%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP051-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 1.04s 0.63s
% Output : Proof 2.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP051-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n002.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 27 09:19:36 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.04/0.63 Command-line arguments: --no-flatten-goal
% 1.04/0.63
% 1.04/0.63 % SZS status Unsatisfiable
% 1.04/0.63
% 1.78/0.74 % SZS output start Proof
% 1.78/0.74 Axiom 1 (single_axiom): multiply(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))) = Y.
% 1.78/0.74
% 1.78/0.74 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z))) = Y.
% 1.78/0.74 Proof:
% 1.78/0.74 multiply(inverse(multiply(X, inverse(multiply(multiply(Y, inverse(multiply(inverse(Z), Z))), Z)))), multiply(X, inverse(Z)))
% 1.78/0.74 = { by axiom 1 (single_axiom) R->L }
% 1.78/0.74 multiply(multiply(inverse(multiply(W, inverse(multiply(multiply(inverse(multiply(X, inverse(multiply(multiply(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)))))
% 1.78/0.74 = { by axiom 1 (single_axiom) }
% 1.78/0.74 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)))))
% 1.78/0.74 = { by axiom 1 (single_axiom) }
% 1.78/0.74 Y
% 1.78/0.74
% 1.78/0.74 Lemma 3: multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(Z, inverse(W))))), inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(W))))) = inverse(multiply(Z, inverse(multiply(multiply(Y, inverse(multiply(inverse(W), W))), W)))).
% 1.78/0.74 Proof:
% 1.78/0.74 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(Z, inverse(W))))), inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(W)))))
% 1.78/0.75 = { by lemma 2 R->L }
% 1.78/0.75 multiply(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(Z, inverse(multiply(multiply(Y, inverse(multiply(inverse(W), W))), W)))), multiply(Z, inverse(W)))))), multiply(X, inverse(multiply(Z, inverse(W))))), inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(W)))))
% 1.78/0.75 = { by axiom 1 (single_axiom) }
% 1.78/0.75 inverse(multiply(Z, inverse(multiply(multiply(Y, inverse(multiply(inverse(W), W))), W))))
% 1.78/0.75
% 1.78/0.75 Lemma 4: inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))) = Y.
% 1.78/0.75 Proof:
% 1.78/0.75 inverse(multiply(X, inverse(multiply(multiply(multiply(Y, multiply(X, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))))
% 1.78/0.75 = { by lemma 3 R->L }
% 1.78/0.75 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)))))
% 1.78/0.75 = { by axiom 1 (single_axiom) }
% 1.78/0.75 Y
% 1.78/0.75
% 1.78/0.75 Lemma 5: multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z)) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z)).
% 1.78/0.75 Proof:
% 1.78/0.75 multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z))
% 1.78/0.75 = { by lemma 4 R->L }
% 1.78/0.75 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))))))
% 1.78/0.75 = { by lemma 2 R->L }
% 1.78/0.75 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))))))
% 1.78/0.75 = { by axiom 1 (single_axiom) R->L }
% 1.78/0.75 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))))))))
% 1.78/0.75 = { by axiom 1 (single_axiom) }
% 1.78/0.75 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))))))))
% 1.78/0.75 = { by axiom 1 (single_axiom) R->L }
% 1.78/0.75 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))))))))
% 1.78/0.75 = { by axiom 1 (single_axiom) }
% 1.78/0.75 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))))))
% 1.78/0.75 = { by lemma 2 }
% 1.78/0.75 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))))))
% 1.78/0.75 = { by lemma 4 }
% 1.78/0.75 multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z))
% 1.78/0.75
% 1.78/0.75 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)).
