TSTP Solution File: GRP595-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP595-1 : 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 : n021.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 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP595-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % 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 : n021.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 : Mon Aug 28 21:13:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.42 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.42
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.19/0.44 Axiom 2 (single_axiom): inverse(double_divide(double_divide(X, Y), inverse(double_divide(X, inverse(double_divide(Z, Y)))))) = Z.
% 0.19/0.44
% 0.19/0.44 Lemma 3: multiply(multiply(multiply(X, Y), Z), double_divide(Z, X)) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(multiply(multiply(X, Y), Z), double_divide(Z, X))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 multiply(multiply(inverse(double_divide(Y, X)), Z), double_divide(Z, X))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 multiply(inverse(double_divide(Z, inverse(double_divide(Y, X)))), double_divide(Z, X))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 inverse(double_divide(double_divide(Z, X), inverse(double_divide(Z, inverse(double_divide(Y, X))))))
% 0.19/0.44 = { by axiom 2 (single_axiom) }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Lemma 4: multiply(X, double_divide(double_divide(Y, Z), multiply(Z, X))) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(X, double_divide(double_divide(Y, Z), multiply(Z, X)))
% 0.19/0.44 = { by lemma 3 R->L }
% 0.19/0.44 multiply(multiply(multiply(multiply(Z, X), Y), double_divide(Y, Z)), double_divide(double_divide(Y, Z), multiply(Z, X)))
% 0.19/0.44 = { by lemma 3 }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Lemma 5: double_divide(multiply(X, double_divide(Y, multiply(Z, X))), Z) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 double_divide(multiply(X, double_divide(Y, multiply(Z, X))), Z)
% 0.19/0.44 = { by lemma 3 R->L }
% 0.19/0.44 multiply(multiply(multiply(multiply(multiply(Z, X), multiply(X, double_divide(Y, multiply(Z, X)))), double_divide(multiply(X, double_divide(Y, multiply(Z, X))), Z)), double_divide(Y, multiply(Z, X))), double_divide(double_divide(Y, multiply(Z, X)), multiply(multiply(Z, X), multiply(X, double_divide(Y, multiply(Z, X))))))
% 0.19/0.44 = { by lemma 3 }
% 0.19/0.44 multiply(multiply(X, double_divide(Y, multiply(Z, X))), double_divide(double_divide(Y, multiply(Z, X)), multiply(multiply(Z, X), multiply(X, double_divide(Y, multiply(Z, X))))))
% 0.19/0.44 = { by lemma 4 }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Lemma 6: multiply(X, double_divide(Y, multiply(multiply(Z, W), X))) = double_divide(multiply(W, Y), Z).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(X, double_divide(Y, multiply(multiply(Z, W), X)))
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 double_divide(multiply(W, double_divide(multiply(X, double_divide(Y, multiply(multiply(Z, W), X))), multiply(Z, W))), Z)
% 0.19/0.44 = { by lemma 5 }
% 0.19/0.44 double_divide(multiply(W, Y), Z)
% 0.19/0.44
% 0.19/0.44 Lemma 7: double_divide(multiply(X, double_divide(Y, Z)), multiply(W, multiply(Z, double_divide(X, W)))) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 double_divide(multiply(X, double_divide(Y, Z)), multiply(W, multiply(Z, double_divide(X, W))))
% 0.19/0.44 = { by lemma 6 R->L }
% 0.19/0.44 multiply(V, double_divide(double_divide(Y, Z), multiply(multiply(multiply(W, multiply(Z, double_divide(X, W))), X), V)))
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 multiply(V, double_divide(double_divide(multiply(double_divide(X, W), double_divide(double_divide(Y, Z), multiply(multiply(multiply(W, multiply(Z, double_divide(X, W))), X), double_divide(X, W)))), multiply(multiply(W, multiply(Z, double_divide(X, W))), X)), multiply(multiply(multiply(W, multiply(Z, double_divide(X, W))), X), V)))
% 0.19/0.44 = { by lemma 3 }
% 0.19/0.44 multiply(V, double_divide(double_divide(multiply(double_divide(X, W), double_divide(double_divide(Y, Z), multiply(Z, double_divide(X, W)))), multiply(multiply(W, multiply(Z, double_divide(X, W))), X)), multiply(multiply(multiply(W, multiply(Z, double_divide(X, W))), X), V)))
% 0.19/0.44 = { by lemma 4 }
% 0.19/0.44 multiply(double_divide(X, W), double_divide(double_divide(Y, Z), multiply(Z, double_divide(X, W))))
% 0.19/0.44 = { by lemma 4 }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Lemma 8: double_divide(X, multiply(Y, multiply(Z, double_divide(multiply(multiply(Z, X), W), Y)))) = W.
