%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP062-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10:09:11 AM UTC 2026
% Result : Unsatisfiable 1.75s 0.68s
% Output : Proof 3.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP062-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:15:39 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.75/0.68 Command-line arguments: --no-flatten-goal
% 1.75/0.68
% 1.75/0.68 % SZS status Unsatisfiable
% 1.75/0.68
% 2.84/0.88 % SZS output start Proof
% 2.84/0.88 Axiom 1 (single_axiom): inverse(multiply(X, multiply(Y, multiply(multiply(Z, inverse(Z)), inverse(multiply(W, multiply(X, Y))))))) = W.
% 2.84/0.88
% 2.84/0.88 Lemma 2: inverse(multiply(X, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))), multiply(multiply(V, inverse(V)), Z)))) = W.
% 2.84/0.88 Proof:
% 2.84/0.88 inverse(multiply(X, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))), multiply(multiply(V, inverse(V)), Z))))
% 2.84/0.88 = { by axiom 1 (single_axiom) R->L }
% 2.84/0.88 inverse(multiply(X, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))), multiply(multiply(V, inverse(V)), inverse(multiply(W, multiply(X, multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, X)))))))))))
% 2.84/0.88 = { by axiom 1 (single_axiom) }
% 2.84/0.88 W
% 2.84/0.88
% 2.84/0.88 Lemma 3: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 2.84/0.88 Proof:
% 2.84/0.88 multiply(Y, inverse(Y))
% 2.84/0.88 = { by lemma 2 R->L }
% 2.84/0.88 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, V))))))), multiply(multiply(S, inverse(S)), T))))
% 2.84/0.88 = { by lemma 2 R->L }
% 2.84/0.89 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, inverse(multiply(multiply(multiply(X2, inverse(X2)), Z), multiply(multiply(multiply(Y2, inverse(Y2)), inverse(multiply(V, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, V)))), multiply(multiply(X2, inverse(X2)), Z))))), multiply(multiply(Z2, inverse(Z2)), V))))))), multiply(multiply(S, inverse(S)), T))))
% 2.84/0.89 = { by lemma 2 }
% 2.84/0.89 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, inverse(multiply(multiply(multiply(X2, inverse(X2)), Z), multiply(multiply(multiply(Y2, inverse(Y2)), W), multiply(multiply(Z2, inverse(Z2)), V))))))), multiply(multiply(S, inverse(S)), T))))
% 2.84/0.89 = { by lemma 2 R->L }
% 2.84/0.89 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, inverse(multiply(multiply(multiply(X2, inverse(X2)), Z), multiply(multiply(multiply(Y2, inverse(Y2)), inverse(multiply(V, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Z, multiply(W, V)))), multiply(multiply(X2, inverse(X2)), Z))))), multiply(multiply(Z2, inverse(Z2)), V))))))), multiply(multiply(S, inverse(S)), T))))
% 2.84/0.89 = { by lemma 2 }
% 2.84/0.89 inverse(multiply(inverse(multiply(Z, multiply(W, V))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(T, multiply(multiply(X, inverse(X)), inverse(multiply(Z, multiply(W, V))))))), multiply(multiply(S, inverse(S)), T))))
% 2.84/0.89 = { by lemma 2 }
% 2.84/0.89 multiply(X, inverse(X))
% 2.84/0.89
% 2.84/0.89 Lemma 4: inverse(multiply(X, multiply(inverse(X), multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W)))))))) = Z.
% 2.84/0.89 Proof:
% 2.84/0.89 inverse(multiply(X, multiply(inverse(X), multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))))))
% 2.84/0.89 = { by lemma 3 }
% 2.84/0.89 inverse(multiply(X, multiply(inverse(X), multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(X, inverse(X))))))))
% 2.84/0.89 = { by axiom 1 (single_axiom) }
% 2.84/0.89 Z
% 2.84/0.89
% 2.84/0.89 Lemma 5: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(Z, inverse(Z)), W), multiply(multiply(V, inverse(V)), U)))) = multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(W, U)))).
% 2.84/0.89 Proof:
% 2.84/0.89 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(Z, inverse(Z)), W), multiply(multiply(V, inverse(V)), U))))
% 2.84/0.89 = { by lemma 2 R->L }
% 2.84/0.89 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(U, multiply(multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(W, U)))), multiply(multiply(X, inverse(X)), Y))))), multiply(multiply(V, inverse(V)), U))))
% 2.84/0.89 = { by lemma 2 }
% 2.84/0.89 multiply(multiply(T, inverse(T)), inverse(multiply(Y, multiply(W, U))))
% 2.84/0.89
% 2.84/0.89 Lemma 6: multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(Y, W)))) = inverse(W).
% 2.84/0.89 Proof:
% 2.84/0.89 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(Y, W))))
% 2.84/0.89 = { by lemma 5 R->L }
% 2.84/0.89 inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(Y, multiply(Z, inverse(Z))))), multiply(multiply(multiply(U, inverse(U)), Y), multiply(multiply(T, inverse(T)), W))))
% 2.84/0.89 = { by lemma 4 R->L }
% 2.84/0.89 inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(Y, multiply(Z, inverse(Z))))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(W, multiply(inverse(W), multiply(multiply(V, inverse(V)), inverse(multiply(Y, multiply(Z, inverse(Z))))))))), multiply(multiply(T, inverse(T)), W))))
% 2.84/0.89 = { by lemma 2 }
% 2.84/0.89 inverse(W)
% 2.84/0.89
% 2.84/0.89 Lemma 7: multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(W, inverse(W))))) = inverse(inverse(Y)).
% 2.84/0.89 Proof:
% 2.84/0.89 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(W, inverse(W)))))
% 2.84/0.89 = { by lemma 3 }
% 2.84/0.89 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Y, multiply(Z, inverse(Z)))), multiply(Y, inverse(Y)))))
% 2.84/0.89 = { by lemma 6 }
% 2.84/0.89 inverse(inverse(Y))
% 2.84/0.89
% 2.84/0.89 Lemma 8: inverse(multiply(X, multiply(Y, inverse(Y)))) = inverse(multiply(Z, multiply(inverse(Z), inverse(inverse(X))))).