% 1.78/0.75 Proof:
% 1.78/0.75 multiply(inverse(X), multiply(multiply(inverse(multiply(Y, inverse(multiply(X, Z)))), multiply(Y, inverse(Z))), W))
% 1.78/0.75 = { by axiom 1 (single_axiom) R->L }
% 1.78/0.75 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))
% 1.78/0.75 = { by lemma 5 R->L }
% 1.78/0.75 multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, W))
% 1.78/0.75
% 1.78/0.75 Lemma 7: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 1.78/0.75 Proof:
% 1.78/0.75 multiply(inverse(Y), Y)
% 1.78/0.76 = { by axiom 1 (single_axiom) R->L }
% 1.78/0.76 multiply(inverse(Y), multiply(multiply(inverse(multiply(U, inverse(multiply(Y, W)))), multiply(U, inverse(W))), inverse(multiply(inverse(W), W))))
% 1.78/0.76 = { by lemma 6 }
% 1.78/0.76 multiply(inverse(multiply(V, inverse(multiply(inverse(W), W)))), multiply(V, inverse(multiply(inverse(W), W))))
% 1.78/0.76 = { by lemma 6 R->L }
% 1.78/0.76 multiply(inverse(X), multiply(multiply(inverse(multiply(Z, inverse(multiply(X, W)))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W))))
% 1.78/0.76 = { by axiom 1 (single_axiom) }
% 1.78/0.76 multiply(inverse(X), X)
% 1.78/0.76
% 1.78/0.76 Lemma 8: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 1.78/0.76 Proof:
% 1.78/0.76 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 1.78/0.76 = { by lemma 4 R->L }
% 1.78/0.76 multiply(inverse(multiply(W, inverse(multiply(V, inverse(multiply(multiply(multiply(Y, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), multiply(W, Z))
% 1.78/0.76 = { by lemma 5 }
% 1.78/0.76 multiply(inverse(multiply(X, inverse(multiply(V, inverse(multiply(multiply(multiply(Y, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), multiply(X, Z))
% 1.78/0.76 = { by lemma 4 }
% 1.78/0.76 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 1.78/0.76
% 1.78/0.76 Lemma 9: multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Y), Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 1.78/0.76 Proof:
% 1.78/0.76 multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Y), Z))
% 1.78/0.76 = { by lemma 7 }
% 1.78/0.76 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 1.78/0.76 = { by lemma 8 R->L }
% 1.78/0.76 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 1.78/0.76
% 1.78/0.76 Lemma 10: multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(Y), Y))), inverse(Z))), inverse(multiply(inverse(W), W))) = inverse(Z).
% 1.78/0.76 Proof:
% 1.78/0.76 multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(Y), Y))), inverse(Z))), inverse(multiply(inverse(W), W)))
% 1.78/0.76 = { by lemma 9 }
% 1.78/0.76 multiply(multiply(inverse(multiply(V, inverse(multiply(inverse(Y), Y)))), multiply(V, inverse(Z))), inverse(multiply(inverse(W), W)))
% 1.78/0.76 = { by lemma 7 }
% 1.78/0.76 multiply(multiply(inverse(multiply(V, inverse(multiply(inverse(Y), Y)))), multiply(V, inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 1.78/0.76 = { by lemma 7 }
% 1.78/0.76 multiply(multiply(inverse(multiply(V, inverse(multiply(inverse(Z), Z)))), multiply(V, inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 1.78/0.76 = { by axiom 1 (single_axiom) }
% 1.78/0.76 inverse(Z)
% 1.78/0.76
% 1.78/0.76 Lemma 11: multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(Y), Y))), Z)), inverse(multiply(inverse(W), W))) = Z.
% 1.78/0.76 Proof:
% 1.78/0.76 multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(Y), Y))), Z)), inverse(multiply(inverse(W), W)))
% 1.78/0.76 = { by lemma 4 R->L }
% 1.78/0.76 multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(Y), Y))), inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U)))))), inverse(multiply(inverse(W), W)))
% 1.78/0.76 = { by lemma 10 }
% 1.78/0.76 inverse(multiply(V, inverse(multiply(multiply(multiply(Z, multiply(V, inverse(U))), inverse(multiply(inverse(U), U))), U))))
% 1.78/0.76 = { by lemma 4 }
% 1.78/0.76 Z
% 1.78/0.76
% 1.78/0.76 Lemma 12: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 1.78/0.76 Proof:
% 1.78/0.76 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 1.78/0.76 = { by lemma 7 }
% 1.78/0.76 multiply(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)))
% 1.78/0.76 = { by lemma 10 }
% 1.78/0.76 inverse(multiply(inverse(Z), Z))
% 1.78/0.76
% 1.78/0.76 Lemma 13: inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))), W)))) = inverse(multiply(X, inverse(W))).
