TSTP Solution File: GRP432-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP432-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:18:24 EDT 2023
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : GRP432-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.35 % Computer : n002.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Mon Aug 28 23:13:05 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.45 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.45
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Axiom 1 (single_axiom): multiply(X, inverse(multiply(Y, multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, Y))), X)))) = W.
% 0.21/0.49
% 0.21/0.49 Lemma 2: multiply(X, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V))), multiply(Z, X)))) = W.
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(X, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V))), multiply(Z, X))))
% 0.21/0.49 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.49 multiply(X, inverse(multiply(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V))), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(W, multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Z, W))), multiply(V, inverse(V)))))), X))))
% 0.21/0.49 = { by axiom 1 (single_axiom) }
% 0.21/0.49 W
% 0.21/0.49
% 0.21/0.49 Lemma 3: multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W))) = multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, V)))).
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))
% 0.21/0.49 = { by lemma 2 R->L }
% 0.21/0.49 multiply(V, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(Z, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))))), multiply(U, inverse(U))), multiply(Z, V))))
% 0.21/0.49 = { by axiom 1 (single_axiom) }
% 0.21/0.50 multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, V))))
% 0.21/0.50
% 0.21/0.50 Lemma 4: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(Y, inverse(Y))
% 0.21/0.50 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.50 multiply(Z, inverse(multiply(inverse(multiply(W, V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(W, V))))), Z))))
% 0.21/0.50 = { by lemma 2 R->L }
% 0.21/0.50 multiply(Z, inverse(multiply(inverse(multiply(W, V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(W, multiply(S, inverse(multiply(multiply(multiply(multiply(X, inverse(X)), inverse(multiply(W, V))), multiply(X2, inverse(X2))), multiply(W, S))))))))), Z))))
% 0.21/0.50 = { by lemma 3 R->L }
% 0.21/0.50 multiply(Z, inverse(multiply(inverse(multiply(W, V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(Y, inverse(Y)), inverse(multiply(W, multiply(multiply(multiply(T, inverse(T)), inverse(multiply(multiply(multiply(X, inverse(X)), inverse(multiply(W, V))), W))), multiply(Y, inverse(Y)))))))), Z))))
% 0.21/0.50 = { by axiom 1 (single_axiom) }
% 0.21/0.50 multiply(Z, inverse(multiply(inverse(multiply(W, V)), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(multiply(X, inverse(X)), inverse(multiply(W, V))))), Z))))
% 0.21/0.50 = { by axiom 1 (single_axiom) }
% 0.21/0.50 multiply(X, inverse(X))
% 0.21/0.50
% 0.21/0.50 Lemma 5: multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, X)))) = inverse(W).
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, X))))
% 0.21/0.50 = { by lemma 4 }
% 0.21/0.50 multiply(X, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(W, inverse(W)))), multiply(Z, inverse(Z))), multiply(W, X))))
% 0.21/0.50 = { by lemma 2 }
% 0.21/0.50 inverse(W)
% 0.21/0.50
% 0.21/0.50 Lemma 6: multiply(inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z)))), inverse(multiply(Z, multiply(W, inverse(W))))) = Y.
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z)))), inverse(multiply(Z, multiply(W, inverse(W)))))
% 0.21/0.50 = { by lemma 4 }
% 0.21/0.50 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z)))), inverse(multiply(Z, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))))))))
% 0.21/0.50 = { by axiom 1 (single_axiom) }
% 0.21/0.50 Y
% 0.21/0.50
% 0.21/0.50 Lemma 7: multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, inverse(W))))) = X.
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(X, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.21/0.50 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.50 multiply(multiply(V, inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(multiply(multiply(U, inverse(U)), inverse(multiply(X, multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z)))))), V)))), inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.21/0.50 = { by lemma 5 }
% 0.21/0.50 multiply(inverse(multiply(multiply(U, inverse(U)), inverse(multiply(X, multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))))))), inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(Z, inverse(Z))), multiply(W, inverse(W)))))
% 0.21/0.50 = { by lemma 6 }
% 0.21/0.50 X
% 0.21/0.50
% 0.21/0.50 Lemma 8: inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))) = multiply(Z, inverse(Z)).