% 2.84/0.89 Proof:
% 2.84/0.89 inverse(multiply(X, multiply(Y, inverse(Y))))
% 2.84/0.89 = { by lemma 4 R->L }
% 2.84/0.89 inverse(multiply(Z, multiply(inverse(Z), multiply(multiply(W, inverse(W)), inverse(multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), multiply(V, inverse(V))))))))
% 2.84/0.89 = { by lemma 7 }
% 2.84/0.89 inverse(multiply(Z, multiply(inverse(Z), inverse(inverse(X)))))
% 2.84/0.89
% 2.84/0.89 Lemma 9: multiply(multiply(X, multiply(Y, multiply(multiply(Z, inverse(Z)), inverse(multiply(W, multiply(X, Y)))))), W) = multiply(V, inverse(V)).
% 2.84/0.89 Proof:
% 2.84/0.89 multiply(multiply(X, multiply(Y, multiply(multiply(Z, inverse(Z)), inverse(multiply(W, multiply(X, Y)))))), W)
% 2.84/0.89 = { by axiom 1 (single_axiom) R->L }
% 2.84/0.89 multiply(multiply(X, multiply(Y, multiply(multiply(Z, inverse(Z)), inverse(multiply(W, multiply(X, Y)))))), inverse(multiply(X, multiply(Y, multiply(multiply(Z, inverse(Z)), inverse(multiply(W, multiply(X, Y))))))))
% 2.84/0.89 = { by lemma 3 R->L }
% 2.84/0.89 multiply(V, inverse(V))
% 2.84/0.89
% 2.84/0.89 Lemma 10: multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(inverse(Y), inverse(inverse(inverse(multiply(Z, inverse(Z))))))))) = inverse(multiply(W, inverse(W))).
% 2.84/0.89 Proof:
% 2.84/0.89 multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(inverse(Y), inverse(inverse(inverse(multiply(Z, inverse(Z)))))))))
% 2.84/0.89 = { by lemma 8 R->L }
% 2.84/0.89 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(V, inverse(V)))))
% 2.84/0.89 = { by lemma 9 R->L }
% 2.84/0.89 multiply(multiply(X, inverse(X)), inverse(multiply(inverse(multiply(multiply(U, multiply(T, multiply(multiply(S, inverse(S)), inverse(multiply(multiply(W, inverse(W)), multiply(U, T)))))), multiply(W, inverse(W)))), multiply(V, inverse(V)))))
% 2.84/0.89 = { by lemma 7 }
% 2.84/0.89 inverse(inverse(multiply(U, multiply(T, multiply(multiply(S, inverse(S)), inverse(multiply(multiply(W, inverse(W)), multiply(U, T))))))))
% 2.84/0.89 = { by axiom 1 (single_axiom) }
% 2.84/0.89 inverse(multiply(W, inverse(W)))
% 2.84/0.89
% 2.84/0.89 Lemma 11: inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(Z, inverse(Z)), multiply(multiply(W, inverse(W)), V)))) = multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(inverse(multiply(T, inverse(T))), V)))).
% 2.84/0.89 Proof:
% 2.84/0.89 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(Z, inverse(Z)), multiply(multiply(W, inverse(W)), V))))
% 2.84/0.89 = { by lemma 3 }
% 2.84/0.89 inverse(multiply(multiply(multiply(X, inverse(X)), Y), multiply(multiply(multiply(T, inverse(T)), inverse(multiply(T, inverse(T)))), multiply(multiply(W, inverse(W)), V))))
% 2.84/0.89 = { by lemma 5 }
% 2.84/0.89 multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(inverse(multiply(T, inverse(T))), V))))
% 2.84/0.89
% 2.84/0.89 Lemma 12: inverse(multiply(inverse(multiply(X, inverse(X))), multiply(multiply(Y, inverse(Y)), multiply(multiply(Z, inverse(Z)), W)))) = inverse(W).
% 2.84/0.89 Proof:
% 2.84/0.89 inverse(multiply(inverse(multiply(X, inverse(X))), multiply(multiply(Y, inverse(Y)), multiply(multiply(Z, inverse(Z)), W))))
% 2.84/0.89 = { by lemma 10 R->L }
% 2.84/0.89 inverse(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(U, inverse(U))), multiply(inverse(inverse(multiply(U, inverse(U)))), inverse(inverse(inverse(multiply(U, inverse(U))))))))), multiply(multiply(Y, inverse(Y)), multiply(multiply(Z, inverse(Z)), W))))
% 2.84/0.89 = { by lemma 11 }
% 2.84/0.89 multiply(multiply(T, inverse(T)), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(U))), multiply(inverse(inverse(multiply(U, inverse(U)))), inverse(inverse(inverse(multiply(U, inverse(U)))))))), multiply(inverse(multiply(U, inverse(U))), W))))
% 2.84/0.89 = { by lemma 6 }
% 2.84/0.89 inverse(W)
% 2.84/0.89
% 2.84/0.89 Lemma 13: inverse(multiply(inverse(X), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))), multiply(multiply(V, inverse(V)), Z)))) = X.
% 2.84/0.89 Proof:
% 2.84/0.89 inverse(multiply(inverse(X), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(W, inverse(W))))), multiply(multiply(V, inverse(V)), Z))))
% 2.84/0.89 = { by lemma 3 }
% 2.84/0.89 inverse(multiply(inverse(X), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, multiply(X, inverse(X))))), multiply(multiply(V, inverse(V)), Z))))
% 2.84/0.89 = { by lemma 2 }
% 2.84/0.89 X
% 2.84/0.89
% 2.84/0.89 Lemma 14: multiply(Z, multiply(inverse(Z), inverse(inverse(X)))) = multiply(X, multiply(Y, inverse(Y))).
% 2.84/0.90 Proof:
% 2.84/0.90 multiply(Z, multiply(inverse(Z), inverse(inverse(X))))
% 2.84/0.90 = { by lemma 13 R->L }
% 2.84/0.90 inverse(multiply(inverse(multiply(Z, multiply(inverse(Z), inverse(inverse(X))))), multiply(multiply(multiply(W, inverse(W)), inverse(multiply(V, multiply(U, inverse(U))))), multiply(multiply(T, inverse(T)), V))))
% 2.84/0.90 = { by lemma 8 R->L }
% 2.84/0.90 inverse(multiply(inverse(multiply(X, multiply(Y, inverse(Y)))), multiply(multiply(multiply(W, inverse(W)), inverse(multiply(V, multiply(U, inverse(U))))), multiply(multiply(T, inverse(T)), V))))
% 2.84/0.90 = { by lemma 13 }
% 2.84/0.90 multiply(X, multiply(Y, inverse(Y)))
% 2.84/0.90
% 2.84/0.90 Lemma 15: inverse(multiply(Z, multiply(inverse(Z), inverse(Y)))) = inverse(multiply(X, multiply(inverse(X), inverse(Y)))).
