%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP049-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:09:09 AM UTC 2026
% Result : Unsatisfiable 10.04s 1.75s
% Output : Proof 11.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP049-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:16:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.04/1.75 Command-line arguments: --no-flatten-goal
% 10.04/1.75
% 10.04/1.75 % SZS status Unsatisfiable
% 10.04/1.75
% 11.54/1.91 % SZS output start Proof
% 11.54/1.91 Axiom 1 (single_axiom): multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(Y, multiply(inverse(Y), Y)))))) = Z.
% 11.54/1.91
% 11.54/1.91 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))) = multiply(X, inverse(multiply(inverse(W), inverse(multiply(Y, multiply(inverse(Y), Y)))))).
% 11.54/1.91 Proof:
% 11.54/1.91 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z)))))
% 11.54/1.91 = { by axiom 1 (single_axiom) R->L }
% 11.54/1.91 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 11.54/1.91 = { by axiom 1 (single_axiom) }
% 11.54/1.91 multiply(X, inverse(multiply(inverse(W), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 11.54/1.91
% 11.54/1.91 Lemma 3: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z))))) = W.
% 11.54/1.91 Proof:
% 11.54/1.91 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z)))))
% 11.54/1.91 = { by lemma 2 }
% 11.54/1.91 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 11.54/1.91 = { by axiom 1 (single_axiom) }
% 11.54/1.92 W
% 11.54/1.92
% 11.54/1.92 Lemma 4: multiply(inverse(multiply(X, Y)), inverse(multiply(Z, inverse(multiply(multiply(X, Z), multiply(inverse(multiply(X, Z)), multiply(X, Z))))))) = inverse(multiply(Y, multiply(inverse(Y), Y))).
% 11.54/1.92 Proof:
% 11.54/1.92 multiply(inverse(multiply(X, Y)), inverse(multiply(Z, inverse(multiply(multiply(X, Z), multiply(inverse(multiply(X, Z)), multiply(X, Z)))))))
% 11.54/1.92 = { by lemma 3 R->L }
% 11.54/1.92 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Z))), inverse(multiply(Y, multiply(inverse(Y), Y))))), inverse(multiply(multiply(X, Z), multiply(inverse(multiply(X, Z)), multiply(X, Z)))))))
% 11.54/1.92 = { by lemma 3 }
% 11.54/1.92 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), U)), multiply(inverse(multiply(W, V)), X))), inverse(multiply(U, multiply(inverse(U), U))))), Z))), inverse(multiply(Y, multiply(inverse(Y), Y))))), inverse(multiply(multiply(X, Z), multiply(inverse(multiply(X, Z)), multiply(X, Z)))))))
% 11.54/1.92 = { by lemma 3 }
% 11.54/1.92 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(Y, multiply(inverse(Y), Y))))), inverse(multiply(multiply(X, Z), multiply(inverse(multiply(X, Z)), multiply(X, Z)))))))
% 11.54/1.92 = { by axiom 1 (single_axiom) }
% 11.54/1.92 inverse(multiply(Y, multiply(inverse(Y), Y)))
% 11.54/1.92
% 11.54/1.92 Lemma 5: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), inverse(multiply(Y, multiply(inverse(Y), Y))))))) = Z.
% 11.54/1.92 Proof:
% 11.54/1.92 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 11.54/1.92 = { by lemma 2 R->L }
% 11.54/1.92 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z)), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.92 = { by axiom 1 (single_axiom) }
% 11.54/1.92 Z
% 11.54/1.92
% 11.54/1.92 Lemma 6: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y)))) = Z.
% 11.54/1.92 Proof:
% 11.54/1.92 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), inverse(multiply(Y, multiply(inverse(Y), Y))))
% 11.54/1.92 = { by lemma 4 R->L }
% 11.54/1.92 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(Z)))), multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(Z), inverse(multiply(multiply(X, inverse(Z)), multiply(inverse(multiply(X, inverse(Z))), multiply(X, inverse(Z)))))))))
% 11.54/1.92 = { by lemma 5 }
% 11.54/1.92 Z
% 11.54/1.92
% 11.54/1.92 Lemma 7: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W)) = multiply(inverse(multiply(V, Z)), multiply(V, W)).
