%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP443-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n013.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 11:38:54 EDT 2022
% Result : Unsatisfiable 2.24s 2.43s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of clauses : 95 ( 95 unt; 0 nHn; 2 RR)
% Number of literals : 95 ( 94 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 353 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X,multiply(Y,multiply(multiply(Z,inverse(Z)),inverse(multiply(U,multiply(X,Y))))))) = U,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(3,plain,
inverse(multiply(X,multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,multiply(U,X)))),multiply(multiply(V,inverse(V)),Z)))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(5,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(Z,U)))),multiply(multiply(multiply(V,inverse(V)),Y),multiply(multiply(W,inverse(W)),Z)))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(6,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),U),multiply(multiply(V,inverse(V)),W)))) = multiply(multiply(X1,inverse(X1)),inverse(multiply(Y,multiply(U,W)))),
inference('PARAMODULATE',[status(thm)],[3,3,theory(equality)]) ).
cnf(26,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(Z,U))),multiply(Y,Z)))) = U,
inference('PARAMODULATE',[status(thm)],[5,6,theory(equality)]) ).
cnf(69,plain,
multiply(multiply(X,inverse(X)),Y) = multiply(multiply(Z,inverse(Z)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[26,3,theory(equality)]),single_axiom,theory(equality)]) ).
cnf(91,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,69,theory(equality)]),single_axiom,theory(equality)]) ).
cnf(102,plain,
inverse(multiply(multiply(X,inverse(X)),multiply(multiply(multiply(Y,inverse(Y)),Z),multiply(multiply(U,inverse(U)),V)))) = multiply(multiply(W,inverse(W)),inverse(multiply(inverse(multiply(X1,inverse(X1))),multiply(Z,V)))),
inference('PARAMODULATE',[status(thm)],[6,69,theory(equality)]) ).
cnf(117,plain,
multiply(X,inverse(X)) = multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z)))),
inference('PARAMODULATE',[status(thm)],[69,91,theory(equality)]) ).
cnf(118,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),multiply(Y,U)))) = inverse(U),
inference('PARAMODULATE',[status(thm)],[26,91,theory(equality)]) ).
cnf(119,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(inverse(Y),Z))),multiply(U,inverse(U))))) = Z,
inference('PARAMODULATE',[status(thm)],[26,91,theory(equality)]) ).
cnf(120,plain,
inverse(multiply(X,multiply(inverse(X),multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,multiply(U,inverse(U)))))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,91,theory(equality)]) ).
cnf(121,plain,
multiply(multiply(X,multiply(Y,multiply(multiply(Z,inverse(Z)),inverse(multiply(U,multiply(X,Y)))))),U) = multiply(V,inverse(V)),
inference('PARAMODULATE',[status(thm)],[91,single_axiom,theory(equality)]) ).
cnf(122,plain,
inverse(multiply(inverse(X),multiply(multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,multiply(U,inverse(U))))),multiply(multiply(V,inverse(V)),Z)))) = X,
inference('PARAMODULATE',[status(thm)],[3,91,theory(equality)]) ).
cnf(128,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),U),multiply(multiply(V,inverse(V)),inverse(U))))) = multiply(multiply(W,inverse(W)),inverse(multiply(Y,multiply(X1,inverse(X1))))),
inference('PARAMODULATE',[status(thm)],[6,91,theory(equality)]) ).
cnf(136,plain,
inverse(multiply(multiply(X,inverse(X)),multiply(inverse(multiply(Y,inverse(Y))),multiply(multiply(Z,inverse(Z)),inverse(multiply(U,multiply(V,inverse(V)))))))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,117,theory(equality)]) ).
cnf(272,plain,
inverse(multiply(X,multiply(Y,inverse(Y)))) = inverse(multiply(X,multiply(Z,inverse(Z)))),
inference('PARAMODULATE',[status(thm)],[single_axiom,118,theory(equality)]) ).
