TSTP Solution File: GRP200-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP200-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n028.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 11:37:31 EDT 2022
% Result : Unsatisfiable 2.28s 2.49s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of clauses : 113 ( 113 unt; 0 nHn; 6 RR)
% Number of literals : 113 ( 112 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 207 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(right_identity,axiom,
multiply(X,identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(multiply_left_division,axiom,
multiply(X,left_division(X,Y)) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_left_division) ).
cnf(left_division_multiply,axiom,
left_division(X,multiply(X,Y)) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_division_multiply) ).
cnf(multiply_right_division,axiom,
multiply(right_division(X,Y),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_right_division) ).
cnf(right_division_multiply,axiom,
right_division(multiply(X,Y),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_division_multiply) ).
cnf(right_inverse,axiom,
multiply(X,right_inverse(X)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(left_inverse,axiom,
multiply(left_inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(moufang1,axiom,
multiply(multiply(X,multiply(Y,Z)),X) = multiply(multiply(X,Y),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang1) ).
cnf(prove_moufang2,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang2) ).
cnf(14,plain,
left_division(X,X) = identity,
inference('PARAMODULATE',[status(thm)],[left_division_multiply,right_identity,theory(equality)]) ).
cnf(15,plain,
left_division(X,identity) = right_inverse(X),
inference('PARAMODULATE',[status(thm)],[left_division_multiply,right_inverse,theory(equality)]) ).
cnf(16,plain,
right_inverse(left_inverse(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[left_division_multiply,left_inverse,theory(equality)]),15,theory(equality)]) ).
cnf(18,plain,
left_division(right_division(X,Y),X) = Y,
inference('PARAMODULATE',[status(thm)],[left_division_multiply,multiply_right_division,theory(equality)]) ).
cnf(20,plain,
right_division(identity,X) = left_inverse(X),
inference('PARAMODULATE',[status(thm)],[right_division_multiply,left_inverse,theory(equality)]) ).
cnf(22,plain,
right_division(X,left_division(Y,X)) = Y,
inference('PARAMODULATE',[status(thm)],[right_division_multiply,multiply_left_division,theory(equality)]) ).
cnf(23,plain,
multiply(multiply(X,Y),X) = multiply(X,multiply(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[moufang1,left_identity,theory(equality)]),right_identity,theory(equality)]) ).
cnf(24,plain,
multiply(X,X) = multiply(multiply(X,left_inverse(Y)),multiply(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[moufang1,left_inverse,theory(equality)]),right_identity,theory(equality)]) ).
cnf(25,plain,
multiply(X,X) = multiply(multiply(X,Y),multiply(right_inverse(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[moufang1,right_inverse,theory(equality)]),right_identity,theory(equality)]) ).
cnf(26,plain,
right_division(multiply(multiply(X,Y),multiply(Z,X)),X) = multiply(X,multiply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[right_division_multiply,moufang1,theory(equality)]) ).
cnf(28,plain,
multiply(multiply(X,Y),X) = multiply(multiply(X,right_division(Y,Z)),multiply(Z,X)),
inference('PARAMODULATE',[status(thm)],[moufang1,multiply_right_division,theory(equality)]) ).
cnf(29,plain,
multiply(multiply(X,Y),X) = multiply(multiply(X,Z),multiply(left_division(Z,Y),X)),
inference('PARAMODULATE',[status(thm)],[moufang1,multiply_left_division,theory(equality)]) ).
cnf(31,plain,
multiply(multiply(X,multiply(Y,Z)),multiply(multiply(U,Y),X)) = multiply(multiply(X,multiply(Y,multiply(Z,U))),multiply(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[moufang1,moufang1,theory(equality)]),moufang1,theory(equality)]) ).
cnf(34,plain,
X = multiply(X,multiply(right_inverse(X),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[23,right_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(36,plain,
right_division(multiply(X,multiply(Y,X)),X) = multiply(X,Y),
inference('PARAMODULATE',[status(thm)],[right_division_multiply,23,theory(equality)]) ).
cnf(38,plain,
right_division(multiply(multiply(X,Y),X),multiply(Y,X)) = X,
inference('PARAMODULATE',[status(thm)],[right_division_multiply,23,theory(equality)]) ).
cnf(39,plain,
left_division(X,multiply(multiply(X,Y),X)) = multiply(Y,X),
inference('PARAMODULATE',[status(thm)],[left_division_multiply,23,theory(equality)]) ).