% 11.54/1.92 Proof:
% 11.54/1.92 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))
% 11.54/1.92 = { by lemma 5 R->L }
% 11.54/1.92 multiply(inverse(multiply(V, Z)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), inverse(multiply(Z, multiply(inverse(Z), Z)))))))
% 11.54/1.92 = { by lemma 3 }
% 11.54/1.92 multiply(inverse(multiply(V, Z)), multiply(V, W))
% 11.54/1.92
% 11.54/1.92 Lemma 8: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 11.54/1.92 Proof:
% 11.54/1.92 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 11.54/1.92 = { by lemma 3 R->L }
% 11.54/1.92 multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 11.54/1.92 = { by lemma 5 }
% 11.54/1.92 multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))
% 11.54/1.92 = { by lemma 5 R->L }
% 11.54/1.92 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))), inverse(multiply(Y, multiply(inverse(Y), Y)))))))
% 11.54/1.92 = { by lemma 3 }
% 11.54/1.92 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 11.54/1.92
% 11.54/1.92 Lemma 9: multiply(V, multiply(inverse(multiply(inverse(multiply(U, Z)), multiply(U, V))), W)) = multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))), W)).
% 11.54/1.92 Proof:
% 11.54/1.92 multiply(V, multiply(inverse(multiply(inverse(multiply(U, Z)), multiply(U, V))), W))
% 11.54/1.92 = { by lemma 7 R->L }
% 11.54/1.92 multiply(V, multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 11.54/1.92 = { by lemma 3 R->L }
% 11.54/1.92 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), inverse(multiply(Z, multiply(inverse(Z), Z))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), Z)), multiply(inverse(multiply(X2, Y2)), V))), W))
% 11.54/1.92 = { by lemma 8 R->L }
% 11.54/1.92 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), inverse(multiply(Z, multiply(inverse(Z), Z))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 11.54/1.92 = { by lemma 3 }
% 11.54/1.92 multiply(X, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), Z)), multiply(inverse(multiply(T, S)), X))), W))
% 11.54/1.92 = { by lemma 7 }
% 11.54/1.92 multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Y, X))), W))
% 11.54/1.92
% 11.54/1.92 Lemma 10: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 11.54/1.92 Proof:
% 11.54/1.92 multiply(inverse(Y), Y)
% 11.54/1.92 = { by lemma 6 R->L }
% 11.54/1.92 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Y)))), inverse(multiply(W, multiply(inverse(W), W)))))
% 11.54/1.92 = { by lemma 9 R->L }
% 11.54/1.93 multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, inverse(X)))), inverse(multiply(W, multiply(inverse(W), W)))))
% 11.54/1.93 = { by lemma 6 }
% 11.54/1.93 multiply(inverse(X), X)
% 11.54/1.93
% 11.54/1.93 Lemma 11: multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z))))))) = inverse(multiply(X, multiply(inverse(X), X))).
