TSTP Solution File: BOO068-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO068-1 : 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 : n031.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 : Wed Aug 30 18:11:36 EDT 2023
% Result : Unsatisfiable 2.52s 0.78s
% Output : Proof 3.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : BOO068-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 08:19:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.52/0.78 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 2.52/0.78
% 2.52/0.78 % SZS status Unsatisfiable
% 2.52/0.78
% 3.28/0.80 % SZS output start Proof
% 3.28/0.80 Axiom 1 (single_axiom): multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, V), U, multiply(Z, W, T))), multiply(W, multiply(T, U, V), Z)) = Y.
% 3.28/0.80
% 3.28/0.80 Lemma 2: multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, multiply(V, multiply(U, T, S), X2)), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(Z, W, multiply(Y2, inverse(Y2), Z2)))), multiply(W, Z2, Z)) = Y.
% 3.28/0.80 Proof:
% 3.28/0.80 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, multiply(V, multiply(U, T, S), X2)), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(Z, W, multiply(Y2, inverse(Y2), Z2)))), multiply(W, Z2, Z))
% 3.28/0.80 = { by axiom 1 (single_axiom) R->L }
% 3.28/0.80 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, multiply(V, multiply(U, T, S), X2)), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(Z, W, multiply(Y2, inverse(Y2), Z2)))), multiply(W, multiply(multiply(Y2, inverse(Y2), Z2), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(V, multiply(U, T, S), X2)), Z))
% 3.28/0.80 = { by axiom 1 (single_axiom) }
% 3.28/0.80 Y
% 3.28/0.80
% 3.28/0.80 Lemma 3: multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, inverse(Z), multiply(W, inverse(W), V))), multiply(inverse(Z), V, Z)) = Y.
% 3.28/0.80 Proof:
% 3.28/0.80 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, inverse(Z), multiply(W, inverse(W), V))), multiply(inverse(Z), V, Z))
% 3.28/0.80 = { by axiom 1 (single_axiom) R->L }
% 3.28/0.80 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, multiply(multiply(U, inverse(U), inverse(Z)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(S, multiply(Z2, Y2, X2), T)), multiply(W, inverse(W), V))), multiply(inverse(Z), V, Z))
% 3.28/0.80 = { by lemma 2 R->L }
% 3.28/0.80 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), multiply(Z, multiply(multiply(U, inverse(U), inverse(Z)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(S, multiply(Z2, Y2, X2), T)), multiply(W, inverse(W), V))), inverse(multiply(multiply(multiply(W, inverse(W), V), Z, multiply(S, multiply(Z2, Y2, X2), T)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(multiply(W, inverse(W), V), Z, multiply(U, inverse(U), inverse(Z))))), multiply(Z, inverse(Z), multiply(W, inverse(W), V)))), multiply(inverse(Z), V, Z))
% 3.28/0.80 = { by lemma 2 }
% 3.28/0.80 Y
% 3.28/0.80
% 3.28/0.80 Lemma 4: multiply(inverse(X), Y, X) = Y.
% 3.28/0.80 Proof:
% 3.28/0.80 multiply(inverse(X), Y, X)
% 3.28/0.80 = { by axiom 1 (single_axiom) R->L }
% 3.28/0.80 multiply(multiply(multiply(X, inverse(X), multiply(Z, inverse(Z), Y)), inverse(multiply(X, inverse(X), multiply(Z, inverse(Z), Y))), multiply(inverse(X), Y, X)), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 3.28/0.80 = { by lemma 3 }
% 3.28/0.80 multiply(multiply(Z, inverse(Z), Y), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 3.28/0.80 = { by axiom 1 (single_axiom) }
% 3.28/0.80 Y
% 3.28/0.80
% 3.28/0.80 Lemma 5: multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V)) = multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z).
% 3.28/0.80 Proof:
% 3.28/0.80 multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 3.28/0.80 = { by axiom 1 (single_axiom) R->L }
% 3.28/0.80 multiply(multiply(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 3.28/0.80 = { by axiom 1 (single_axiom) }
% 3.28/0.80 multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)
% 3.28/0.80
% 3.28/0.80 Lemma 6: multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), Z)), Z), X) = Y.
% 3.28/0.80 Proof:
% 3.28/0.80 multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), Z)), Z), X)
% 3.28/0.80 = { by lemma 5 R->L }
% 3.28/0.80 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 3.28/0.81 = { by axiom 1 (single_axiom) }
% 3.28/0.81 Y
% 3.28/0.81
% 3.28/0.81 Lemma 7: inverse(multiply(X, inverse(X), Y)) = inverse(Y).
