%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP056-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:10 AM UTC 2026
% Result : Unsatisfiable 0.59s 0.51s
% Output : Proof 1.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP056-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:12:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.59/0.51 Command-line arguments: --no-flatten-goal
% 0.59/0.51
% 0.59/0.51 % SZS status Unsatisfiable
% 0.59/0.51
% 0.59/0.61 % SZS output start Proof
% 0.59/0.61 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.
% 0.59/0.61
% 0.59/0.61 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z))) = Y.
% 0.59/0.61 Proof:
% 0.59/0.61 multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z)))
% 0.59/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.59/0.61 multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))), Z)))), multiply(X, inverse(Z)))), 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)))))
% 0.59/0.61 = { by axiom 1 (single_axiom) }
% 0.59/0.61 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)))))
% 0.59/0.61 = { by axiom 1 (single_axiom) }
% 0.59/0.61 Y
% 0.59/0.61
% 0.59/0.61 Lemma 3: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z))) = Y.
% 0.59/0.61 Proof:
% 0.59/0.61 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(X, inverse(Z)))), inverse(multiply(inverse(Z), Z)))), Z)))
% 0.59/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.59/0.61 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)))))
% 0.59/0.61 = { by lemma 2 }
% 0.59/0.61 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)))))
% 0.59/0.61 = { by axiom 1 (single_axiom) }
% 0.59/0.61 Y
% 0.59/0.61
% 0.59/0.61 Lemma 4: multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(Z))) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z))).
% 0.59/0.61 Proof:
% 0.59/0.61 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(Z)))
% 0.59/0.62 = { by lemma 3 R->L }
% 0.59/0.62 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))))))
% 0.59/0.62 = { by lemma 2 R->L }
% 0.59/0.62 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))))))
% 0.59/0.62 = { by axiom 1 (single_axiom) R->L }
% 0.59/0.62 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))))))))
% 0.59/0.62 = { by axiom 1 (single_axiom) }
% 0.59/0.62 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))))))))
% 0.59/0.62 = { by axiom 1 (single_axiom) R->L }
% 0.59/0.62 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))))))))
% 0.59/0.62 = { by axiom 1 (single_axiom) }
% 1.61/0.63 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))))))
% 1.61/0.63 = { by lemma 2 }
% 1.61/0.63 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))))))
% 1.61/0.63 = { by lemma 3 }
% 1.61/0.63 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z)))
% 1.61/0.63
% 1.61/0.63 Lemma 5: 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))).
% 1.61/0.63 Proof:
% 1.61/0.63 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Z)))), multiply(Y, inverse(Z)))), inverse(W)))
% 1.61/0.63 = { by axiom 1 (single_axiom) R->L }
% 1.61/0.63 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)))
% 1.61/0.63 = { by lemma 4 R->L }
% 1.61/0.63 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(W)))
% 1.61/0.63
% 1.61/0.63 Lemma 6: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 1.61/0.63 Proof:
% 1.61/0.63 multiply(inverse(Y), Y)
% 1.61/0.63 = { by axiom 1 (single_axiom) R->L }
% 1.61/0.63 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(Y), W)))), multiply(U, inverse(W)))), inverse(multiply(inverse(W), W))))
% 1.61/0.63 = { by lemma 5 }
% 1.61/0.63 multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(multiply(inverse(W), W))))
% 1.61/0.63 = { by lemma 5 R->L }
% 1.61/0.63 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), W)))), multiply(Z, inverse(W)))), inverse(multiply(inverse(W), W))))
% 1.61/0.63 = { by axiom 1 (single_axiom) }
% 1.61/0.63 multiply(inverse(X), X)
% 1.61/0.63
% 1.61/0.63 Lemma 7: multiply(inverse(multiply(inverse(W), W)), multiply(inverse(inverse(Y)), inverse(Z))) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z))).