% 11.54/1.93 Proof:
% 11.54/1.93 multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z)))))))
% 11.54/1.93 = { by lemma 2 R->L }
% 11.54/1.93 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.93 = { by lemma 3 R->L }
% 11.54/1.93 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T))))), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.93 = { by lemma 5 R->L }
% 11.54/1.93 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T))))), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))), inverse(multiply(X2, multiply(inverse(X2), X2)))))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.93 = { by axiom 1 (single_axiom) R->L }
% 11.54/1.93 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))))), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))), inverse(multiply(X2, multiply(inverse(X2), X2)))))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.93 = { by axiom 1 (single_axiom) R->L }
% 11.54/1.93 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))))), Z)), W)), inverse(multiply(Z, multiply(inverse(Z), Z))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))))))))), inverse(multiply(X2, multiply(inverse(X2), X2)))))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.94 = { by axiom 1 (single_axiom) }
% 11.54/1.94 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(multiply(Y2, inverse(multiply(inverse(W), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))))))))), inverse(multiply(X2, multiply(inverse(X2), X2)))))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.94 = { by axiom 1 (single_axiom) R->L }
% 11.54/1.94 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))))), X)), W)), inverse(multiply(X, multiply(inverse(X), X))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))))))))), inverse(multiply(X2, multiply(inverse(X2), X2)))))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.94 = { by axiom 1 (single_axiom) }
% 11.54/1.94 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T)))))), inverse(multiply(Z2, multiply(inverse(Z2), Z2))))))), X)), W)), inverse(multiply(X, multiply(inverse(X), X))))), inverse(multiply(X2, multiply(inverse(X2), X2)))))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.94 = { by axiom 1 (single_axiom) }
% 11.54/1.94 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T))))), X)), W)), inverse(multiply(X, multiply(inverse(X), X))))), inverse(multiply(X2, multiply(inverse(X2), X2)))))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.94 = { by lemma 5 }
% 11.54/1.94 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), T)), multiply(inverse(multiply(V, U)), Y))), inverse(multiply(T, multiply(inverse(T), T))))), X)), W)), inverse(multiply(X, multiply(inverse(X), X))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.94 = { by lemma 3 }
% 11.54/1.94 multiply(inverse(multiply(Y, X)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), W)), inverse(multiply(X, multiply(inverse(X), X))))), inverse(multiply(W, multiply(inverse(W), W))))))
% 11.54/1.94 = { by lemma 2 }
% 11.54/1.94 multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(inverse(inverse(multiply(X, multiply(inverse(X), X)))), inverse(multiply(X, multiply(inverse(X), X)))))))
% 11.54/1.94 = { by lemma 5 }
% 11.54/1.94 inverse(multiply(X, multiply(inverse(X), X)))
% 11.54/1.94
% 11.54/1.94 Lemma 12: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 11.54/1.94 Proof:
% 11.54/1.94 inverse(multiply(inverse(X), X))
% 11.54/1.94 = { by lemma 10 }
% 11.54/1.94 inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z))))))), multiply(inverse(inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z))))))))
% 11.54/1.94 = { by lemma 10 }
% 11.54/1.94 inverse(multiply(inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z))))), multiply(inverse(inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z)))))), inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z))))))))
% 11.54/1.94 = { by lemma 11 R->L }
% 11.54/1.94 multiply(inverse(multiply(W, inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z))))))), multiply(W, inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z)))))))
% 11.54/1.94 = { by lemma 10 R->L }
% 11.54/1.94 multiply(inverse(Y), Y)
% 11.54/1.94
% 11.54/1.94 Lemma 13: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(multiply(inverse(W), W), multiply(inverse(Y), Z)).
% 11.54/1.94 Proof:
% 11.54/1.94 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 11.54/1.95 = { by lemma 8 }
% 11.54/1.95 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 11.54/1.95 = { by lemma 10 R->L }
% 11.54/1.95 multiply(inverse(multiply(inverse(V), V)), multiply(inverse(Y), Z))
% 11.54/1.95 = { by lemma 12 }
% 11.54/1.95 multiply(multiply(inverse(W), W), multiply(inverse(Y), Z))
% 11.54/1.95
% 11.54/1.95 Lemma 14: multiply(multiply(inverse(X), X), multiply(inverse(Y), multiply(inverse(Z), Z))) = inverse(multiply(Y, multiply(inverse(W), W))).
