TSTP Solution File: GRP082-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP082-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n008.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 : 600s
% DateTime : Sat Jul 16 11:36:04 EDT 2022
% Result : Unsatisfiable 2.13s 2.39s
% Output : Refutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 3
% Syntax : Number of clauses : 108 ( 104 unt; 0 nHn; 8 RR)
% Number of literals : 114 ( 113 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 404 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,double_divide(Y,Z))),double_divide(U,double_divide(Y,U))))) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X,Y) = inverse(double_divide(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(4,plain,
( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
| inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
inference('REWRITE',[status(thm)],[prove_these_axioms,multiply,theory(equality)]) ).
cnf(5,plain,
double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,double_divide(inverse(U),Z))))) = inverse(double_divide(inverse(double_divide(U,double_divide(V,Y))),double_divide(W,double_divide(V,W)))),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(7,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(inverse(X),Z)))),double_divide(U,double_divide(Y,U)))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,5,theory(equality)]) ).
cnf(8,plain,
double_divide(inverse(X),double_divide(inverse(Y),inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(U,double_divide(inverse(X),U)))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,5,theory(equality)]) ).
cnf(11,plain,
double_divide(inverse(inverse(double_divide(X,double_divide(Y,Z)))),inverse(double_divide(double_divide(inverse(U),inverse(double_divide(inverse(double_divide(U,Z)),double_divide(V,double_divide(inverse(X),V))))),double_divide(W,double_divide(X1,W))))) = double_divide(Y,X1),
inference('PARAMODULATE',[status(thm)],[single_axiom,5,theory(equality)]) ).
cnf(20,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(inverse(double_divide(Y,double_divide(Z,double_divide(U,double_divide(X,U))))),double_divide(V,double_divide(Z,V)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,5,theory(equality)]),11,theory(equality)]) ).
cnf(26,plain,
double_divide(inverse(inverse(double_divide(X,double_divide(Y,double_divide(inverse(X),Z))))),inverse(double_divide(Z,double_divide(U,double_divide(V,U))))) = double_divide(Y,V),
inference('PARAMODULATE',[status(thm)],[single_axiom,7,theory(equality)]) ).
cnf(36,plain,
double_divide(X,double_divide(inverse(Y),inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(U,double_divide(X,U)))))) = Z,
inference('PARAMODULATE',[status(thm)],[8,7,theory(equality)]) ).
cnf(37,plain,
inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,double_divide(U,Z)))) = inverse(double_divide(inverse(double_divide(X,Y)),double_divide(V,double_divide(U,V)))),
inference('PARAMODULATE',[status(thm)],[7,36,theory(equality)]) ).
cnf(42,plain,
double_divide(X,double_divide(Y,X)) = double_divide(Z,double_divide(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[36,7,theory(equality)]),26,theory(equality)]) ).
cnf(56,plain,
double_divide(X,double_divide(Y,X)) = double_divide(double_divide(Z,Y),double_divide(U,double_divide(Z,U))),
inference('PARAMODULATE',[status(thm)],[42,42,theory(equality)]) ).
cnf(57,plain,
double_divide(inverse(X),inverse(double_divide(inverse(double_divide(Y,double_divide(Z,Y))),double_divide(U,double_divide(Z,U))))) = X,
inference('PARAMODULATE',[status(thm)],[single_axiom,42,theory(equality)]) ).
cnf(58,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(inverse(X),Y)))),double_divide(Z,double_divide(U,Z)))) = U,
inference('PARAMODULATE',[status(thm)],[7,42,theory(equality)]) ).
cnf(73,plain,
double_divide(X,double_divide(double_divide(Y,Z),X)) = double_divide(double_divide(U,double_divide(Y,U)),double_divide(V,double_divide(Z,V))),
inference('PARAMODULATE',[status(thm)],[42,56,theory(equality)]) ).
cnf(82,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(Z,Y)))),double_divide(U,double_divide(double_divide(V,Z),U)))) = double_divide(V,inverse(X)),
inference('PARAMODULATE',[status(thm)],[7,56,theory(equality)]) ).