% 0.21/0.50 Proof:
% 0.21/0.50 inverse(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))))
% 0.21/0.50 = { by lemma 5 R->L }
% 0.21/0.50 multiply(W, inverse(multiply(multiply(multiply(V, inverse(V)), multiply(U, inverse(U))), multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), W))))
% 0.21/0.50 = { by lemma 7 R->L }
% 0.21/0.50 multiply(W, inverse(multiply(multiply(multiply(multiply(V, inverse(V)), inverse(multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), multiply(Z, inverse(Z))))), multiply(U, inverse(U))), multiply(multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))), W))))
% 0.21/0.50 = { by lemma 2 }
% 0.21/0.50 multiply(Z, inverse(Z))
% 0.21/0.50
% 0.21/0.50 Lemma 9: multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y))) = multiply(Z, inverse(Z)).
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(multiply(X, inverse(X)), multiply(Y, inverse(Y)))
% 0.21/0.50 = { by lemma 8 R->L }
% 0.21/0.50 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(V, inverse(V)))), multiply(Y, inverse(Y)))
% 0.21/0.50 = { by lemma 8 R->L }
% 0.21/0.50 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(V, inverse(V)))), inverse(multiply(multiply(U, inverse(U)), multiply(T, inverse(T)))))
% 0.21/0.50 = { by lemma 8 R->L }
% 0.21/0.50 multiply(inverse(multiply(multiply(W, inverse(W)), inverse(multiply(multiply(Z, inverse(Z)), multiply(U, inverse(U)))))), inverse(multiply(multiply(U, inverse(U)), multiply(T, inverse(T)))))
% 0.21/0.50 = { by lemma 6 }
% 0.21/0.50 multiply(Z, inverse(Z))
% 0.21/0.50
% 0.21/0.50 Lemma 10: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(X, multiply(Y, inverse(Y)))
% 0.21/0.50 = { by lemma 8 R->L }
% 0.21/0.50 multiply(X, inverse(multiply(multiply(Z, inverse(Z)), multiply(W, inverse(W)))))
% 0.21/0.50 = { by lemma 9 R->L }
% 0.21/0.50 multiply(X, inverse(multiply(multiply(multiply(V, inverse(V)), multiply(U, inverse(U))), multiply(W, inverse(W)))))
% 0.21/0.50 = { by lemma 7 }
% 0.21/0.50 X
% 0.21/0.50
% 0.21/0.50 Lemma 11: inverse(multiply(multiply(X, inverse(X)), inverse(Y))) = Y.
% 0.21/0.50 Proof:
% 0.21/0.50 inverse(multiply(multiply(X, inverse(X)), inverse(Y)))
% 0.21/0.50 = { by lemma 10 R->L }
% 0.21/0.50 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(Y))), multiply(Z, inverse(Z)))
% 0.21/0.50 = { by lemma 8 R->L }
% 0.21/0.50 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(Y))), inverse(multiply(multiply(W, inverse(W)), multiply(V, inverse(V)))))
% 0.21/0.50 = { by lemma 10 R->L }
% 0.21/0.50 multiply(inverse(multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(W, inverse(W)))))), inverse(multiply(multiply(W, inverse(W)), multiply(V, inverse(V)))))
% 0.21/0.50 = { by lemma 6 }
% 0.21/0.50 Y
% 0.21/0.50
% 0.21/0.50 Lemma 12: multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(W, V)))) = multiply(X, inverse(multiply(multiply(Y, multiply(Z, inverse(Z))), multiply(W, X)))).
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(W, V))))
% 0.21/0.50 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.50 multiply(V, inverse(multiply(multiply(multiply(multiply(T, inverse(T)), inverse(multiply(W, multiply(multiply(multiply(S, inverse(S)), inverse(multiply(Y, W))), multiply(T, inverse(T)))))), multiply(U, inverse(U))), multiply(W, V))))
% 0.21/0.50 = { by lemma 2 }
% 0.21/0.50 multiply(multiply(multiply(S, inverse(S)), inverse(multiply(Y, W))), multiply(T, inverse(T)))
% 0.21/0.50 = { by lemma 2 R->L }
% 0.21/0.50 multiply(X, inverse(multiply(multiply(multiply(multiply(T, inverse(T)), inverse(multiply(W, multiply(multiply(multiply(S, inverse(S)), inverse(multiply(Y, W))), multiply(T, inverse(T)))))), multiply(Z, inverse(Z))), multiply(W, X))))
% 0.21/0.50 = { by axiom 1 (single_axiom) }
% 0.21/0.50 multiply(X, inverse(multiply(multiply(Y, multiply(Z, inverse(Z))), multiply(W, X))))
% 0.21/0.50
% 0.21/0.50 Lemma 13: inverse(multiply(X, inverse(multiply(Y, multiply(Z, X))))) = multiply(Y, Z).