% 3.28/0.81 Proof:
% 3.28/0.81 inverse(multiply(X, inverse(X), Y))
% 3.28/0.81 = { by lemma 4 R->L }
% 3.28/0.81 multiply(inverse(X), inverse(multiply(X, inverse(X), Y)), X)
% 3.28/0.81 = { by lemma 4 R->L }
% 3.28/0.81 multiply(inverse(X), multiply(inverse(Y), inverse(multiply(X, inverse(X), Y)), Y), X)
% 3.28/0.81 = { by lemma 6 }
% 3.28/0.81 inverse(Y)
% 3.28/0.81
% 3.28/0.81 Lemma 8: multiply(X, inverse(Y), Y) = X.
% 3.28/0.81 Proof:
% 3.28/0.81 multiply(X, inverse(Y), Y)
% 3.28/0.81 = { by lemma 4 R->L }
% 3.28/0.81 multiply(inverse(Z), multiply(X, inverse(Y), Y), Z)
% 3.28/0.81 = { by lemma 7 R->L }
% 3.28/0.81 multiply(inverse(Z), multiply(X, inverse(multiply(Z, inverse(Z), Y)), Y), Z)
% 3.28/0.81 = { by lemma 5 R->L }
% 3.28/0.81 multiply(multiply(Z, inverse(Z), X), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 3.28/0.81 = { by axiom 1 (single_axiom) }
% 3.28/0.81 X
% 3.28/0.81
% 3.28/0.81 Lemma 9: multiply(X, inverse(X), Y) = Y.
% 3.28/0.81 Proof:
% 3.28/0.81 multiply(X, inverse(X), Y)
% 3.28/0.81 = { by lemma 8 R->L }
% 3.28/0.81 multiply(multiply(X, inverse(X), Y), inverse(Z), Z)
% 3.28/0.81 = { by lemma 7 R->L }
% 3.28/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), Z)), Z)
% 3.28/0.81 = { by lemma 8 R->L }
% 3.28/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), Z))), Z)
% 3.28/0.81 = { by lemma 6 R->L }
% 3.28/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), Z))), multiply(inverse(Z), multiply(Z, inverse(multiply(Z, inverse(Z), W)), W), Z))
% 3.28/0.81 = { by axiom 1 (single_axiom) }
% 3.28/0.81 Y
% 3.28/0.81
% 3.28/0.81 Lemma 10: inverse(inverse(X)) = X.
% 3.28/0.81 Proof:
% 3.28/0.81 inverse(inverse(X))
% 3.28/0.81 = { by lemma 4 R->L }
% 3.28/0.81 multiply(inverse(X), inverse(inverse(X)), X)
% 3.28/0.81 = { by lemma 9 }
% 3.28/0.81 X
% 3.28/0.81
% 3.28/0.81 Lemma 11: multiply(X, Y, inverse(Y)) = X.
% 3.28/0.81 Proof:
% 3.28/0.81 multiply(X, Y, inverse(Y))
% 3.28/0.81 = { by lemma 10 R->L }
% 3.28/0.81 multiply(X, inverse(inverse(Y)), inverse(Y))
% 3.28/0.81 = { by lemma 8 }
% 3.28/0.81 X
% 3.28/0.81
% 3.28/0.81 Lemma 12: multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, W, Z)), multiply(multiply(Z, inverse(multiply(V, inverse(V), U)), U), multiply(V, W, V), inverse(V))) = Y.
% 3.28/0.81 Proof:
% 3.28/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, W, Z)), multiply(multiply(Z, inverse(multiply(V, inverse(V), U)), U), multiply(V, W, V), inverse(V)))
% 3.28/0.81 = { by axiom 1 (single_axiom) R->L }
% 3.28/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, W, multiply(multiply(V, inverse(V), Z), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(S, multiply(Z2, Y2, X2), T)))), multiply(multiply(Z, inverse(multiply(V, inverse(V), U)), U), multiply(V, W, V), inverse(V)))
% 3.28/0.81 = { by lemma 5 }
% 3.28/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, W, multiply(inverse(V), multiply(Z, inverse(multiply(V, inverse(V), U)), U), V))), multiply(multiply(Z, inverse(multiply(V, inverse(V), U)), U), multiply(V, W, V), inverse(V)))
% 3.28/0.81 = { by lemma 6 R->L }
% 3.28/0.81 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(inverse(V), multiply(Z, inverse(multiply(V, inverse(V), U)), U), V), W, multiply(inverse(V), multiply(Z, inverse(multiply(V, inverse(V), U)), U), V))), multiply(multiply(Z, inverse(multiply(V, inverse(V), U)), U), multiply(V, W, V), inverse(V)))
% 3.28/0.81 = { by axiom 1 (single_axiom) }
% 3.28/0.81 Y
% 3.28/0.81
% 3.28/0.81 Lemma 13: multiply(X, inverse(multiply(Y, Z, Y)), Y) = X.