cnf(273,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,multiply(Z,inverse(Z)))),multiply(U,inverse(U))))) = inverse(inverse(Y)),
inference('PARAMODULATE',[status(thm)],[118,91,theory(equality)]) ).
cnf(275,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z)))),multiply(multiply(U,inverse(U)),V)))) = inverse(V),
inference('PARAMODULATE',[status(thm)],[118,69,theory(equality)]) ).
cnf(278,plain,
inverse(inverse(multiply(X,inverse(X)))) = inverse(inverse(multiply(Y,inverse(Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,117,theory(equality)]),273,theory(equality)]) ).
cnf(307,plain,
multiply(X,inverse(X)) = multiply(inverse(multiply(Y,inverse(Y))),inverse(inverse(multiply(Z,inverse(Z))))),
inference('PARAMODULATE',[status(thm)],[91,278,theory(equality)]) ).
cnf(342,plain,
multiply(X,inverse(X)) = multiply(multiply(Y,multiply(Z,inverse(Z))),inverse(multiply(Y,multiply(U,inverse(U))))),
inference('PARAMODULATE',[status(thm)],[91,272,theory(equality)]) ).
cnf(343,plain,
inverse(multiply(multiply(X,inverse(X)),multiply(Y,inverse(Y)))) = inverse(multiply(multiply(Z,inverse(Z)),multiply(U,inverse(U)))),
inference('PARAMODULATE',[status(thm)],[272,69,theory(equality)]) ).
cnf(399,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = inverse(inverse(inverse(multiply(Y,inverse(Y))))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,307,theory(equality)]),273,theory(equality)]) ).
cnf(426,plain,
multiply(multiply(X,inverse(X)),Y) = multiply(multiply(inverse(inverse(multiply(Z,inverse(Z)))),inverse(inverse(inverse(multiply(U,inverse(U)))))),Y),
inference('PARAMODULATE',[status(thm)],[69,399,theory(equality)]) ).
cnf(493,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(X,multiply(Z,inverse(Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,342,theory(equality)]),122,theory(equality)]) ).
cnf(513,plain,
multiply(multiply(X,inverse(X)),multiply(Y,inverse(Y))) = multiply(multiply(Z,inverse(Z)),multiply(U,inverse(U))),
inference('PARAMODULATE',[status(thm)],[69,493,theory(equality)]) ).
cnf(594,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(inverse(multiply(Y,inverse(Y))),multiply(inverse(multiply(Z,inverse(Z))),U)))),multiply(multiply(V,inverse(V)),multiply(W,inverse(W))))) = U,
inference('PARAMODULATE',[status(thm)],[5,513,theory(equality)]) ).
cnf(596,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(Z,inverse(Z)),multiply(U,inverse(U))))) = multiply(multiply(V,inverse(V)),inverse(multiply(Y,multiply(inverse(multiply(W,inverse(W))),inverse(multiply(X1,inverse(X1))))))),
inference('PARAMODULATE',[status(thm)],[6,513,theory(equality)]) ).
cnf(605,plain,
inverse(multiply(X,multiply(inverse(X),Y))) = inverse(multiply(Z,multiply(inverse(Z),Y))),
inference('PARAMODULATE',[status(thm)],[single_axiom,119,theory(equality)]) ).
cnf(611,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(inverse(Y),Z)))),multiply(multiply(multiply(U,inverse(U)),V),multiply(multiply(W,inverse(W)),inverse(V))))) = Z,
inference('PARAMODULATE',[status(thm)],[6,119,theory(equality)]) ).
cnf(652,plain,
inverse(multiply(X,multiply(inverse(X),inverse(inverse(Y))))) = inverse(multiply(Y,multiply(Z,inverse(Z)))),
inference('PARAMODULATE',[status(thm)],[272,605,theory(equality)]) ).
cnf(653,plain,
multiply(X,inverse(X)) = multiply(multiply(Y,multiply(inverse(Y),Z)),inverse(multiply(U,multiply(inverse(U),Z)))),
inference('PARAMODULATE',[status(thm)],[91,605,theory(equality)]) ).