% 11.54/1.95 Proof:
% 11.54/1.95 multiply(multiply(inverse(X), X), multiply(inverse(Y), multiply(inverse(Z), Z)))
% 11.54/1.95 = { by lemma 12 R->L }
% 11.54/1.95 multiply(multiply(inverse(X), X), multiply(inverse(Y), inverse(multiply(inverse(inverse(multiply(V, multiply(inverse(V), V)))), inverse(multiply(V, multiply(inverse(V), V)))))))
% 11.54/1.95 = { by lemma 13 R->L }
% 11.54/1.95 multiply(inverse(multiply(U, Y)), multiply(U, inverse(multiply(inverse(inverse(multiply(V, multiply(inverse(V), V)))), inverse(multiply(V, multiply(inverse(V), V)))))))
% 11.54/1.95 = { by lemma 11 }
% 11.54/1.95 inverse(multiply(Y, multiply(inverse(Y), Y)))
% 11.54/1.95 = { by lemma 10 R->L }
% 11.54/1.95 inverse(multiply(Y, multiply(inverse(W), W)))
% 11.54/1.95
% 11.54/1.95 Lemma 15: inverse(multiply(X, inverse(multiply(multiply(Y, X), multiply(inverse(multiply(Y, X)), multiply(Y, X)))))) = multiply(Y, inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z)))))).
% 11.54/1.95 Proof:
% 11.54/1.95 inverse(multiply(X, inverse(multiply(multiply(Y, X), multiply(inverse(multiply(Y, X)), multiply(Y, X))))))
% 11.54/1.95 = { by axiom 1 (single_axiom) R->L }
% 11.54/1.95 multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), inverse(multiply(X, inverse(multiply(multiply(Y, X), multiply(inverse(multiply(Y, X)), multiply(Y, X)))))))), inverse(multiply(Z, multiply(inverse(Z), Z))))))
% 11.54/1.95 = { by lemma 4 }
% 11.54/1.95 multiply(Y, inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), Z)))), inverse(multiply(Z, multiply(inverse(Z), Z))))))
% 11.54/1.95
% 11.54/1.95 Lemma 16: inverse(multiply(X, multiply(inverse(Y), Y))) = multiply(inverse(X), multiply(inverse(Z), Z)).
% 11.54/1.95 Proof:
% 11.54/1.95 inverse(multiply(X, multiply(inverse(Y), Y)))
% 11.54/1.95 = { by lemma 12 R->L }
% 11.54/1.95 inverse(multiply(X, inverse(multiply(inverse(W), W))))
% 11.54/1.95 = { by lemma 12 R->L }
% 11.54/1.95 inverse(multiply(X, inverse(inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))))))
% 11.54/1.95 = { by lemma 12 }
% 11.54/1.95 inverse(multiply(X, inverse(inverse(multiply(multiply(inverse(X), X), multiply(inverse(V), V))))))
% 11.54/1.95 = { by lemma 14 R->L }
% 11.54/1.95 inverse(multiply(X, inverse(multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))))))
% 11.54/1.95 = { by lemma 15 }
% 11.54/1.95 multiply(inverse(X), inverse(multiply(inverse(inverse(multiply(U, multiply(inverse(U), U)))), inverse(multiply(U, multiply(inverse(U), U))))))
% 11.54/1.95 = { by lemma 12 }
% 11.54/1.95 multiply(inverse(X), multiply(inverse(Z), Z))
% 11.54/1.95
% 11.54/1.95 Lemma 17: inverse(multiply(multiply(inverse(X), X), inverse(multiply(Y, multiply(inverse(Z), Z))))) = Y.
% 11.54/1.95 Proof:
% 11.54/1.95 inverse(multiply(multiply(inverse(X), X), inverse(multiply(Y, multiply(inverse(Z), Z)))))
% 11.54/1.95 = { by lemma 10 }
% 11.54/1.95 inverse(multiply(multiply(inverse(X), X), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 11.54/1.95 = { by lemma 12 R->L }
% 11.54/1.95 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), inverse(multiply(Y, multiply(inverse(Y), Y)))))
% 11.54/1.95 = { by lemma 3 }
% 11.54/1.95 Y
% 11.54/1.95
% 11.54/1.95 Lemma 18: inverse(multiply(inverse(X), multiply(inverse(Y), Y))) = X.
