%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP052-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 1.95s 0.70s
% Output : Proof 3.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP052-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:19:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.95/0.70 Command-line arguments: --no-flatten-goal
% 1.95/0.70
% 1.95/0.70 % SZS status Unsatisfiable
% 1.95/0.70
% 2.85/0.88 % SZS output start Proof
% 2.85/0.88 Axiom 1 (single_axiom): multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(X, inverse(Y))), Z))), Y))) = Z.
% 2.85/0.88
% 2.85/0.88 Lemma 2: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X)) = multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z))).
% 2.85/0.88 Proof:
% 2.85/0.88 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))
% 2.85/0.88 = { by axiom 1 (single_axiom) R->L }
% 2.85/0.89 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))))), Z)))
% 2.85/0.89 = { by axiom 1 (single_axiom) }
% 2.85/0.89 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z)))
% 2.85/0.89
% 2.85/0.89 Lemma 3: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X)) = W.
% 2.85/0.89 Proof:
% 2.85/0.89 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X))
% 2.85/0.89 = { by lemma 2 }
% 2.85/0.89 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), W))), Z)))
% 2.85/0.89 = { by axiom 1 (single_axiom) }
% 2.85/0.89 W
% 2.85/0.89
% 2.85/0.89 Lemma 4: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y)))) = Z.
% 2.85/0.89 Proof:
% 2.85/0.89 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y))))
% 2.85/0.89 = { by lemma 2 R->L }
% 2.85/0.89 multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), inverse(W))), Z))), W)))
% 2.85/0.89 = { by axiom 1 (single_axiom) }
% 2.85/0.89 Z
% 2.85/0.89
% 2.85/0.89 Lemma 5: multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z)) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z)).
% 2.85/0.89 Proof:
% 2.85/0.89 multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z))
% 2.85/0.89 = { by lemma 3 R->L }
% 2.85/0.89 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(U))), inverse(Y))), multiply(inverse(multiply(V, inverse(U))), Z)))), Y))))
% 2.85/0.89 = { by lemma 4 }
% 2.85/0.89 multiply(inverse(multiply(inverse(multiply(V, inverse(U))), inverse(Y))), multiply(inverse(multiply(V, inverse(U))), Z))
% 2.85/0.89 = { by lemma 4 R->L }
% 2.85/0.89 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(U))), inverse(Y))), multiply(inverse(multiply(V, inverse(U))), Z)))), Y))))
% 2.85/0.89 = { by lemma 3 }
% 2.85/0.89 multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z))
% 2.85/0.89
% 2.85/0.89 Lemma 6: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 2.85/0.89 Proof:
% 2.85/0.89 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 2.85/0.89 = { by axiom 1 (single_axiom) R->L }
% 2.85/0.90 multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(V))), multiply(inverse(multiply(W, Y)), multiply(W, Z))))), V)))
% 2.85/0.90 = { by lemma 3 R->L }
% 2.85/0.90 multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(V))), multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), multiply(W, Z))))), V)))
% 2.85/0.90 = { by lemma 3 R->L }
% 2.85/0.90 multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), inverse(V))), multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), multiply(W, Z))))), V)))
% 2.85/0.90 = { by lemma 5 }
% 2.85/0.90 multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), inverse(V))), multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), multiply(X, Z))))), V)))
% 2.85/0.90 = { by lemma 5 R->L }
% 2.85/0.90 multiply(inverse(multiply(X, Y)), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(V))), multiply(inverse(multiply(X, Y)), multiply(X, Z))))), V)))
% 2.85/0.90 = { by axiom 1 (single_axiom) }
% 2.85/0.90 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 2.85/0.90
% 2.85/0.90 Lemma 7: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X) = multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(Z, Y)))).
% 2.85/0.90 Proof:
% 2.85/0.90 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X)
% 2.85/0.90 = { by lemma 4 R->L }
% 2.85/0.90 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X))), Y))))
% 2.85/0.90 = { by axiom 1 (single_axiom) }
% 2.85/0.90 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(Z, Y))))
% 2.85/0.90
% 2.85/0.90 Lemma 8: multiply(X, multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z))))) = multiply(inverse(multiply(W, V)), multiply(W, V)).