% 2.84/0.90 Proof:
% 2.84/0.90 inverse(multiply(Z, multiply(inverse(Z), inverse(Y))))
% 2.84/0.90 = { by axiom 1 (single_axiom) R->L }
% 2.84/0.90 inverse(multiply(Z, multiply(inverse(Z), inverse(inverse(multiply(W, multiply(V, multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(W, V)))))))))))
% 2.84/0.90 = { by lemma 7 R->L }
% 2.84/0.90 inverse(multiply(Z, multiply(inverse(Z), multiply(multiply(Y2, inverse(Y2)), inverse(multiply(inverse(multiply(multiply(W, multiply(V, multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(W, V)))))), multiply(S, inverse(S)))), multiply(Z2, inverse(Z2))))))))
% 2.84/0.90 = { by lemma 4 }
% 2.84/0.90 inverse(multiply(multiply(W, multiply(V, multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(W, V)))))), multiply(S, inverse(S))))
% 2.84/0.90 = { by lemma 4 R->L }
% 2.84/0.90 inverse(multiply(X, multiply(inverse(X), multiply(multiply(T, inverse(T)), inverse(multiply(inverse(multiply(multiply(W, multiply(V, multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(W, V)))))), multiply(S, inverse(S)))), multiply(X2, inverse(X2))))))))
% 2.84/0.90 = { by lemma 7 }
% 2.84/0.90 inverse(multiply(X, multiply(inverse(X), inverse(inverse(multiply(W, multiply(V, multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(W, V)))))))))))
% 2.84/0.90 = { by axiom 1 (single_axiom) }
% 2.84/0.90 inverse(multiply(X, multiply(inverse(X), inverse(Y))))
% 2.84/0.90
% 2.84/0.90 Lemma 16: multiply(Z, multiply(inverse(Z), Y)) = multiply(X, multiply(inverse(X), Y)).
% 2.84/0.90 Proof:
% 2.84/0.90 multiply(Z, multiply(inverse(Z), Y))
% 2.84/0.90 = { by lemma 13 R->L }
% 2.84/0.90 inverse(multiply(inverse(multiply(Z, multiply(inverse(Z), Y))), multiply(multiply(multiply(W, inverse(W)), inverse(multiply(V, multiply(U, inverse(U))))), multiply(multiply(T, inverse(T)), V))))
% 2.84/0.90 = { by axiom 1 (single_axiom) R->L }
% 2.84/0.90 inverse(multiply(inverse(multiply(Z, multiply(inverse(Z), inverse(multiply(S, multiply(X2, multiply(multiply(Y2, inverse(Y2)), inverse(multiply(Y, multiply(S, X2)))))))))), multiply(multiply(multiply(W, inverse(W)), inverse(multiply(V, multiply(U, inverse(U))))), multiply(multiply(T, inverse(T)), V))))
% 2.84/0.90 = { by lemma 15 }
% 2.84/0.90 inverse(multiply(inverse(multiply(X, multiply(inverse(X), inverse(multiply(S, multiply(X2, multiply(multiply(Y2, inverse(Y2)), inverse(multiply(Y, multiply(S, X2)))))))))), multiply(multiply(multiply(W, inverse(W)), inverse(multiply(V, multiply(U, inverse(U))))), multiply(multiply(T, inverse(T)), V))))
% 2.84/0.90 = { by axiom 1 (single_axiom) }
% 2.84/0.90 inverse(multiply(inverse(multiply(X, multiply(inverse(X), Y))), multiply(multiply(multiply(W, inverse(W)), inverse(multiply(V, multiply(U, inverse(U))))), multiply(multiply(T, inverse(T)), V))))
% 2.84/0.90 = { by lemma 13 }
% 2.84/0.90 multiply(X, multiply(inverse(X), Y))
% 2.84/0.90
% 2.84/0.90 Lemma 17: multiply(X, multiply(inverse(X), multiply(inverse(inverse(Y)), Z))) = multiply(Y, multiply(W, multiply(inverse(W), Z))).
% 2.84/0.90 Proof:
% 2.84/0.90 multiply(X, multiply(inverse(X), multiply(inverse(inverse(Y)), Z)))
% 2.84/0.90 = { by lemma 16 }
% 2.84/0.90 multiply(Y, multiply(inverse(Y), multiply(inverse(inverse(Y)), Z)))
% 2.84/0.90 = { by lemma 16 R->L }
% 2.84/0.90 multiply(Y, multiply(W, multiply(inverse(W), Z)))
% 2.84/0.90
% 2.84/0.90 Lemma 18: multiply(X, multiply(inverse(X), multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, multiply(inverse(W), inverse(inverse(V))))))))))) = inverse(multiply(multiply(U, inverse(U)), V)).
% 2.84/0.90 Proof:
% 2.84/0.90 multiply(X, multiply(inverse(X), multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, multiply(inverse(W), inverse(inverse(V)))))))))))
% 2.84/0.90 = { by lemma 8 R->L }
% 2.84/0.90 multiply(X, multiply(inverse(X), multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(V, multiply(T, inverse(T))))))))))
% 2.84/0.90 = { by lemma 17 }
% 2.84/0.90 multiply(multiply(Y, inverse(Y)), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(V, multiply(T, inverse(T))))), multiply(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(V, multiply(T, inverse(T)))))), inverse(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(V, multiply(T, inverse(T))))))))))
% 3.56/0.90 = { by lemma 13 R->L }
% 3.56/0.90 multiply(multiply(Y, inverse(Y)), inverse(multiply(inverse(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(V, multiply(T, inverse(T))))), multiply(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(V, multiply(T, inverse(T)))))), inverse(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(V, multiply(T, inverse(T)))))))))), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(V, multiply(T, inverse(T))))), multiply(multiply(U, inverse(U)), V)))))
% 3.56/0.90 = { by lemma 6 }
% 3.56/0.90 inverse(multiply(multiply(U, inverse(U)), V))
% 3.56/0.90
% 3.56/0.90 Lemma 19: multiply(X, multiply(Y, multiply(inverse(Y), inverse(inverse(inverse(X)))))) = inverse(multiply(Z, inverse(Z))).