cnf(739,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(inverse(Y),inverse(inverse(inverse(multiply(Z,multiply(U,inverse(U)))))))))) = inverse(inverse(Z)),
inference('PARAMODULATE',[status(thm)],[118,652,theory(equality)]) ).
cnf(821,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),inverse(Y)),multiply(multiply(U,inverse(U)),inverse(inverse(V)))))) = multiply(multiply(W,inverse(W)),inverse(multiply(V,multiply(X1,inverse(X1))))),
inference('PARAMODULATE',[status(thm)],[6,652,theory(equality)]) ).
cnf(822,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),U),multiply(multiply(V,inverse(V)),inverse(U))))) = multiply(multiply(W,inverse(W)),inverse(multiply(X1,multiply(inverse(X1),inverse(inverse(Y)))))),
inference('PARAMODULATE',[status(thm)],[6,652,theory(equality)]) ).
cnf(890,plain,
inverse(inverse(multiply(X,multiply(inverse(X),Y)))) = inverse(inverse(multiply(Z,multiply(inverse(Z),Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[118,653,theory(equality)]),273,theory(equality)]) ).
cnf(899,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Z,multiply(inverse(Z),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,653,theory(equality)]),122,theory(equality)]) ).
cnf(919,plain,
multiply(X,multiply(inverse(X),inverse(inverse(Y)))) = multiply(Y,multiply(Z,inverse(Z))),
inference('PARAMODULATE',[status(thm)],[493,899,theory(equality)]) ).
cnf(920,plain,
multiply(X,multiply(inverse(X),multiply(Y,inverse(Y)))) = multiply(Z,multiply(inverse(Z),multiply(U,inverse(U)))),
inference('PARAMODULATE',[status(thm)],[899,493,theory(equality)]) ).
cnf(921,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(multiply(Z,inverse(Z)),multiply(inverse(multiply(U,inverse(U))),Y)),
inference('PARAMODULATE',[status(thm)],[69,899,theory(equality)]) ).
cnf(922,plain,
multiply(X,multiply(Y,multiply(inverse(Y),Z))) = multiply(U,multiply(inverse(U),multiply(inverse(inverse(X)),Z))),
inference('PARAMODULATE',[status(thm)],[899,899,theory(equality)]) ).
cnf(1037,plain,
multiply(multiply(X,inverse(X)),Y) = multiply(multiply(inverse(multiply(Z,multiply(inverse(Z),U))),inverse(inverse(multiply(V,multiply(inverse(V),U))))),Y),
inference('PARAMODULATE',[status(thm)],[69,890,theory(equality)]) ).
cnf(1619,plain,
inverse(multiply(inverse(X),multiply(multiply(Y,inverse(Y)),multiply(multiply(Z,inverse(Z)),inverse(multiply(U,multiply(inverse(U),multiply(V,inverse(V))))))))) = X,
inference('PARAMODULATE',[status(thm)],[single_axiom,920,theory(equality)]) ).
cnf(1679,plain,
inverse(multiply(X,multiply(inverse(X),inverse(multiply(multiply(multiply(Y,inverse(Y)),Z),multiply(multiply(multiply(U,inverse(U)),V),multiply(multiply(W,inverse(W)),inverse(V)))))))) = Z,
inference('PARAMODULATE',[status(thm)],[120,6,theory(equality)]) ).
cnf(1772,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),inverse(Y)),multiply(multiply(U,inverse(U)),multiply(multiply(V,inverse(V)),inverse(multiply(W,multiply(X1,inverse(X1))))))))) = multiply(multiply(Y1,inverse(Y1)),W),
inference('PARAMODULATE',[status(thm)],[6,120,theory(equality)]) ).
cnf(1964,plain,
multiply(X,multiply(inverse(X),multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z))) = multiply(multiply(U,inverse(U)),multiply(V,multiply(inverse(V),Z))),
inference('PARAMODULATE',[status(thm)],[921,899,theory(equality)]) ).