% 3.28/0.81 Proof:
% 3.28/0.81 multiply(X, inverse(multiply(Y, Z, Y)), Y)
% 3.28/0.81 = { by lemma 8 R->L }
% 3.28/0.81 multiply(X, inverse(multiply(Y, Z, Y)), multiply(Y, inverse(W), W))
% 3.28/0.81 = { by lemma 7 R->L }
% 3.28/0.81 multiply(X, inverse(multiply(Y, Z, Y)), multiply(Y, inverse(multiply(inverse(Z), inverse(inverse(Z)), W)), W))
% 3.28/0.81 = { by lemma 11 R->L }
% 3.28/0.81 multiply(X, inverse(multiply(Y, Z, Y)), multiply(multiply(Y, inverse(multiply(inverse(Z), inverse(inverse(Z)), W)), W), inverse(Z), inverse(inverse(Z))))
% 3.28/0.81 = { by lemma 9 R->L }
% 3.28/0.81 multiply(multiply(V, inverse(V), X), inverse(multiply(Y, Z, Y)), multiply(multiply(Y, inverse(multiply(inverse(Z), inverse(inverse(Z)), W)), W), inverse(Z), inverse(inverse(Z))))
% 3.28/0.81 = { by lemma 3 R->L }
% 3.28/0.81 multiply(multiply(V, inverse(V), X), inverse(multiply(Y, Z, Y)), multiply(multiply(Y, inverse(multiply(inverse(Z), inverse(inverse(Z)), W)), W), multiply(multiply(inverse(Z), inverse(inverse(Z)), inverse(Z)), inverse(multiply(U, inverse(U), multiply(T, inverse(T), S))), multiply(inverse(U), S, U)), inverse(inverse(Z))))
% 3.28/0.81 = { by lemma 10 }
% 3.28/0.81 multiply(multiply(V, inverse(V), X), inverse(multiply(Y, Z, Y)), multiply(multiply(Y, inverse(multiply(inverse(Z), inverse(inverse(Z)), W)), W), multiply(multiply(inverse(Z), Z, inverse(Z)), inverse(multiply(U, inverse(U), multiply(T, inverse(T), S))), multiply(inverse(U), S, U)), inverse(inverse(Z))))
% 3.28/0.81 = { by lemma 9 }
% 3.28/0.81 multiply(multiply(V, inverse(V), X), inverse(multiply(Y, Z, Y)), multiply(multiply(Y, inverse(multiply(inverse(Z), inverse(inverse(Z)), W)), W), multiply(multiply(inverse(Z), Z, inverse(Z)), inverse(multiply(T, inverse(T), S)), multiply(inverse(U), S, U)), inverse(inverse(Z))))
% 3.28/0.81 = { by lemma 9 }
% 3.28/0.81 multiply(multiply(V, inverse(V), X), inverse(multiply(Y, Z, Y)), multiply(multiply(Y, inverse(multiply(inverse(Z), inverse(inverse(Z)), W)), W), multiply(multiply(inverse(Z), Z, inverse(Z)), inverse(S), multiply(inverse(U), S, U)), inverse(inverse(Z))))
% 3.28/0.81 = { by lemma 4 }
% 3.28/0.81 multiply(multiply(V, inverse(V), X), inverse(multiply(Y, Z, Y)), multiply(multiply(Y, inverse(multiply(inverse(Z), inverse(inverse(Z)), W)), W), multiply(multiply(inverse(Z), Z, inverse(Z)), inverse(S), S), inverse(inverse(Z))))
% 3.28/0.81 = { by lemma 8 }
% 3.28/0.81 multiply(multiply(V, inverse(V), X), inverse(multiply(Y, Z, Y)), multiply(multiply(Y, inverse(multiply(inverse(Z), inverse(inverse(Z)), W)), W), multiply(inverse(Z), Z, inverse(Z)), inverse(inverse(Z))))
% 3.28/0.81 = { by lemma 12 }
% 3.28/0.81 X
% 3.28/0.81
% 3.28/0.81 Lemma 14: multiply(X, Y, X) = X.