% 1.78/0.76 Proof:
% 1.78/0.76 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))), W))))
% 1.78/0.76 = { by lemma 7 }
% 1.78/0.76 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(W), W))), W))))
% 1.78/0.76 = { by lemma 7 }
% 1.78/0.76 inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(multiply(X, inverse(W))), multiply(X, inverse(W))), inverse(multiply(inverse(W), W))), W))))
% 1.78/0.76 = { by lemma 4 }
% 1.78/0.76 inverse(multiply(X, inverse(W)))
% 1.78/0.76
% 1.78/0.76 Lemma 14: multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), Z)) = multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(Y), Y))), Z)).
% 1.78/0.76 Proof:
% 1.78/0.76 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(V), V), Z))
% 1.78/0.76 = { by lemma 7 }
% 1.78/0.76 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(multiply(S, inverse(inverse(multiply(inverse(T), T))))), multiply(S, inverse(inverse(multiply(inverse(T), T))))), Z))
% 1.78/0.76 = { by lemma 12 R->L }
% 1.78/0.76 multiply(inverse(multiply(inverse(W), W)), multiply(multiply(inverse(multiply(S, inverse(multiply(multiply(inverse(W), W), inverse(multiply(inverse(T), T)))))), multiply(S, inverse(inverse(multiply(inverse(T), T))))), Z))
% 1.78/0.76 = { by lemma 6 }
% 1.78/0.76 multiply(inverse(multiply(U, inverse(multiply(inverse(inverse(multiply(inverse(T), T))), inverse(multiply(inverse(T), T)))))), multiply(U, Z))
% 1.78/0.76 = { by lemma 7 R->L }
% 1.78/0.76 multiply(inverse(multiply(U, inverse(multiply(inverse(Y), Y)))), multiply(U, Z))
% 1.78/0.76 = { by lemma 9 R->L }
% 1.78/0.76 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(multiply(inverse(Y), Y))), Z))
% 1.78/0.76
% 1.78/0.76 Lemma 15: multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 1.78/0.76 Proof:
% 1.78/0.76 multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y)))
% 1.78/0.76 = { by lemma 12 R->L }
% 1.78/0.76 multiply(inverse(multiply(inverse(X), X)), multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))))
% 1.78/0.76 = { by lemma 14 }
% 1.78/0.76 multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))
% 1.78/0.76 = { by lemma 7 R->L }
% 1.78/0.76 multiply(inverse(Z), Z)
% 1.78/0.76
% 1.78/0.76 Lemma 16: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 1.78/0.76 Proof:
% 1.78/0.76 inverse(multiply(inverse(X), X))
% 1.78/0.76 = { by lemma 12 R->L }
% 1.78/0.76 multiply(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W)))
% 1.78/0.76 = { by lemma 13 R->L }
% 1.78/0.76 multiply(multiply(inverse(multiply(Z, inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(W), W))), W)))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W)))
% 1.78/0.76 = { by lemma 3 R->L }
% 1.78/0.76 multiply(multiply(multiply(multiply(inverse(multiply(U, inverse(multiply(inverse(V), V)))), multiply(U, inverse(multiply(Z, inverse(W))))), inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(W))))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W)))
% 2.44/0.76 = { by lemma 15 R->L }
% 2.44/0.76 multiply(multiply(multiply(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(T), T)), inverse(multiply(inverse(S), S)))))), multiply(U, inverse(multiply(Z, inverse(W))))), inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(W))))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W)))
% 2.44/0.76 = { by lemma 12 R->L }
% 2.44/0.76 multiply(multiply(multiply(multiply(inverse(multiply(U, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(Y2), Y2))), inverse(multiply(inverse(S), S)))))), multiply(U, inverse(multiply(Z, inverse(W))))), inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(W))))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W)))
% 2.44/0.76 = { by lemma 13 }
% 2.44/0.76 multiply(multiply(multiply(multiply(inverse(multiply(U, inverse(inverse(multiply(inverse(S), S))))), multiply(U, inverse(multiply(Z, inverse(W))))), inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(W))))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W)))
% 2.44/0.76 = { by lemma 3 }
% 2.44/0.76 multiply(multiply(inverse(multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(S), S)), inverse(multiply(inverse(W), W))), W)))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W)))
% 2.44/0.76 = { by lemma 15 }
% 2.44/0.76 multiply(multiply(inverse(multiply(Z, inverse(multiply(multiply(inverse(Y), Y), W)))), multiply(Z, inverse(W))), inverse(multiply(inverse(W), W)))
% 2.44/0.76 = { by axiom 1 (single_axiom) }
% 2.44/0.76 multiply(inverse(Y), Y)
% 2.44/0.76
% 2.44/0.76 Lemma 17: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(multiply(inverse(W), W), multiply(inverse(Y), Z)).
