TSTP Solution File: GRP426-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP426-1 : 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 01:18:23 EDT 2023
% Result : Unsatisfiable 0.15s 0.38s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GRP426-1 : TPTP v8.1.2. Released v2.6.0.
% 0.06/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Aug 29 01:15:46 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.38 Command-line arguments: --no-flatten-goal
% 0.15/0.38
% 0.15/0.38 % SZS status Unsatisfiable
% 0.15/0.38
% 0.15/0.44 % SZS output start Proof
% 0.15/0.44 Axiom 1 (single_axiom): multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Z)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z))) = Y.
% 0.15/0.44
% 0.15/0.44 Lemma 2: multiply(inverse(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(inverse(Y), Z)))), multiply(W, inverse(Z))).
% 0.15/0.44 Proof:
% 0.15/0.44 multiply(inverse(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)))))
% 0.15/0.44 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.44 multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(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)))))
% 0.15/0.44 = { by axiom 1 (single_axiom) }
% 0.15/0.44 multiply(inverse(multiply(W, inverse(multiply(inverse(Y), Z)))), multiply(W, inverse(Z)))
% 0.15/0.44
% 0.15/0.44 Lemma 3: multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z))) = Y.
% 0.15/0.44 Proof:
% 0.15/0.44 multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z)))
% 0.15/0.44 = { by lemma 2 R->L }
% 0.15/0.44 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(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)))))
% 0.15/0.44 = { by axiom 1 (single_axiom) }
% 0.15/0.44 Y
% 0.15/0.44
% 0.15/0.44 Lemma 4: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z))) = Y.
% 0.15/0.44 Proof:
% 0.15/0.44 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z)))
% 0.15/0.44 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.44 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(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)))))
% 0.15/0.44 = { by lemma 3 }
% 0.15/0.44 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), multiply(X, inverse(Z)))))), multiply(W, inverse(multiply(X, inverse(Z)))))), inverse(multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))
% 0.15/0.44 = { by axiom 1 (single_axiom) }
% 0.15/0.45 Y
% 0.15/0.45
% 0.15/0.45 Lemma 5: multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(Z))) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z))).
% 0.15/0.45 Proof:
% 0.15/0.45 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(Z)))
% 0.15/0.45 = { by lemma 4 R->L }
% 0.15/0.45 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))
% 0.15/0.45 = { by lemma 3 R->L }
% 0.15/0.45 multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))
% 0.15/0.45 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.45 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(W, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))
% 0.15/0.45 = { by axiom 1 (single_axiom) }
% 0.15/0.45 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))
% 0.15/0.45 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.45 multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), multiply(T, inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))))
% 0.15/0.45 = { by axiom 1 (single_axiom) }
% 0.15/0.45 multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U)), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))), multiply(X, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))
% 0.15/0.45 = { by lemma 3 }
% 0.15/0.45 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), multiply(V, inverse(U)))), inverse(multiply(inverse(U), U)))), U))))))
% 0.15/0.45 = { by lemma 4 }
% 0.15/0.45 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z)))
% 0.15/0.45
% 0.15/0.45 Lemma 6: multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W))) = multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(W))).
% 0.15/0.45 Proof:
% 0.15/0.45 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W)))
% 0.15/0.45 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.45 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W)))
% 0.15/0.45 = { by lemma 5 R->L }
% 0.15/0.45 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(W)))
% 0.15/0.45
% 0.15/0.45 Lemma 7: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.15/0.45 Proof:
% 0.15/0.45 multiply(inverse(Y), Y)
% 0.15/0.45 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.45 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(Y), W)))), multiply(U, inverse(W)))), inverse(multiply(inverse(W), W))))
% 0.15/0.45 = { by lemma 6 }
% 0.15/0.45 multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(multiply(inverse(W), W))))
% 0.15/0.45 = { by lemma 6 R->L }
% 0.15/0.45 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), W)))), multiply(Z, inverse(W)))), inverse(multiply(inverse(W), W))))
% 0.15/0.45 = { by axiom 1 (single_axiom) }
% 0.15/0.45 multiply(inverse(X), X)
% 0.15/0.45
% 0.15/0.45 Lemma 8: multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(W), W))) = Z.
