TSTP Solution File: GRP406-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP406-1 : 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 : n011.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 01:18:18 EDT 2023
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP406-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:04:56 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.48
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Axiom 1 (single_axiom): multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), multiply(inverse(Y), Y))))) = Z.
% 0.20/0.50
% 0.20/0.50 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))) = multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y))))).
% 0.20/0.50 Proof:
% 0.20/0.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z))))
% 0.20/0.50 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.50 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))))), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.20/0.50 = { by axiom 1 (single_axiom) }
% 0.20/0.50 multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 0.20/0.50
% 0.20/0.50 Lemma 3: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y)))))) = Z.
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 0.20/0.50 = { by lemma 2 R->L }
% 0.20/0.50 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z)), multiply(inverse(W), multiply(inverse(W), W)))))
% 0.20/0.50 = { by axiom 1 (single_axiom) }
% 0.20/0.50 Z
% 0.20/0.50
% 0.20/0.50 Lemma 4: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W)) = multiply(inverse(multiply(V, Z)), multiply(V, W)).
% 0.20/0.50 Proof:
% 0.20/0.50 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))
% 0.20/0.50 = { by lemma 3 R->L }
% 0.20/0.50 multiply(inverse(multiply(V, Z)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), multiply(inverse(Z), multiply(inverse(Z), Z))))))
% 0.20/0.50 = { by lemma 2 }
% 0.20/0.50 multiply(inverse(multiply(V, Z)), multiply(V, multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), multiply(inverse(Y), multiply(inverse(Y), Y)))))))
% 0.20/0.50 = { by axiom 1 (single_axiom) }
% 0.20/0.51 multiply(inverse(multiply(V, Z)), multiply(V, W))
% 0.20/0.51
% 0.20/0.51 Lemma 5: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(Y), multiply(inverse(Y), Y)))) = Z.
% 0.20/0.51 Proof:
% 0.20/0.51 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 0.20/0.51 = { by lemma 2 }
% 0.20/0.51 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Z)), multiply(inverse(V), multiply(inverse(V), V)))))
% 0.20/0.51 = { by axiom 1 (single_axiom) }
% 0.20/0.51 Z
% 0.20/0.51
% 0.20/0.51 Lemma 6: multiply(X, multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(X, multiply(inverse(Z), multiply(inverse(Z), Z))))))) = multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W))).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(X, multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(X, multiply(inverse(Z), multiply(inverse(Z), Z)))))))
% 0.20/0.51 = { by lemma 5 R->L }
% 0.20/0.51 multiply(X, multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(Z), multiply(inverse(Z), Z)))))))
% 0.20/0.51 = { by lemma 3 }
% 0.20/0.51 multiply(X, multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U))))
% 0.20/0.51 = { by lemma 5 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U))))
% 0.20/0.51 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(U), multiply(inverse(U), U)))))))
% 0.20/0.51 = { by lemma 2 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), multiply(inverse(U), U))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), U))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), U))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), U)))), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), U))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.51 = { by lemma 3 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), U)))), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), U))))), multiply(inverse(S), multiply(inverse(S), S))))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.51 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), U)))), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), U))))))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(S), multiply(inverse(S), S))))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.51 = { by lemma 2 R->L }
% 0.20/0.51 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(X2, inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(inverse(multiply(inverse(U), U)), U))), Z2)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(multiply(inverse(U), U)), U)), multiply(inverse(multiply(inverse(U), U)), U))))), multiply(inverse(Z2), multiply(inverse(Z2), Z2))))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(S), multiply(inverse(S), S))))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.52 = { by lemma 2 }
% 0.20/0.52 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(X2, inverse(multiply(inverse(inverse(multiply(multiply(X2, inverse(multiply(inverse(Z2), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(Z2), multiply(inverse(Z2), Z2))))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(S), multiply(inverse(S), S))))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.52 = { by lemma 2 R->L }
% 0.20/0.52 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(X2, inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), W)), Z2)), multiply(inverse(W), multiply(inverse(W), W)))), multiply(inverse(Z2), multiply(inverse(Z2), Z2))))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(S), multiply(inverse(S), S))))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.52 = { by lemma 2 }
% 0.20/0.52 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), inverse(multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W)))))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(S), multiply(inverse(S), S))))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.52 = { by axiom 1 (single_axiom) }
% 0.20/0.52 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W)))), multiply(inverse(S), multiply(inverse(S), S))))))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.52 = { by lemma 3 }
% 0.20/0.52 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W)))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(multiply(inverse(U), multiply(inverse(U), U))), multiply(inverse(U), multiply(inverse(U), U))))))))
% 0.20/0.52 = { by lemma 3 }
% 0.20/0.52 multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W)))
% 0.20/0.52
% 0.20/0.52 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.20/0.52 Proof:
% 0.20/0.52 multiply(inverse(a1), a1)
% 0.20/0.52 = { by lemma 3 R->L }
% 0.20/0.52 multiply(inverse(a1), multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(a1), multiply(inverse(Y), multiply(inverse(Y), Y)))))))
% 0.20/0.52 = { by lemma 6 }
% 0.20/0.52 multiply(inverse(multiply(inverse(Z), multiply(inverse(Z), Z))), multiply(inverse(Z), multiply(inverse(Z), Z)))
% 0.20/0.52 = { by lemma 6 R->L }
% 0.20/0.52 multiply(inverse(b1), multiply(inverse(multiply(W, V)), multiply(W, inverse(multiply(inverse(b1), multiply(inverse(V), multiply(inverse(V), V)))))))
% 0.20/0.52 = { by lemma 3 }
% 0.20/0.52 multiply(inverse(b1), b1)
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52
% 0.20/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------