% 2.44/0.76 Proof:
% 2.44/0.76 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 2.44/0.76 = { by lemma 9 R->L }
% 2.44/0.76 multiply(inverse(multiply(inverse(V), V)), multiply(inverse(Y), Z))
% 2.44/0.76 = { by lemma 16 }
% 2.44/0.76 multiply(multiply(inverse(W), W), multiply(inverse(Y), Z))
% 2.44/0.76
% 2.44/0.76 Lemma 18: multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(Z), Z)) = multiply(inverse(multiply(W, Y)), multiply(W, X)).
% 2.44/0.76 Proof:
% 2.44/0.76 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(Z), Z))
% 2.44/0.76 = { by lemma 7 }
% 2.44/0.76 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(X), X))
% 2.44/0.76 = { by lemma 8 R->L }
% 2.44/0.76 multiply(inverse(multiply(W, Y)), multiply(W, X))
% 2.44/0.76
% 2.44/0.76 Lemma 19: multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), multiply(inverse(Z), Z))), multiply(inverse(W), W)) = multiply(multiply(inverse(V), V), multiply(multiply(inverse(U), U), Y)).
% 2.44/0.76 Proof:
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), multiply(inverse(Z), Z))), multiply(inverse(W), W))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(T), T)), multiply(inverse(T), T))))
% 2.44/0.76 = { by lemma 16 }
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(S), S), multiply(inverse(T), T))))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), inverse(multiply(inverse(X2), X2)))), inverse(multiply(multiply(inverse(S), S), multiply(inverse(T), T))))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), inverse(multiply(inverse(X2), X2)))), inverse(multiply(inverse(multiply(inverse(Y2), Y2)), multiply(inverse(T), T))))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), inverse(inverse(multiply(inverse(Z2), Z2))))), inverse(multiply(inverse(multiply(inverse(Y2), Y2)), multiply(inverse(T), T))))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), inverse(inverse(multiply(inverse(Z2), Z2))))), inverse(multiply(inverse(inverse(multiply(inverse(Z2), Z2))), multiply(inverse(T), T))))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), inverse(inverse(multiply(inverse(Z2), Z2))))), inverse(multiply(inverse(inverse(multiply(inverse(Z2), Z2))), inverse(multiply(inverse(Z2), Z2)))))
% 2.44/0.76 = { by lemma 17 R->L }
% 2.44/0.76 multiply(multiply(inverse(multiply(W2, inverse(Y))), multiply(W2, inverse(inverse(multiply(inverse(Z2), Z2))))), inverse(multiply(inverse(inverse(multiply(inverse(Z2), Z2))), inverse(multiply(inverse(Z2), Z2)))))
% 2.44/0.76 = { by lemma 11 R->L }
% 2.44/0.76 multiply(multiply(inverse(multiply(W2, inverse(multiply(multiply(inverse(multiply(inverse(V2), V2)), multiply(inverse(inverse(multiply(inverse(U2), U2))), Y)), inverse(multiply(inverse(Z2), Z2)))))), multiply(W2, inverse(inverse(multiply(inverse(Z2), Z2))))), inverse(multiply(inverse(inverse(multiply(inverse(Z2), Z2))), inverse(multiply(inverse(Z2), Z2)))))
% 2.44/0.76 = { by axiom 1 (single_axiom) }
% 2.44/0.76 multiply(inverse(multiply(inverse(V2), V2)), multiply(inverse(inverse(multiply(inverse(U2), U2))), Y))
% 2.44/0.76 = { by lemma 14 R->L }
% 2.44/0.76 multiply(inverse(multiply(inverse(T2), T2)), multiply(multiply(inverse(U), U), Y))
% 2.44/0.76 = { by lemma 16 }
% 2.44/0.76 multiply(multiply(inverse(V), V), multiply(multiply(inverse(U), U), Y))
% 2.44/0.76
% 2.44/0.76 Lemma 20: multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(multiply(Y, Z))), inverse(Z))), multiply(inverse(W), W)) = Y.