% 3.56/0.90 Proof:
% 3.56/0.90 multiply(X, multiply(Y, multiply(inverse(Y), inverse(inverse(inverse(X))))))
% 3.56/0.90 = { by lemma 14 }
% 3.56/0.90 multiply(X, multiply(inverse(X), multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(inverse(inverse(multiply(W, inverse(W))))))))
% 3.56/0.90 = { by lemma 10 R->L }
% 3.56/0.90 multiply(X, multiply(inverse(X), multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(inverse(multiply(multiply(V, inverse(V)), inverse(multiply(U, multiply(inverse(U), inverse(inverse(inverse(multiply(T, inverse(T))))))))))))))
% 3.56/0.90 = { by lemma 18 }
% 3.56/0.90 inverse(multiply(multiply(T, inverse(T)), inverse(multiply(T, inverse(T)))))
% 3.56/0.90 = { by lemma 3 R->L }
% 3.56/0.90 inverse(multiply(Z, inverse(Z)))
% 3.56/0.90
% 3.56/0.90 Lemma 20: inverse(inverse(inverse(multiply(X, inverse(X))))) = multiply(Y, inverse(Y)).
% 3.56/0.90 Proof:
% 3.56/0.90 inverse(inverse(inverse(multiply(X, inverse(X)))))
% 3.56/0.90 = { by lemma 19 R->L }
% 3.56/0.90 inverse(inverse(multiply(multiply(Y, inverse(Y)), multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(multiply(Y, inverse(Y))))))))))
% 3.56/0.90 = { by lemma 12 R->L }
% 3.56/0.90 inverse(multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(multiply(Y, inverse(Y)))))), multiply(multiply(Z, inverse(Z)), inverse(multiply(multiply(Y, inverse(Y)), multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(inverse(multiply(Y, inverse(Y)))), inverse(inverse(inverse(multiply(Y, inverse(Y)))))))))))))
% 3.56/0.90 = { by axiom 1 (single_axiom) }
% 3.56/0.90 multiply(Y, inverse(Y))
% 3.56/0.90
% 3.56/0.90 Lemma 21: multiply(inverse(multiply(X, inverse(X))), multiply(multiply(Y, inverse(Y)), multiply(multiply(Z, inverse(Z)), W))) = W.
% 3.56/0.90 Proof:
% 3.56/0.90 multiply(inverse(multiply(X, inverse(X))), multiply(multiply(Y, inverse(Y)), multiply(multiply(Z, inverse(Z)), W)))
% 3.56/0.90 = { by lemma 13 R->L }
% 3.56/0.90 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(X))), multiply(multiply(Y, inverse(Y)), multiply(multiply(Z, inverse(Z)), W)))), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(U, multiply(T, inverse(T))))), multiply(multiply(S, inverse(S)), U))))
% 3.56/0.90 = { by lemma 12 }
% 3.56/0.90 inverse(multiply(inverse(W), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(U, multiply(T, inverse(T))))), multiply(multiply(S, inverse(S)), U))))
% 3.56/0.90 = { by lemma 13 }
% 3.56/0.90 W
% 3.56/0.90
% 3.56/0.90 Lemma 22: inverse(inverse(multiply(X, inverse(multiply(Y, inverse(Y)))))) = X.
% 3.56/0.90 Proof:
% 3.56/0.90 inverse(inverse(multiply(X, inverse(multiply(Y, inverse(Y))))))
% 3.56/0.90 = { by lemma 19 R->L }
% 3.56/0.90 inverse(inverse(multiply(X, multiply(inverse(multiply(Z, inverse(Z))), multiply(inverse(inverse(multiply(Z, inverse(Z)))), multiply(inverse(inverse(inverse(multiply(Z, inverse(Z))))), inverse(inverse(inverse(inverse(multiply(Z, inverse(Z))))))))))))
% 3.56/0.90 = { by lemma 20 R->L }
% 3.56/0.90 inverse(inverse(multiply(X, multiply(inverse(multiply(Z, inverse(Z))), multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(inverse(inverse(multiply(Z, inverse(Z))))))))))
% 3.56/0.90 = { by lemma 21 R->L }
% 3.56/0.90 inverse(multiply(inverse(multiply(Z, inverse(Z))), multiply(multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(inverse(inverse(multiply(Z, inverse(Z)))))), multiply(multiply(W, inverse(W)), inverse(multiply(X, multiply(inverse(multiply(Z, inverse(Z))), multiply(inverse(inverse(multiply(Z, inverse(Z)))), inverse(inverse(inverse(multiply(Z, inverse(Z)))))))))))))
% 3.56/0.90 = { by axiom 1 (single_axiom) }
% 3.56/0.90 X
% 3.56/0.90
% 3.56/0.90 Lemma 23: inverse(inverse(multiply(X, inverse(X)))) = multiply(Y, inverse(Y)).
% 3.56/0.90 Proof:
% 3.56/0.90 inverse(inverse(multiply(X, inverse(X))))
% 3.56/0.90 = { by lemma 3 }
% 3.56/0.90 inverse(inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y))))))
% 3.56/0.91 = { by lemma 22 }
% 3.56/0.91 multiply(Y, inverse(Y))
% 3.56/0.91
% 3.56/0.91 Lemma 24: inverse(inverse(multiply(X, multiply(inverse(X), inverse(inverse(Y)))))) = Y.