% 0.15/0.45 Proof:
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(W), W)))
% 0.15/0.46 = { by lemma 7 }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))
% 0.15/0.46 = { by lemma 7 }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Z), Z)))), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))
% 0.15/0.46 = { by axiom 1 (single_axiom) }
% 0.15/0.46 Z
% 0.15/0.46
% 0.15/0.46 Lemma 9: multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 0.15/0.46 Proof:
% 0.15/0.46 multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y)))
% 0.15/0.46 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(X), Z)))), multiply(W, inverse(Z)))), inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(Y), Y)))
% 0.15/0.46 = { by lemma 6 }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(Y), Y)))
% 0.15/0.46 = { by lemma 8 }
% 0.15/0.46 multiply(inverse(Z), Z)
% 0.15/0.46
% 0.15/0.46 Lemma 10: multiply(inverse(multiply(inverse(X), X)), Y) = Y.
% 0.15/0.46 Proof:
% 0.15/0.46 multiply(inverse(multiply(inverse(X), X)), Y)
% 0.15/0.46 = { by lemma 9 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(Y))), multiply(Z, inverse(Y)))), inverse(multiply(inverse(Y), Y)))), Y)
% 0.15/0.46 = { by lemma 8 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(W), W)))), multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(Y))), multiply(Z, inverse(Y)))), inverse(multiply(inverse(Y), Y)))), Y))))), inverse(multiply(inverse(V), V)))
% 0.15/0.46 = { by lemma 4 }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(W), W)))), multiply(Z, inverse(Y)))), inverse(multiply(inverse(V), V)))
% 0.15/0.46 = { by lemma 8 }
% 0.15/0.46 Y
% 0.15/0.46
% 0.15/0.46 Lemma 11: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.15/0.46 Proof:
% 0.15/0.46 inverse(multiply(inverse(X), X))
% 0.15/0.46 = { by lemma 10 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 9 }
% 0.15/0.46 multiply(inverse(Y), Y)
% 0.15/0.46
% 0.15/0.46 Lemma 12: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z))) = multiply(inverse(inverse(Y)), inverse(Z)).
% 0.15/0.46 Proof:
% 0.15/0.46 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z)))
% 0.15/0.46 = { by lemma 5 }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(inverse(W), W)), inverse(Y))), multiply(inverse(multiply(inverse(W), W)), inverse(Z)))
% 0.15/0.46 = { by lemma 10 }
% 0.15/0.46 multiply(inverse(inverse(Y)), multiply(inverse(multiply(inverse(W), W)), inverse(Z)))
% 0.15/0.46 = { by lemma 10 }
% 0.15/0.46 multiply(inverse(inverse(Y)), inverse(Z))
% 0.15/0.46
% 0.15/0.46 Lemma 13: multiply(inverse(inverse(X)), multiply(inverse(Y), Y)) = X.
% 0.15/0.46 Proof:
% 0.15/0.46 multiply(inverse(inverse(X)), multiply(inverse(Y), Y))
% 0.15/0.46 = { by lemma 10 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(X))), multiply(inverse(Y), Y))
% 0.15/0.46 = { by lemma 11 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(inverse(multiply(inverse(W), W))), inverse(X))), multiply(inverse(Y), Y))
% 0.15/0.46 = { by lemma 11 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(inverse(multiply(inverse(W), W))), inverse(X))), inverse(multiply(inverse(V), V)))
% 0.15/0.46 = { by lemma 12 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(W), W)))), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))
% 0.15/0.46 = { by lemma 8 }
% 0.15/0.46 X
% 0.15/0.46
% 0.15/0.46 Lemma 14: inverse(inverse(X)) = X.
% 0.15/0.46 Proof:
% 0.15/0.46 inverse(inverse(X))
% 0.15/0.46 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(inverse(X))), X)))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 10 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(X)))), X)))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 11 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(W), W))), inverse(X)))), X)))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 12 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), X)))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 8 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X)))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 13 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(T), T))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 11 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), inverse(multiply(inverse(U), U)))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 12 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X)))))), multiply(S, inverse(multiply(inverse(U), U))))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 13 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(X))))), multiply(inverse(U), U))))), multiply(S, inverse(multiply(inverse(U), U))))), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 6 }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))))), multiply(X2, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))))))), multiply(Y, inverse(X)))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 12 }
% 0.15/0.46 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))))), multiply(X2, inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))))))), inverse(X))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 11 }
% 0.15/0.46 multiply(inverse(multiply(inverse(multiply(inverse(Y2), Y2)), inverse(X))), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 10 }
% 0.15/0.46 multiply(inverse(inverse(X)), inverse(multiply(inverse(X), X)))
% 0.15/0.46 = { by lemma 7 R->L }
% 0.15/0.46 multiply(inverse(inverse(X)), inverse(multiply(inverse(Z2), Z2)))
% 0.15/0.46 = { by lemma 11 }
% 0.15/0.46 multiply(inverse(inverse(X)), multiply(inverse(W2), W2))
% 0.15/0.46 = { by lemma 13 }
% 0.15/0.46 X
% 0.15/0.46
% 0.15/0.46 Lemma 15: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.15/0.46 Proof:
% 0.15/0.46 multiply(inverse(X), X)
% 0.15/0.46 = { by lemma 7 }
% 0.15/0.46 multiply(inverse(inverse(Y)), inverse(Y))
% 0.15/0.46 = { by lemma 14 }
% 0.15/0.46 multiply(Y, inverse(Y))
% 0.15/0.46
% 0.15/0.46 Lemma 16: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.15/0.46 Proof:
% 0.15/0.46 multiply(X, multiply(Y, inverse(Y)))
% 0.15/0.46 = { by lemma 15 R->L }
% 0.15/0.46 multiply(X, multiply(inverse(Z), Z))
% 0.15/0.46 = { by lemma 14 R->L }
% 0.15/0.46 multiply(inverse(inverse(X)), multiply(inverse(Z), Z))
% 0.15/0.46 = { by lemma 13 }
% 0.15/0.46 X
% 0.15/0.46
% 0.15/0.46 Lemma 17: multiply(multiply(inverse(X), X), Y) = Y.