% 2.85/0.90 Proof:
% 2.85/0.90 multiply(X, multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z)))))
% 2.85/0.90 = { by axiom 1 (single_axiom) R->L }
% 2.85/0.90 multiply(multiply(U, inverse(multiply(multiply(multiply(inverse(T), T), inverse(multiply(inverse(multiply(U, inverse(T))), X))), T))), multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z)))))
% 2.85/0.90 = { by lemma 2 R->L }
% 2.85/0.90 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z)))))
% 2.85/0.90 = { by lemma 7 R->L }
% 2.85/0.91 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(V))), multiply(multiply(inverse(Z), Z), X)))), V))
% 2.85/0.91 = { by lemma 5 R->L }
% 2.85/0.91 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V))
% 2.85/0.91 = { by lemma 6 R->L }
% 3.53/0.91 multiply(inverse(multiply(W, V)), multiply(W, V))
% 3.53/0.91
% 3.53/0.91 Lemma 9: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 3.53/0.91 Proof:
% 3.53/0.91 multiply(inverse(Y), Y)
% 3.53/0.91 = { by axiom 1 (single_axiom) R->L }
% 3.53/0.91 multiply(inverse(Y), multiply(inverse(multiply(S, inverse(X2))), inverse(multiply(multiply(multiply(inverse(Y2), Y2), inverse(multiply(inverse(multiply(inverse(multiply(S, inverse(X2))), inverse(Y2))), Y))), Y2))))
% 3.53/0.91 = { by lemma 2 }
% 3.53/0.91 multiply(inverse(Y), multiply(inverse(multiply(S, inverse(X2))), multiply(S, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(Y)), X2)))))
% 3.53/0.91 = { by lemma 8 }
% 3.53/0.91 multiply(inverse(multiply(U, T)), multiply(U, T))
% 3.53/0.91 = { by lemma 8 R->L }
% 3.53/0.91 multiply(inverse(X), multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(multiply(multiply(inverse(W), W), inverse(X)), W)))))
% 3.53/0.91 = { by lemma 2 R->L }
% 3.53/0.91 multiply(inverse(X), multiply(inverse(multiply(Z, inverse(W))), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(W))), inverse(V))), X))), V))))
% 3.53/0.91 = { by axiom 1 (single_axiom) }
% 3.53/0.91 multiply(inverse(X), X)
% 3.53/0.91
% 3.53/0.91 Lemma 10: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y)))) = multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z).
% 3.53/0.91 Proof:
% 3.53/0.91 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y))))
% 3.53/0.91 = { by lemma 7 R->L }
% 3.53/0.91 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(Z))), multiply(multiply(inverse(Y), Y), inverse(Z))))), Z)
% 3.53/0.91 = { by lemma 9 R->L }
% 3.53/0.91 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(V), V))), Z)
% 3.53/0.91 = { by lemma 9 R->L }
% 3.53/0.91 multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z)
% 3.53/0.91
% 3.53/0.91 Lemma 11: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), Z) = Z.
% 3.53/0.91 Proof:
% 3.53/0.91 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), Z)
% 3.53/0.91 = { by lemma 10 R->L }
% 3.53/0.91 multiply(inverse(multiply(W, inverse(V))), multiply(W, inverse(multiply(multiply(multiply(inverse(V), V), inverse(Z)), V))))
% 3.53/0.91 = { by lemma 2 R->L }
% 3.53/0.91 multiply(inverse(multiply(W, inverse(V))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(V))), inverse(U))), Z))), U)))
% 3.53/0.91 = { by axiom 1 (single_axiom) }
% 3.53/0.91 Z
% 3.53/0.91
% 3.53/0.91 Lemma 12: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(inverse(Y), Z).
% 3.53/0.91 Proof:
% 3.53/0.91 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 3.53/0.91 = { by lemma 6 }
% 3.53/0.91 multiply(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Y)), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 3.53/0.91 = { by lemma 11 }
% 3.53/0.91 multiply(inverse(Y), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 3.53/0.91 = { by lemma 11 }
% 3.53/0.91 multiply(inverse(Y), Z)
% 3.53/0.91
% 3.53/0.91 Lemma 13: multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z)) = multiply(inverse(inverse(Y)), Z).