% 3.56/0.91 Proof:
% 3.56/0.91 inverse(inverse(multiply(X, multiply(inverse(X), inverse(inverse(Y))))))
% 3.56/0.91 = { by lemma 8 R->L }
% 3.56/0.91 inverse(inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 3.56/0.91 = { by lemma 12 R->L }
% 3.56/0.91 inverse(multiply(inverse(multiply(W, inverse(W))), multiply(multiply(V, inverse(V)), multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(Z, inverse(Z))))))))
% 3.56/0.91 = { by lemma 23 R->L }
% 3.56/0.91 inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(multiply(U, inverse(U)), inverse(multiply(Y, multiply(Z, inverse(Z))))))))
% 3.56/0.91 = { by lemma 4 }
% 3.56/0.91 Y
% 3.56/0.91
% 3.56/0.91 Lemma 25: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 3.56/0.91 Proof:
% 3.56/0.91 inverse(multiply(X, inverse(X)))
% 3.56/0.91 = { by lemma 13 R->L }
% 3.56/0.91 inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(inverse(inverse(multiply(W, inverse(W))))))))), multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))))))
% 3.56/0.91 = { by lemma 3 R->L }
% 3.56/0.91 inverse(multiply(inverse(inverse(multiply(X, inverse(X)))), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(inverse(inverse(multiply(W, inverse(W))))))))), multiply(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(inverse(inverse(multiply(W, inverse(W)))))))))), inverse(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(inverse(inverse(multiply(W, inverse(W)))))))))))))))
% 3.56/0.91 = { by lemma 17 R->L }
% 3.56/0.91 inverse(multiply(V, multiply(inverse(V), multiply(inverse(inverse(inverse(inverse(multiply(X, inverse(X)))))), inverse(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(inverse(inverse(multiply(W, inverse(W)))))))))))))))
% 3.56/0.91 = { by lemma 23 }
% 3.56/0.91 inverse(multiply(V, multiply(inverse(V), multiply(inverse(inverse(multiply(U, inverse(U)))), inverse(inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), inverse(inverse(inverse(multiply(W, inverse(W)))))))))))))))
% 3.56/0.91 = { by lemma 18 }
% 3.56/0.91 inverse(inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(W, inverse(W))))))
% 3.56/0.91 = { by lemma 22 }
% 3.56/0.91 multiply(Y, inverse(Y))
% 3.56/0.91
% 3.56/0.91 Lemma 26: inverse(inverse(multiply(X, multiply(inverse(X), Y)))) = multiply(Z, multiply(inverse(Z), inverse(inverse(Y)))).
% 3.56/0.91 Proof:
% 3.56/0.91 inverse(inverse(multiply(X, multiply(inverse(X), Y))))
% 3.56/0.91 = { by lemma 22 R->L }
% 3.56/0.91 inverse(inverse(multiply(X, multiply(inverse(X), inverse(inverse(multiply(Y, inverse(multiply(W, inverse(W))))))))))
% 3.56/0.91 = { by lemma 24 }
% 3.56/0.91 multiply(Y, inverse(multiply(W, inverse(W))))
% 3.56/0.91 = { by lemma 25 }
% 3.56/0.91 multiply(Y, multiply(V, inverse(V)))
% 3.56/0.91 = { by lemma 14 R->L }
% 3.56/0.91 multiply(Z, multiply(inverse(Z), inverse(inverse(Y))))
% 3.56/0.91
% 3.56/0.91 Lemma 27: multiply(X, multiply(Y, inverse(Y))) = X.
% 3.56/0.91 Proof:
% 3.56/0.91 multiply(X, multiply(Y, inverse(Y)))
% 3.56/0.91 = { by lemma 3 }
% 3.56/0.91 multiply(X, multiply(inverse(X), inverse(inverse(X))))
% 3.56/0.91 = { by lemma 24 R->L }
% 3.56/0.91 multiply(X, multiply(inverse(X), inverse(inverse(multiply(Z, multiply(inverse(Z), inverse(inverse(inverse(inverse(X))))))))))
% 3.56/0.91 = { by lemma 26 R->L }
% 3.56/0.91 inverse(inverse(multiply(X, multiply(inverse(X), multiply(Z, multiply(inverse(Z), inverse(inverse(inverse(inverse(X))))))))))
% 3.56/0.91 = { by lemma 19 }
% 3.56/0.91 inverse(inverse(multiply(X, inverse(multiply(W, inverse(W))))))
% 3.56/0.91 = { by lemma 22 }
% 3.56/0.91 X
% 3.56/0.91
% 3.56/0.91 Lemma 28: inverse(inverse(X)) = X.
% 3.56/0.91 Proof:
% 3.56/0.91 inverse(inverse(X))
% 3.56/0.91 = { by lemma 27 R->L }
% 3.56/0.91 inverse(inverse(multiply(X, multiply(Y, inverse(Y)))))
% 3.56/0.91 = { by lemma 8 }
% 3.56/0.91 inverse(inverse(multiply(Z, multiply(inverse(Z), inverse(inverse(X))))))
% 3.56/0.91 = { by lemma 24 }
% 3.56/0.91 X
% 3.56/0.91
% 3.56/0.91 Lemma 29: multiply(X, multiply(inverse(X), Y)) = Y.
% 3.56/0.91 Proof:
% 3.56/0.91 multiply(X, multiply(inverse(X), Y))
% 3.56/0.91 = { by lemma 28 R->L }
% 3.56/0.91 multiply(X, multiply(inverse(X), inverse(inverse(Y))))
% 3.56/0.91 = { by lemma 14 }
% 3.56/0.91 multiply(Y, multiply(Z, inverse(Z)))
% 3.56/0.91 = { by lemma 28 R->L }
% 3.56/0.91 inverse(inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 3.56/0.91 = { by lemma 8 }
% 3.56/0.91 inverse(inverse(multiply(W, multiply(inverse(W), inverse(inverse(Y))))))
% 3.56/0.91 = { by lemma 24 }
% 3.56/0.91 Y
% 3.56/0.91
% 3.56/0.91 Lemma 30: multiply(inverse(X), multiply(X, Y)) = multiply(Z, multiply(inverse(Z), Y)).
% 3.56/0.91 Proof:
% 3.56/0.91 multiply(inverse(X), multiply(X, Y))
% 3.56/0.91 = { by lemma 28 R->L }
% 3.56/0.91 multiply(inverse(X), multiply(inverse(inverse(X)), Y))
% 3.56/0.91 = { by lemma 16 R->L }
% 3.56/0.91 multiply(Z, multiply(inverse(Z), Y))
% 3.56/0.91
% 3.56/0.91 Lemma 31: inverse(multiply(X, multiply(inverse(X), Y))) = multiply(Z, multiply(inverse(Z), inverse(Y))).