% 2.44/0.76 Proof:
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(multiply(Y, Z))), inverse(Z))), multiply(inverse(W), W))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(X), X), multiply(inverse(inverse(multiply(Y, Z))), inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z)))), multiply(inverse(inverse(multiply(Y, Z))), inverse(Z))), inverse(multiply(inverse(Z), Z)))
% 2.44/0.76 = { by axiom 1 (single_axiom) }
% 2.44/0.76 Y
% 2.44/0.76
% 2.44/0.76 Lemma 21: multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), multiply(Z, multiply(inverse(W), W)))) = Z.
% 2.44/0.76 Proof:
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), multiply(Z, multiply(inverse(W), W))))
% 2.44/0.76 = { by lemma 19 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(V), V), multiply(inverse(inverse(multiply(Z, multiply(inverse(W), W)))), multiply(inverse(U), U))), multiply(inverse(T), T))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(V), V), multiply(inverse(inverse(multiply(Z, multiply(inverse(W), W)))), inverse(multiply(inverse(W), W)))), multiply(inverse(T), T))
% 2.44/0.76 = { by lemma 20 }
% 2.44/0.76 Z
% 2.44/0.76
% 2.44/0.76 Lemma 22: multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(inverse(Z), Z)) = multiply(multiply(inverse(W), W), multiply(inverse(Y), multiply(inverse(V), V))).
% 2.44/0.76 Proof:
% 2.44/0.76 multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(inverse(Z), Z))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(inverse(multiply(multiply(inverse(X), X), Y)), inverse(multiply(inverse(U), U)))
% 2.44/0.76 = { by lemma 12 R->L }
% 2.44/0.76 multiply(inverse(multiply(multiply(inverse(X), X), Y)), multiply(multiply(inverse(X), X), inverse(multiply(inverse(T), T))))
% 2.44/0.76 = { by lemma 17 }
% 2.44/0.76 multiply(multiply(inverse(W), W), multiply(inverse(Y), inverse(multiply(inverse(T), T))))
% 2.44/0.76 = { by lemma 16 }
% 2.44/0.76 multiply(multiply(inverse(W), W), multiply(inverse(Y), multiply(inverse(V), V)))
% 2.44/0.76
% 2.44/0.76 Lemma 23: inverse(multiply(X, multiply(inverse(Y), Y))) = multiply(inverse(X), multiply(inverse(Z), Z)).
% 2.44/0.76 Proof:
% 2.44/0.76 inverse(multiply(X, multiply(inverse(Y), Y)))
% 2.44/0.76 = { by lemma 21 R->L }
% 2.44/0.76 multiply(multiply(inverse(W), W), multiply(multiply(inverse(V), V), multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(inverse(U), U))))
% 2.44/0.76 = { by lemma 22 R->L }
% 2.44/0.76 multiply(multiply(inverse(W), W), multiply(inverse(multiply(multiply(inverse(T), T), multiply(X, multiply(inverse(Y), Y)))), multiply(inverse(S), S)))
% 2.44/0.76 = { by lemma 22 R->L }
% 2.44/0.76 multiply(inverse(multiply(multiply(inverse(X2), X2), multiply(multiply(inverse(T), T), multiply(X, multiply(inverse(Y), Y))))), multiply(inverse(Z), Z))
% 2.44/0.76 = { by lemma 21 }
% 2.44/0.76 multiply(inverse(X), multiply(inverse(Z), Z))
% 2.44/0.76
% 2.44/0.76 Lemma 24: multiply(multiply(inverse(X), X), Y) = Y.