% 3.53/0.91 Proof:
% 3.53/0.91 multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z))
% 3.53/0.91 = { by lemma 5 }
% 3.53/0.91 multiply(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), inverse(Y))), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 3.53/0.91 = { by lemma 11 }
% 3.53/0.91 multiply(inverse(inverse(Y)), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 3.53/0.91 = { by lemma 11 }
% 3.53/0.91 multiply(inverse(inverse(Y)), Z)
% 3.53/0.91
% 3.53/0.91 Lemma 14: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(Y)), Z)) = multiply(inverse(inverse(Y)), Z).
% 3.53/0.91 Proof:
% 3.53/0.91 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(Y)), Z))
% 3.53/0.91 = { by lemma 9 }
% 3.53/0.91 multiply(inverse(multiply(inverse(inverse(Y)), inverse(Y))), multiply(inverse(inverse(Y)), Z))
% 3.53/0.91 = { by lemma 13 }
% 3.53/0.91 multiply(inverse(inverse(Y)), Z)
% 3.53/0.91
% 3.53/0.91 Lemma 15: multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X)))))) = Z.
% 3.53/0.91 Proof:
% 3.53/0.92 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X))))))
% 3.53/0.92 = { by lemma 7 R->L }
% 3.53/0.92 multiply(multiply(inverse(X), X), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(W))), Z))), W)))
% 3.53/0.92 = { by axiom 1 (single_axiom) }
% 3.53/0.92 Z
% 3.53/0.92
% 3.53/0.92 Lemma 16: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 3.53/0.92 Proof:
% 3.53/0.92 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 3.53/0.92 = { by lemma 9 }
% 3.53/0.92 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(inverse(V)), U)))), multiply(W, inverse(multiply(inverse(inverse(V)), U))))))
% 3.53/0.92 = { by lemma 9 }
% 3.53/0.92 multiply(multiply(inverse(multiply(inverse(inverse(V)), U)), multiply(inverse(inverse(V)), U)), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(inverse(V)), U)))), multiply(W, inverse(multiply(inverse(inverse(V)), U))))))
% 3.53/0.92 = { by lemma 14 R->L }
% 3.53/0.92 multiply(multiply(inverse(multiply(inverse(inverse(V)), U)), multiply(inverse(inverse(V)), U)), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(inverse(V)), U)))), multiply(W, inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(inverse(V)), U)))))))
% 3.53/0.92 = { by lemma 15 }
% 3.53/0.92 inverse(multiply(inverse(Z), Z))
% 3.53/0.92
% 3.53/0.92 Lemma 17: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 3.53/0.92 Proof:
% 3.53/0.92 inverse(multiply(inverse(X), X))
% 3.53/0.92 = { by lemma 16 R->L }
% 3.53/0.92 multiply(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), multiply(W, inverse(inverse(multiply(inverse(Z), Z)))))))
% 3.53/0.92 = { by lemma 16 R->L }
% 3.53/0.92 multiply(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(W, inverse(inverse(multiply(inverse(Z), Z))))), multiply(W, inverse(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Z), Z))))))))
% 3.53/0.92 = { by lemma 15 }
% 3.53/0.92 multiply(inverse(Y), Y)
% 3.53/0.92
% 3.53/0.92 Lemma 18: multiply(inverse(multiply(inverse(X), X)), Y) = Y.
% 3.53/0.92 Proof:
% 3.53/0.92 multiply(inverse(multiply(inverse(X), X)), Y)
% 3.53/0.92 = { by axiom 1 (single_axiom) R->L }
% 3.53/0.92 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(Z)), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(inverse(Z)), inverse(W))), Y))), W))))
% 3.53/0.92 = { by lemma 14 }
% 3.53/0.92 multiply(inverse(inverse(Z)), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(inverse(Z)), inverse(W))), Y))), W)))
% 3.53/0.92 = { by axiom 1 (single_axiom) }
% 3.53/0.92 Y
% 3.53/0.92
% 3.53/0.92 Lemma 19: multiply(multiply(inverse(X), X), Y) = Y.
% 3.53/0.92 Proof:
% 3.53/0.92 multiply(multiply(inverse(X), X), Y)
% 3.53/0.92 = { by lemma 17 R->L }
% 3.53/0.92 multiply(inverse(multiply(inverse(Z), Z)), Y)
% 3.53/0.92 = { by lemma 18 }
% 3.53/0.92 Y
% 3.53/0.92
% 3.53/0.92 Lemma 20: inverse(multiply(inverse(multiply(inverse(inverse(X)), Y)), X)) = Y.