% 0.21/0.50 Proof:
% 0.21/0.50 inverse(multiply(X, inverse(multiply(Y, multiply(Z, X)))))
% 0.21/0.50 = { by lemma 10 R->L }
% 0.21/0.50 inverse(multiply(X, inverse(multiply(multiply(Y, multiply(W, inverse(W))), multiply(Z, X)))))
% 0.21/0.50 = { by lemma 12 }
% 0.21/0.50 inverse(multiply(multiply(V, inverse(V)), inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, multiply(V, inverse(V)))))))
% 0.21/0.50 = { by lemma 11 }
% 0.21/0.50 multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, multiply(V, inverse(V))))
% 0.21/0.50 = { by lemma 10 }
% 0.21/0.50 multiply(Y, multiply(Z, multiply(V, inverse(V))))
% 0.21/0.50 = { by lemma 10 }
% 0.21/0.50 multiply(Y, Z)
% 0.21/0.50
% 0.21/0.50 Lemma 14: multiply(X, inverse(multiply(multiply(Y, inverse(Y)), multiply(Z, X)))) = inverse(Z).
% 0.21/0.50 Proof:
% 0.21/0.50 multiply(X, inverse(multiply(multiply(Y, inverse(Y)), multiply(Z, X))))
% 0.21/0.50 = { by lemma 9 R->L }
% 0.21/0.51 multiply(X, inverse(multiply(multiply(multiply(W, inverse(W)), multiply(V, inverse(V))), multiply(Z, X))))
% 0.21/0.51 = { by lemma 12 R->L }
% 0.21/0.51 multiply(U, inverse(multiply(multiply(multiply(W, inverse(W)), multiply(T, inverse(T))), multiply(Z, U))))
% 0.21/0.51 = { by lemma 5 }
% 0.21/0.51 inverse(Z)
% 0.21/0.51
% 0.21/0.51 Lemma 15: multiply(X, inverse(multiply(Y, multiply(Z, X)))) = inverse(multiply(Y, Z)).
% 0.21/0.51 Proof:
% 0.21/0.51 multiply(X, inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 11 R->L }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), inverse(X))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 6 R->L }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(X), multiply(X, inverse(multiply(Y, multiply(Z, X)))))))), inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, X)))), multiply(U, inverse(U))))))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 10 R->L }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(X), multiply(multiply(X, multiply(T, inverse(T))), inverse(multiply(Y, multiply(Z, X)))))))), inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, X)))), multiply(U, inverse(U))))))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 13 R->L }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(X), inverse(multiply(S, inverse(multiply(multiply(X, multiply(T, inverse(T))), multiply(inverse(multiply(Y, multiply(Z, X))), S))))))))), inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, X)))), multiply(U, inverse(U))))))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 3 R->L }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(X), inverse(multiply(multiply(multiply(X2, inverse(X2)), inverse(multiply(X, inverse(multiply(Y, multiply(Z, X)))))), multiply(Y2, inverse(Y2)))))))), inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, X)))), multiply(U, inverse(U))))))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 10 R->L }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(X), inverse(multiply(multiply(multiply(multiply(X2, inverse(X2)), inverse(multiply(X, inverse(multiply(Y, multiply(Z, X)))))), multiply(Y2, inverse(Y2))), multiply(X, inverse(X)))))))), inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, X)))), multiply(U, inverse(U))))))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 2 }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(multiply(V, inverse(V)), inverse(inverse(multiply(Y, multiply(Z, X)))))), inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, X)))), multiply(U, inverse(U))))))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 11 }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(Y, multiply(Z, X))), inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, X)))), multiply(U, inverse(U))))))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 10 }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(Y, multiply(Z, X))), inverse(multiply(X, inverse(multiply(Y, multiply(Z, X)))))))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 13 }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(Y, multiply(Z, X))), multiply(Y, Z)))), inverse(multiply(Y, multiply(Z, X))))
% 0.21/0.51 = { by lemma 11 R->L }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(Y, multiply(Z, X))), multiply(Y, Z)))), inverse(multiply(multiply(Z2, inverse(Z2)), inverse(inverse(multiply(Y, multiply(Z, X)))))))
% 0.21/0.51 = { by lemma 14 R->L }
% 0.21/0.51 multiply(inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(Y, multiply(Z, X))), multiply(Y, Z)))), inverse(multiply(multiply(Z2, inverse(Z2)), multiply(multiply(Y, Z), inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(Y, multiply(Z, X))), multiply(Y, Z))))))))
% 0.21/0.51 = { by lemma 14 }
% 0.21/0.51 inverse(multiply(Y, Z))
% 0.21/0.51
% 0.21/0.51 Lemma 16: multiply(X, inverse(multiply(inverse(Y), multiply(multiply(Z, inverse(Z)), X)))) = Y.
