TSTP Solution File: GRP683+1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP683+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n024.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 11:40:19 EDT 2022
% Result : Theorem 1.46s 1.63s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 8
% Syntax : Number of clauses : 157 ( 155 unt; 0 nHn; 5 RR)
% Number of literals : 159 ( 158 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 399 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ld(X,mult(X,X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(2,axiom,
rd(mult(X,X),X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(3,axiom,
mult(X,ld(X,Y)) = ld(X,mult(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
cnf(4,axiom,
mult(rd(X,Y),Y) = rd(mult(X,Y),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
cnf(5,axiom,
ld(ld(X,Y),mult(ld(X,Y),mult(Z,U))) = mult(ld(X,mult(X,Z)),U),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
cnf(6,axiom,
rd(mult(mult(X,Y),rd(Z,U)),rd(Z,U)) = mult(X,rd(mult(Y,U),U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
cnf(7,plain,
mult(rd(mult(X,Y),rd(Z,U)),rd(Z,U)) = mult(X,mult(rd(Y,U),U)),
inference('REWRITE',[status(thm)],[6,4,theory(equality)]) ).
cnf(8,axiom,
ld(X,mult(X,ld(Y,Y))) = rd(mult(rd(X,X),Y),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
cnf(9,plain,
ld(X,mult(X,ld(Y,Y))) = mult(rd(rd(X,X),Y),Y),
inference('REWRITE',[status(thm)],[8,4,theory(equality)]) ).
cnf(10,negated_conjecture,
( mult('SKOLEMAAAS1',ld('SKOLEMAAAS2',mult('SKOLEMAAAS2','SKOLEMAAAS3'))) != mult('SKOLEMAAAS1','SKOLEMAAAS3')
| mult(rd(mult('SKOLEMAAAS1','SKOLEMAAAS2'),'SKOLEMAAAS2'),'SKOLEMAAAS3') != mult('SKOLEMAAAS1','SKOLEMAAAS3') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(11,plain,
( mult('SKOLEMAAAS1',ld('SKOLEMAAAS2',mult('SKOLEMAAAS2','SKOLEMAAAS3'))) != mult('SKOLEMAAAS1','SKOLEMAAAS3')
| mult(mult(rd('SKOLEMAAAS1','SKOLEMAAAS2'),'SKOLEMAAAS2'),'SKOLEMAAAS3') != mult('SKOLEMAAAS1','SKOLEMAAAS3') ),
inference('REWRITE',[status(thm)],[10,4,theory(equality)]) ).
cnf(12,plain,
mult(rd(X,X),X) = X,
inference('REWRITE',[status(thm)],[2,4,theory(equality)]) ).
cnf(14,plain,
ld(X,X) = rd(X,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,12,theory(equality)]),1,3,9,theory(equality)]) ).
cnf(15,plain,
ld(X,mult(X,ld(Y,Y))) = mult(rd(ld(X,X),Y),Y),
inference('REWRITE',[status(thm)],[9,14,theory(equality)]) ).
cnf(16,plain,
mult(ld(X,X),X) = X,
inference('REWRITE',[status(thm)],[12,14,theory(equality)]) ).
cnf(17,plain,
mult(rd(X,ld(X,Y)),ld(X,Y)) = rd(ld(X,mult(X,Y)),ld(X,Y)),
inference('PARAMODULATE',[status(thm)],[4,3,theory(equality)]) ).
cnf(18,plain,
mult(rd(rd(ld(X,X),Y),Y),Y) = rd(ld(X,mult(X,ld(Y,Y))),Y),
inference('PARAMODULATE',[status(thm)],[4,15,theory(equality)]) ).
cnf(19,plain,
ld(X,mult(X,mult(Y,Z))) = mult(ld(X,mult(X,Y)),Z),
inference('PARAMODULATE',[status(thm)],[5,1,theory(equality)]) ).
cnf(21,plain,
ld(ld(X,Y),mult(ld(X,Y),Z)) = mult(ld(X,mult(X,ld(Z,Z))),Z),
inference('PARAMODULATE',[status(thm)],[5,16,theory(equality)]) ).
cnf(23,plain,
mult(rd(ld(X,mult(X,Y)),Z),Z) = rd(ld(ld(X,U),mult(ld(X,U),mult(Y,Z))),Z),
inference('PARAMODULATE',[status(thm)],[4,5,theory(equality)]) ).