cnf(41,plain,
multiply(multiply(X,right_division(Y,X)),X) = multiply(X,Y),
inference('PARAMODULATE',[status(thm)],[23,multiply_right_division,theory(equality)]) ).
cnf(44,plain,
multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)),
inference('PARAMODULATE',[status(thm)],[moufang1,23,theory(equality)]) ).
cnf(47,plain,
multiply(multiply(multiply(X,Y),X),X) = multiply(multiply(X,Y),multiply(X,X)),
inference('PARAMODULATE',[status(thm)],[moufang1,23,theory(equality)]) ).
cnf(56,plain,
identity = multiply(right_inverse(X),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[left_division_multiply,34,theory(equality)]),14,theory(equality)]) ).
cnf(57,plain,
left_inverse(X) = right_inverse(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[right_division_multiply,56,theory(equality)]),20,theory(equality)]) ).
cnf(58,plain,
left_inverse(left_inverse(X)) = X,
inference('REWRITE',[status(thm)],[16,57,theory(equality)]) ).
cnf(59,plain,
multiply(X,X) = multiply(multiply(X,Y),multiply(left_inverse(Y),X)),
inference('REWRITE',[status(thm)],[25,57,theory(equality)]) ).
cnf(60,plain,
multiply(X,left_inverse(X)) = identity,
inference('REWRITE',[status(thm)],[right_inverse,57,theory(equality)]) ).
cnf(62,plain,
right_division(multiply(X,X),multiply(Y,X)) = multiply(X,left_inverse(Y)),
inference('PARAMODULATE',[status(thm)],[right_division_multiply,24,theory(equality)]) ).
cnf(63,plain,
left_division(multiply(X,left_inverse(Y)),multiply(X,X)) = multiply(Y,X),
inference('PARAMODULATE',[status(thm)],[left_division_multiply,24,theory(equality)]) ).
cnf(76,plain,
right_division(multiply(X,Y),X) = multiply(X,right_division(Y,X)),
inference('PARAMODULATE',[status(thm)],[36,multiply_right_division,theory(equality)]) ).
cnf(97,plain,
left_division(X,multiply(multiply(X,Y),multiply(Z,X))) = multiply(multiply(Y,Z),X),
inference('PARAMODULATE',[status(thm)],[39,moufang1,theory(equality)]) ).
cnf(98,plain,
left_division(b,multiply(multiply(b,multiply(a,b)),multiply(c,b))) != multiply(a,multiply(b,multiply(c,b))),
inference('REWRITE',[status(thm)],[prove_moufang2,97,theory(equality)]) ).
cnf(103,plain,
left_division(b,multiply(multiply(multiply(b,a),b),multiply(c,b))) != multiply(a,multiply(b,multiply(c,b))),
inference('PARAMODULATE',[status(thm)],[98,23,theory(equality)]) ).
cnf(105,plain,
multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[23,41,theory(equality)]),multiply_right_division,moufang1,theory(equality)]) ).
cnf(107,plain,
right_division(left_division(X,multiply(multiply(X,multiply(X,X)),Y)),multiply(X,Y)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[38,41,theory(equality)]),multiply_right_division,97,105,theory(equality)]) ).
cnf(115,plain,
left_division(multiply(X,Y),multiply(X,X)) = multiply(left_inverse(Y),X),
inference('PARAMODULATE',[status(thm)],[left_division_multiply,59,theory(equality)]) ).
cnf(132,plain,
right_division(multiply(X,X),Y) = multiply(X,left_inverse(right_division(Y,X))),
inference('PARAMODULATE',[status(thm)],[62,multiply_right_division,theory(equality)]) ).
cnf(137,plain,
left_division(X,multiply(multiply(X,multiply(X,X)),Y)) = multiply(X,multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,76,theory(equality)]),multiply_right_division,97,105,theory(equality)]) ).
cnf(151,plain,
multiply(multiply(X,X),left_inverse(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[105,60,theory(equality)]),right_identity,theory(equality)]) ).
cnf(154,plain,
left_division(multiply(X,X),multiply(X,multiply(X,Y))) = Y,
inference('PARAMODULATE',[status(thm)],[left_division_multiply,105,theory(equality)]) ).
cnf(157,plain,
left_division(X,multiply(multiply(X,X),Y)) = multiply(X,Y),
inference('PARAMODULATE',[status(thm)],[left_division_multiply,105,theory(equality)]) ).