cnf(146,plain,
double_divide(inverse(X),double_divide(Y,inverse(double_divide(Z,double_divide(Y,Z))))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,73,theory(equality)]),82,theory(equality)]) ).
cnf(173,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(double_divide(Z,double_divide(U,Z)),double_divide(V,double_divide(W,V)))))),double_divide(X1,double_divide(Y,X1)))) = double_divide(double_divide(U,W),inverse(X)),
inference('PARAMODULATE',[status(thm)],[7,73,theory(equality)]) ).
cnf(189,plain,
double_divide(X,double_divide(inverse(Y),X)) = double_divide(double_divide(Z,inverse(double_divide(U,double_divide(Z,U)))),Y),
inference('PARAMODULATE',[status(thm)],[42,146,theory(equality)]) ).
cnf(190,plain,
double_divide(inverse(X),double_divide(Y,inverse(double_divide(double_divide(Z,Y),double_divide(U,double_divide(Z,U)))))) = X,
inference('PARAMODULATE',[status(thm)],[146,42,theory(equality)]) ).
cnf(347,plain,
double_divide(X,double_divide(Y,inverse(double_divide(Z,double_divide(Y,Z))))) = double_divide(inverse(double_divide(U,double_divide(V,double_divide(inverse(U),V)))),double_divide(W,double_divide(X,W))),
inference('PARAMODULATE',[status(thm)],[146,58,theory(equality)]) ).
cnf(353,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(inverse(X),Y)))),double_divide(double_divide(inverse(Z),inverse(double_divide(inverse(double_divide(Z,U)),double_divide(V,double_divide(W,V))))),U))) = W,
inference('PARAMODULATE',[status(thm)],[58,36,theory(equality)]) ).
cnf(368,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(inverse(X),Y)))),double_divide(inverse(double_divide(inverse(double_divide(Z,U)),double_divide(V,double_divide(inverse(W),V)))),inverse(double_divide(inverse(double_divide(W,double_divide(X1,U))),double_divide(Y1,double_divide(X1,Y1))))))) = inverse(Z),
inference('PARAMODULATE',[status(thm)],[58,5,theory(equality)]) ).
cnf(436,plain,
double_divide(X,double_divide(inverse(Y),X)) = double_divide(double_divide(Z,inverse(double_divide(double_divide(inverse(U),inverse(double_divide(inverse(double_divide(U,V)),double_divide(W,double_divide(Z,W))))),V))),Y),
inference('PARAMODULATE',[status(thm)],[189,36,theory(equality)]) ).
cnf(437,plain,
double_divide(X,double_divide(inverse(Y),inverse(double_divide(inverse(double_divide(double_divide(Z,inverse(double_divide(U,double_divide(Z,U)))),V)),double_divide(W,double_divide(X,W)))))) = double_divide(inverse(V),Y),
inference('PARAMODULATE',[status(thm)],[36,189,theory(equality)]) ).
cnf(449,plain,
inverse(double_divide(X,double_divide(Y,inverse(double_divide(Z,double_divide(Y,Z)))))) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[58,189,theory(equality)]),58,theory(equality)]) ).
cnf(467,plain,
inverse(double_divide(X,double_divide(Y,X))) = inverse(double_divide(Z,double_divide(Y,Z))),
inference('PARAMODULATE',[status(thm)],[449,42,theory(equality)]) ).
cnf(468,plain,
inverse(double_divide(double_divide(X,Y),double_divide(Z,double_divide(X,Z)))) = inverse(double_divide(U,double_divide(Y,U))),
inference('PARAMODULATE',[status(thm)],[449,56,theory(equality)]) ).
cnf(470,plain,
inverse(double_divide(X,double_divide(Y,inverse(double_divide(double_divide(Z,Y),double_divide(U,double_divide(Z,U))))))) = X,
inference('PARAMODULATE',[status(thm)],[449,42,theory(equality)]) ).
cnf(472,plain,
inverse(double_divide(double_divide(X,inverse(double_divide(Y,double_divide(X,Y)))),Z)) = inverse(double_divide(U,double_divide(inverse(Z),U))),
inference('PARAMODULATE',[status(thm)],[449,189,theory(equality)]) ).