cnf(1980,plain,
inverse(multiply(inverse(X),multiply(Y,multiply(multiply(Z,inverse(Z)),inverse(multiply(multiply(U,inverse(U)),multiply(inverse(multiply(V,inverse(V))),Y))))))) = X,
inference('PARAMODULATE',[status(thm)],[single_axiom,921,theory(equality)]) ).
cnf(2000,plain,
inverse(multiply(X,multiply(inverse(X),multiply(multiply(Y,inverse(Y)),inverse(multiply(multiply(Z,inverse(Z)),multiply(inverse(multiply(U,inverse(U))),inverse(inverse(V))))))))) = V,
inference('PARAMODULATE',[status(thm)],[120,921,theory(equality)]) ).
cnf(2004,plain,
multiply(X,multiply(inverse(X),multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z))) = multiply(multiply(U,inverse(U)),multiply(multiply(V,inverse(V)),multiply(inverse(multiply(W,inverse(W))),Z))),
inference('PARAMODULATE',[status(thm)],[921,921,theory(equality)]) ).
cnf(2244,plain,
multiply(X,multiply(Y,multiply(inverse(Y),multiply(Z,inverse(Z))))) = multiply(U,multiply(inverse(U),multiply(V,multiply(inverse(V),inverse(inverse(inverse(inverse(X)))))))),
inference('PARAMODULATE',[status(thm)],[922,919,theory(equality)]) ).
cnf(2581,plain,
multiply(X,multiply(inverse(X),inverse(multiply(Y,inverse(Y))))) = multiply(Z,inverse(Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[919,121,theory(equality)]),single_axiom,theory(equality)]) ).
cnf(2683,plain,
inverse(multiply(inverse(X),multiply(inverse(multiply(Y,inverse(Y))),multiply(multiply(Z,inverse(Z)),inverse(multiply(U,inverse(U))))))) = X,
inference('PARAMODULATE',[status(thm)],[single_axiom,2581,theory(equality)]) ).
cnf(2722,plain,
inverse(X) = multiply(inverse(X),inverse(multiply(Y,inverse(Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[26,2581,theory(equality)]),118,theory(equality)]) ).
cnf(2723,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(Z,inverse(Z)),multiply(U,inverse(U))))) = multiply(multiply(V,inverse(V)),inverse(multiply(Y,inverse(multiply(W,inverse(W)))))),
inference('REWRITE',[status(thm)],[596,2722,theory(equality)]) ).
cnf(2724,plain,
X = multiply(X,inverse(multiply(Y,inverse(Y)))),
inference('PARAMODULATE',[status(thm)],[2722,3,theory(equality)]) ).
cnf(2725,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(Z,inverse(Z)),multiply(U,inverse(U))))) = multiply(multiply(V,inverse(V)),inverse(Y)),
inference('REWRITE',[status(thm)],[2723,2724,theory(equality)]) ).
cnf(2747,plain,
inverse(multiply(inverse(X),multiply(inverse(multiply(Y,inverse(Y))),multiply(Z,inverse(Z))))) = X,
inference('REWRITE',[status(thm)],[2683,2724,theory(equality)]) ).
cnf(2749,plain,
X = multiply(X,inverse(multiply(inverse(multiply(Y,inverse(Y))),inverse(inverse(multiply(Z,inverse(Z))))))),
inference('PARAMODULATE',[status(thm)],[2724,278,theory(equality)]) ).
cnf(2761,plain,
X = multiply(X,inverse(multiply(multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z))),inverse(multiply(multiply(U,inverse(U)),multiply(V,inverse(V))))))),
inference('PARAMODULATE',[status(thm)],[2724,343,theory(equality)]) ).
cnf(2767,plain,
multiply(multiply(X,inverse(X)),multiply(inverse(multiply(Y,inverse(Y))),multiply(multiply(Z,inverse(Z)),U))) = U,
inference('PARAMODULATE',[status(thm)],[26,2747,theory(equality)]) ).