cnf(184,plain,
multiply(multiply(X,multiply(X,Y)),multiply(multiply(Z,X),X)) = multiply(multiply(multiply(X,X),Y),multiply(Z,multiply(X,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[moufang1,105,theory(equality)]),31,theory(equality)]) ).
cnf(186,plain,
right_division(X,left_inverse(X)) = multiply(X,X),
inference('PARAMODULATE',[status(thm)],[right_division_multiply,151,theory(equality)]) ).
cnf(187,plain,
left_division(multiply(X,X),X) = left_inverse(X),
inference('PARAMODULATE',[status(thm)],[left_division_multiply,151,theory(equality)]) ).
cnf(190,plain,
X = multiply(left_inverse(X),multiply(X,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[39,151,theory(equality)]),154,theory(equality)]) ).
cnf(193,plain,
right_division(left_inverse(X),X) = multiply(left_inverse(X),left_inverse(X)),
inference('PARAMODULATE',[status(thm)],[186,58,theory(equality)]) ).
cnf(197,plain,
left_division(left_inverse(X),X) = multiply(X,X),
inference('PARAMODULATE',[status(thm)],[left_division_multiply,190,theory(equality)]) ).
cnf(213,plain,
right_division(left_inverse(X),X) = left_division(X,left_inverse(X)),
inference('REWRITE',[status(thm)],[193,58,197,theory(equality)]) ).
cnf(223,plain,
multiply(multiply(multiply(X,Y),X),X) = multiply(multiply(X,Y),left_division(left_inverse(X),X)),
inference('REWRITE',[status(thm)],[47,197,theory(equality)]) ).
cnf(226,plain,
left_division(multiply(X,left_inverse(Y)),left_division(left_inverse(X),X)) = multiply(Y,X),
inference('REWRITE',[status(thm)],[63,197,theory(equality)]) ).
cnf(236,plain,
multiply(left_division(left_inverse(X),X),Y) = multiply(X,multiply(X,Y)),
inference('REWRITE',[status(thm)],[105,197,theory(equality)]) ).
cnf(250,plain,
right_division(left_division(X,multiply(multiply(X,left_division(left_inverse(X),X)),Y)),multiply(X,Y)) = X,
inference('REWRITE',[status(thm)],[107,197,theory(equality)]) ).
cnf(255,plain,
left_division(multiply(X,Y),left_division(left_inverse(X),X)) = multiply(left_inverse(Y),X),
inference('REWRITE',[status(thm)],[115,197,theory(equality)]) ).
cnf(271,plain,
right_division(left_division(left_inverse(X),X),Y) = multiply(X,left_inverse(right_division(Y,X))),
inference('REWRITE',[status(thm)],[132,197,theory(equality)]) ).
cnf(272,plain,
left_division(X,multiply(multiply(X,left_division(left_inverse(X),X)),Y)) = multiply(left_division(left_inverse(X),X),Y),
inference('REWRITE',[status(thm)],[137,236,197,theory(equality)]) ).
cnf(273,plain,
right_division(multiply(left_division(left_inverse(X),X),Y),multiply(X,Y)) = X,
inference('REWRITE',[status(thm)],[250,272,theory(equality)]) ).
cnf(276,plain,
left_division(X,multiply(left_division(left_inverse(X),X),Y)) = multiply(X,Y),
inference('REWRITE',[status(thm)],[157,197,theory(equality)]) ).
cnf(284,plain,
multiply(multiply(left_division(left_inverse(X),X),Y),multiply(multiply(Z,X),X)) = multiply(multiply(left_division(left_inverse(X),X),Y),multiply(Z,left_division(left_inverse(X),X))),
inference('REWRITE',[status(thm)],[184,236,197,theory(equality)]) ).
cnf(285,plain,
right_division(X,left_inverse(X)) = left_division(left_inverse(X),X),
inference('REWRITE',[status(thm)],[186,197,theory(equality)]) ).
cnf(286,plain,
left_division(left_division(left_inverse(X),X),X) = left_inverse(X),
inference('REWRITE',[status(thm)],[187,197,theory(equality)]) ).
cnf(291,plain,
multiply(left_division(left_inverse(X),X),X) = multiply(X,left_division(left_inverse(X),X)),
inference('PARAMODULATE',[status(thm)],[23,197,theory(equality)]) ).