cnf(521,plain,
double_divide(X,inverse(inverse(double_divide(Y,double_divide(Z,double_divide(inverse(Y),U)))))) = inverse(double_divide(U,double_divide(V,double_divide(double_divide(X,Z),V)))),
inference('PARAMODULATE',[status(thm)],[20,7,theory(equality)]) ).
cnf(522,plain,
double_divide(X,inverse(inverse(double_divide(Y,double_divide(Z,double_divide(inverse(Y),Z)))))) = inverse(double_divide(U,double_divide(V,double_divide(double_divide(X,U),V)))),
inference('PARAMODULATE',[status(thm)],[20,58,theory(equality)]) ).
cnf(559,plain,
double_divide(double_divide(X,double_divide(Y,X)),inverse(Z)) = double_divide(double_divide(U,double_divide(Y,U)),inverse(Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,73,theory(equality)]),173,theory(equality)]) ).
cnf(619,plain,
double_divide(double_divide(X,double_divide(Y,X)),Z) = double_divide(double_divide(U,double_divide(Y,U)),Z),
inference('PARAMODULATE',[status(thm)],[559,7,theory(equality)]) ).
cnf(972,plain,
inverse(double_divide(X,double_divide(Y,double_divide(Z,Y)))) = inverse(double_divide(X,double_divide(U,double_divide(Z,U)))),
inference('PARAMODULATE',[status(thm)],[37,7,theory(equality)]) ).
cnf(974,plain,
inverse(double_divide(X,double_divide(double_divide(Y,Z),double_divide(U,double_divide(Y,U))))) = inverse(double_divide(X,double_divide(V,double_divide(Z,V)))),
inference('PARAMODULATE',[status(thm)],[972,42,theory(equality)]) ).
cnf(1015,plain,
inverse(double_divide(X,double_divide(inverse(Y),X))) = inverse(double_divide(double_divide(Z,inverse(double_divide(double_divide(U,Z),double_divide(V,double_divide(U,V))))),Y)),
inference('PARAMODULATE',[status(thm)],[467,190,theory(equality)]) ).
cnf(1058,plain,
double_divide(X,double_divide(Y,X)) = double_divide(double_divide(Z,double_divide(inverse(Y),Z)),double_divide(U,double_divide(double_divide(V,inverse(double_divide(double_divide(W,V),double_divide(X1,double_divide(W,X1))))),U))),
inference('PARAMODULATE',[status(thm)],[73,190,theory(equality)]) ).
cnf(1110,plain,
inverse(double_divide(double_divide(X,inverse(Y)),double_divide(Z,double_divide(X,Z)))) = inverse(double_divide(double_divide(U,inverse(double_divide(double_divide(V,U),double_divide(W,double_divide(V,W))))),Y)),
inference('PARAMODULATE',[status(thm)],[468,190,theory(equality)]) ).
cnf(1156,plain,
inverse(double_divide(double_divide(X,inverse(Y)),double_divide(Z,double_divide(X,Z)))) = inverse(double_divide(inverse(double_divide(inverse(double_divide(Y,U)),double_divide(V,double_divide(inverse(W),V)))),inverse(double_divide(inverse(double_divide(W,double_divide(X1,U))),double_divide(Y1,double_divide(X1,Y1)))))),
inference('PARAMODULATE',[status(thm)],[468,5,theory(equality)]) ).
cnf(1661,plain,
inverse(double_divide(X,double_divide(Y,double_divide(Z,double_divide(inverse(Y),Z))))) = inverse(double_divide(X,double_divide(U,double_divide(double_divide(V,inverse(double_divide(double_divide(W,V),double_divide(X1,double_divide(W,X1))))),U)))),
inference('PARAMODULATE',[status(thm)],[974,190,theory(equality)]) ).
cnf(1689,plain,
double_divide(X,Y) = inverse(double_divide(Z,double_divide(X,double_divide(inverse(Z),inverse(double_divide(U,double_divide(Y,U))))))),
inference('PARAMODULATE',[status(thm)],[57,26,theory(equality)]) ).