% 11.54/1.95 Proof:
% 11.54/1.95 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 11.54/1.95 = { by lemma 16 R->L }
% 11.54/1.95 inverse(inverse(multiply(X, multiply(inverse(Z), Z))))
% 11.54/1.95 = { by lemma 14 R->L }
% 11.54/1.95 inverse(multiply(multiply(inverse(W), W), multiply(inverse(X), multiply(inverse(V), V))))
% 11.54/1.95 = { by lemma 16 R->L }
% 11.54/1.95 inverse(multiply(multiply(inverse(W), W), inverse(multiply(X, multiply(inverse(U), U)))))
% 11.54/1.95 = { by lemma 17 }
% 11.54/1.95 X
% 11.54/1.95
% 11.54/1.95 Lemma 19: multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), Z)) = multiply(W, multiply(inverse(W), Z)).
% 11.54/1.95 Proof:
% 11.54/1.95 multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), Z))
% 11.54/1.95 = { by lemma 12 R->L }
% 11.54/1.95 multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(V), V)), Z))
% 11.54/1.95 = { by lemma 13 R->L }
% 11.54/1.95 multiply(inverse(multiply(inverse(W), multiply(inverse(V), V))), multiply(inverse(W), Z))
% 11.54/1.95 = { by lemma 18 }
% 11.54/1.95 multiply(W, multiply(inverse(W), Z))
% 11.54/1.95
% 11.54/1.95 Lemma 20: multiply(X, multiply(inverse(X), multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 11.54/1.95 Proof:
% 11.54/1.95 multiply(X, multiply(inverse(X), multiply(inverse(Y), Y)))
% 11.54/1.95 = { by lemma 16 R->L }
% 11.54/1.95 multiply(X, inverse(multiply(X, multiply(inverse(W), W))))
% 11.54/1.95 = { by lemma 14 R->L }
% 11.54/1.95 multiply(X, multiply(multiply(inverse(V), V), multiply(inverse(X), multiply(inverse(U), U))))
% 11.54/1.95 = { by lemma 16 R->L }
% 11.54/1.95 multiply(X, multiply(multiply(inverse(V), V), inverse(multiply(X, multiply(inverse(T), T)))))
% 11.54/1.95 = { by lemma 14 R->L }
% 11.54/1.95 multiply(X, multiply(multiply(inverse(V), V), multiply(multiply(inverse(S), S), multiply(inverse(X), multiply(inverse(X2), X2)))))
% 11.54/1.95 = { by lemma 16 R->L }
% 11.54/1.95 multiply(X, multiply(multiply(inverse(V), V), multiply(multiply(inverse(S), S), inverse(multiply(X, multiply(inverse(Y2), Y2))))))
% 11.54/1.95 = { by lemma 12 R->L }
% 11.54/1.95 multiply(X, multiply(multiply(inverse(V), V), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(X, multiply(inverse(Y2), Y2))))))
% 11.54/1.95 = { by lemma 13 R->L }
% 11.54/1.95 multiply(X, multiply(inverse(multiply(inverse(multiply(inverse(X), Z2)), multiply(inverse(X), X))), multiply(inverse(multiply(inverse(X), Z2)), inverse(multiply(X, multiply(inverse(Y2), Y2))))))
% 11.54/1.95 = { by lemma 9 }
% 11.54/1.95 multiply(multiply(inverse(W2), W2), multiply(inverse(multiply(inverse(multiply(inverse(X), Z2)), multiply(inverse(X), multiply(inverse(W2), W2)))), multiply(inverse(multiply(inverse(X), Z2)), inverse(multiply(X, multiply(inverse(Y2), Y2))))))
% 11.54/1.95 = { by lemma 13 R->L }
% 11.54/1.95 multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(X), Z2)), multiply(inverse(X), multiply(inverse(W2), W2))))), multiply(V2, multiply(inverse(multiply(inverse(X), Z2)), inverse(multiply(X, multiply(inverse(Y2), Y2))))))
% 11.54/1.95 = { by lemma 16 R->L }
% 11.54/1.95 multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(X), Z2)), inverse(multiply(X, multiply(inverse(Y2), Y2)))))), multiply(V2, multiply(inverse(multiply(inverse(X), Z2)), inverse(multiply(X, multiply(inverse(Y2), Y2))))))
% 11.54/1.95 = { by lemma 10 R->L }
% 11.54/1.95 multiply(inverse(Z), Z)
% 11.54/1.95
% 11.54/1.95 Lemma 21: multiply(X, multiply(inverse(X), multiply(inverse(inverse(Y)), multiply(inverse(Z), Z)))) = Y.
