))), multiply(multiply(inverse(Y4), Y4), inverse(multiply(inverse(U2), U2)))), inverse(multiply(inverse(multiply(inverse(U2), U2)), multiply(inverse(U2), U2))))
% 0.20/0.51 = { by axiom 1 (single_axiom) }
% 0.20/0.51 Y
% 0.20/0.51
% 0.20/0.51 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(multiply(inverse(b2), b2), a2)
% 0.20/0.52 = { by lemma 12 R->L }
% 0.20/0.52 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), a2)
% 0.20/0.52 = { by lemma 16 R->L }
% 0.20/0.52 multiply(multiply(inverse(multiply(Z, inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), a2)))), multiply(Z, multiply(inverse(W), W))), multiply(inverse(V), V))
% 0.20/0.52 = { by lemma 14 }
% 0.20/0.52 multiply(multiply(inverse(multiply(Z, inverse(a2))), multiply(Z, multiply(inverse(W), W))), multiply(inverse(V), V))
% 0.20/0.52 = { by lemma 16 }
% 0.20/0.52 a2
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52
% 0.20/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
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