cnf(1731,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(inverse(X),Y)))),double_divide(inverse(double_divide(Z,double_divide(U,double_divide(V,U)))),double_divide(W,V)))) = inverse(inverse(double_divide(X1,double_divide(W,double_divide(inverse(X1),Z))))),
inference('PARAMODULATE',[status(thm)],[58,26,theory(equality)]) ).
cnf(1831,plain,
double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
inference('PARAMODULATE',[status(thm)],[1689,146,theory(equality)]) ).
cnf(2051,plain,
double_divide(X,inverse(double_divide(double_divide(inverse(double_divide(double_divide(Y,inverse(double_divide(Z,double_divide(Y,Z)))),U)),double_divide(V,double_divide(X,V))),W))) = double_divide(inverse(U),W),
inference('REWRITE',[status(thm)],[437,1831,theory(equality)]) ).
cnf(2072,plain,
inverse(double_divide(inverse(double_divide(X,double_divide(Y,double_divide(inverse(X),Y)))),double_divide(inverse(double_divide(double_divide(inverse(double_divide(Z,U)),double_divide(V,double_divide(W,V))),Z)),U))) = W,
inference('REWRITE',[status(thm)],[353,1831,theory(equality)]) ).
cnf(2129,plain,
double_divide(X,double_divide(inverse(Y),X)) = double_divide(double_divide(Z,inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(U,V)),double_divide(W,double_divide(Z,W))),U)),V))),Y),
inference('REWRITE',[status(thm)],[436,1831,theory(equality)]) ).
cnf(2182,plain,
double_divide(X,inverse(double_divide(double_divide(inverse(double_divide(Y,Z)),double_divide(U,double_divide(X,U))),Y))) = Z,
inference('REWRITE',[status(thm)],[36,1831,theory(equality)]) ).
cnf(2205,plain,
inverse(inverse(double_divide(double_divide(double_divide(inverse(double_divide(X,double_divide(Y,Z))),double_divide(U,double_divide(Y,U))),double_divide(inverse(double_divide(V,Z)),double_divide(W,double_divide(inverse(X),W)))),double_divide(X1,double_divide(Y1,double_divide(inverse(X1),Y1)))))) = inverse(V),
inference('REWRITE',[status(thm)],[368,1831,theory(equality)]) ).
cnf(2214,plain,
inverse(double_divide(double_divide(X,inverse(Y)),double_divide(Z,double_divide(X,Z)))) = inverse(inverse(double_divide(double_divide(inverse(double_divide(U,double_divide(V,W))),double_divide(X1,double_divide(V,X1))),double_divide(inverse(double_divide(Y,W)),double_divide(Y1,double_divide(inverse(U),Y1)))))),
inference('REWRITE',[status(thm)],[1156,1831,theory(equality)]) ).
cnf(2252,plain,
inverse(double_divide(double_divide(inverse(double_divide(X,double_divide(Y,Z))),double_divide(U,double_divide(Y,U))),X)) = Z,
inference('REWRITE',[status(thm)],[single_axiom,1831,theory(equality)]) ).
cnf(2338,plain,
double_divide(X,double_divide(inverse(Y),X)) = inverse(double_divide(double_divide(Z,Y),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,1831,theory(equality)]),1831,theory(equality)]) ).
cnf(2371,plain,
double_divide(inverse(X),Y) = inverse(double_divide(double_divide(Y,double_divide(Z,inverse(double_divide(U,double_divide(Z,U))))),X)),
inference('PARAMODULATE',[status(thm)],[1831,449,theory(equality)]) ).
cnf(2402,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(Y,double_divide(inverse(double_divide(Z,double_divide(U,double_divide(inverse(Z),U)))),double_divide(V,double_divide(X,V))))),
inference('PARAMODULATE',[status(thm)],[1831,58,theory(equality)]) ).
cnf(2404,plain,
double_divide(inverse(X),Y) = inverse(double_divide(double_divide(inverse(double_divide(Z,double_divide(U,double_divide(inverse(Z),U)))),double_divide(V,double_divide(Y,V))),X)),
inference('PARAMODULATE',[status(thm)],[1831,58,theory(equality)]) ).