cnf(310,plain,
left_division(left_division(left_division(multiply(X,Y),left_division(left_inverse(X),X)),left_division(Y,left_inverse(Y))),left_division(X,left_inverse(X))) = multiply(Y,left_inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[226,58,theory(equality)]),58,255,theory(equality)]) ).
cnf(317,plain,
right_division(left_division(left_inverse(X),X),Y) = left_division(left_division(left_division(Y,left_division(left_inverse(right_division(Y,X)),right_division(Y,X))),left_division(X,left_inverse(X))),left_division(right_division(Y,X),left_inverse(right_division(Y,X)))),
inference('REWRITE',[status(thm)],[271,multiply_right_division,310,theory(equality)]) ).
cnf(342,plain,
right_division(left_division(multiply(X,Y),left_division(left_inverse(X),X)),X) = left_inverse(Y),
inference('PARAMODULATE',[status(thm)],[right_division_multiply,255,theory(equality)]) ).
cnf(365,plain,
right_division(multiply(X,multiply(Y,Z)),Z) = multiply(Z,multiply(left_division(Z,X),Y)),
inference('PARAMODULATE',[status(thm)],[26,multiply_left_division,theory(equality)]) ).
cnf(393,plain,
right_division(multiply(multiply(X,Y),X),multiply(Z,X)) = multiply(X,right_division(Y,Z)),
inference('PARAMODULATE',[status(thm)],[right_division_multiply,28,theory(equality)]) ).
cnf(427,plain,
multiply(multiply(X,Y),X) = multiply(Z,multiply(left_division(left_division(X,Z),Y),X)),
inference('PARAMODULATE',[status(thm)],[29,multiply_left_division,theory(equality)]) ).
cnf(460,plain,
right_division(multiply(multiply(left_division(left_inverse(X),X),Y),left_division(left_inverse(X),X)),multiply(X,multiply(Y,left_division(left_inverse(X),X)))) = X,
inference('PARAMODULATE',[status(thm)],[273,23,theory(equality)]) ).
cnf(521,plain,
left_division(X,left_division(X,multiply(multiply(left_division(left_inverse(X),X),Y),multiply(Z,left_division(left_inverse(X),X))))) = multiply(multiply(multiply(Y,Z),X),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[39,44,theory(equality)]),284,236,97,theory(equality)]) ).
cnf(522,plain,
left_division(X,left_division(X,multiply(multiply(left_division(left_inverse(X),X),X),multiply(Y,left_division(left_inverse(X),X))))) = multiply(multiply(X,Y),left_division(left_inverse(X),X)),
inference('REWRITE',[status(thm)],[223,521,theory(equality)]) ).
cnf(587,plain,
left_division(X,left_division(left_inverse(left_division(left_inverse(X),X)),left_division(left_inverse(X),X))) = multiply(X,left_division(left_inverse(X),X)),
inference('PARAMODULATE',[status(thm)],[276,197,theory(equality)]) ).
cnf(588,plain,
left_division(X,multiply(left_division(X,left_division(left_inverse(left_division(left_inverse(X),X)),left_division(left_inverse(X),X))),Y)) = multiply(left_division(left_inverse(X),X),Y),
inference('REWRITE',[status(thm)],[272,587,theory(equality)]) ).
cnf(590,plain,
multiply(left_division(left_inverse(X),X),X) = left_division(X,left_division(left_inverse(left_division(left_inverse(X),X)),left_division(left_inverse(X),X))),
inference('REWRITE',[status(thm)],[291,587,theory(equality)]) ).
cnf(594,plain,
multiply(X,multiply(Y,left_division(left_inverse(X),X))) = multiply(multiply(X,Y),left_division(left_inverse(X),X)),
inference('REWRITE',[status(thm)],[522,276,588,590,theory(equality)]) ).
cnf(596,plain,
multiply(left_division(left_inverse(X),X),right_division(Y,multiply(X,Y))) = X,
inference('REWRITE',[status(thm)],[460,393,594,theory(equality)]) ).
cnf(609,plain,
left_inverse(X) = right_division(Y,multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[left_division_multiply,596,theory(equality)]),286,theory(equality)]) ).
cnf(610,plain,
left_division(left_inverse(X),Y) = multiply(X,Y),
inference('PARAMODULATE',[status(thm)],[18,609,theory(equality)]) ).