cnf(27,plain,
ld(ld(X,Y),mult(ld(X,Y),mult(ld(X,Z),U))) = mult(ld(X,ld(X,mult(X,Z))),U),
inference('PARAMODULATE',[status(thm)],[5,3,theory(equality)]) ).
cnf(36,plain,
mult(rd(X,rd(Y,Z)),rd(Y,Z)) = mult(ld(X,X),mult(rd(X,Z),Z)),
inference('PARAMODULATE',[status(thm)],[7,16,theory(equality)]) ).
cnf(37,plain,
mult(ld(mult(X,Y),mult(X,Y)),mult(rd(mult(X,Y),Z),Z)) = mult(X,mult(rd(Y,Z),Z)),
inference('REWRITE',[status(thm)],[7,36,theory(equality)]) ).
cnf(38,plain,
mult(ld(mult(X,Y),mult(X,Y)),mult(mult(rd(X,Y),Y),Y)) = mult(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,4,theory(equality)]),16,14,theory(equality)]) ).
cnf(40,plain,
mult(ld(ld(X,mult(X,Y)),ld(X,mult(X,Y))),mult(rd(ld(X,mult(X,Y)),Z),Z)) = mult(X,mult(rd(ld(X,Y),Z),Z)),
inference('PARAMODULATE',[status(thm)],[37,3,theory(equality)]) ).
cnf(43,plain,
mult(X,mult(rd(ld(X,ld(Y,Y)),Z),Z)) = mult(rd(ld(X,X),Y),mult(rd(Y,Z),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,15,theory(equality)]),40,theory(equality)]) ).
cnf(47,plain,
ld(X,mult(X,ld(ld(X,X),ld(X,X)))) = ld(X,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,14,theory(equality)]),16,theory(equality)]) ).
cnf(48,plain,
mult(X,Y) = mult(X,mult(rd(Y,mult(X,Y)),mult(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,14,theory(equality)]),16,theory(equality)]) ).
cnf(53,plain,
ld(X,mult(X,mult(X,Y))) = mult(X,Y),
inference('PARAMODULATE',[status(thm)],[19,1,theory(equality)]) ).
cnf(54,plain,
ld(X,mult(X,Y)) = mult(ld(X,mult(X,ld(Y,Y))),Y),
inference('PARAMODULATE',[status(thm)],[19,16,theory(equality)]) ).
cnf(55,plain,
ld(ld(X,Y),mult(ld(X,Y),Z)) = ld(X,mult(X,Z)),
inference('REWRITE',[status(thm)],[21,54,theory(equality)]) ).
cnf(66,plain,
ld(X,mult(X,mult(ld(X,Y),Z))) = mult(ld(X,ld(X,mult(X,Y))),Z),
inference('REWRITE',[status(thm)],[27,55,theory(equality)]) ).
cnf(69,plain,
mult(rd(ld(X,mult(X,Y)),Z),Z) = rd(ld(X,mult(X,mult(Y,Z))),Z),
inference('REWRITE',[status(thm)],[23,55,theory(equality)]) ).
cnf(77,plain,
ld(ld(X,X),X) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[53,16,theory(equality)]),16,theory(equality)]) ).
cnf(78,plain,
ld(X,mult(X,mult(mult(X,Y),Z))) = mult(mult(X,Y),Z),
inference('PARAMODULATE',[status(thm)],[19,53,theory(equality)]) ).
cnf(81,plain,
ld(X,ld(X,mult(X,Y))) = ld(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,55,theory(equality)]),3,theory(equality)]) ).
cnf(83,plain,
ld(X,mult(X,mult(ld(X,Y),Z))) = mult(ld(X,Y),Z),
inference('REWRITE',[status(thm)],[66,81,theory(equality)]) ).
cnf(84,plain,
ld(mult(X,Y),mult(mult(X,Y),Z)) = ld(X,mult(X,Z)),
inference('PARAMODULATE',[status(thm)],[55,53,theory(equality)]) ).
cnf(88,plain,
ld(ld(X,mult(X,Y)),ld(X,mult(X,mult(Y,Z)))) = ld(X,mult(X,Z)),
inference('PARAMODULATE',[status(thm)],[55,19,theory(equality)]) ).