cnf(2412,plain,
inverse(double_divide(double_divide(X,Y),X)) = inverse(double_divide(double_divide(Z,Y),Z)),
inference('PARAMODULATE',[status(thm)],[2338,2338,theory(equality)]) ).
cnf(2521,plain,
double_divide(X,double_divide(double_divide(Y,inverse(Z)),X)) = inverse(double_divide(double_divide(U,double_divide(inverse(double_divide(Z,double_divide(V,double_divide(W,double_divide(Y,W))))),double_divide(X1,double_divide(V,X1)))),U)),
inference('PARAMODULATE',[status(thm)],[2338,20,theory(equality)]) ).
cnf(2540,plain,
double_divide(double_divide(X,Y),X) = double_divide(double_divide(Z,Y),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[146,2412,theory(equality)]),146,theory(equality)]) ).
cnf(2543,plain,
inverse(double_divide(X,inverse(X))) = double_divide(inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2412,146,theory(equality)]),2371,theory(equality)]) ).
cnf(2575,plain,
double_divide(double_divide(X,double_divide(Y,Z)),X) = double_divide(double_divide(U,double_divide(Y,U)),Z),
inference('PARAMODULATE',[status(thm)],[619,2540,theory(equality)]) ).
cnf(2666,plain,
double_divide(inverse(X),X) = double_divide(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[2543,2543,theory(equality)]) ).
cnf(2667,plain,
inverse(double_divide(X,inverse(X))) = inverse(double_divide(Y,inverse(Y))),
inference('PARAMODULATE',[status(thm)],[1831,2543,theory(equality)]) ).
cnf(2668,plain,
( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
inference('REWRITE',[status(thm)],[4,2667,theory(equality)]) ).
cnf(2669,plain,
inverse(double_divide(inverse(double_divide(X,inverse(X))),Y)) = Y,
inference('PARAMODULATE',[status(thm)],[2252,2543,theory(equality)]) ).
cnf(2677,plain,
double_divide(double_divide(inverse(X),X),inverse(Y)) = inverse(double_divide(Y,double_divide(Z,inverse(Z)))),
inference('PARAMODULATE',[status(thm)],[1831,2543,theory(equality)]) ).
cnf(2680,plain,
inverse(double_divide(X,double_divide(inverse(Y),X))) = inverse(double_divide(Y,inverse(double_divide(Z,inverse(Z))))),
inference('PARAMODULATE',[status(thm)],[467,2543,theory(equality)]) ).
cnf(2746,plain,
double_divide(X,inverse(double_divide(double_divide(inverse(inverse(double_divide(Y,inverse(Y)))),double_divide(Z,double_divide(X,Z))),inverse(U)))) = U,
inference('PARAMODULATE',[status(thm)],[2182,2543,theory(equality)]) ).
cnf(2751,plain,
inverse(double_divide(inverse(double_divide(X,inverse(double_divide(Y,inverse(Y))))),double_divide(Z,double_divide(inverse(double_divide(inverse(X),U)),Z)))) = U,
inference('PARAMODULATE',[status(thm)],[7,2543,theory(equality)]) ).
cnf(2789,plain,
inverse(double_divide(double_divide(inverse(X),X),Y)) = Y,
inference('PARAMODULATE',[status(thm)],[2252,2666,theory(equality)]) ).
cnf(2792,plain,
double_divide(double_divide(inverse(X),X),inverse(Y)) = double_divide(double_divide(Z,Y),Z),
inference('PARAMODULATE',[status(thm)],[2540,2666,theory(equality)]) ).
cnf(2797,plain,
inverse(X) = inverse(double_divide(double_divide(Y,X),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2412,2666,theory(equality)]),2789,theory(equality)]) ).
cnf(2802,plain,
double_divide(X,double_divide(double_divide(Y,inverse(Z)),X)) = double_divide(Y,inverse(Z)),
inference('REWRITE',[status(thm)],[2521,20,2797,theory(equality)]) ).
cnf(2806,plain,
double_divide(X,double_divide(Y,X)) = double_divide(double_divide(Z,double_divide(inverse(Y),Z)),double_divide(U,inverse(double_divide(double_divide(V,U),double_divide(W,double_divide(V,W)))))),
inference('REWRITE',[status(thm)],[1058,2802,theory(equality)]) ).