% 11.54/1.95 Proof:
% 11.54/1.95 multiply(X, multiply(inverse(X), multiply(inverse(inverse(Y)), multiply(inverse(Z), Z))))
% 11.54/1.95 = { by lemma 12 R->L }
% 11.54/1.95 multiply(X, multiply(inverse(X), multiply(inverse(inverse(Y)), inverse(multiply(inverse(W), W)))))
% 11.54/1.95 = { by lemma 20 R->L }
% 11.54/1.95 multiply(X, multiply(inverse(X), multiply(inverse(inverse(Y)), inverse(multiply(V, multiply(inverse(V), multiply(inverse(U), U)))))))
% 11.54/1.95 = { by lemma 16 R->L }
% 11.54/1.95 multiply(X, multiply(inverse(X), multiply(inverse(inverse(Y)), inverse(multiply(V, inverse(multiply(V, multiply(inverse(V), V))))))))
% 11.54/1.96 = { by lemma 18 R->L }
% 11.54/1.96 multiply(X, multiply(inverse(X), multiply(inverse(inverse(Y)), inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(T), T))), inverse(multiply(V, multiply(inverse(V), V))))))))
% 11.54/1.96 = { by lemma 19 R->L }
% 11.54/1.96 multiply(multiply(inverse(S), S), multiply(multiply(inverse(X2), X2), multiply(inverse(inverse(Y)), inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(T), T))), inverse(multiply(V, multiply(inverse(V), V))))))))
% 11.54/1.96 = { by lemma 13 R->L }
% 11.54/1.96 multiply(multiply(inverse(S), S), multiply(inverse(multiply(Y2, inverse(Y))), multiply(Y2, inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(T), T))), inverse(multiply(V, multiply(inverse(V), V))))))))
% 11.54/1.96 = { by lemma 13 R->L }
% 11.54/1.96 multiply(inverse(multiply(Z2, multiply(Y2, inverse(Y)))), multiply(Z2, multiply(Y2, inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(T), T))), inverse(multiply(V, multiply(inverse(V), V))))))))
% 11.54/1.96 = { by lemma 16 R->L }
% 11.54/1.96 multiply(inverse(multiply(Z2, multiply(Y2, inverse(Y)))), multiply(Z2, multiply(Y2, inverse(multiply(inverse(inverse(multiply(V, multiply(inverse(V), V)))), inverse(multiply(V, multiply(inverse(V), V))))))))
% 11.54/1.96 = { by lemma 15 R->L }
% 11.54/1.96 multiply(inverse(multiply(Z2, multiply(Y2, inverse(Y)))), multiply(Z2, inverse(multiply(inverse(Y), inverse(multiply(multiply(Y2, inverse(Y)), multiply(inverse(multiply(Y2, inverse(Y))), multiply(Y2, inverse(Y)))))))))
% 11.54/1.96 = { by lemma 5 }
% 11.54/1.96 Y
% 11.54/1.96
% 11.54/1.96 Lemma 22: multiply(multiply(inverse(X), X), Y) = Y.
% 11.54/1.96 Proof:
% 11.54/1.96 multiply(multiply(inverse(X), X), Y)
% 11.54/1.96 = { by lemma 21 R->L }
% 11.54/1.96 multiply(Z, multiply(inverse(Z), multiply(inverse(inverse(multiply(multiply(inverse(X), X), Y))), multiply(inverse(W), W))))
% 11.54/1.96 = { by lemma 18 R->L }
% 11.54/1.96 multiply(Z, multiply(inverse(Z), multiply(inverse(inverse(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), multiply(inverse(V), V)))))), multiply(inverse(W), W))))
% 11.54/1.96 = { by lemma 17 }
% 11.54/1.96 multiply(Z, multiply(inverse(Z), multiply(inverse(inverse(Y)), multiply(inverse(W), W))))
% 11.54/1.96 = { by lemma 21 }
% 11.54/1.96 Y
% 11.54/1.96
% 11.54/1.96 Lemma 23: multiply(X, multiply(inverse(X), Y)) = Y.