% 3.53/0.92 Proof:
% 3.53/0.92 inverse(multiply(inverse(multiply(inverse(inverse(X)), Y)), X))
% 3.53/0.92 = { by lemma 19 R->L }
% 3.53/0.92 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(inverse(X)), Y))), X))
% 3.53/0.92 = { by lemma 19 R->L }
% 3.53/0.92 multiply(multiply(inverse(Z), Z), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(inverse(X)), Y))), X)))
% 3.53/0.92 = { by lemma 19 R->L }
% 3.53/0.92 multiply(multiply(inverse(Z), Z), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), inverse(X))), Y))), X)))
% 3.53/0.92 = { by axiom 1 (single_axiom) }
% 3.53/0.92 Y
% 3.53/0.92
% 3.53/0.92 Lemma 21: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 3.53/0.92 Proof:
% 3.53/0.92 inverse(multiply(inverse(X), Y))
% 3.53/0.92 = { by lemma 12 R->L }
% 3.53/0.92 inverse(multiply(inverse(multiply(inverse(Y), X)), multiply(inverse(Y), Y)))
% 3.53/0.92 = { by lemma 18 R->L }
% 3.53/0.92 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Y), X))), multiply(inverse(Y), Y)))
% 3.53/0.92 = { by lemma 17 R->L }
% 3.53/0.92 inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(Y), Y))), multiply(inverse(Y), X))), multiply(inverse(Y), Y)))
% 3.53/0.92 = { by lemma 20 }
% 3.53/0.92 multiply(inverse(Y), X)
% 3.53/0.92
% 3.53/0.92 Lemma 22: multiply(X, multiply(inverse(X), Y)) = Y.
% 3.53/0.92 Proof:
% 3.53/0.92 multiply(X, multiply(inverse(X), Y))
% 3.53/0.92 = { by lemma 12 R->L }
% 3.53/0.92 multiply(X, multiply(inverse(multiply(inverse(inverse(Z)), X)), multiply(inverse(inverse(Z)), Y)))
% 3.53/0.92 = { by lemma 20 R->L }
% 3.53/0.92 multiply(inverse(multiply(inverse(multiply(inverse(inverse(Z)), X)), Z)), multiply(inverse(multiply(inverse(inverse(Z)), X)), multiply(inverse(inverse(Z)), Y)))
% 3.53/0.92 = { by lemma 12 }
% 3.53/0.92 multiply(inverse(Z), multiply(inverse(inverse(Z)), Y))
% 3.53/0.92 = { by lemma 13 R->L }
% 3.53/0.92 multiply(inverse(Z), multiply(inverse(multiply(inverse(multiply(W, multiply(inverse(V), U))), inverse(Z))), multiply(inverse(multiply(W, multiply(inverse(V), U))), Y)))
% 3.53/0.92 = { by lemma 21 R->L }
% 3.53/0.92 multiply(inverse(Z), multiply(inverse(multiply(inverse(multiply(W, multiply(inverse(V), U))), inverse(Z))), multiply(inverse(multiply(W, inverse(multiply(inverse(U), V)))), Y)))
% 3.53/0.93 = { by lemma 21 R->L }
% 3.53/0.93 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, multiply(inverse(V), U))), inverse(Z))), multiply(inverse(multiply(W, inverse(multiply(inverse(U), V)))), Y))), Z))
% 3.53/0.93 = { by lemma 19 R->L }
% 3.53/0.93 inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(multiply(W, multiply(inverse(V), U))), inverse(Z))), multiply(inverse(multiply(W, inverse(multiply(inverse(U), V)))), Y)))), Z))
% 3.53/0.93 = { by lemma 21 R->L }
% 3.53/0.93 inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(U), V)))), inverse(Z))), multiply(inverse(multiply(W, inverse(multiply(inverse(U), V)))), Y)))), Z))
% 3.53/0.93 = { by lemma 3 }
% 3.53/0.93 Y
% 3.53/0.93
% 3.53/0.93 Lemma 23: inverse(inverse(X)) = X.