cnf(2808,plain,
inverse(double_divide(X,double_divide(Y,double_divide(Z,double_divide(inverse(Y),Z))))) = X,
inference('REWRITE',[status(thm)],[1661,470,2802,theory(equality)]) ).
cnf(2809,plain,
inverse(double_divide(double_divide(inverse(double_divide(X,double_divide(Y,Z))),double_divide(U,double_divide(Y,U))),double_divide(inverse(double_divide(V,Z)),double_divide(W,double_divide(inverse(X),W))))) = inverse(V),
inference('REWRITE',[status(thm)],[2205,2808,theory(equality)]) ).
cnf(2811,plain,
inverse(double_divide(double_divide(X,inverse(Y)),double_divide(Z,double_divide(X,Z)))) = inverse(inverse(Y)),
inference('REWRITE',[status(thm)],[2214,2809,theory(equality)]) ).
cnf(2821,plain,
inverse(inverse(X)) = inverse(double_divide(double_divide(Y,inverse(double_divide(double_divide(Z,Y),double_divide(U,double_divide(Z,U))))),X)),
inference('REWRITE',[status(thm)],[1110,2811,theory(equality)]) ).
cnf(2830,plain,
inverse(double_divide(X,double_divide(inverse(Y),X))) = inverse(inverse(Y)),
inference('REWRITE',[status(thm)],[1015,2821,theory(equality)]) ).
cnf(2845,plain,
inverse(inverse(X)) = inverse(double_divide(X,inverse(double_divide(Y,inverse(Y))))),
inference('REWRITE',[status(thm)],[2680,2830,theory(equality)]) ).
cnf(2847,plain,
inverse(double_divide(inverse(inverse(X)),double_divide(Y,double_divide(inverse(double_divide(inverse(X),Z)),Y)))) = Z,
inference('REWRITE',[status(thm)],[2751,2845,theory(equality)]) ).
cnf(2849,plain,
( inverse(inverse(a2)) != a2
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
inference('REWRITE',[status(thm)],[2668,2845,theory(equality)]) ).
cnf(2855,plain,
inverse(double_divide(double_divide(X,inverse(double_divide(Y,double_divide(X,Y)))),Z)) = inverse(inverse(Z)),
inference('REWRITE',[status(thm)],[472,2830,theory(equality)]) ).
cnf(2863,plain,
double_divide(X,inverse(double_divide(double_divide(inverse(inverse(Y)),double_divide(Z,double_divide(X,Z))),U))) = double_divide(inverse(Y),U),
inference('REWRITE',[status(thm)],[2051,2855,theory(equality)]) ).
cnf(2865,plain,
inverse(double_divide(X,double_divide(Y,inverse(Y)))) = X,
inference('REWRITE',[status(thm)],[2746,1831,2863,theory(equality)]) ).
cnf(2866,plain,
double_divide(double_divide(inverse(X),X),inverse(Y)) = Y,
inference('REWRITE',[status(thm)],[2677,2865,theory(equality)]) ).
cnf(2867,plain,
X = double_divide(double_divide(Y,X),Y),
inference('REWRITE',[status(thm)],[2792,2866,theory(equality)]) ).
cnf(2881,plain,
double_divide(X,Y) = double_divide(double_divide(Z,double_divide(X,Z)),Y),
inference('REWRITE',[status(thm)],[2575,2867,theory(equality)]) ).
cnf(2882,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference('REWRITE',[status(thm)],[2806,190,2881,theory(equality)]) ).
cnf(2883,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[2847,2867,1831,2882,theory(equality)]) ).
cnf(2888,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference('REWRITE',[status(thm)],[2849,2883,theory(equality)]) ).
cnf(2889,plain,
double_divide(X,double_divide(Y,double_divide(Z,double_divide(inverse(Y),U)))) = inverse(double_divide(U,double_divide(X,Z))),
inference('REWRITE',[status(thm)],[521,2883,2882,theory(equality)]) ).