% 3.56/0.91 Proof:
% 3.56/0.91 inverse(multiply(X, multiply(inverse(X), Y)))
% 3.56/0.91 = { by lemma 24 R->L }
% 3.56/0.91 inverse(inverse(multiply(W, multiply(inverse(W), inverse(inverse(inverse(multiply(X, multiply(inverse(X), Y)))))))))
% 3.56/0.91 = { by lemma 26 }
% 3.56/0.91 inverse(inverse(multiply(W, multiply(inverse(W), inverse(multiply(V, multiply(inverse(V), inverse(inverse(Y)))))))))
% 3.56/0.91 = { by lemma 26 }
% 3.56/0.91 multiply(Z, multiply(inverse(Z), inverse(inverse(inverse(multiply(V, multiply(inverse(V), inverse(inverse(Y)))))))))
% 3.56/0.91 = { by lemma 24 }
% 3.56/0.91 multiply(Z, multiply(inverse(Z), inverse(Y)))
% 3.56/0.91
% 3.56/0.91 Lemma 32: multiply(multiply(X, inverse(X)), Y) = Y.
% 3.56/0.91 Proof:
% 3.56/0.91 multiply(multiply(X, inverse(X)), Y)
% 3.56/0.91 = { by lemma 29 R->L }
% 3.56/0.91 multiply(Z, multiply(inverse(Z), multiply(multiply(X, inverse(X)), Y)))
% 3.56/0.91 = { by lemma 30 R->L }
% 3.56/0.91 multiply(inverse(multiply(W, inverse(W))), multiply(multiply(W, inverse(W)), multiply(multiply(X, inverse(X)), Y)))
% 3.56/0.91 = { by lemma 21 }
% 3.56/0.91 Y
% 3.56/0.91
% 3.56/0.91 Lemma 33: inverse(multiply(X, inverse(multiply(Y, X)))) = Y.
% 3.56/0.91 Proof:
% 3.56/0.91 inverse(multiply(X, inverse(multiply(Y, X))))
% 3.56/0.91 = { by lemma 32 R->L }
% 3.56/0.91 inverse(multiply(X, inverse(multiply(Y, multiply(multiply(Z, inverse(Z)), X)))))
% 3.56/0.91 = { by lemma 32 R->L }
% 3.56/0.91 inverse(multiply(X, multiply(multiply(W, inverse(W)), inverse(multiply(Y, multiply(multiply(Z, inverse(Z)), X))))))
% 3.56/0.91 = { by lemma 32 R->L }
% 3.56/0.91 inverse(multiply(multiply(Z, inverse(Z)), multiply(X, multiply(multiply(W, inverse(W)), inverse(multiply(Y, multiply(multiply(Z, inverse(Z)), X)))))))
% 3.56/0.91 = { by axiom 1 (single_axiom) }
% 3.56/0.91 Y
% 3.56/0.91
% 3.56/0.91 Lemma 34: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 3.56/0.91 Proof:
% 3.56/0.91 multiply(X, inverse(multiply(Y, X)))
% 3.56/0.91 = { by lemma 28 R->L }
% 3.56/0.91 inverse(inverse(multiply(X, inverse(multiply(Y, X)))))
% 3.56/0.91 = { by lemma 29 R->L }
% 3.56/0.91 multiply(Z, multiply(inverse(Z), inverse(inverse(multiply(X, inverse(multiply(Y, X)))))))
% 3.56/0.91 = { by lemma 31 R->L }
% 3.56/0.91 inverse(multiply(W, multiply(inverse(W), inverse(multiply(X, inverse(multiply(Y, X)))))))
% 3.56/0.91 = { by lemma 33 }
% 3.56/0.91 inverse(multiply(W, multiply(inverse(W), Y)))
% 3.56/0.91 = { by lemma 31 }
% 3.56/0.91 multiply(V, multiply(inverse(V), inverse(Y)))
% 3.56/0.91 = { by lemma 29 }
% 3.56/0.91 inverse(Y)
% 3.56/0.91
% 3.56/0.91 Lemma 35: inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 3.56/0.91 Proof:
% 3.56/0.91 inverse(multiply(X, Y))
% 3.56/0.91 = { by lemma 29 R->L }
% 3.56/0.91 multiply(Z, multiply(inverse(Z), inverse(multiply(X, Y))))
% 3.56/0.91 = { by lemma 30 R->L }
% 3.56/0.91 multiply(inverse(Y), multiply(Y, inverse(multiply(X, Y))))
% 3.56/0.91 = { by lemma 27 R->L }
% 3.56/0.91 multiply(inverse(multiply(Y, multiply(inverse(Y), inverse(inverse(Y))))), multiply(Y, inverse(multiply(X, Y))))
% 3.56/0.91 = { by lemma 28 R->L }
% 3.56/0.91 inverse(inverse(multiply(inverse(multiply(Y, multiply(inverse(Y), inverse(inverse(Y))))), multiply(Y, inverse(multiply(X, Y))))))
% 3.56/0.91 = { by lemma 34 }
% 3.56/0.91 inverse(inverse(multiply(inverse(multiply(Y, multiply(inverse(Y), inverse(inverse(Y))))), inverse(X))))
% 3.56/0.91 = { by lemma 28 }
% 3.56/0.91 multiply(inverse(multiply(Y, multiply(inverse(Y), inverse(inverse(Y))))), inverse(X))
% 3.56/0.91 = { by lemma 31 }
% 3.56/0.91 multiply(multiply(W, multiply(inverse(W), inverse(inverse(inverse(Y))))), inverse(X))
% 3.56/0.91 = { by lemma 29 }
% 3.56/0.91 multiply(inverse(inverse(inverse(Y))), inverse(X))
% 3.56/0.91 = { by lemma 28 }
% 3.56/0.91 multiply(inverse(Y), inverse(X))
% 3.56/0.91
% 3.56/0.91 Lemma 36: multiply(multiply(X, multiply(inverse(X), inverse(inverse(inverse(Y))))), Y) = multiply(Z, inverse(Z)).