% 2.44/0.76 Proof:
% 2.44/0.76 multiply(multiply(inverse(X), X), Y)
% 2.44/0.76 = { by lemma 11 R->L }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(inverse(multiply(inverse(W), W))), Y)), inverse(multiply(inverse(V), V))))
% 2.44/0.76 = { by lemma 16 }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(multiply(inverse(U), U), multiply(inverse(inverse(multiply(inverse(W), W))), Y)), inverse(multiply(inverse(V), V))))
% 2.44/0.76 = { by lemma 16 }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(multiply(inverse(U), U), multiply(inverse(inverse(multiply(inverse(W), W))), Y)), multiply(inverse(T), T)))
% 2.44/0.76 = { by lemma 16 }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(multiply(inverse(U), U), multiply(inverse(multiply(inverse(S), S)), Y)), multiply(inverse(T), T)))
% 2.44/0.76 = { by lemma 17 R->L }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(inverse(multiply(X2, multiply(inverse(S), S))), multiply(X2, Y)), multiply(inverse(T), T)))
% 2.44/0.76 = { by lemma 18 R->L }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(inverse(multiply(inverse(Y), multiply(inverse(S), S))), multiply(inverse(Y2), Y2)), multiply(inverse(T), T)))
% 2.44/0.76 = { by lemma 23 R->L }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(inverse(inverse(multiply(Y, multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(Z2), Z2))))), multiply(inverse(Y2), Y2)), multiply(inverse(T), T)))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(inverse(inverse(multiply(Y, multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))))), multiply(inverse(Y2), Y2)), multiply(inverse(T), T)))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(inverse(inverse(multiply(Y, multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))))), multiply(inverse(Y2), Y2)), inverse(multiply(inverse(W2), W2))))
% 2.44/0.76 = { by lemma 23 R->L }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(multiply(inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(W2), W2)), multiply(inverse(W2), W2)))))), multiply(inverse(Y2), Y2)), inverse(multiply(inverse(W2), W2))))
% 2.44/0.76 = { by lemma 23 R->L }
% 2.44/0.76 multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(W2), W2)), multiply(inverse(W2), W2))))), multiply(inverse(V2), V2))), inverse(multiply(inverse(W2), W2))))
% 2.44/0.76 = { by lemma 17 R->L }
% 2.44/0.76 multiply(inverse(multiply(U2, multiply(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(W2), W2)), multiply(inverse(W2), W2))))), multiply(inverse(V2), V2)))), multiply(U2, inverse(multiply(inverse(W2), W2))))
% 2.44/0.76 = { by lemma 23 R->L }
% 2.44/0.76 multiply(inverse(multiply(U2, inverse(multiply(multiply(Y, inverse(multiply(inverse(multiply(inverse(W2), W2)), multiply(inverse(W2), W2)))), multiply(inverse(W2), W2))))), multiply(U2, inverse(multiply(inverse(W2), W2))))
% 2.44/0.76 = { by lemma 2 }
% 2.44/0.76 Y
% 2.44/0.76
% 2.44/0.76 Lemma 25: multiply(X, multiply(inverse(Y), Y)) = X.
% 2.44/0.76 Proof:
% 2.44/0.76 multiply(X, multiply(inverse(Y), Y))
% 2.44/0.76 = { by lemma 24 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(Z), Z), X), multiply(inverse(Y), Y))
% 2.44/0.76 = { by lemma 16 R->L }
% 2.44/0.76 multiply(multiply(inverse(multiply(inverse(W), W)), X), multiply(inverse(Y), Y))
% 2.44/0.76 = { by lemma 24 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(V), V), multiply(inverse(multiply(inverse(W), W)), X)), multiply(inverse(Y), Y))
% 2.44/0.76 = { by lemma 17 R->L }
% 2.44/0.76 multiply(multiply(inverse(multiply(U, multiply(inverse(W), W))), multiply(U, X)), multiply(inverse(Y), Y))
% 2.44/0.76 = { by lemma 18 R->L }
% 2.44/0.76 multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(W), W))), multiply(inverse(T), T)), multiply(inverse(Y), Y))
% 2.44/0.76 = { by lemma 24 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(S), S), multiply(inverse(multiply(inverse(X), multiply(inverse(W), W))), multiply(inverse(T), T))), multiply(inverse(Y), Y))
% 2.44/0.76 = { by lemma 23 R->L }
% 2.44/0.76 multiply(multiply(multiply(inverse(S), S), multiply(inverse(inverse(multiply(X, multiply(inverse(X2), X2)))), multiply(inverse(T), T))), multiply(inverse(Y), Y))
% 2.44/0.77 = { by lemma 19 }
% 2.44/0.77 multiply(multiply(inverse(Y2), Y2), multiply(multiply(inverse(Z2), Z2), multiply(X, multiply(inverse(X2), X2))))
% 2.44/0.77 = { by lemma 21 }
% 2.44/0.77 X
% 2.44/0.77
% 2.44/0.77 Lemma 26: inverse(inverse(X)) = X.