cnf(2768,plain,
inverse(inverse(multiply(X,multiply(Y,inverse(Y))))) = X,
inference('REWRITE',[status(thm)],[136,2767,theory(equality)]) ).
cnf(2774,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,multiply(inverse(Y),inverse(Z))))) = inverse(inverse(Z)),
inference('REWRITE',[status(thm)],[739,2768,theory(equality)]) ).
cnf(2775,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),U),multiply(multiply(V,inverse(V)),inverse(U))))) = inverse(inverse(inverse(Y))),
inference('REWRITE',[status(thm)],[822,2774,theory(equality)]) ).
cnf(2778,plain,
inverse(multiply(X,multiply(inverse(X),inverse(inverse(inverse(Y)))))) = Y,
inference('REWRITE',[status(thm)],[1679,2775,theory(equality)]) ).
cnf(2782,plain,
inverse(inverse(inverse(inverse(multiply(X,multiply(inverse(X),Y)))))) = Y,
inference('REWRITE',[status(thm)],[611,2775,theory(equality)]) ).
cnf(2784,plain,
inverse(inverse(inverse(X))) = multiply(multiply(Y,inverse(Y)),inverse(multiply(X,multiply(Z,inverse(Z))))),
inference('REWRITE',[status(thm)],[128,2775,theory(equality)]) ).
cnf(2806,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),inverse(Y)),multiply(multiply(U,inverse(U)),inverse(inverse(inverse(V))))))) = multiply(multiply(W,inverse(W)),V),
inference('REWRITE',[status(thm)],[1772,2784,theory(equality)]) ).
cnf(2818,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(multiply(multiply(Z,inverse(Z)),inverse(Y)),multiply(multiply(U,inverse(U)),inverse(inverse(V)))))) = inverse(inverse(inverse(V))),
inference('REWRITE',[status(thm)],[821,2784,theory(equality)]) ).
cnf(2819,plain,
inverse(inverse(inverse(inverse(X)))) = multiply(multiply(Y,inverse(Y)),X),
inference('REWRITE',[status(thm)],[2806,2818,theory(equality)]) ).
cnf(2890,plain,
multiply(X,multiply(inverse(X),multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z))) = inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(U,inverse(U))),Z))))))))),
inference('REWRITE',[status(thm)],[2004,2819,theory(equality)]) ).
cnf(2892,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(Y))))))))) = Y,
inference('REWRITE',[status(thm)],[2000,2778,2819,theory(equality)]) ).
cnf(2900,plain,
inverse(multiply(inverse(X),multiply(Y,inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(Z,inverse(Z))),Y))))))))))))) = X,
inference('REWRITE',[status(thm)],[1980,2819,theory(equality)]) ).
cnf(2918,plain,
multiply(X,multiply(inverse(X),multiply(inverse(inverse(multiply(Y,inverse(Y)))),Z))) = Z,
inference('REWRITE',[status(thm)],[1964,2782,2819,theory(equality)]) ).
cnf(2920,plain,
X = inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(Y,inverse(Y))),X))))))))),
inference('REWRITE',[status(thm)],[2890,2918,theory(equality)]) ).
cnf(2921,plain,
inverse(multiply(inverse(X),multiply(Y,inverse(Y)))) = X,
inference('REWRITE',[status(thm)],[2900,2920,theory(equality)]) ).
cnf(2943,plain,
inverse(multiply(inverse(X),inverse(inverse(inverse(inverse(inverse(multiply(Y,inverse(Y))))))))) = X,
inference('REWRITE',[status(thm)],[1619,2782,2819,theory(equality)]) ).
cnf(3036,plain,
X = multiply(X,inverse(inverse(inverse(multiply(Y,inverse(Y)))))),
inference('REWRITE',[status(thm)],[2761,2943,2819,theory(equality)]) ).
cnf(3117,plain,
inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(X,inverse(X))),multiply(inverse(multiply(Y,inverse(Y))),Z))))))),inverse(inverse(inverse(inverse(multiply(U,inverse(U)))))))) = Z,
inference('REWRITE',[status(thm)],[594,2819,theory(equality)]) ).