% 3.56/0.91 Proof:
% 3.56/0.91 multiply(multiply(X, multiply(inverse(X), inverse(inverse(inverse(Y))))), Y)
% 3.56/0.91 = { by lemma 31 R->L }
% 3.56/0.91 multiply(inverse(multiply(Y, multiply(inverse(Y), inverse(inverse(Y))))), Y)
% 3.56/0.91 = { by lemma 25 R->L }
% 3.56/0.91 multiply(inverse(multiply(Y, inverse(multiply(W, inverse(W))))), Y)
% 3.56/0.91 = { by lemma 22 R->L }
% 3.56/0.91 multiply(inverse(multiply(Y, inverse(multiply(W, inverse(W))))), inverse(inverse(multiply(Y, inverse(multiply(W, inverse(W)))))))
% 3.56/0.91 = { by lemma 3 R->L }
% 3.56/0.91 multiply(Z, inverse(Z))
% 3.56/0.91
% 3.56/0.91 Lemma 37: multiply(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), Z)) = multiply(W, multiply(inverse(W), Z)).
% 3.56/0.91 Proof:
% 3.56/0.91 multiply(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), Z))
% 3.56/0.91 = { by lemma 25 R->L }
% 3.56/0.91 multiply(multiply(X, inverse(X)), multiply(inverse(multiply(X, inverse(X))), Z))
% 3.56/0.91 = { by lemma 16 R->L }
% 3.56/0.91 multiply(W, multiply(inverse(W), Z))
% 3.56/0.91
% 3.56/0.91 Lemma 38: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 3.56/0.91 Proof:
% 3.56/0.91 multiply(inverse(X), X)
% 3.56/0.91 = { by lemma 13 R->L }
% 3.56/0.91 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), inverse(inverse(inverse(multiply(V, inverse(V))))))), multiply(V, inverse(V))))), multiply(multiply(U, inverse(U)), multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), inverse(inverse(inverse(multiply(V, inverse(V))))))))))))
% 3.56/0.91 = { by lemma 36 }
% 3.56/0.91 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))), multiply(multiply(U, inverse(U)), multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), inverse(inverse(inverse(multiply(V, inverse(V))))))))))))
% 3.56/0.91 = { by lemma 37 }
% 3.56/0.91 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), inverse(inverse(inverse(multiply(V, inverse(V))))))))))))
% 3.56/0.91 = { by lemma 30 }
% 3.56/0.91 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(W, inverse(W)), multiply(T, multiply(inverse(T), multiply(inverse(multiply(W, inverse(W))), inverse(inverse(inverse(multiply(V, inverse(V))))))))))))
% 3.56/0.91 = { by lemma 20 }
% 3.56/0.91 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(W, inverse(W)), multiply(T, multiply(inverse(T), multiply(inverse(multiply(W, inverse(W))), multiply(S, inverse(S)))))))))
% 3.56/0.91 = { by lemma 30 R->L }
% 3.56/0.91 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), multiply(S, inverse(S)))))))))
% 3.56/0.91 = { by lemma 37 R->L }
% 3.56/0.91 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), multiply(multiply(X2, inverse(X2)), multiply(multiply(Y2, inverse(Y2)), multiply(S, inverse(S)))))))))
% 3.56/0.91 = { by lemma 23 R->L }
% 3.56/0.91 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(multiply(Y2, inverse(Y2)), multiply(S, inverse(S)))))))))
% 3.56/0.92 = { by lemma 23 R->L }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(W, inverse(W)), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(multiply(Y2, inverse(Y2)), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 9 R->L }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(multiply(W2, multiply(V2, multiply(multiply(U2, inverse(U2)), inverse(multiply(multiply(T2, inverse(T2)), multiply(W2, V2)))))), multiply(T2, inverse(T2))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(multiply(Y2, inverse(Y2)), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 14 R->L }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(S2, multiply(inverse(S2), inverse(inverse(multiply(W2, multiply(V2, multiply(multiply(U2, inverse(U2)), inverse(multiply(multiply(T2, inverse(T2)), multiply(W2, V2)))))))))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(multiply(Y2, inverse(Y2)), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by axiom 1 (single_axiom) }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(S2, multiply(inverse(S2), inverse(multiply(T2, inverse(T2))))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(multiply(Y2, inverse(Y2)), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 20 R->L }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(S2, multiply(inverse(S2), inverse(inverse(inverse(inverse(multiply(X3, inverse(X3)))))))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(multiply(Y2, inverse(Y2)), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 20 R->L }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(S2, multiply(inverse(S2), inverse(inverse(inverse(inverse(multiply(X3, inverse(X3)))))))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(inverse(inverse(inverse(multiply(Y3, inverse(Y3))))), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 6 R->L }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(S2, multiply(inverse(S2), inverse(inverse(multiply(multiply(Z3, inverse(Z3)), inverse(multiply(inverse(multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(inverse(multiply(W3, inverse(W3)))), inverse(inverse(inverse(multiply(W3, inverse(W3)))))))), multiply(inverse(multiply(W3, inverse(W3))), inverse(multiply(X3, inverse(X3))))))))))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(inverse(inverse(inverse(multiply(Y3, inverse(Y3))))), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 11 R->L }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(S2, multiply(inverse(S2), inverse(inverse(inverse(multiply(multiply(multiply(V3, inverse(V3)), inverse(multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(inverse(multiply(W3, inverse(W3)))), inverse(inverse(inverse(multiply(W3, inverse(W3))))))))), multiply(multiply(Z2, inverse(Z2)), multiply(multiply(X3, inverse(X3)), inverse(multiply(X3, inverse(X3))))))))))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(inverse(inverse(inverse(multiply(Y3, inverse(Y3))))), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 3 R->L }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(S2, multiply(inverse(S2), inverse(inverse(inverse(multiply(multiply(multiply(V3, inverse(V3)), inverse(multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(inverse(multiply(W3, inverse(W3)))), inverse(inverse(inverse(multiply(W3, inverse(W3))))))))), multiply(multiply(Z2, inverse(Z2)), multiply(inverse(multiply(Z2, inverse(Z2))), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(inverse(inverse(inverse(multiply(Y3, inverse(Y3))))), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 