% 2.44/0.77 Proof:
% 2.44/0.77 inverse(inverse(X))
% 2.44/0.77 = { by lemma 25 R->L }
% 2.44/0.77 multiply(inverse(inverse(X)), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y)))
% 2.44/0.77 = { by lemma 23 R->L }
% 2.44/0.77 multiply(inverse(inverse(X)), inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(Z), Z))))
% 2.44/0.77 = { by lemma 25 R->L }
% 2.44/0.77 multiply(multiply(inverse(inverse(X)), multiply(inverse(W), W)), inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(Z), Z))))
% 2.44/0.77 = { by lemma 16 R->L }
% 2.44/0.77 multiply(multiply(inverse(inverse(X)), inverse(multiply(inverse(Z), Z))), inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(Z), Z))))
% 2.44/0.77 = { by lemma 16 R->L }
% 2.44/0.77 multiply(multiply(inverse(inverse(X)), inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))
% 2.44/0.77 = { by lemma 24 R->L }
% 2.44/0.77 multiply(multiply(multiply(inverse(V), V), multiply(inverse(inverse(X)), inverse(multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))
% 2.44/0.77 = { by lemma 17 R->L }
% 2.44/0.77 multiply(multiply(inverse(multiply(U, inverse(X))), multiply(U, inverse(multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))
% 2.44/0.77 = { by lemma 25 R->L }
% 2.44/0.77 multiply(multiply(inverse(multiply(U, inverse(multiply(X, multiply(inverse(Z), Z))))), multiply(U, inverse(multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))
% 2.44/0.77 = { by axiom 1 (single_axiom) }
% 2.44/0.77 X
% 2.44/0.77
% 2.44/0.77 Lemma 27: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 2.44/0.77 Proof:
% 2.44/0.77 multiply(inverse(X), X)
% 2.44/0.77 = { by lemma 7 }
% 2.44/0.77 multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(Y)), inverse(Y))))), multiply(Z, inverse(multiply(inverse(inverse(Y)), inverse(Y)))))
% 2.44/0.77 = { by lemma 26 }
% 2.44/0.77 multiply(inverse(multiply(Z, inverse(multiply(Y, inverse(Y))))), multiply(Z, inverse(multiply(inverse(inverse(Y)), inverse(Y)))))
% 2.44/0.77 = { by lemma 17 }
% 2.44/0.77 multiply(multiply(inverse(W), W), multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(multiply(inverse(inverse(Y)), inverse(Y)))))
% 2.44/0.77 = { by lemma 24 }
% 2.44/0.77 multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(multiply(inverse(inverse(Y)), inverse(Y))))
% 2.44/0.77 = { by lemma 26 }
% 2.44/0.77 multiply(multiply(Y, inverse(Y)), inverse(multiply(inverse(inverse(Y)), inverse(Y))))
% 2.44/0.77 = { by lemma 16 }
% 2.44/0.77 multiply(multiply(Y, inverse(Y)), multiply(inverse(V), V))
% 2.44/0.77 = { by lemma 25 }
% 2.44/0.77 multiply(Y, inverse(Y))
% 2.44/0.77
% 2.44/0.77 Lemma 28: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = inverse(multiply(inverse(Z), Y)).
% 2.44/0.77 Proof:
% 2.44/0.77 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 2.44/0.77 = { by lemma 18 R->L }
% 2.44/0.77 multiply(inverse(multiply(inverse(Z), Y)), multiply(inverse(W), W))
% 2.44/0.77 = { by lemma 25 }
% 2.44/0.77 inverse(multiply(inverse(Z), Y))
% 2.44/0.77
% 2.44/0.77 Lemma 29: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 2.44/0.77 Proof:
% 2.44/0.77 inverse(multiply(inverse(X), Y))
% 2.44/0.77 = { by lemma 28 R->L }
% 2.44/0.77 multiply(inverse(multiply(Z, Y)), multiply(Z, X))
% 2.44/0.77 = { by lemma 9 R->L }
% 2.44/0.77 multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Y), X))
% 2.44/0.77 = { by lemma 16 }
% 2.44/0.77 multiply(multiply(inverse(V), V), multiply(inverse(Y), X))
% 2.44/0.77 = { by lemma 24 }
% 2.44/0.77 multiply(inverse(Y), X)
% 2.44/0.77
% 2.44/0.77 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)).