% 0.15/0.46 Proof:
% 0.15/0.46 multiply(multiply(inverse(X), X), Y)
% 0.15/0.46 = { by lemma 11 R->L }
% 0.15/0.46 multiply(inverse(multiply(inverse(Z), Z)), Y)
% 0.15/0.46 = { by lemma 10 }
% 0.15/0.46 Y
% 0.15/0.46
% 0.15/0.46 Lemma 18: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 0.15/0.46 Proof:
% 0.15/0.46 inverse(multiply(X, inverse(Y)))
% 0.15/0.46 = { by lemma 16 R->L }
% 0.15/0.46 multiply(inverse(multiply(X, inverse(Y))), multiply(Z, inverse(Z)))
% 0.15/0.46 = { by lemma 14 R->L }
% 0.15/0.46 multiply(inverse(multiply(X, inverse(Y))), inverse(inverse(multiply(Z, inverse(Z)))))
% 0.15/0.46 = { by lemma 17 R->L }
% 0.15/0.46 multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(inverse(W), W), inverse(multiply(Z, inverse(Z))))))
% 0.15/0.46 = { by lemma 15 }
% 0.15/0.46 multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(V, inverse(V)), inverse(multiply(Z, inverse(Z))))))
% 0.15/0.46 = { by lemma 16 R->L }
% 0.15/0.46 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(U, inverse(U)))), inverse(multiply(multiply(V, inverse(V)), inverse(multiply(Z, inverse(Z))))))
% 0.15/0.46 = { by lemma 15 R->L }
% 0.15/0.47 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(U, inverse(U)))), inverse(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.15/0.47 = { by lemma 15 R->L }
% 0.15/0.47 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(U, inverse(U)))), inverse(multiply(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.15/0.47 = { by lemma 15 R->L }
% 0.15/0.47 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.15/0.47 = { by lemma 14 R->L }
% 0.15/0.47 multiply(inverse(multiply(multiply(X, inverse(Y)), multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.15/0.47 = { by lemma 14 R->L }
% 0.15/0.47 multiply(inverse(multiply(multiply(X, inverse(Y)), inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.15/0.47 = { by lemma 14 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(inverse(multiply(X, inverse(Y)))), inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.15/0.47 = { by lemma 12 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(multiply(S, inverse(multiply(X, inverse(Y))))), multiply(S, inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))), inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))))
% 0.15/0.47 = { by lemma 2 }
% 0.15/0.47 multiply(inverse(multiply(X2, inverse(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(T), T)))))))), multiply(X2, inverse(multiply(X, inverse(inverse(multiply(inverse(T), T)))))))
% 0.15/0.47 = { by lemma 12 }
% 0.15/0.47 multiply(inverse(inverse(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(T), T))))))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.15/0.47 = { by lemma 14 }
% 0.15/0.47 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(inverse(multiply(inverse(T), T))))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.15/0.47 = { by lemma 5 R->L }
% 0.15/0.47 multiply(multiply(inverse(multiply(Y2, inverse(Y))), multiply(Y2, inverse(inverse(multiply(inverse(T), T))))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.15/0.47 = { by lemma 12 }
% 0.15/0.47 multiply(multiply(inverse(inverse(Y)), inverse(inverse(multiply(inverse(T), T)))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.15/0.47 = { by lemma 14 }
% 0.15/0.47 multiply(multiply(Y, inverse(inverse(multiply(inverse(T), T)))), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.15/0.47 = { by lemma 14 }
% 0.15/0.47 multiply(multiply(Y, multiply(inverse(T), T)), inverse(multiply(X, inverse(inverse(multiply(inverse(T), T))))))
% 0.15/0.47 = { by lemma 14 }
% 0.15/0.47 multiply(multiply(Y, multiply(inverse(T), T)), inverse(multiply(X, multiply(inverse(T), T))))
% 0.15/0.47 = { by lemma 15 }
% 0.15/0.47 multiply(multiply(Y, multiply(Z2, inverse(Z2))), inverse(multiply(X, multiply(inverse(T), T))))
% 0.15/0.47 = { by lemma 15 }
% 0.15/0.47 multiply(multiply(Y, multiply(Z2, inverse(Z2))), inverse(multiply(X, multiply(W2, inverse(W2)))))
% 0.15/0.47 = { by lemma 16 }
% 0.15/0.47 multiply(Y, inverse(multiply(X, multiply(W2, inverse(W2)))))
% 0.15/0.47 = { by lemma 16 }
% 0.15/0.47 multiply(Y, inverse(X))
% 0.15/0.47
% 0.15/0.47 Lemma 19: multiply(inverse(X), inverse(Y)) = inverse(multiply(Y, X)).