% 11.54/1.96 Proof:
% 11.54/1.96 multiply(X, multiply(inverse(X), Y))
% 11.54/1.96 = { by lemma 19 R->L }
% 11.54/1.96 multiply(multiply(inverse(Z), Z), multiply(multiply(inverse(W), W), Y))
% 11.54/1.96 = { by lemma 22 }
% 11.54/1.96 multiply(multiply(inverse(Z), Z), Y)
% 11.54/1.96 = { by lemma 22 }
% 11.54/1.96 Y
% 11.54/1.96
% 11.54/1.96 Lemma 24: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(X).
% 11.54/1.96 Proof:
% 11.54/1.96 multiply(inverse(X), multiply(inverse(Y), Y))
% 11.54/1.96 = { by lemma 16 R->L }
% 11.54/1.96 inverse(multiply(X, multiply(inverse(X), X)))
% 11.54/1.96 = { by lemma 23 }
% 11.54/1.96 inverse(X)
% 11.54/1.96
% 11.54/1.96 Lemma 25: inverse(inverse(X)) = X.
% 11.54/1.96 Proof:
% 11.54/1.96 inverse(inverse(X))
% 11.54/1.96 = { by lemma 24 R->L }
% 11.54/1.96 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 11.54/1.96 = { by lemma 18 }
% 11.54/1.96 X
% 11.54/1.96
% 11.54/1.96 Lemma 26: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 11.54/1.96 Proof:
% 11.54/1.96 multiply(inverse(X), X)
% 11.54/1.96 = { by lemma 20 R->L }
% 11.54/1.96 multiply(Y, multiply(inverse(Y), multiply(inverse(Z), Z)))
% 11.54/1.96 = { by lemma 24 }
% 11.54/1.96 multiply(Y, inverse(Y))
% 11.54/1.96
% 11.54/1.96 Lemma 27: multiply(multiply(X, inverse(X)), Y) = Y.
% 11.54/1.96 Proof:
% 11.54/1.96 multiply(multiply(X, inverse(X)), Y)
% 11.54/1.96 = { by lemma 26 R->L }
% 11.54/1.96 multiply(multiply(inverse(Z), Z), Y)
% 11.54/1.96 = { by lemma 22 }
% 11.54/1.96 Y
% 11.54/1.96
% 11.54/1.96 Lemma 28: multiply(X, multiply(Y, inverse(Y))) = X.