cnf(620,plain,
left_division(left_inverse(X),left_division(X,Y)) = Y,
inference('REWRITE',[status(thm)],[multiply_left_division,610,theory(equality)]) ).
cnf(744,plain,
right_division(left_division(left_inverse(X),left_division(left_inverse(Y),Z)),Z) = left_division(left_inverse(Z),left_division(left_inverse(left_division(Z,X)),Y)),
inference('REWRITE',[status(thm)],[365,610,theory(equality)]) ).
cnf(756,plain,
left_division(left_inverse(right_division(X,Y)),Y) = X,
inference('REWRITE',[status(thm)],[multiply_right_division,610,theory(equality)]) ).
cnf(757,plain,
left_division(X,left_division(left_inverse(X),Y)) = Y,
inference('REWRITE',[status(thm)],[left_division_multiply,610,theory(equality)]) ).
cnf(764,plain,
left_division(left_inverse(left_division(left_inverse(X),Y)),X) = left_division(left_inverse(X),left_division(left_inverse(Y),X)),
inference('REWRITE',[status(thm)],[23,610,theory(equality)]) ).
cnf(785,plain,
left_division(X,left_division(left_inverse(left_division(left_inverse(X),Y)),left_division(left_inverse(Z),X))) = left_division(left_inverse(left_division(left_inverse(Y),Z)),X),
inference('REWRITE',[status(thm)],[97,610,theory(equality)]) ).
cnf(796,plain,
left_division(left_inverse(left_division(left_inverse(X),X)),Y) = left_division(left_inverse(X),left_division(left_inverse(X),Y)),
inference('REWRITE',[status(thm)],[236,610,theory(equality)]) ).
cnf(807,plain,
left_division(left_division(left_inverse(X),Y),left_division(left_inverse(X),X)) = left_division(Y,X),
inference('REWRITE',[status(thm)],[255,58,610,theory(equality)]) ).
cnf(862,plain,
right_division(left_division(X,Y),Y) = left_inverse(X),
inference('REWRITE',[status(thm)],[342,807,610,theory(equality)]) ).
cnf(913,plain,
left_division(left_inverse(left_division(left_inverse(X),Y)),X) = left_division(left_inverse(Z),left_division(left_inverse(left_division(left_division(X,Z),Y)),X)),
inference('REWRITE',[status(thm)],[427,610,theory(equality)]) ).
cnf(976,plain,
left_division(left_inverse(left_division(left_inverse(left_division(left_inverse(a),b)),c)),b) != left_division(left_inverse(a),left_division(left_inverse(left_division(left_inverse(b),c)),b)),
inference('REWRITE',[status(thm)],[103,785,764,610,theory(equality)]) ).
cnf(979,plain,
right_division(X,Y) = left_inverse(right_division(Y,X)),
inference('PARAMODULATE',[status(thm)],[22,756,theory(equality)]) ).
cnf(1000,plain,
right_division(left_division(left_inverse(X),X),Y) = left_division(left_division(left_division(Y,left_division(right_division(X,Y),right_division(Y,X))),left_division(X,left_inverse(X))),left_division(right_division(Y,X),right_division(X,Y))),
inference('REWRITE',[status(thm)],[317,979,theory(equality)]) ).
cnf(1003,plain,
left_division(X,left_inverse(X)) = left_inverse(left_division(left_inverse(X),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[979,285,theory(equality)]),213,theory(equality)]) ).
cnf(1026,plain,
left_division(left_division(X,left_inverse(X)),Y) = left_division(left_inverse(X),left_division(left_inverse(X),Y)),
inference('REWRITE',[status(thm)],[796,1003,theory(equality)]) ).
cnf(1064,plain,
left_division(left_inverse(X),X) = left_inverse(left_division(X,left_inverse(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[979,213,theory(equality)]),285,theory(equality)]) ).
cnf(1084,plain,
left_division(X,left_division(left_inverse(Y),Y)) = left_division(left_division(Y,X),Y),
inference('PARAMODULATE',[status(thm)],[807,620,theory(equality)]) ).
cnf(1087,plain,
left_division(left_division(X,Y),left_division(X,left_inverse(X))) = left_division(Y,left_inverse(X)),
inference('PARAMODULATE',[status(thm)],[807,58,theory(equality)]) ).