10 }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(S2, multiply(inverse(S2), inverse(inverse(inverse(multiply(inverse(multiply(Y3, inverse(Y3))), multiply(multiply(Z2, inverse(Z2)), multiply(inverse(multiply(Z2, inverse(Z2))), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(inverse(inverse(inverse(multiply(Y3, inverse(Y3))))), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 17 R->L }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(multiply(S2, multiply(inverse(S2), inverse(inverse(inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(inverse(inverse(inverse(multiply(Y3, inverse(Y3))))), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))), multiply(inverse(multiply(W, inverse(W))), multiply(inverse(inverse(multiply(W, inverse(W)))), multiply(inverse(inverse(inverse(multiply(Y3, inverse(Y3))))), inverse(inverse(multiply(Z2, inverse(Z2)))))))))))
% 3.56/0.92 = { by lemma 36 }
% 3.56/0.92 multiply(inverse(X), inverse(multiply(inverse(X), multiply(inverse(inverse(X)), inverse(inverse(inverse(X)))))))
% 3.56/0.92 = { by lemma 31 }
% 3.56/0.92 multiply(inverse(X), multiply(inverse(inverse(X)), multiply(inverse(inverse(inverse(X))), inverse(inverse(inverse(inverse(X)))))))
% 3.56/0.92 = { by lemma 16 R->L }
% 3.56/0.92 multiply(Y, multiply(inverse(Y), multiply(inverse(inverse(inverse(X))), inverse(inverse(inverse(inverse(X)))))))
% 3.56/0.92 = { by lemma 14 R->L }
% 3.56/0.92 multiply(Y, multiply(U3, multiply(inverse(U3), inverse(inverse(inverse(Y))))))
% 3.56/0.92 = { by lemma 26 R->L }
% 3.56/0.92 multiply(Y, inverse(inverse(multiply(T3, multiply(inverse(T3), inverse(Y))))))
% 3.56/0.92 = { by lemma 28 R->L }
% 3.56/0.92 multiply(Y, inverse(inverse(multiply(T3, multiply(inverse(T3), inverse(inverse(inverse(Y))))))))
% 3.56/0.92 = { by lemma 24 }
% 3.56/0.92 multiply(Y, inverse(Y))
% 3.56/0.92
% 3.56/0.92 Lemma 39: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 3.56/0.92 Proof:
% 3.56/0.92 inverse(multiply(X, inverse(Y)))
% 3.56/0.92 = { by lemma 34 R->L }
% 3.56/0.92 inverse(multiply(X, multiply(inverse(X), inverse(multiply(Y, inverse(X))))))
% 3.56/0.92 = { by lemma 15 R->L }
% 3.56/0.92 inverse(multiply(Z, multiply(inverse(Z), inverse(multiply(Y, inverse(X))))))
% 3.56/0.92 = { by lemma 31 }
% 3.56/0.92 multiply(W, multiply(inverse(W), inverse(inverse(multiply(Y, inverse(X))))))
% 3.56/0.92 = { by lemma 29 }
% 3.56/0.92 inverse(inverse(multiply(Y, inverse(X))))
% 3.56/0.92 = { by lemma 28 }
% 3.56/0.92 multiply(Y, inverse(X))
% 3.56/0.92
% 3.56/0.92 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 3.56/0.92 Proof:
% 3.56/0.92 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 3.56/0.92 = { by lemma 38 }
% 3.56/0.92 tuple(multiply(X, inverse(X)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 3.56/0.92 = { by lemma 38 }
% 3.56/0.92 tuple(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), a2), multiply(multiply(a3, b3), c3))
% 3.56/0.92 = { by lemma 32 }
% 3.56/0.92 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 3.56/0.92 = { by lemma 28 R->L }
% 3.56/0.92 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), inverse(inverse(c3))))
% 3.56/0.92 = { by lemma 39 R->L }
% 3.56/0.92 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(multiply(a3, b3)))))
% 3.56/0.92 = { by lemma 28 R->L }
% 3.56/0.92 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(multiply(a3, inverse(inverse(b3)))))))
% 3.56/0.92 = { by lemma 39 R->L }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(a3)))))))
% 3.56/0.93 = { by lemma 28 R->L }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(inverse(inverse(a3)))))))))
% 3.56/0.93 = { by lemma 29 R->L }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(multiply(a3, multiply(inverse(a3), inverse(inverse(a3)))))))))))
% 3.56/0.93 = { by lemma 25 R->L }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(multiply(a3, inverse(multiply(Z, inverse(Z)))))))))))
% 3.56/0.93 = { by lemma 9 R->L }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(multiply(a3, inverse(multiply(multiply(b3, multiply(c3, multiply(multiply(W, inverse(W)), inverse(multiply(a3, multiply(b3, c3)))))), a3))))))))))
% 3.56/0.93 = { by lemma 34 }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(inverse(multiply(b3, multiply(c3, multiply(multiply(W, inverse(W)), inverse(multiply(a3, multiply(b3, c3))))))))))))))
% 3.56/0.93 = { by lemma 35 }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(multiply(inverse(multiply(c3, multiply(multiply(W, inverse(W)), inverse(multiply(a3, multiply(b3, c3)))))), inverse(b3)))))))))
% 3.56/0.93 = { by lemma 35 }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(multiply(multiply(inverse(multiply(multiply(W, inverse(W)), inverse(multiply(a3, multiply(b3, c3))))), inverse(c3)), inverse(b3)))))))))
% 3.56/0.93 = { by lemma 39 }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(multiply(multiply(multiply(multiply(a3, multiply(b3, c3)), inverse(multiply(W, inverse(W)))), inverse(c3)), inverse(b3)))))))))
% 3.56/0.93 = { by lemma 25 }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(multiply(multiply(multiply(multiply(a3, multiply(b3, c3)), multiply(inverse(multiply(a3, multiply(b3, c3))), inverse(inverse(multiply(a3, multiply(b3, c3)))))), inverse(c3)), inverse(b3)))))))))
% 3.56/0.93 = { by lemma 29 }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(multiply(multiply(inverse(inverse(multiply(a3, multiply(b3, c3)))), inverse(c3)), inverse(b3)))))))))
% 3.56/0.93 = { by lemma 28 }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(inverse(multiply(inverse(b3), inverse(multiply(multiply(multiply(a3, multiply(b3, c3)), inverse(c3)), inverse(b3)))))))))
% 3.56/0.93 = { by lemma 33 }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), inverse(multiply(multiply(a3, multiply(b3, c3)), inverse(c3))))))
% 3.56/0.93 = { by lemma 33 }
% 3.56/0.93 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 3.56/0.93 = { by lemma 38 R->L }
% 3.56/0.93 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 3.56/0.93 % SZS output end Proof
% 3.56/0.93
% 3.56/0.93 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------