cnf(89,plain,
mult(ld(X,Y),ld(X,mult(X,Z))) = mult(ld(X,Y),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,55,theory(equality)]),83,55,theory(equality)]) ).
cnf(90,plain,
ld(ld(X,Y),ld(X,mult(X,Z))) = ld(X,mult(X,ld(ld(X,Y),Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[55,3,theory(equality)]),55,theory(equality)]) ).
cnf(91,plain,
ld(ld(X,X),ld(X,X)) = ld(X,X),
inference('REWRITE',[status(thm)],[47,1,3,90,theory(equality)]) ).
cnf(93,plain,
mult(ld(X,X),ld(X,X)) = ld(X,X),
inference('PARAMODULATE',[status(thm)],[16,91,theory(equality)]) ).
cnf(94,plain,
ld(ld(X,Y),ld(X,mult(X,Z))) = ld(ld(X,Y),Z),
inference('PARAMODULATE',[status(thm)],[81,55,theory(equality)]) ).
cnf(95,plain,
ld(ld(X,mult(X,Y)),mult(Y,Z)) = ld(X,mult(X,Z)),
inference('REWRITE',[status(thm)],[88,94,theory(equality)]) ).
cnf(97,plain,
mult(ld(ld(X,mult(X,Y)),Y),mult(rd(ld(X,mult(X,Y)),Z),Z)) = mult(X,mult(rd(ld(X,Y),Z),Z)),
inference('REWRITE',[status(thm)],[40,94,theory(equality)]) ).
cnf(114,plain,
ld(ld(X,mult(X,Y)),mult(Y,X)) = X,
inference('PARAMODULATE',[status(thm)],[1,95,theory(equality)]) ).
cnf(116,plain,
ld(X,ld(ld(X,mult(X,Y)),mult(Y,Z))) = ld(X,Z),
inference('PARAMODULATE',[status(thm)],[81,95,theory(equality)]) ).
cnf(117,plain,
ld(ld(X,mult(X,ld(Y,Y))),Y) = ld(X,mult(X,Y)),
inference('PARAMODULATE',[status(thm)],[95,16,theory(equality)]) ).
cnf(120,plain,
ld(ld(X,mult(X,Y)),ld(Y,mult(Y,Z))) = ld(X,mult(X,ld(Y,Z))),
inference('PARAMODULATE',[status(thm)],[95,3,theory(equality)]) ).
cnf(127,plain,
ld(ld(X,mult(X,Y)),Y) = mult(rd(ld(X,X),Y),Y),
inference('REWRITE',[status(thm)],[15,1,120,theory(equality)]) ).
cnf(128,plain,
mult(rd(rd(ld(X,X),Y),Y),Y) = rd(ld(ld(X,mult(X,Y)),Y),Y),
inference('REWRITE',[status(thm)],[18,1,120,theory(equality)]) ).
cnf(129,plain,
ld(X,mult(X,Y)) = mult(ld(ld(X,mult(X,Y)),Y),Y),
inference('REWRITE',[status(thm)],[54,1,120,theory(equality)]) ).
cnf(135,plain,
ld(ld(ld(X,mult(X,Y)),Y),Y) = ld(X,mult(X,Y)),
inference('REWRITE',[status(thm)],[117,1,120,theory(equality)]) ).
cnf(140,plain,
mult(X,ld(ld(X,mult(X,Y)),mult(Y,Z))) = mult(X,Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,95,theory(equality)]),53,theory(equality)]) ).
cnf(142,plain,
ld(ld(ld(X,mult(X,Y)),Y),ld(Y,Y)) = ld(ld(X,mult(X,Y)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[95,93,theory(equality)]),1,120,theory(equality)]) ).
cnf(143,plain,
ld(ld(ld(X,mult(X,Y)),ld(Y,mult(Y,Z))),mult(ld(Y,Z),U)) = ld(ld(X,mult(X,Y)),mult(Y,U)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[95,89,theory(equality)]),53,120,theory(equality)]) ).
cnf(160,plain,
ld(ld(ld(rd(mult(X,Y),Z),mult(rd(mult(X,Y),Z),mult(X,Y))),mult(X,Y)),mult(X,mult(rd(Y,Z),Z))) = mult(rd(mult(X,Y),Z),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[114,37,theory(equality)]),53,120,84,theory(equality)]) ).