cnf(1090,plain,
left_division(left_division(right_division(X,Y),Z),left_division(right_division(X,Y),right_division(Y,X))) = left_division(Z,right_division(Y,X)),
inference('PARAMODULATE',[status(thm)],[807,979,theory(equality)]) ).
cnf(1103,plain,
left_division(X,left_division(right_division(Y,X),right_division(X,Y))) = left_division(Y,right_division(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1084,18,theory(equality)]),979,theory(equality)]) ).
cnf(1104,plain,
right_division(left_division(left_inverse(X),X),Y) = left_division(left_inverse(X),right_division(X,Y)),
inference('REWRITE',[status(thm)],[1000,1090,1087,1103,theory(equality)]) ).
cnf(1272,plain,
left_division(left_inverse(X),left_division(left_inverse(left_division(X,Y)),Y)) = left_division(left_inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[862,1026,theory(equality)]),1064,744,theory(equality)]) ).
cnf(1911,plain,
left_division(left_inverse(X),left_inverse(left_division(Y,X))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[862,1272,theory(equality)]),58,22,1104,theory(equality)]) ).
cnf(1967,plain,
left_division(X,Y) = left_inverse(left_division(Y,X)),
inference('PARAMODULATE',[status(thm)],[757,1911,theory(equality)]) ).
cnf(2342,plain,
left_division(left_division(X,left_inverse(Y)),Y) = left_division(left_inverse(Z),left_division(left_division(X,left_division(Y,Z)),Y)),
inference('REWRITE',[status(thm)],[913,1967,theory(equality)]) ).
cnf(2678,plain,
left_division(left_division(c,left_division(b,left_inverse(a))),b) != left_division(left_inverse(a),left_division(left_division(c,left_inverse(b)),b)),
inference('REWRITE',[status(thm)],[976,1967,theory(equality)]) ).
cnf(3330,plain,
left_division(X,left_division(left_division(Y,left_inverse(Z)),Z)) = left_division(left_division(Y,left_division(Z,X)),Z),
inference('PARAMODULATE',[status(thm)],[757,2342,theory(equality)]) ).
cnf(3331,plain,
$false,
inference('REWRITE',[status(thm)],[2678,3330,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP200-1 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % Command : run-snark %s %d
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 07:05:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.47 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.48 *
% 0.21/0.48 *
% 0.21/0.49 #<PACKAGE "SNARK-USER">
% 0.21/0.49 *
% 0.21/0.49 SNARK-TPTP-OPTIONS
% 0.21/0.49 *
% 0.21/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.49 (USE-FACTORING :POS)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.49 *
% 0.21/0.49 "."
% 0.21/0.49 *
% 0.21/0.49 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T07:05:23
% 0.21/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2022-06-14T07:05:23
% 0.21/0.50
% 0.21/0.50 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.21/0.50 ; Recognized right identity assertion (= (|multiply| ?X |identity|) ?X).
% 0.21/0.50 ; Recognized possible right inverse assertion (= (|multiply| ?X (|right_inverse| ?X)) |identity|).
% 2.28/2.49 ; Recognized possible left inverse assertion (= (|multiply| (|left_inverse| ?X) ?X) |identity|).
% 2.28/2.49
% 2.28/2.49 #||
% 2.28/2.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.28/2.49 % SZS output start Refutation
% See solution above
% 2.28/2.51 ||#
% 2.28/2.51
% 2.28/2.51 ; Summary of computation:
% 2.28/2.51 ; 9038 formulas have been input or derived (from 158 formulas).
% 2.28/2.51 ; 3331 (37%) were retained. Of these,
% 2.28/2.51 ; 2444 (73%) were simplified or subsumed later,
% 2.28/2.51 ; 887 (27%) are still being kept.
% 2.28/2.51 ;
% 2.28/2.51 ; Run time in seconds excluding printing time:
% 2.28/2.51 ; 0.002 0% Read assertion file (1 call)
% 2.28/2.51 ; 0.000 0% Assert (10 calls)
% 2.28/2.51 ; 0.392 20% Process new row (8,850 calls)
% 2.28/2.51 ; 0.013 1% Resolution (314 calls)
% 2.28/2.51 ; 0.165 8% Paramodulation (157 calls)
% 2.28/2.51 ; 0.619 31% Forward simplification (8,347 calls)
% 2.28/2.51 ; 0.389 19% Backward simplification (3,331 calls)
% 2.28/2.51 ; 0.355 18% Ordering (43,143 calls)
% 2.28/2.51 ; 0.000 0% Sortal reasoning (32 calls)
% 2.28/2.51 ; 0.000 0% Purity testing (1 call)
% 2.28/2.51 ; 0.064 3% Other
% 2.28/2.51 ; 1.999 Total
% 2.28/2.51 ; 2.020 Real time
% 2.28/2.51 ;
% 2.28/2.51 ; Term-hash-array has 9,860 terms in all.