% 0.19/0.44 Proof:
% 0.19/0.44 double_divide(X, multiply(Y, multiply(Z, double_divide(multiply(multiply(Z, X), W), Y))))
% 0.19/0.44 = { by lemma 3 R->L }
% 0.19/0.44 double_divide(multiply(multiply(multiply(Z, X), W), double_divide(W, Z)), multiply(Y, multiply(Z, double_divide(multiply(multiply(Z, X), W), Y))))
% 0.19/0.44 = { by lemma 7 }
% 0.19/0.44 W
% 0.19/0.44
% 0.19/0.44 Lemma 9: multiply(multiply(X, double_divide(multiply(multiply(X, double_divide(Y, Z)), W), Z)), W) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(multiply(X, double_divide(multiply(multiply(X, double_divide(Y, Z)), W), Z)), W)
% 0.19/0.44 = { by lemma 8 R->L }
% 0.19/0.44 multiply(multiply(X, double_divide(multiply(multiply(X, double_divide(Y, Z)), W), Z)), double_divide(double_divide(Y, Z), multiply(Z, multiply(X, double_divide(multiply(multiply(X, double_divide(Y, Z)), W), Z)))))
% 0.19/0.44 = { by lemma 4 }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(multiply(a3, b3), c3)
% 0.19/0.44 = { by lemma 7 R->L }
% 0.19/0.44 multiply(multiply(a3, b3), double_divide(multiply(multiply(a3, multiply(b3, c3)), double_divide(c3, a3)), multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by axiom 1 (multiply) }
% 0.19/0.44 multiply(multiply(a3, b3), double_divide(inverse(double_divide(double_divide(c3, a3), multiply(a3, multiply(b3, c3)))), multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 multiply(multiply(a3, b3), double_divide(inverse(double_divide(double_divide(c3, a3), multiply(a3, multiply(b3, double_divide(multiply(multiply(b3, double_divide(c3, a3)), double_divide(c3, multiply(a3, multiply(b3, double_divide(c3, a3))))), a3))))), multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by lemma 8 }
% 0.19/0.44 multiply(multiply(a3, b3), double_divide(inverse(double_divide(c3, multiply(a3, multiply(b3, double_divide(c3, a3))))), multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by axiom 1 (multiply) R->L }
% 0.19/0.44 multiply(multiply(a3, b3), double_divide(multiply(multiply(a3, multiply(b3, double_divide(c3, a3))), c3), multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by lemma 4 R->L }
% 0.19/0.44 multiply(multiply(a3, b3), double_divide(multiply(multiply(a3, multiply(Y, double_divide(double_divide(multiply(b3, double_divide(c3, a3)), multiply(Z, multiply(a3, double_divide(b3, Z)))), multiply(multiply(Z, multiply(a3, double_divide(b3, Z))), Y)))), c3), multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by lemma 7 }
% 0.19/0.44 multiply(multiply(a3, b3), double_divide(multiply(multiply(a3, multiply(Y, double_divide(c3, multiply(multiply(Z, multiply(a3, double_divide(b3, Z))), Y)))), c3), multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by lemma 6 }
% 0.19/0.44 multiply(multiply(a3, b3), double_divide(multiply(multiply(a3, double_divide(multiply(multiply(a3, double_divide(b3, Z)), c3), Z)), c3), multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 multiply(multiply(a3, b3), double_divide(b3, multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 multiply(multiply(a3, double_divide(multiply(multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)), double_divide(b3, multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X))))), X)), double_divide(b3, multiply(X, multiply(a3, double_divide(multiply(a3, multiply(b3, c3)), X)))))
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 multiply(a3, multiply(b3, c3))
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44
% 0.19/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------