cnf(175,plain,
ld(ld(rd(X,mult(Y,X)),mult(rd(X,mult(Y,X)),Y)),mult(Y,X)) = mult(rd(X,mult(Y,X)),mult(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[114,48,theory(equality)]),84,theory(equality)]) ).
cnf(208,plain,
ld(ld(X,Y),mult(ld(X,mult(X,Z)),U)) = ld(ld(X,Y),mult(Z,U)),
inference('PARAMODULATE',[status(thm)],[94,19,theory(equality)]) ).
cnf(213,plain,
ld(ld(ld(X,mult(X,Y)),mult(Y,Z)),Z) = mult(rd(ld(ld(X,mult(X,Y)),Y),Z),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[127,94,theory(equality)]),208,theory(equality)]) ).
cnf(238,plain,
ld(ld(X,mult(X,Y)),Y) = rd(ld(X,mult(X,Y)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,129,theory(equality)]),95,213,theory(equality)]) ).
cnf(247,plain,
mult(X,mult(rd(ld(X,Y),Z),Z)) = mult(ld(ld(X,mult(X,Y)),Y),mult(rd(Y,Z),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,129,theory(equality)]),97,94,theory(equality)]) ).
cnf(248,plain,
mult(ld(ld(X,mult(X,Y)),Y),ld(ld(Y,mult(Y,Z)),Z)) = mult(rd(ld(X,X),Y),mult(rd(Y,Z),Z)),
inference('REWRITE',[status(thm)],[43,127,142,1,120,247,theory(equality)]) ).
cnf(290,plain,
ld(X,Y) = ld(X,ld(Z,mult(Z,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[116,89,theory(equality)]),116,143,120,theory(equality)]) ).
cnf(304,plain,
ld(ld(X,mult(X,Y)),Z) = ld(X,mult(X,ld(Y,Z))),
inference('REWRITE',[status(thm)],[120,290,theory(equality)]) ).
cnf(313,plain,
ld(X,ld(Y,Z)) = ld(X,ld(ld(U,mult(U,Y)),Z)),
inference('PARAMODULATE',[status(thm)],[290,304,theory(equality)]) ).
cnf(318,plain,
ld(X,mult(X,mult(ld(Y,Z),U))) = mult(ld(ld(X,mult(X,Y)),Z),U),
inference('PARAMODULATE',[status(thm)],[19,304,theory(equality)]) ).
cnf(323,plain,
mult(X,ld(ld(X,mult(X,Y)),Z)) = mult(X,ld(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,304,theory(equality)]),53,theory(equality)]) ).
cnf(324,plain,
mult(X,ld(Y,mult(Y,Z))) = mult(X,Z),
inference('REWRITE',[status(thm)],[140,323,theory(equality)]) ).
cnf(328,plain,
mult(mult(rd('SKOLEMAAAS1','SKOLEMAAAS2'),'SKOLEMAAAS2'),'SKOLEMAAAS3') != mult('SKOLEMAAAS1','SKOLEMAAAS3'),
inference('REWRITE',[status(thm)],[11,324,theory(equality)]) ).
cnf(339,plain,
mult(X,ld(ld(Y,mult(Y,Z)),U)) = mult(X,ld(Z,U)),
inference('PARAMODULATE',[status(thm)],[324,304,theory(equality)]) ).
cnf(341,plain,
mult(ld(ld(X,mult(X,Y)),Y),ld(Z,Z)) = mult(rd(ld(X,X),Y),mult(rd(Y,Z),Z)),
inference('REWRITE',[status(thm)],[248,339,theory(equality)]) ).
cnf(344,plain,
mult(rd(X,ld(Y,mult(Y,Z))),Z) = rd(mult(X,Z),ld(Y,mult(Y,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,324,theory(equality)]),324,theory(equality)]) ).
cnf(347,plain,
mult(X,ld(ld(mult(Y,Z),mult(Y,Z)),mult(Y,mult(rd(Z,U),U)))) = mult(X,mult(rd(mult(Y,Z),U),U)),
inference('PARAMODULATE',[status(thm)],[324,37,theory(equality)]) ).
cnf(367,plain,
mult(rd(X,ld(X,X)),ld(X,X)) = rd(X,ld(X,X)),
inference('PARAMODULATE',[status(thm)],[17,1,theory(equality)]) ).