cnf(3199,plain,
inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X))))))),inverse(inverse(inverse(inverse(Y)))))))))) = inverse(Y),
inference('REWRITE',[status(thm)],[275,2819,theory(equality)]) ).
cnf(3219,plain,
inverse(inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(X)))),inverse(inverse(inverse(inverse(Y)))))))))) = inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(Z,inverse(Z))),multiply(X,Y))))))),
inference('REWRITE',[status(thm)],[102,2819,theory(equality)]) ).
cnf(3225,plain,
inverse(multiply(inverse(X),inverse(inverse(inverse(inverse(multiply(Y,inverse(Y)))))))) = X,
inference('REWRITE',[status(thm)],[3117,3199,3219,theory(equality)]) ).
cnf(3383,plain,
inverse(inverse(inverse(inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(inverse(inverse(Y))))))))) = Y,
inference('REWRITE',[status(thm)],[2767,2819,theory(equality)]) ).
cnf(3426,plain,
inverse(inverse(inverse(inverse(X)))) = multiply(inverse(inverse(multiply(Y,inverse(Y)))),X),
inference('REWRITE',[status(thm)],[426,3036,2819,theory(equality)]) ).
cnf(3446,plain,
multiply(X,multiply(inverse(X),inverse(inverse(inverse(inverse(Y)))))) = Y,
inference('REWRITE',[status(thm)],[2918,3426,theory(equality)]) ).
cnf(3451,plain,
multiply(X,multiply(Y,multiply(inverse(Y),multiply(Z,inverse(Z))))) = multiply(U,multiply(inverse(U),X)),
inference('REWRITE',[status(thm)],[2244,3446,theory(equality)]) ).
cnf(3483,plain,
inverse(inverse(inverse(inverse(X)))) = multiply(multiply(inverse(multiply(Y,multiply(inverse(Y),Z))),inverse(inverse(multiply(U,multiply(inverse(U),Z))))),X),
inference('REWRITE',[status(thm)],[1037,2819,theory(equality)]) ).
cnf(3507,plain,
inverse(inverse(inverse(X))) = inverse(inverse(inverse(inverse(inverse(X))))),
inference('REWRITE',[status(thm)],[2725,3225,2819,theory(equality)]) ).
cnf(3525,plain,
inverse(inverse(inverse(inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(Y))))))) = Y,
inference('REWRITE',[status(thm)],[2892,3507,theory(equality)]) ).
cnf(3526,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[3383,3525,theory(equality)]) ).
cnf(3555,plain,
X = multiply(X,multiply(Y,inverse(Y))),
inference('REWRITE',[status(thm)],[2749,2921,3526,theory(equality)]) ).
cnf(3559,plain,
X = multiply(Y,multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[3451,3555,theory(equality)]) ).
cnf(3575,plain,
X = multiply(multiply(inverse(Y),Y),X),
inference('REWRITE',[status(thm)],[3483,3559,3526,theory(equality)]) ).
cnf(3576,plain,
$false,
inference('REWRITE',[status(thm)],[prove_these_axioms_2,3575,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP443-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 06:39:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.44 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 *
% 0.19/0.45 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T06:39:44
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n013.cluster.edu at 2022-06-13T06:39:44
% 2.24/2.43
% 2.24/2.43
% 2.24/2.43 #||
% 2.24/2.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.24/2.43 % SZS output start Refutation
% See solution above
% 2.24/2.47 ||#
% 2.24/2.47
% 2.24/2.47 ; Summary of computation:
% 2.24/2.47 ; 13123 formulas have been input or derived (from 49 formulas).
% 2.24/2.47 ; 3576 (27%) were retained. Of these,
% 2.24/2.47 ; 3553 (99%) were simplified or subsumed later,
% 2.24/2.47 ; 23 ( 1%) are still being kept.