cnf(2913,plain,
double_divide(inverse(X),Y) = inverse(double_divide(double_divide(inverse(double_divide(Z,inverse(Z))),Y),X)),
inference('REWRITE',[status(thm)],[2404,2882,theory(equality)]) ).
cnf(2914,plain,
inverse(X) = double_divide(double_divide(Y,inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(Z,U)),Y),Z)),U))),X),
inference('REWRITE',[status(thm)],[2129,2882,theory(equality)]) ).
cnf(2922,plain,
double_divide(X,double_divide(Y,inverse(Y))) = inverse(X),
inference('REWRITE',[status(thm)],[522,2883,2882,theory(equality)]) ).
cnf(2925,plain,
double_divide(inverse(double_divide(double_divide(inverse(double_divide(X,Y)),Z),X)),Y) = Z,
inference('REWRITE',[status(thm)],[2072,2669,2882,theory(equality)]) ).
cnf(2926,plain,
inverse(X) = double_divide(double_divide(Y,inverse(Y)),X),
inference('REWRITE',[status(thm)],[2914,2925,theory(equality)]) ).
cnf(2928,plain,
inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,Y))) = double_divide(Z,inverse(X)),
inference('REWRITE',[status(thm)],[82,2882,theory(equality)]) ).
cnf(2938,plain,
inverse(X) = double_divide(inverse(double_divide(Y,inverse(Y))),X),
inference('REWRITE',[status(thm)],[347,2922,2882,theory(equality)]) ).
cnf(2939,plain,
double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
inference('REWRITE',[status(thm)],[2913,2938,theory(equality)]) ).
cnf(2943,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('REWRITE',[status(thm)],[2888,2939,theory(equality)]) ).
cnf(2952,plain,
double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
inference('REWRITE',[status(thm)],[2402,2938,2882,theory(equality)]) ).
cnf(2954,plain,
double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
inference('REWRITE',[status(thm)],[2943,2952,theory(equality)]) ).
cnf(2964,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(Z,double_divide(X,double_divide(inverse(Z),Y))),
inference('REWRITE',[status(thm)],[1731,2883,2928,2926,2952,2882,theory(equality)]) ).
cnf(2968,plain,
double_divide(X,inverse(double_divide(Y,inverse(Z)))) = inverse(double_divide(Z,double_divide(X,Y))),
inference('REWRITE',[status(thm)],[2889,2964,theory(equality)]) ).
cnf(2997,plain,
double_divide(inverse(X),double_divide(Y,Z)) = inverse(double_divide(Y,inverse(double_divide(Z,X)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2968,1831,theory(equality)]),2883,1831,theory(equality)]) ).
cnf(2998,plain,
$false,
inference('REWRITE',[status(thm)],[2954,2883,2952,2997,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP082-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.12/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 06:44:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 *
% 0.18/0.45 *
% 0.18/0.45 #<PACKAGE "SNARK-USER">
% 0.18/0.45 *
% 0.18/0.45 SNARK-TPTP-OPTIONS
% 0.18/0.45 *
% 0.18/0.45 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.45 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.45 (USE-FACTORING :POS)
% 0.18/0.45 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.45 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.45 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.45 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.45 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.45 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.45 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.45 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.45 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.45 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.45 *
% 0.18/0.45 "."
% 0.18/0.45 *
% 0.18/0.45 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T06:44:22
% 0.18/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n008.cluster.edu at 2022-06-13T06:44:22
% 2.13/2.39
% 2.13/2.39
% 2.13/2.39 #||
% 2.13/2.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.13/2.39 % SZS output start Refutation
% See solution above
% 2.22/2.41 ||#
% 2.22/2.41
% 2.22/2.41 ; Summary of computation:
% 2.22/2.41 ; 11210 formulas have been input or derived (from 56 formulas).
% 2.22/2.41 ; 2998 (27%) were retained. Of these,
% 2.22/2.41 ; 2945 (98%) were simplified or subsumed later,
% 2.22/2.41 ; 53 ( 2%) are still being kept.