% 1.61/0.63 Proof:
% 1.61/0.63 multiply(inverse(multiply(inverse(W), W)), multiply(inverse(inverse(Y)), inverse(Z)))
% 1.61/0.63 = { by lemma 6 }
% 1.61/0.63 multiply(inverse(multiply(inverse(inverse(Y)), inverse(Y))), multiply(inverse(inverse(Y)), inverse(Z)))
% 1.61/0.63 = { by lemma 4 R->L }
% 1.61/0.63 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z)))
% 1.61/0.63
% 1.61/0.63 Lemma 8: multiply(inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(Y), Y))), inverse(Z)))), inverse(multiply(inverse(W), W))) = Z.
% 1.61/0.63 Proof:
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(Y), Y))), inverse(Z)))), inverse(multiply(inverse(W), W)))
% 1.61/0.63 = { by lemma 7 }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Y), Y)))), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W)))
% 1.61/0.63 = { by lemma 6 }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Y), Y)))), multiply(V, inverse(Z)))), inverse(multiply(inverse(Z), Z)))
% 1.61/0.63 = { by lemma 6 }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(Z)))), inverse(multiply(inverse(Z), Z)))
% 1.61/0.63 = { by axiom 1 (single_axiom) }
% 1.61/0.63 Z
% 1.61/0.63
% 1.61/0.63 Lemma 9: multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 1.61/0.63 Proof:
% 1.61/0.63 multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y)))
% 1.61/0.63 = { by lemma 6 }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(Y), Y)))
% 1.61/0.63 = { by lemma 8 }
% 1.61/0.63 multiply(inverse(Z), Z)
% 1.61/0.63
% 1.61/0.63 Lemma 10: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z)))), W))) = multiply(X, inverse(W)).
% 1.61/0.63 Proof:
% 1.61/0.63 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z)))), W)))
% 1.61/0.63 = { by lemma 6 }
% 1.61/0.63 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(W), W)))), W)))
% 1.61/0.63 = { by lemma 6 }
% 1.61/0.63 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(W))), multiply(X, inverse(W)))), inverse(multiply(inverse(W), W)))), W)))
% 1.61/0.63 = { by lemma 3 }
% 1.61/0.63 multiply(X, inverse(W))
% 1.61/0.63
% 1.61/0.63 Lemma 11: multiply(X, inverse(multiply(inverse(multiply(inverse(Y), Y)), Z))) = multiply(X, inverse(Z)).
% 1.61/0.63 Proof:
% 1.61/0.63 multiply(X, inverse(multiply(inverse(multiply(inverse(Y), Y)), Z)))
% 1.61/0.63 = { by lemma 9 R->L }
% 1.61/0.63 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(V), V)))), Z)))
% 1.61/0.63 = { by lemma 10 }
% 1.61/0.63 multiply(X, inverse(Z))
% 1.61/0.63
% 1.61/0.63 Lemma 12: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 1.61/0.63 Proof:
% 1.61/0.63 inverse(multiply(inverse(X), X))
% 1.61/0.63 = { by axiom 1 (single_axiom) R->L }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(W))))), multiply(Z, inverse(inverse(W))))), inverse(multiply(inverse(inverse(W)), inverse(W))))
% 1.61/0.63 = { by lemma 11 R->L }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(W)))))), multiply(Z, inverse(inverse(W))))), inverse(multiply(inverse(inverse(W)), inverse(W))))
% 1.61/0.63 = { by lemma 7 }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), inverse(multiply(inverse(X), X)))), multiply(inverse(multiply(inverse(U), U)), inverse(W)))))), multiply(Z, inverse(inverse(W))))), inverse(multiply(inverse(inverse(W)), inverse(W))))
% 1.61/0.63 = { by lemma 9 }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(T), T)), multiply(inverse(multiply(inverse(U), U)), inverse(W)))))), multiply(Z, inverse(inverse(W))))), inverse(multiply(inverse(inverse(W)), inverse(W))))
% 1.61/0.63 = { by lemma 11 }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(U), U)), inverse(W))))), multiply(Z, inverse(inverse(W))))), inverse(multiply(inverse(inverse(W)), inverse(W))))
% 1.61/0.63 = { by lemma 11 }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(W)))), multiply(Z, inverse(inverse(W))))), inverse(multiply(inverse(inverse(W)), inverse(W))))
% 1.61/0.63 = { by lemma 9 }
% 1.61/0.63 multiply(inverse(Y), Y)
% 1.61/0.63
% 1.61/0.63 Lemma 13: multiply(inverse(multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), inverse(Z)))), multiply(inverse(W), W)) = Z.