% 2.24/2.47 ;
% 2.24/2.47 ; Run time in seconds excluding printing time:
% 2.24/2.47 ; 0.001 0% Read assertion file (1 call)
% 2.24/2.47 ; 0.000 0% Assert (2 calls)
% 2.24/2.47 ; 0.551 28% Process new row (11,713 calls)
% 2.24/2.47 ; 0.006 0% Resolution (96 calls)
% 2.24/2.47 ; 0.181 9% Paramodulation (48 calls)
% 2.24/2.47 ; 0.610 31% Forward simplification (11,431 calls)
% 2.24/2.47 ; 0.523 27% Backward simplification (3,576 calls)
% 2.24/2.47 ; 0.034 2% Ordering (17,066 calls)
% 2.24/2.47 ; 0.000 0% Sortal reasoning (32 calls)
% 2.24/2.47 ; 0.000 0% Purity testing (1 call)
% 2.24/2.47 ; 0.058 3% Other
% 2.24/2.47 ; 1.964 Total
% 2.24/2.47 ; 2.013 Real time
% 2.24/2.47 ;
% 2.24/2.47 ; Term-hash-array has 13,482 terms in all.
% 2.24/2.47 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 2.24/2.47 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 2.24/2.47 ; Path-index has 63 entries (9,714 at peak, 13,786 added, 13,723 deleted).
% 2.24/2.47 ; Path-index has 21,388 nodes (25,388 at peak, 33,262 added, 11,874 deleted).
% 2.24/2.47 ; Trie-index has 63 entries (9,714 at peak, 13,786 added, 13,723 deleted).
% 2.24/2.47 ; Trie-index has 259 nodes (87,065 at peak, 120,060 added, 119,801 deleted).
% 2.24/2.47 ; Retrieved 21,951 generalization terms in 122,040 calls.
% 2.24/2.47 ; Retrieved 6,629 instance terms in 3,593 calls.
% 2.24/2.47 ; Retrieved 49,013 unifiable terms in 600 calls.
% 2.24/2.47 ;
% 2.24/2.47 ; The agenda of backward simplifiable rows to process has 858 entries:
% 2.24/2.47 ; 858 with value 0
% 2.24/2.47 ; The agenda of rows to process has 207 entries:
% 2.24/2.47 ; 3 with value 40 22 with value 49 3 with value 58
% 2.24/2.47 ; 6 with value 41 17 with value 50 2 with value 59
% 2.24/2.47 ; 7 with value 42 22 with value 51 2 with value 62
% 2.24/2.47 ; 8 with value 43 18 with value 52 3 with value 63
% 2.24/2.47 ; 8 with value 44 8 with value 53 1 with value 64
% 2.24/2.47 ; 5 with value 45 14 with value 54 1 with value 65
% 2.24/2.47 ; 14 with value 46 5 with value 55 2 with value 67
% 2.24/2.47 ; 15 with value 47 2 with value 56 3 with value 68
% 2.24/2.47 ; 12 with value 48 4 with value 57
% 2.24/2.47 ; The agenda of rows to give has 19 entries:
% 2.24/2.47 ; 2 with value (4 21) 2 with value (4 25) 2 with value (4 31)
% 2.24/2.47 ; 2 with value (4 22) 2 with value (4 26) 1 with value (4 33)
% 2.24/2.47 ; 2 with value (4 23) 1 with value (4 28) 1 with value (4 35)
% 2.24/2.47 ; 4 with value (4 24)
% 2.24/2.47 Evaluation took:
% 2.24/2.47 2.014 seconds of real time
% 2.24/2.47 1.862935 seconds of user run time
% 2.24/2.47 0.150787 seconds of system run time
% 2.24/2.47 [Run times include 0.364 seconds GC run time.]
% 2.24/2.47 0 calls to %EVAL
% 2.24/2.47 0 page faults and
% 2.24/2.47 171,675,072 bytes consed.
% 2.24/2.47 :PROOF-FOUND
% 2.24/2.47 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T06:39:46
% 2.24/2.47 :PROOF-FOUND
% 2.24/2.47 *
%------------------------------------------------------------------------------