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(inverse(X), inverse(Y))
% 0.15/0.47 = { by lemma 18 R->L }
% 0.15/0.47 inverse(multiply(Y, inverse(inverse(X))))
% 0.15/0.47 = { by lemma 14 }
% 0.15/0.47 inverse(multiply(Y, X))
% 0.15/0.47
% 0.15/0.47 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(multiply(a3, b3), c3)
% 0.15/0.47 = { by lemma 14 R->L }
% 0.15/0.47 multiply(multiply(a3, inverse(inverse(b3))), c3)
% 0.15/0.47 = { by lemma 18 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), c3)
% 0.15/0.47 = { by lemma 16 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(c3, multiply(X, inverse(X))))
% 0.15/0.47 = { by lemma 15 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(c3, multiply(inverse(inverse(b3)), inverse(b3))))
% 0.15/0.47 = { by lemma 14 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(c3, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3))))))
% 0.15/0.47 = { by lemma 14 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(inverse(c3)), inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3))))))
% 0.15/0.47 = { by lemma 12 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(multiply(Y, inverse(c3))), multiply(Y, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3)))))))
% 0.15/0.47 = { by lemma 14 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(inverse(multiply(inverse(multiply(Y, inverse(c3))), multiply(Y, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3)))))))))
% 0.15/0.47 = { by lemma 17 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(multiply(inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3)))), inverse(multiply(inverse(inverse(b3)), inverse(b3)))), inverse(inverse(multiply(inverse(multiply(Y, inverse(c3))), multiply(Y, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3))))))))))
% 0.15/0.47 = { by lemma 18 R->L }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(c3))), multiply(Y, inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(b3)), inverse(b3)))), inverse(multiply(inverse(inverse(b3)), inverse(b3))))))))
% 0.15/0.47 = { by lemma 2 }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(c3), inverse(b3))))), multiply(Z, inverse(inverse(b3))))))
% 0.15/0.47 = { by lemma 12 }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(multiply(inverse(inverse(multiply(inverse(c3), inverse(b3)))), inverse(inverse(b3)))))
% 0.15/0.47 = { by lemma 18 }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(b3), inverse(inverse(inverse(multiply(inverse(c3), inverse(b3)))))))
% 0.15/0.47 = { by lemma 14 }
% 0.15/0.47 multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(b3), inverse(multiply(inverse(c3), inverse(b3)))))
% 0.15/0.47 = { by lemma 12 }
% 0.15/0.47 multiply(inverse(inverse(a3)), inverse(multiply(inverse(c3), inverse(b3))))
% 0.15/0.47 = { by lemma 19 }
% 0.15/0.47 inverse(multiply(multiply(inverse(c3), inverse(b3)), inverse(a3)))
% 0.15/0.47 = { by lemma 18 }
% 0.15/0.47 multiply(a3, inverse(multiply(inverse(c3), inverse(b3))))
% 0.15/0.47 = { by lemma 19 R->L }
% 0.15/0.47 multiply(a3, multiply(inverse(inverse(b3)), inverse(inverse(c3))))
% 0.15/0.47 = { by lemma 14 }
% 0.15/0.47 multiply(a3, multiply(inverse(inverse(b3)), c3))
% 0.15/0.47 = { by lemma 14 }
% 0.15/0.47 multiply(a3, multiply(b3, c3))
% 0.15/0.47 % SZS output end Proof
% 0.15/0.47
% 0.15/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------