TSTP Solution File: GRP598-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP598-1 : 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 : n012.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 01:19:03 EDT 2023
% Result : Unsatisfiable 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP598-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.36 % Computer : n012.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Aug 29 01:47:54 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.22/0.43 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.43
% 0.22/0.43 % SZS status Unsatisfiable
% 0.22/0.43
% 0.22/0.45 % SZS output start Proof
% 0.22/0.45 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.22/0.45 Axiom 2 (single_axiom): double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y))))) = Z.
% 0.22/0.45
% 0.22/0.45 Lemma 3: double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X)) = Z.
% 0.22/0.45 Proof:
% 0.22/0.45 double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(Z)), X))
% 0.22/0.45 = { by axiom 1 (multiply) }
% 0.22/0.45 double_divide(double_divide(X, Y), multiply(inverse(double_divide(inverse(Z), Y)), X))
% 0.22/0.45 = { by axiom 1 (multiply) }
% 0.22/0.45 double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(inverse(Z), Y)))))
% 0.22/0.45 = { by axiom 2 (single_axiom) }
% 0.22/0.45 Z
% 0.22/0.45
% 0.22/0.45 Lemma 4: multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X)) = inverse(Y).
% 0.22/0.45 Proof:
% 0.22/0.45 multiply(multiply(multiply(X, inverse(Y)), Z), double_divide(Z, X))
% 0.22/0.46 = { by axiom 1 (multiply) }
% 0.22/0.46 inverse(double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.22/0.46 = { by lemma 3 }
% 0.22/0.46 inverse(Y)
% 0.22/0.46
% 0.22/0.46 Lemma 5: double_divide(double_divide(X, Y), multiply(multiply(Y, multiply(Z, W)), X)) = double_divide(W, Z).
% 0.22/0.46 Proof:
% 0.22/0.46 double_divide(double_divide(X, Y), multiply(multiply(Y, multiply(Z, W)), X))
% 0.22/0.46 = { by axiom 1 (multiply) }
% 0.22/0.46 double_divide(double_divide(X, Y), multiply(multiply(Y, inverse(double_divide(W, Z))), X))
% 0.22/0.46 = { by lemma 3 }
% 0.22/0.46 double_divide(W, Z)
% 0.22/0.46
% 0.22/0.46 Lemma 6: multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y) = inverse(W).
% 0.22/0.46 Proof:
% 0.22/0.46 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), Y)
% 0.22/0.46 = { by lemma 3 R->L }
% 0.22/0.46 multiply(multiply(multiply(multiply(multiply(X, inverse(Y)), Z), inverse(W)), double_divide(Z, X)), double_divide(double_divide(Z, X), multiply(multiply(X, inverse(Y)), Z)))
% 0.22/0.46 = { by lemma 4 }
% 0.22/0.46 inverse(W)
% 0.22/0.46
% 0.22/0.46 Lemma 7: multiply(multiply(multiply(X, multiply(Y, Z)), W), double_divide(W, X)) = multiply(Y, Z).
% 0.22/0.46 Proof:
% 0.22/0.46 multiply(multiply(multiply(X, multiply(Y, Z)), W), double_divide(W, X))
% 0.22/0.46 = { by axiom 1 (multiply) }
% 0.22/0.46 multiply(multiply(multiply(X, inverse(double_divide(Z, Y))), W), double_divide(W, X))
% 0.22/0.46 = { by lemma 4 }
% 0.22/0.46 inverse(double_divide(Z, Y))
% 0.22/0.46 = { by axiom 1 (multiply) R->L }
% 0.22/0.46 multiply(Y, Z)
% 0.22/0.46
% 0.22/0.46 Lemma 8: multiply(multiply(inverse(X), multiply(Y, Z)), X) = multiply(Y, Z).
% 0.22/0.46 Proof:
% 0.22/0.46 multiply(multiply(inverse(X), multiply(Y, Z)), X)
% 0.22/0.46 = { by lemma 3 R->L }
% 0.22/0.46 multiply(multiply(inverse(X), double_divide(double_divide(W, V), multiply(multiply(V, inverse(multiply(Y, Z))), W))), X)
% 0.22/0.46 = { by lemma 6 R->L }
% 0.22/0.46 multiply(multiply(multiply(multiply(multiply(multiply(multiply(V, inverse(multiply(Y, Z))), W), inverse(X)), double_divide(W, V)), multiply(Y, Z)), double_divide(double_divide(W, V), multiply(multiply(V, inverse(multiply(Y, Z))), W))), X)
% 0.22/0.46 = { by lemma 3 R->L }
% 0.22/0.46 multiply(multiply(multiply(multiply(multiply(multiply(multiply(V, inverse(multiply(Y, Z))), W), inverse(X)), double_divide(W, V)), multiply(Y, Z)), double_divide(double_divide(W, V), multiply(multiply(V, inverse(multiply(Y, Z))), W))), double_divide(double_divide(double_divide(W, V), multiply(multiply(V, inverse(multiply(Y, Z))), W)), multiply(multiply(multiply(multiply(V, inverse(multiply(Y, Z))), W), inverse(X)), double_divide(W, V))))
% 0.22/0.46 = { by lemma 7 }
% 0.22/0.46 multiply(Y, Z)
% 0.22/0.46
% 0.22/0.46 Lemma 9: multiply(multiply(X, Y), double_divide(Z, inverse(Z))) = multiply(X, Y).