% 2.44/0.77 Proof:
% 2.44/0.77 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 2.44/0.77 = { by lemma 24 }
% 2.44/0.77 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 2.44/0.77 = { by lemma 27 }
% 2.44/0.77 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 4 R->L }
% 2.44/0.77 tuple(a2, multiply(multiply(a3, inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))))), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 4 R->L }
% 2.44/0.77 tuple(a2, multiply(multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V)))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))))), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 24 R->L }
% 2.44/0.77 tuple(a2, multiply(multiply(multiply(inverse(U), U), multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V)))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 25 R->L }
% 2.44/0.77 tuple(a2, multiply(multiply(multiply(multiply(inverse(U), U), multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V)))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), multiply(inverse(T), T)), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 24 R->L }
% 2.44/0.77 tuple(a2, multiply(multiply(multiply(multiply(inverse(U), U), multiply(inverse(multiply(multiply(inverse(S), S), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), multiply(inverse(T), T)), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 16 R->L }
% 2.44/0.77 tuple(a2, multiply(multiply(multiply(multiply(inverse(U), U), multiply(inverse(multiply(inverse(multiply(inverse(X2), X2)), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), multiply(inverse(T), T)), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 26 R->L }
% 2.44/0.77 tuple(a2, multiply(multiply(multiply(multiply(inverse(U), U), multiply(inverse(inverse(inverse(multiply(inverse(multiply(inverse(X2), X2)), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), multiply(inverse(T), T)), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 28 R->L }
% 2.44/0.77 tuple(a2, multiply(multiply(multiply(multiply(inverse(U), U), multiply(inverse(inverse(multiply(inverse(multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))), multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(inverse(X2), X2))))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), multiply(inverse(T), T)), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 28 R->L }
% 2.44/0.77 tuple(a2, multiply(multiply(multiply(multiply(inverse(U), U), multiply(inverse(multiply(inverse(multiply(Y2, multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(inverse(X2), X2)))), multiply(Y2, multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), multiply(inverse(T), T)), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 25 }
% 2.44/0.77 tuple(a2, multiply(multiply(multiply(multiply(inverse(U), U), multiply(inverse(multiply(inverse(multiply(Y2, multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))))), multiply(Y2, multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), multiply(inverse(T), T)), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 28 }
% 2.44/0.77 tuple(a2, multiply(multiply(multiply(multiply(inverse(U), U), multiply(inverse(inverse(multiply(inverse(multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))), multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))))), multiply(inverse(T), T)), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 20 }
% 2.44/0.77 tuple(a2, multiply(inverse(multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))), c3), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 29 R->L }
% 2.44/0.77 tuple(a2, inverse(multiply(inverse(c3), multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V)))))), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 28 R->L }
% 2.44/0.77 tuple(a2, multiply(inverse(multiply(inverse(multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(inverse(Z2), Z2))), multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V)))))), multiply(inverse(multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(inverse(Z2), Z2))), c3)), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 25 }
% 2.44/0.77 tuple(a2, multiply(inverse(multiply(inverse(multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(inverse(Z2), Z2))), multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V)))))), multiply(inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))), c3)), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 29 }
% 2.44/0.77 tuple(a2, multiply(multiply(inverse(multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))), multiply(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z))), multiply(inverse(Z2), Z2))), multiply(inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))), c3)), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 28 }
% 2.44/0.77 tuple(a2, multiply(inverse(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V))))), multiply(inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))), c3)), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 29 }
% 2.44/0.77 tuple(a2, multiply(multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V)))), multiply(inverse(Z2), Z2)), multiply(inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))), c3)), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 25 }
% 2.44/0.77 tuple(a2, multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(a3, multiply(W, inverse(V))), inverse(multiply(inverse(V), V))), V)))), multiply(inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))), c3)), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 4 }
% 2.44/0.77 tuple(a2, multiply(a3, multiply(inverse(multiply(Y, inverse(multiply(multiply(multiply(b3, multiply(Y, inverse(Z))), inverse(multiply(inverse(Z), Z))), Z)))), c3)), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 4 }
% 2.44/0.77 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 2.44/0.77 = { by lemma 27 R->L }
% 2.44/0.77 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 2.44/0.77 % SZS output end Proof
% 2.44/0.77
% 2.44/0.77 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------