% 1.61/0.63 Proof:
% 1.61/0.63 multiply(inverse(multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), inverse(Z)))), multiply(inverse(W), W))
% 1.61/0.63 = { by lemma 12 R->L }
% 1.61/0.63 multiply(inverse(multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(V), V)), inverse(Z)))), multiply(inverse(W), W))
% 1.61/0.63 = { by lemma 12 R->L }
% 1.61/0.63 multiply(inverse(multiply(multiply(inverse(X), X), multiply(inverse(inverse(multiply(inverse(U), U))), inverse(Z)))), multiply(inverse(W), W))
% 1.61/0.63 = { by lemma 12 R->L }
% 1.61/0.63 multiply(inverse(multiply(multiply(inverse(X), X), multiply(inverse(inverse(multiply(inverse(U), U))), inverse(Z)))), inverse(multiply(inverse(T), T)))
% 1.61/0.63 = { by lemma 12 R->L }
% 1.61/0.63 multiply(inverse(multiply(inverse(multiply(inverse(S), S)), multiply(inverse(inverse(multiply(inverse(U), U))), inverse(Z)))), inverse(multiply(inverse(T), T)))
% 1.61/0.63 = { by lemma 8 }
% 1.61/0.63 Z
% 1.61/0.63
% 1.61/0.63 Lemma 14: multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, inverse(Z))) = multiply(multiply(inverse(W), W), multiply(multiply(inverse(V), V), inverse(Z))).
% 1.61/0.63 Proof:
% 1.61/0.63 multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, inverse(Z)))
% 1.61/0.64 = { by lemma 12 R->L }
% 1.61/0.64 multiply(inverse(multiply(X, inverse(multiply(inverse(U), U)))), multiply(X, inverse(Z)))
% 1.61/0.64 = { by lemma 7 R->L }
% 1.61/0.64 multiply(inverse(multiply(inverse(T), T)), multiply(inverse(inverse(multiply(inverse(U), U))), inverse(Z)))
% 1.61/0.64 = { by lemma 12 }
% 1.61/0.64 multiply(multiply(inverse(W), W), multiply(inverse(inverse(multiply(inverse(U), U))), inverse(Z)))
% 1.61/0.64 = { by lemma 12 }
% 1.61/0.64 multiply(multiply(inverse(W), W), multiply(inverse(multiply(inverse(S), S)), inverse(Z)))
% 1.61/0.64 = { by lemma 12 }
% 1.61/0.64 multiply(multiply(inverse(W), W), multiply(multiply(inverse(V), V), inverse(Z)))
% 1.61/0.64
% 1.61/0.64 Lemma 15: multiply(multiply(inverse(X), X), Y) = Y.
% 1.61/0.64 Proof:
% 1.61/0.64 multiply(multiply(inverse(X), X), Y)
% 1.61/0.64 = { by lemma 13 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(multiply(inverse(W), W), inverse(multiply(multiply(inverse(X), X), Y))))), multiply(inverse(V), V))
% 1.61/0.64 = { by lemma 12 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(U), U)), Y))))), multiply(inverse(V), V))
% 1.61/0.64 = { by lemma 9 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(inverse(T), T)), inverse(multiply(inverse(S), S)))), Y))))), multiply(inverse(V), V))
% 1.61/0.64 = { by lemma 14 R->L }
% 1.61/0.64 multiply(inverse(multiply(inverse(multiply(X2, multiply(inverse(Y2), Y2))), multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(T), T)), inverse(multiply(inverse(S), S)))), Y))))), multiply(inverse(V), V))
% 1.61/0.64 = { by lemma 10 }
% 1.61/0.64 multiply(inverse(multiply(inverse(multiply(X2, multiply(inverse(Y2), Y2))), multiply(X2, inverse(Y)))), multiply(inverse(V), V))
% 1.61/0.64 = { by lemma 14 }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z2), Z2), multiply(multiply(inverse(W2), W2), inverse(Y)))), multiply(inverse(V), V))
% 1.61/0.64 = { by lemma 13 }
% 1.61/0.64 Y
% 1.61/0.64
% 1.61/0.64 Lemma 16: multiply(inverse(inverse(X)), multiply(inverse(Y), Y)) = X.