% 3.53/0.93 Proof:
% 3.53/0.93 inverse(inverse(X))
% 3.53/0.93 = { by lemma 22 R->L }
% 3.53/0.93 inverse(multiply(inverse(Y), multiply(inverse(inverse(Y)), inverse(X))))
% 3.53/0.93 = { by lemma 18 R->L }
% 3.53/0.93 inverse(multiply(inverse(Y), multiply(inverse(inverse(Y)), inverse(multiply(inverse(multiply(inverse(Z), Z)), X)))))
% 3.53/0.93 = { by lemma 17 R->L }
% 3.53/0.93 inverse(multiply(inverse(Y), multiply(inverse(inverse(Y)), inverse(multiply(inverse(inverse(multiply(inverse(W), W))), X)))))
% 3.53/0.93 = { by lemma 12 R->L }
% 3.53/0.93 inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(Y)), inverse(multiply(inverse(inverse(multiply(inverse(W), W))), X)))), Y)), multiply(inverse(multiply(inverse(inverse(Y)), inverse(multiply(inverse(inverse(multiply(inverse(W), W))), X)))), multiply(inverse(inverse(Y)), inverse(multiply(inverse(inverse(multiply(inverse(W), W))), X))))))
% 3.53/0.93 = { by lemma 9 R->L }
% 3.53/0.93 inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(Y)), inverse(multiply(inverse(inverse(multiply(inverse(W), W))), X)))), Y)), multiply(inverse(W), W)))
% 3.53/0.93 = { by lemma 20 }
% 3.53/0.93 inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(W), W))), X)), multiply(inverse(W), W)))
% 3.53/0.93 = { by lemma 20 }
% 3.53/0.93 X
% 3.53/0.93
% 3.53/0.93 Lemma 24: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 3.53/0.93 Proof:
% 3.53/0.93 multiply(inverse(X), X)
% 3.53/0.93 = { by lemma 22 R->L }
% 3.53/0.93 multiply(Y, multiply(inverse(Y), multiply(inverse(X), X)))
% 3.53/0.93 = { by lemma 9 }
% 3.53/0.93 multiply(Y, multiply(inverse(Y), multiply(inverse(multiply(Z, W)), multiply(Z, W))))
% 3.53/0.93 = { by lemma 8 R->L }
% 3.53/0.93 multiply(Y, multiply(inverse(Y), multiply(inverse(inverse(Y)), multiply(inverse(multiply(V, inverse(U))), multiply(V, inverse(multiply(multiply(multiply(inverse(U), U), inverse(inverse(Y))), U)))))))
% 3.53/0.93 = { by lemma 10 }
% 3.53/0.93 multiply(Y, multiply(inverse(Y), multiply(inverse(inverse(Y)), multiply(multiply(multiply(inverse(T), T), inverse(multiply(inverse(S), S))), inverse(Y)))))
% 3.53/0.93 = { by lemma 11 }
% 3.53/0.93 multiply(Y, multiply(inverse(Y), multiply(inverse(inverse(Y)), inverse(Y))))
% 3.53/0.93 = { by lemma 22 }
% 3.53/0.93 multiply(Y, inverse(Y))
% 3.53/0.93
% 3.53/0.93 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)).
% 3.53/0.93 Proof:
% 3.53/0.93 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 3.53/0.93 = { by lemma 19 }
% 3.53/0.93 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 3.53/0.93 = { by lemma 24 }
% 3.53/0.93 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 3.53/0.93 = { by lemma 23 R->L }
% 3.53/0.93 tuple(a2, multiply(multiply(inverse(inverse(a3)), b3), c3), multiply(X, inverse(X)))
% 3.53/0.93 = { by lemma 21 R->L }
% 3.53/0.93 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), c3), multiply(X, inverse(X)))
% 3.53/0.93 = { by lemma 22 R->L }
% 3.53/0.93 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(b3), multiply(inverse(inverse(b3)), c3))), multiply(X, inverse(X)))
% 3.53/0.93 = { by lemma 23 }
% 3.53/0.94 tuple(a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), multiply(inverse(b3), multiply(b3, c3))), multiply(X, inverse(X)))
% 3.53/0.94 = { by lemma 13 }
% 3.53/0.94 tuple(a2, multiply(inverse(inverse(a3)), multiply(b3, c3)), multiply(X, inverse(X)))
% 3.53/0.94 = { by lemma 23 }
% 3.53/0.94 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 3.53/0.94 = { by lemma 24 R->L }
% 3.53/0.94 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 3.53/0.94 % SZS output end Proof
% 3.53/0.94
% 3.53/0.94 RESULT: Unsatisfiable (the axioms are contradictory).
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