% 0.21/0.51 Proof:
% 0.21/0.51 multiply(X, inverse(multiply(inverse(Y), multiply(multiply(Z, inverse(Z)), X))))
% 0.21/0.51 = { by lemma 4 }
% 0.21/0.51 multiply(X, inverse(multiply(inverse(Y), multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), X))))
% 0.21/0.51 = { by axiom 1 (single_axiom) }
% 0.21/0.51 Y
% 0.21/0.51
% 0.21/0.51 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.21/0.51 Proof:
% 0.21/0.51 multiply(multiply(a3, b3), c3)
% 0.21/0.51 = { by lemma 16 R->L }
% 0.21/0.51 multiply(X, inverse(multiply(inverse(multiply(multiply(a3, b3), c3)), multiply(multiply(Y, inverse(Y)), X))))
% 0.21/0.51 = { by lemma 10 R->L }
% 0.21/0.51 multiply(X, inverse(multiply(inverse(multiply(multiply(multiply(a3, multiply(Z, inverse(Z))), b3), c3)), multiply(multiply(Y, inverse(Y)), X))))
% 0.21/0.51 = { by lemma 13 R->L }
% 0.21/0.51 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(c3, inverse(multiply(multiply(a3, multiply(Z, inverse(Z))), multiply(b3, c3))))), c3)), multiply(multiply(Y, inverse(Y)), X))))
% 0.21/0.51 = { by lemma 10 R->L }
% 0.21/0.51 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(multiply(c3, multiply(W, inverse(W))), inverse(multiply(multiply(a3, multiply(Z, inverse(Z))), multiply(b3, c3))))), c3)), multiply(multiply(Y, inverse(Y)), X))))
% 0.21/0.51 = { by lemma 15 R->L }
% 0.21/0.51 multiply(X, inverse(multiply(inverse(multiply(multiply(V, inverse(multiply(multiply(c3, multiply(W, inverse(W))), multiply(inverse(multiply(multiply(a3, multiply(Z, inverse(Z))), multiply(b3, c3))), V)))), c3)), multiply(multiply(Y, inverse(Y)), X))))
% 0.21/0.51 = { by lemma 3 R->L }
% 0.21/0.51 multiply(X, inverse(multiply(inverse(multiply(multiply(multiply(multiply(U, inverse(U)), inverse(multiply(c3, inverse(multiply(multiply(a3, multiply(Z, inverse(Z))), multiply(b3, c3)))))), multiply(T, inverse(T))), c3)), multiply(multiply(Y, inverse(Y)), X))))
% 0.21/0.51 = { by lemma 15 R->L }
% 0.21/0.51 multiply(X, inverse(multiply(multiply(S, inverse(multiply(multiply(multiply(multiply(U, inverse(U)), inverse(multiply(c3, inverse(multiply(multiply(a3, multiply(Z, inverse(Z))), multiply(b3, c3)))))), multiply(T, inverse(T))), multiply(c3, S)))), multiply(multiply(Y, inverse(Y)), X))))
% 0.21/0.51 = { by lemma 2 }
% 0.21/0.51 multiply(X, inverse(multiply(inverse(multiply(multiply(a3, multiply(Z, inverse(Z))), multiply(b3, c3))), multiply(multiply(Y, inverse(Y)), X))))
% 0.21/0.51 = { by lemma 10 }
% 0.21/0.51 multiply(X, inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), multiply(multiply(Y, inverse(Y)), X))))
% 0.21/0.51 = { by lemma 16 }
% 0.21/0.51 multiply(a3, multiply(b3, c3))
% 0.21/0.51 % SZS output end Proof
% 0.21/0.51
% 0.21/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------