% 1.61/0.64 Proof:
% 1.61/0.64 multiply(inverse(inverse(X)), multiply(inverse(Y), Y))
% 1.61/0.64 = { by lemma 15 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(X))), multiply(inverse(Y), Y))
% 1.61/0.64 = { by lemma 15 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(W), W), multiply(multiply(inverse(Z), Z), inverse(X)))), multiply(inverse(Y), Y))
% 1.61/0.64 = { by lemma 13 }
% 1.61/0.64 X
% 1.61/0.64
% 1.61/0.64 Lemma 17: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z))) = multiply(multiply(inverse(W), W), multiply(inverse(inverse(Y)), inverse(Z))).
% 1.61/0.64 Proof:
% 1.61/0.64 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Z)))
% 1.61/0.64 = { by lemma 7 R->L }
% 1.61/0.64 multiply(inverse(multiply(inverse(V), V)), multiply(inverse(inverse(Y)), inverse(Z)))
% 1.61/0.64 = { by lemma 12 }
% 1.61/0.64 multiply(multiply(inverse(W), W), multiply(inverse(inverse(Y)), inverse(Z)))
% 1.61/0.64
% 1.61/0.64 Lemma 18: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(X).
% 1.61/0.64 Proof:
% 1.61/0.64 multiply(inverse(X), multiply(inverse(Y), Y))
% 1.61/0.64 = { by lemma 15 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), X)), multiply(inverse(Y), Y))
% 1.61/0.64 = { by lemma 16 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(X)), multiply(inverse(W), W)))), multiply(inverse(Y), Y))
% 1.61/0.64 = { by lemma 12 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(X)), multiply(inverse(W), W)))), inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))))
% 1.61/0.64 = { by lemma 12 }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(X)), multiply(inverse(W), W)))), inverse(multiply(multiply(inverse(U), U), multiply(inverse(V), V))))
% 1.61/0.64 = { by lemma 12 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(X)), inverse(multiply(inverse(T), T))))), inverse(multiply(multiply(inverse(U), U), multiply(inverse(V), V))))
% 1.61/0.64 = { by lemma 12 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(X)), inverse(multiply(inverse(T), T))))), inverse(multiply(inverse(multiply(inverse(S), S)), multiply(inverse(V), V))))
% 1.61/0.64 = { by lemma 12 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(X)), inverse(inverse(multiply(inverse(X2), X2)))))), inverse(multiply(inverse(multiply(inverse(S), S)), multiply(inverse(V), V))))
% 1.61/0.64 = { by lemma 12 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(X)), inverse(inverse(multiply(inverse(X2), X2)))))), inverse(multiply(inverse(inverse(multiply(inverse(X2), X2))), multiply(inverse(V), V))))
% 1.61/0.64 = { by lemma 12 R->L }
% 1.61/0.64 multiply(inverse(multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(X)), inverse(inverse(multiply(inverse(X2), X2)))))), inverse(multiply(inverse(inverse(multiply(inverse(X2), X2))), inverse(multiply(inverse(X2), X2)))))
% 1.61/0.64 = { by lemma 17 R->L }
% 1.61/0.64 multiply(inverse(multiply(inverse(multiply(Y2, inverse(X))), multiply(Y2, inverse(inverse(multiply(inverse(X2), X2)))))), inverse(multiply(inverse(inverse(multiply(inverse(X2), X2))), inverse(multiply(inverse(X2), X2)))))
% 1.61/0.64 = { by lemma 8 R->L }
