TSTP Solution File: GRP603-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP603-1 : 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 : n025.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 01:19:05 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP603-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Tue Aug 29 02:43:24 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.19/0.42 Axiom 2 (single_axiom): inverse(double_divide(inverse(double_divide(X, inverse(double_divide(Y, double_divide(X, Z))))), Z)) = Y.
% 0.19/0.42
% 0.19/0.42 Lemma 3: multiply(X, multiply(multiply(double_divide(Y, X), Z), Y)) = Z.
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(X, multiply(multiply(double_divide(Y, X), Z), Y))
% 0.19/0.42 = { by axiom 1 (multiply) }
% 0.19/0.42 multiply(X, multiply(inverse(double_divide(Z, double_divide(Y, X))), Y))
% 0.19/0.42 = { by axiom 1 (multiply) }
% 0.19/0.42 multiply(X, inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))))
% 0.19/0.42 = { by axiom 1 (multiply) }
% 0.19/0.42 inverse(double_divide(inverse(double_divide(Y, inverse(double_divide(Z, double_divide(Y, X))))), X))
% 0.19/0.42 = { by axiom 2 (single_axiom) }
% 0.19/0.42 Z
% 0.19/0.42
% 0.19/0.42 Lemma 4: multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X) = multiply(Z, multiply(W, Y)).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)
% 0.19/0.42 = { by lemma 3 R->L }
% 0.19/0.42 multiply(Z, multiply(multiply(double_divide(Y, Z), multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)), Y))
% 0.19/0.42 = { by lemma 3 }
% 0.19/0.42 multiply(Z, multiply(W, Y))
% 0.19/0.42
% 0.19/0.42 Lemma 5: multiply(double_divide(X, Y), multiply(Y, multiply(Z, X))) = Z.
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))
% 0.19/0.42 = { by lemma 4 R->L }
% 0.19/0.42 multiply(double_divide(X, Y), multiply(multiply(double_divide(W, double_divide(X, Y)), Z), W))
% 0.19/0.42 = { by lemma 3 }
% 0.19/0.42 Z
% 0.19/0.42
% 0.19/0.42 Lemma 6: double_divide(multiply(X, W), double_divide(W, Z)) = multiply(double_divide(X, Y), multiply(Y, Z)).
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(multiply(X, W), double_divide(W, Z))
% 0.19/0.42 = { by lemma 5 R->L }
% 0.19/0.42 multiply(double_divide(X, Y), multiply(Y, multiply(double_divide(multiply(X, W), double_divide(W, Z)), X)))
% 0.19/0.42 = { by lemma 5 R->L }
% 0.19/0.42 multiply(double_divide(X, Y), multiply(Y, multiply(double_divide(multiply(X, W), double_divide(W, Z)), multiply(double_divide(W, Z), multiply(Z, multiply(X, W))))))
% 0.19/0.42 = { by lemma 5 }
% 0.19/0.42 multiply(double_divide(X, Y), multiply(Y, Z))
% 0.19/0.42
% 0.19/0.42 Lemma 7: double_divide(multiply(X, Y), double_divide(Y, multiply(Z, X))) = Z.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(multiply(X, Y), double_divide(Y, multiply(Z, X)))
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.42 multiply(double_divide(X, W), multiply(W, multiply(Z, X)))
% 0.19/0.42 = { by lemma 5 }
% 0.19/0.42 Z
% 0.19/0.42
% 0.19/0.42 Lemma 8: multiply(double_divide(X, multiply(Y, Z)), multiply(Z, X)) = inverse(Y).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(double_divide(X, multiply(Y, Z)), multiply(Z, X))
% 0.19/0.42 = { by axiom 1 (multiply) }
% 0.19/0.42 inverse(double_divide(multiply(Z, X), double_divide(X, multiply(Y, Z))))
% 0.19/0.42 = { by lemma 7 }
% 0.19/0.42 inverse(Y)
% 0.19/0.42
% 0.19/0.42 Lemma 9: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(multiply(X, inverse(X)), Y)
% 0.19/0.42 = { by lemma 7 R->L }
% 0.19/0.42 multiply(multiply(double_divide(multiply(Z, W), double_divide(W, multiply(X, Z))), inverse(X)), Y)
% 0.19/0.42 = { by lemma 8 R->L }
% 0.19/0.42 multiply(multiply(double_divide(multiply(Z, W), double_divide(W, multiply(X, Z))), multiply(double_divide(W, multiply(X, Z)), multiply(Z, W))), Y)
% 0.19/0.42 = { by lemma 6 R->L }
% 0.19/0.42 multiply(double_divide(multiply(multiply(Z, W), V), double_divide(V, multiply(Z, W))), Y)
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.43 multiply(multiply(double_divide(multiply(Z, W), double_divide(W, multiply(double_divide(Y, double_divide(U, T)), Z))), multiply(double_divide(W, multiply(double_divide(Y, double_divide(U, T)), Z)), multiply(Z, W))), Y)
% 0.19/0.43 = { by lemma 8 }
% 0.19/0.43 multiply(multiply(double_divide(multiply(Z, W), double_divide(W, multiply(double_divide(Y, double_divide(U, T)), Z))), inverse(double_divide(Y, double_divide(U, T)))), Y)
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 multiply(multiply(double_divide(Y, double_divide(U, T)), inverse(double_divide(Y, double_divide(U, T)))), Y)
% 0.19/0.43 = { by lemma 4 }
% 0.19/0.43 multiply(T, multiply(inverse(double_divide(Y, double_divide(U, T))), U))
% 0.19/0.43 = { by axiom 1 (multiply) R->L }
% 0.19/0.43 multiply(T, multiply(multiply(double_divide(U, T), Y), U))
% 0.19/0.43 = { by lemma 3 }
% 0.19/0.43 Y
% 0.19/0.43
% 0.19/0.43 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(multiply(a3, b3), c3)
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 multiply(multiply(a3, b3), multiply(multiply(a3, inverse(a3)), c3))
% 0.19/0.43 = { by lemma 8 R->L }
% 0.19/0.43 multiply(multiply(a3, b3), multiply(multiply(a3, multiply(double_divide(c3, multiply(a3, b3)), multiply(b3, c3))), c3))
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 multiply(multiply(a3, b3), multiply(multiply(multiply(double_divide(multiply(a3, multiply(b3, c3)), double_divide(multiply(b3, c3), a3)), double_divide(c3, multiply(a3, b3))), multiply(a3, multiply(b3, c3))), c3))
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 multiply(multiply(a3, b3), multiply(multiply(multiply(double_divide(multiply(a3, multiply(b3, c3)), double_divide(multiply(b3, c3), multiply(multiply(X, inverse(X)), a3))), double_divide(c3, multiply(a3, b3))), multiply(a3, multiply(b3, c3))), c3))
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 multiply(multiply(a3, b3), multiply(multiply(multiply(multiply(X, inverse(X)), double_divide(c3, multiply(a3, b3))), multiply(a3, multiply(b3, c3))), c3))
% 0.19/0.43 = { by lemma 9 }
% 0.19/0.43 multiply(multiply(a3, b3), multiply(multiply(double_divide(c3, multiply(a3, b3)), multiply(a3, multiply(b3, c3))), c3))
% 0.19/0.43 = { by lemma 3 }
% 0.19/0.43 multiply(a3, multiply(b3, c3))
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43
% 0.19/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------