% 11.54/1.96 Proof:
% 11.54/1.96 multiply(X, multiply(Y, inverse(Y)))
% 11.54/1.96 = { by lemma 26 R->L }
% 11.54/1.96 multiply(X, multiply(inverse(X), X))
% 11.54/1.96 = { by lemma 23 }
% 11.54/1.96 X
% 11.54/1.96
% 11.54/1.96 Lemma 29: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 11.54/1.96 Proof:
% 11.54/1.96 inverse(multiply(inverse(X), Y))
% 11.54/1.96 = { by lemma 28 R->L }
% 11.54/1.96 multiply(inverse(multiply(inverse(X), Y)), multiply(Z, inverse(Z)))
% 11.54/1.96 = { by lemma 26 R->L }
% 11.54/1.96 multiply(inverse(multiply(inverse(X), Y)), multiply(inverse(X), X))
% 11.54/1.96 = { by lemma 13 }
% 11.54/1.96 multiply(multiply(inverse(W), W), multiply(inverse(Y), X))
% 11.54/1.96 = { by lemma 26 }
% 11.54/1.96 multiply(multiply(V, inverse(V)), multiply(inverse(Y), X))
% 11.54/1.96 = { by lemma 27 }
% 11.54/1.96 multiply(inverse(Y), X)
% 11.54/1.96
% 11.54/1.96 Lemma 30: multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 11.54/1.96 Proof:
% 11.54/1.96 multiply(multiply(X, Y), Z)
% 11.54/1.96 = { by lemma 27 R->L }
% 11.54/1.96 multiply(multiply(X, Y), multiply(multiply(W, inverse(W)), Z))
% 11.54/1.96 = { by lemma 26 R->L }
% 11.54/1.96 multiply(multiply(X, Y), multiply(multiply(inverse(V), V), Z))
% 11.54/1.96 = { by lemma 12 R->L }
% 11.54/1.96 multiply(multiply(X, Y), multiply(inverse(multiply(inverse(U), U)), Z))
% 11.54/1.96 = { by lemma 26 }
% 11.54/1.96 multiply(multiply(X, Y), multiply(inverse(multiply(T, inverse(T))), Z))
% 11.54/1.96 = { by lemma 28 R->L }
% 11.54/1.96 multiply(multiply(multiply(X, Y), multiply(S, inverse(S))), multiply(inverse(multiply(T, inverse(T))), Z))
% 11.54/1.96 = { by lemma 26 R->L }
% 11.54/1.96 multiply(multiply(multiply(X, Y), multiply(inverse(multiply(X, Y)), multiply(X, Y))), multiply(inverse(multiply(T, inverse(T))), Z))
% 11.54/1.96 = { by lemma 26 R->L }
% 11.54/1.96 multiply(multiply(multiply(X, Y), multiply(inverse(multiply(X, Y)), multiply(X, Y))), multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Y))), Z))
% 11.54/1.96 = { by lemma 25 R->L }
% 11.54/1.96 multiply(inverse(inverse(multiply(multiply(X, Y), multiply(inverse(multiply(X, Y)), multiply(X, Y))))), multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Y))), Z))
% 11.54/1.96 = { by lemma 29 R->L }
% 11.54/1.96 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Y))), Z)), inverse(multiply(multiply(X, Y), multiply(inverse(multiply(X, Y)), multiply(X, Y))))))
% 11.54/1.96 = { by axiom 1 (single_axiom) R->L }
% 11.54/1.96 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Y))), Z)), inverse(multiply(multiply(X, Y), multiply(inverse(multiply(X, Y)), multiply(X, Y)))))))), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 11.54/1.96 = { by axiom 1 (single_axiom) }
% 11.54/1.96 multiply(X, inverse(multiply(inverse(Z), inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 11.54/1.96 = { by lemma 29 }
% 11.54/1.96 multiply(X, multiply(inverse(inverse(multiply(Y, multiply(inverse(Y), Y)))), Z))
% 11.54/1.96 = { by lemma 25 }
% 11.54/1.96 multiply(X, multiply(multiply(Y, multiply(inverse(Y), Y)), Z))
% 11.54/1.96 = { by lemma 23 }
% 11.54/1.96 multiply(X, multiply(Y, Z))
% 11.54/1.96
% 11.54/1.96 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)).
% 11.54/1.96 Proof:
% 11.54/1.96 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 11.54/1.96 = { by lemma 26 }
% 11.54/1.96 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 11.54/1.96 = { by lemma 30 }
% 11.54/1.96 tuple(multiply(inverse(b2), multiply(b2, a2)), multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 11.54/1.96 = { by lemma 25 R->L }
% 11.54/1.96 tuple(multiply(inverse(b2), multiply(inverse(inverse(b2)), a2)), multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 11.54/1.96 = { by lemma 23 }
% 11.54/1.96 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 11.54/1.96 = { by lemma 30 }
% 11.54/1.96 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 11.54/1.96 = { by lemma 26 R->L }
% 11.54/1.96 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 11.54/1.96 % SZS output end Proof
% 11.54/1.96
% 11.54/1.96 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------