% 1.61/0.64 multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(multiply(inverse(W2), W2))), inverse(X)))), inverse(multiply(inverse(X2), X2)))))), multiply(Y2, inverse(inverse(multiply(inverse(X2), X2)))))), inverse(multiply(inverse(inverse(multiply(inverse(X2), X2))), inverse(multiply(inverse(X2), X2)))))
% 1.61/0.64 = { by axiom 1 (single_axiom) }
% 1.61/0.64 multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(multiply(inverse(W2), W2))), inverse(X)))
% 1.61/0.64 = { by lemma 12 }
% 1.61/0.64 multiply(multiply(inverse(V2), V2), multiply(inverse(inverse(multiply(inverse(W2), W2))), inverse(X)))
% 1.61/0.64 = { by lemma 12 }
% 1.61/0.64 multiply(multiply(inverse(V2), V2), multiply(inverse(multiply(inverse(U2), U2)), inverse(X)))
% 1.61/0.64 = { by lemma 12 }
% 1.61/0.64 multiply(multiply(inverse(V2), V2), multiply(multiply(inverse(T2), T2), inverse(X)))
% 1.61/0.64 = { by lemma 15 }
% 1.61/0.64 multiply(multiply(inverse(T2), T2), inverse(X))
% 1.61/0.64 = { by lemma 15 }
% 1.61/0.64 inverse(X)
% 1.61/0.64
% 1.61/0.64 Lemma 19: inverse(inverse(X)) = X.
% 1.61/0.64 Proof:
% 1.61/0.64 inverse(inverse(X))
% 1.61/0.64 = { by lemma 18 R->L }
% 1.61/0.64 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 1.61/0.64 = { by lemma 12 R->L }
% 1.61/0.64 inverse(multiply(inverse(X), inverse(multiply(inverse(Z), Z))))
% 1.61/0.64 = { by lemma 16 R->L }
% 1.61/0.65 multiply(inverse(inverse(inverse(multiply(inverse(X), inverse(multiply(inverse(Z), Z)))))), multiply(inverse(W), W))
% 1.61/0.65 = { by lemma 12 R->L }
% 1.61/0.65 multiply(inverse(inverse(inverse(multiply(inverse(X), inverse(inverse(multiply(inverse(V), V))))))), multiply(inverse(W), W))
% 1.61/0.65 = { by lemma 12 R->L }
% 1.61/0.65 multiply(inverse(inverse(inverse(multiply(inverse(X), inverse(inverse(multiply(inverse(V), V))))))), inverse(multiply(inverse(V), V)))
% 1.61/0.65 = { by lemma 18 R->L }
% 1.61/0.65 multiply(inverse(inverse(inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))))))), inverse(multiply(inverse(V), V)))
% 1.61/0.65 = { by lemma 15 R->L }
% 1.61/0.65 multiply(multiply(inverse(U), U), multiply(inverse(inverse(inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))))))), inverse(multiply(inverse(V), V))))
% 1.61/0.65 = { by lemma 17 R->L }
% 1.61/0.65 multiply(inverse(multiply(T, inverse(inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V)))))))), multiply(T, inverse(multiply(inverse(V), V))))
% 1.61/0.65 = { by lemma 18 R->L }
% 1.61/0.65 multiply(inverse(multiply(T, inverse(multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))))), multiply(inverse(V), V))))), multiply(T, inverse(multiply(inverse(V), V))))
% 1.61/0.65 = { by lemma 2 }
% 1.61/0.65 X
% 1.61/0.65
% 1.61/0.65 Lemma 20: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 1.61/0.65 Proof:
% 1.61/0.65 multiply(inverse(X), X)
% 1.61/0.65 = { by lemma 6 }
% 1.61/0.65 multiply(inverse(inverse(Y)), inverse(Y))
% 1.61/0.65 = { by lemma 19 }
% 1.61/0.65 multiply(Y, inverse(Y))
% 1.61/0.65
% 1.61/0.65 Lemma 21: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 1.61/0.65 Proof:
% 1.61/0.65 inverse(multiply(X, inverse(Y)))
% 1.61/0.65 = { by lemma 18 R->L }
% 1.61/0.65 multiply(inverse(multiply(X, inverse(Y))), multiply(inverse(inverse(X)), inverse(X)))
% 1.61/0.65 = { by lemma 19 R->L }
% 1.61/0.65 multiply(inverse(multiply(inverse(inverse(X)), inverse(Y))), multiply(inverse(inverse(X)), inverse(X)))