% 3.28/0.81 Proof:
% 3.28/0.81 multiply(X, Y, X)
% 3.28/0.81 = { by lemma 8 R->L }
% 3.28/0.81 multiply(multiply(X, Y, X), inverse(Z), Z)
% 3.28/0.81 = { by lemma 4 R->L }
% 3.28/0.81 multiply(multiply(X, Y, X), inverse(Z), multiply(inverse(W), Z, W))
% 3.28/0.81 = { by lemma 9 R->L }
% 3.28/0.81 multiply(multiply(X, Y, X), inverse(multiply(V, inverse(V), Z)), multiply(inverse(W), Z, W))
% 3.28/0.81 = { by lemma 9 R->L }
% 3.28/0.81 multiply(multiply(X, Y, X), inverse(multiply(W, inverse(W), multiply(V, inverse(V), Z))), multiply(inverse(W), Z, W))
% 3.28/0.81 = { by lemma 13 R->L }
% 3.28/0.81 multiply(multiply(multiply(X, Y, X), inverse(multiply(X, Y, X)), X), inverse(multiply(W, inverse(W), multiply(V, inverse(V), Z))), multiply(inverse(W), Z, W))
% 3.28/0.81 = { by lemma 3 }
% 3.28/0.81 X
% 3.28/0.81
% 3.28/0.81 Lemma 15: multiply(X, X, Y) = X.
% 3.28/0.81 Proof:
% 3.28/0.81 multiply(X, X, Y)
% 3.28/0.81 = { by lemma 8 R->L }
% 3.28/0.81 multiply(multiply(X, X, Y), inverse(Z), Z)
% 3.28/0.81 = { by lemma 14 R->L }
% 3.28/0.81 multiply(multiply(X, X, Y), inverse(Z), multiply(Z, Z, Z))
% 3.28/0.81 = { by lemma 14 R->L }
% 3.28/0.81 multiply(multiply(X, X, Y), inverse(multiply(Z, Z, Z)), multiply(Z, Z, Z))
% 3.28/0.81 = { by lemma 14 R->L }
% 3.28/0.81 multiply(multiply(X, X, Y), inverse(multiply(Z, Z, Z)), multiply(Z, multiply(Z, W, Z), Z))
% 3.28/0.81 = { by lemma 14 R->L }
% 3.28/0.81 multiply(multiply(X, X, Y), inverse(multiply(multiply(Z, Z, Z), W, multiply(Z, Z, Z))), multiply(Z, multiply(Z, W, Z), Z))
% 3.28/0.81 = { by lemma 5 }
% 3.28/0.81 multiply(X, multiply(Y, inverse(multiply(X, X, V)), V), X)
% 3.28/0.81 = { by lemma 14 }
% 3.28/0.81 X
% 3.28/0.81
% 3.28/0.81 Goal 1 (prove_tba_axioms_2): multiply(b, a, a) = a.
% 3.28/0.81 Proof:
% 3.28/0.81 multiply(b, a, a)
% 3.28/0.81 = { by lemma 8 R->L }
% 3.28/0.81 multiply(multiply(b, a, a), inverse(X), X)
% 3.28/0.81 = { by lemma 13 R->L }
% 3.28/0.81 multiply(multiply(b, a, a), inverse(X), multiply(X, inverse(multiply(X, inverse(X), X)), X))
% 3.28/0.81 = { by lemma 11 R->L }
% 3.28/0.81 multiply(multiply(b, a, a), inverse(X), multiply(multiply(X, inverse(multiply(X, inverse(X), X)), X), X, inverse(X)))
% 3.28/0.81 = { by lemma 15 R->L }
% 3.28/0.81 multiply(multiply(b, a, a), inverse(X), multiply(multiply(X, inverse(multiply(X, inverse(X), X)), X), multiply(X, X, X), inverse(X)))
% 3.28/0.81 = { by lemma 15 R->L }
% 3.28/0.81 multiply(multiply(b, a, a), inverse(multiply(X, X, X)), multiply(multiply(X, inverse(multiply(X, inverse(X), X)), X), multiply(X, X, X), inverse(X)))
% 3.28/0.81 = { by axiom 1 (single_axiom) R->L }
% 3.28/0.81 multiply(multiply(multiply(multiply(b, a, b), inverse(multiply(b, a, b)), multiply(b, a, a)), inverse(multiply(multiply(b, a, b), inverse(multiply(b, a, b)), multiply(b, a, a))), multiply(a, multiply(a, inverse(multiply(b, a, b)), b), b)), inverse(multiply(X, X, X)), multiply(multiply(X, inverse(multiply(X, inverse(X), X)), X), multiply(X, X, X), inverse(X)))
% 3.28/0.81 = { by lemma 12 }
% 3.28/0.81 multiply(a, multiply(a, inverse(multiply(b, a, b)), b), b)
% 3.28/0.81 = { by lemma 13 }
% 3.28/0.81 multiply(a, a, b)
% 3.28/0.81 = { by lemma 15 }
% 3.28/0.81 a
% 3.28/0.81 % SZS output end Proof
% 3.28/0.81
% 3.28/0.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------