% 0.22/0.46 Proof:
% 0.22/0.46 multiply(multiply(X, Y), double_divide(Z, inverse(Z)))
% 0.22/0.46 = { by lemma 8 R->L }
% 0.22/0.46 multiply(multiply(multiply(inverse(Z), multiply(X, Y)), Z), double_divide(Z, inverse(Z)))
% 0.22/0.46 = { by lemma 7 }
% 0.22/0.46 multiply(X, Y)
% 0.22/0.46
% 0.22/0.46 Lemma 10: multiply(multiply(inverse(X), X), inverse(Y)) = inverse(Y).
% 0.22/0.46 Proof:
% 0.22/0.46 multiply(multiply(inverse(X), X), inverse(Y))
% 0.22/0.46 = { by axiom 1 (multiply) }
% 0.22/0.46 multiply(inverse(double_divide(X, inverse(X))), inverse(Y))
% 0.22/0.46 = { by lemma 9 R->L }
% 0.22/0.46 multiply(multiply(inverse(double_divide(X, inverse(X))), inverse(Y)), double_divide(X, inverse(X)))
% 0.22/0.46 = { by lemma 3 R->L }
% 0.22/0.46 multiply(multiply(inverse(double_divide(X, inverse(X))), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), double_divide(X, inverse(X)))
% 0.22/0.46 = { by lemma 6 R->L }
% 0.22/0.46 multiply(multiply(multiply(multiply(multiply(multiply(multiply(W, inverse(inverse(Y))), Z), inverse(double_divide(X, inverse(X)))), double_divide(Z, W)), inverse(Y)), double_divide(double_divide(Z, W), multiply(multiply(W, inverse(inverse(Y))), Z))), double_divide(X, inverse(X)))
% 0.22/0.46 = { by lemma 6 }
% 0.22/0.46 inverse(Y)
% 0.22/0.46
% 0.22/0.46 Lemma 11: inverse(inverse(X)) = X.
% 0.22/0.46 Proof:
% 0.22/0.46 inverse(inverse(X))
% 0.22/0.46 = { by lemma 4 R->L }
% 0.22/0.46 inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))
% 0.22/0.46 = { by lemma 3 R->L }
% 0.22/0.46 double_divide(double_divide(W, V), multiply(multiply(V, inverse(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))))), W))
% 0.22/0.46 = { by lemma 4 R->L }
% 0.22/0.46 double_divide(double_divide(W, V), multiply(multiply(V, multiply(multiply(multiply(multiply(inverse(U), U), inverse(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))))), inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), double_divide(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))), multiply(inverse(U), U)))), W))
% 0.22/0.46 = { by lemma 5 R->L }
% 0.22/0.46 double_divide(double_divide(W, V), multiply(multiply(V, multiply(multiply(multiply(multiply(inverse(U), U), inverse(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))))), inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), double_divide(double_divide(T, S), multiply(multiply(S, multiply(multiply(inverse(U), U), inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))))), T)))), W))
% 0.22/0.46 = { by lemma 10 }
% 0.22/0.46 double_divide(double_divide(W, V), multiply(multiply(V, multiply(multiply(multiply(multiply(inverse(U), U), inverse(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))))), inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), double_divide(double_divide(T, S), multiply(multiply(S, inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), T)))), W))
% 0.22/0.46 = { by lemma 3 }
% 0.22/0.46 double_divide(double_divide(W, V), multiply(multiply(V, multiply(multiply(multiply(multiply(inverse(U), U), inverse(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))))), inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), W))
% 0.22/0.46 = { by lemma 10 }
% 0.22/0.46 double_divide(double_divide(W, V), multiply(multiply(V, multiply(multiply(inverse(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), W))
% 0.22/0.46 = { by axiom 1 (multiply) }
% 0.22/0.46 double_divide(double_divide(W, V), multiply(multiply(V, multiply(inverse(double_divide(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))), inverse(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))))), multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))), W))
% 0.22/0.46 = { by lemma 9 R->L }
% 0.22/0.46 double_divide(double_divide(W, V), multiply(multiply(V, multiply(multiply(inverse(double_divide(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))), inverse(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y)))))), multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))), double_divide(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))), inverse(inverse(multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))))))), W))
% 0.22/0.46 = { by lemma 8 }
% 0.22/0.46 double_divide(double_divide(W, V), multiply(multiply(V, multiply(multiply(multiply(Y, inverse(X)), Z), double_divide(Z, Y))), W))
% 0.22/0.46 = { by lemma 5 }
% 0.22/0.46 double_divide(double_divide(Z, Y), multiply(multiply(Y, inverse(X)), Z))
% 0.22/0.46 = { by lemma 3 }
% 0.22/0.46 X
% 0.22/0.46
% 0.22/0.46 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.22/0.46 Proof:
% 0.22/0.46 multiply(multiply(inverse(b2), b2), a2)
% 0.22/0.46 = { by lemma 11 R->L }
% 0.22/0.46 multiply(multiply(inverse(b2), b2), inverse(inverse(a2)))
% 0.22/0.46 = { by lemma 10 }
% 0.22/0.46 inverse(inverse(a2))
% 0.22/0.46 = { by lemma 11 }
% 0.22/0.46 a2
% 0.22/0.46 % SZS output end Proof
% 0.22/0.46
% 0.22/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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