% 1.61/0.65 = { by lemma 17 }
% 1.61/0.65 multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(Y)), inverse(X)))
% 1.61/0.65 = { by lemma 15 }
% 1.61/0.65 multiply(inverse(inverse(Y)), inverse(X))
% 1.61/0.65 = { by lemma 19 }
% 1.61/0.65 multiply(Y, inverse(X))
% 1.61/0.65
% 1.61/0.65 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1)).
% 1.61/0.65 Proof:
% 1.61/0.65 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 1.61/0.65 = { by lemma 15 }
% 1.61/0.65 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 1.61/0.65 = { by lemma 20 }
% 1.61/0.65 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 19 R->L }
% 1.61/0.65 tuple(a2, multiply(multiply(a3, b3), inverse(inverse(c3))), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 19 R->L }
% 1.61/0.65 tuple(a2, multiply(inverse(inverse(multiply(a3, b3))), inverse(inverse(c3))), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 15 R->L }
% 1.61/0.65 tuple(a2, multiply(multiply(inverse(Y), Y), multiply(inverse(inverse(multiply(a3, b3))), inverse(inverse(c3)))), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 17 R->L }
% 1.61/0.65 tuple(a2, multiply(inverse(multiply(b3, inverse(multiply(a3, b3)))), multiply(b3, inverse(inverse(c3)))), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 19 }
% 1.61/0.65 tuple(a2, multiply(inverse(multiply(b3, inverse(multiply(a3, b3)))), multiply(b3, c3)), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 21 }
% 1.61/0.65 tuple(a2, multiply(multiply(multiply(a3, b3), inverse(b3)), multiply(b3, c3)), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 19 R->L }
% 1.61/0.65 tuple(a2, multiply(multiply(multiply(inverse(inverse(a3)), b3), inverse(b3)), multiply(b3, c3)), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 15 R->L }
% 1.61/0.65 tuple(a2, multiply(multiply(multiply(multiply(multiply(inverse(b3), b3), inverse(inverse(a3))), b3), inverse(b3)), multiply(b3, c3)), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 19 R->L }
% 1.61/0.65 tuple(a2, multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(b3), b3), inverse(inverse(a3))), b3))), inverse(b3)), multiply(b3, c3)), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 15 R->L }
% 1.61/0.65 tuple(a2, multiply(multiply(multiply(inverse(Z), Z), multiply(inverse(inverse(multiply(multiply(multiply(inverse(b3), b3), inverse(inverse(a3))), b3))), inverse(b3))), multiply(b3, c3)), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 17 R->L }
% 1.61/0.65 tuple(a2, multiply(multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(b3), b3), inverse(inverse(a3))), b3)))), multiply(W, inverse(b3))), multiply(b3, c3)), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 21 R->L }
% 1.61/0.65 tuple(a2, multiply(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(a3), inverse(multiply(inverse(b3), b3)))), b3)))), multiply(W, inverse(b3))), multiply(b3, c3)), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 2 }
% 1.61/0.65 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 1.61/0.65 = { by lemma 20 R->L }
% 1.61/0.65 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 1.61/0.65 % SZS output end Proof
% 1.61/0.65
% 1.61/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------