% 2.22/2.41 ;
% 2.22/2.41 ; Run time in seconds excluding printing time:
% 2.22/2.41 ; 0.001 0% Read assertion file (1 call)
% 2.22/2.41 ; 0.000 0% Assert (3 calls)
% 2.22/2.41 ; 0.399 21% Process new row (11,101 calls)
% 2.22/2.41 ; 0.009 0% Resolution (110 calls)
% 2.22/2.41 ; 0.181 9% Paramodulation (55 calls)
% 2.22/2.41 ; 0.000 0% Condensing (5 calls)
% 2.22/2.41 ; 0.000 0% Forward subsumption (5 calls)
% 2.22/2.41 ; 0.000 0% Backward subsumption (4 calls)
% 2.22/2.41 ; 0.000 0% Clause clause subsumption (2 calls)
% 2.22/2.41 ; 0.632 33% Forward simplification (10,129 calls)
% 2.22/2.41 ; 0.565 29% Backward simplification (2,997 calls)
% 2.22/2.41 ; 0.101 5% Ordering (34,549 calls)
% 2.22/2.41 ; 0.000 0% Sortal reasoning (32 calls)
% 2.22/2.41 ; 0.000 0% Purity testing (1 call)
% 2.22/2.41 ; 0.049 3% Other
% 2.22/2.41 ; 1.937 Total
% 2.22/2.41 ; 1.952 Real time
% 2.22/2.41 ;
% 2.22/2.41 ; Term-hash-array has 11,883 terms in all.
% 2.22/2.41 ; Feature-vector-row-index has 0 entries (2 at peak, 4 added, 4 deleted).
% 2.22/2.41 ; Feature-vector-row-index has 1 node (44 at peak, 93 added, 92 deleted).
% 2.22/2.41 ; Retrieved 1 possibly forward subsuming row in 5 calls.
% 2.22/2.41 ; Retrieved 1 possibly backward subsumed row in 4 calls.
% 2.22/2.41 ; Path-index has 221 entries (9,183 at peak, 12,707 added, 12,486 deleted).
% 2.22/2.41 ; Path-index has 9,701 nodes (13,674 at peak, 15,962 added, 6,261 deleted).
% 2.22/2.41 ; Trie-index has 221 entries (9,183 at peak, 12,707 added, 12,486 deleted).
% 2.22/2.41 ; Trie-index has 846 nodes (52,284 at peak, 72,682 added, 71,836 deleted).
% 2.22/2.41 ; Retrieved 55,028 generalization terms in 105,266 calls.
% 2.22/2.41 ; Retrieved 28,280 instance terms in 3,055 calls.
% 2.22/2.41 ; Retrieved 76,963 unifiable terms in 586 calls.
% 2.22/2.41 ;
% 2.22/2.41 ; The agenda of rows to process has 21 entries:
% 2.22/2.41 ; 1 with value 31 4 with value 34 2 with value 36
% 2.22/2.41 ; 4 with value 32 4 with value 35 4 with value 37
% 2.22/2.41 ; 2 with value 33
% 2.22/2.41 ; The agenda of rows to give has 43 entries:
% 2.22/2.41 ; 4 with value (4 23) 4 with value (4 28) 3 with value (4 32)
% 2.22/2.41 ; 7 with value (4 24) 3 with value (4 29) 2 with value (4 34)
% 2.22/2.41 ; 7 with value (4 25) 2 with value (4 30) 2 with value (4 35)
% 2.22/2.41 ; 3 with value (4 26) 1 with value (4 31) 1 with value (4 36)
% 2.22/2.41 ; 4 with value (4 27)
% 2.22/2.41 Evaluation took:
% 2.22/2.41 1.952 seconds of real time
% 2.22/2.41 1.807704 seconds of user run time
% 2.22/2.41 0.144986 seconds of system run time
% 2.22/2.41 [Run times include 0.252 seconds GC run time.]
% 2.22/2.41 0 calls to %EVAL
% 2.22/2.41 0 page faults and
% 2.22/2.41 152,196,360 bytes consed.
% 2.22/2.41 :PROOF-FOUND
% 2.22/2.41 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T06:44:24
% 2.22/2.41 :PROOF-FOUND
% 2.22/2.41 *
%------------------------------------------------------------------------------