% 2.28/2.51 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 2.28/2.51 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 2.28/2.51 ; Path-index has 2,630 entries (3,260 at peak, 10,699 added, 8,069 deleted).
% 2.28/2.51 ; Path-index has 8,288 nodes (9,317 at peak, 15,281 added, 6,993 deleted).
% 2.28/2.51 ; Trie-index has 2,630 entries (3,260 at peak, 10,699 added, 8,069 deleted).
% 2.28/2.51 ; Trie-index has 14,358 nodes (22,993 at peak, 76,732 added, 62,374 deleted).
% 2.28/2.51 ; Retrieved 250,622 generalization terms in 115,701 calls.
% 2.28/2.51 ; Retrieved 48,484 instance terms in 3,944 calls.
% 2.28/2.51 ; Retrieved 40,782 unifiable terms in 1,036 calls.
% 2.28/2.51 ;
% 2.28/2.51 ; The agenda of backward simplifiable rows to process has 1 entry:
% 2.28/2.51 ; 1 with value 0
% 2.28/2.51 ; The agenda of rows to process has 145 entries:
% 2.28/2.51 ; 4 with value 24 6 with value 33 8 with value 42
% 2.28/2.51 ; 1 with value 25 11 with value 34 4 with value 43
% 2.28/2.51 ; 3 with value 26 4 with value 35 6 with value 44
% 2.28/2.51 ; 2 with value 27 11 with value 36 4 with value 45
% 2.28/2.51 ; 5 with value 28 9 with value 37 4 with value 46
% 2.28/2.51 ; 10 with value 29 4 with value 38 4 with value 47
% 2.28/2.51 ; 6 with value 30 10 with value 39 1 with value 48
% 2.28/2.51 ; 7 with value 31 5 with value 40 1 with value 49
% 2.28/2.51 ; 11 with value 32 3 with value 41 1 with value 62
% 2.28/2.51 ; The agenda of rows to give has 838 entries:
% 2.28/2.51 ; 9 with value (4 24) 50 with value (4 37) 5 with value (4 50)
% 2.28/2.51 ; 16 with value (4 25) 40 with value (4 38) 3 with value (4 51)
% 2.28/2.51 ; 23 with value (4 26) 35 with value (4 39) 4 with value (4 52)
% 2.28/2.51 ; 42 with value (4 27) 29 with value (4 40) 3 with value (4 53)
% 2.28/2.51 ; 55 with value (4 28) 17 with value (4 41) 1 with value (4 54)
% 2.28/2.51 ; 41 with value (4 29) 17 with value (4 42) 1 with value (4 57)
% 2.28/2.51 ; 48 with value (4 30) 9 with value (4 43) 2 with value (4 58)
% 2.28/2.51 ; 41 with value (4 31) 6 with value (4 44) 2 with value (4 59)
% 2.28/2.51 ; 68 with value (4 32) 6 with value (4 45) 1 with value (4 60)
% 2.28/2.51 ; 70 with value (4 33) 6 with value (4 46) 1 with value (4 62)
% 2.28/2.51 ; 65 with value (4 34) 6 with value (4 47) 1 with value (4 64)
% 2.28/2.51 ; 53 with value (4 35) 7 with value (4 48) 1 with value (4 76)
% 2.28/2.51 ; 50 with value (4 36) 4 with value (4 49)
% 2.28/2.51 Evaluation took:
% 2.28/2.51 2.021 seconds of real time
% 2.28/2.51 1.871437 seconds of user run time
% 2.28/2.51 0.148705 seconds of system run time
% 2.28/2.51 [Run times include 0.201 seconds GC run time.]
% 2.28/2.51 0 calls to %EVAL
% 2.28/2.51 0 page faults and
% 2.28/2.51 147,955,496 bytes consed.
% 2.28/2.51 :PROOF-FOUND
% 2.28/2.51 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T07:05:25
% 2.28/2.51 :PROOF-FOUND
% 2.28/2.51 *
%------------------------------------------------------------------------------