cnf(398,plain,
mult(rd(X,ld(Y,Y)),ld(Y,Y)) = mult(ld(X,X),mult(rd(X,Y),Y)),
inference('PARAMODULATE',[status(thm)],[36,14,theory(equality)]) ).
cnf(400,plain,
X = rd(X,ld(X,X)),
inference('REWRITE',[status(thm)],[367,16,14,398,theory(equality)]) ).
cnf(403,plain,
mult(ld(rd(X,rd(Y,Z)),rd(X,rd(Y,Z))),mult(rd(rd(X,rd(Y,Z)),Z),Z)) = rd(mult(ld(X,X),mult(rd(X,Z),Z)),rd(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,36,theory(equality)]),36,theory(equality)]) ).
cnf(406,plain,
rd(X,Y) = mult(ld(rd(X,Y),rd(X,Y)),mult(rd(rd(X,Y),Y),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[36,14,theory(equality)]),16,theory(equality)]) ).
cnf(409,plain,
mult(rd(X,ld(ld(Y,mult(Y,Z)),Z)),ld(Z,Z)) = mult(ld(X,X),mult(rd(X,Z),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[36,238,theory(equality)]),339,theory(equality)]) ).
cnf(414,plain,
mult(mult(ld(X,X),mult(rd(X,Y),Y)),rd(Z,Y)) = mult(X,mult(rd(rd(Z,Y),Y),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[36,4,theory(equality)]),53,84,55,3,347,36,theory(equality)]) ).
cnf(428,plain,
mult(rd(X,Y),Y) = mult(ld(X,X),mult(ld(X,X),mult(rd(X,Y),Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[36,400,theory(equality)]),398,theory(equality)]) ).
cnf(471,plain,
mult(X,mult(Y,Z)) = mult(X,mult(mult(rd(Y,Z),Z),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[324,38,theory(equality)]),77,theory(equality)]) ).
cnf(472,plain,
ld(rd(X,Y),mult(rd(X,Y),mult(X,Y))) = mult(mult(rd(X,Y),Y),Y),
inference('PARAMODULATE',[status(thm)],[78,471,theory(equality)]) ).
cnf(521,plain,
mult(rd(ld(X,mult(X,rd(ld(Y,Y),Z))),Z),Z) = rd(ld(ld(X,mult(X,Z)),Z),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[69,127,theory(equality)]),304,339,theory(equality)]) ).
cnf(581,plain,
mult(ld(X,X),mult(rd(X,Y),Y)) = mult(rd(X,Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[398,91,theory(equality)]),428,398,theory(equality)]) ).
cnf(587,plain,
rd(X,Y) = mult(rd(rd(X,Y),Y),Y),
inference('REWRITE',[status(thm)],[406,581,theory(equality)]) ).
cnf(593,plain,
rd(ld(X,X),Y) = rd(ld(ld(X,mult(X,Y)),Y),Y),
inference('REWRITE',[status(thm)],[128,587,theory(equality)]) ).
cnf(610,plain,
mult(rd(ld(X,mult(X,rd(ld(Y,Y),Z))),Z),Z) = rd(ld(X,X),Z),
inference('REWRITE',[status(thm)],[521,593,theory(equality)]) ).
cnf(636,plain,
mult(rd(X,ld(Y,Y)),ld(Y,Y)) = mult(rd(X,Y),Y),
inference('REWRITE',[status(thm)],[398,581,theory(equality)]) ).
cnf(637,plain,
mult(mult(rd(X,Y),Y),rd(Z,Y)) = mult(X,rd(Z,Y)),
inference('REWRITE',[status(thm)],[414,587,581,theory(equality)]) ).
cnf(638,plain,
mult(rd(X,rd(Y,Z)),rd(Y,Z)) = mult(rd(X,Z),Z),
inference('REWRITE',[status(thm)],[36,581,theory(equality)]) ).
cnf(640,plain,
mult(rd(rd(X,rd(Y,Z)),Z),Z) = rd(mult(rd(X,Z),Z),rd(Y,Z)),
inference('REWRITE',[status(thm)],[403,581,theory(equality)]) ).
cnf(642,plain,
mult(rd(X,ld(ld(Y,mult(Y,Z)),Z)),ld(Z,Z)) = mult(rd(X,Z),Z),
inference('REWRITE',[status(thm)],[409,581,theory(equality)]) ).
cnf(687,plain,
rd(X,rd(Y,Z)) = rd(mult(rd(X,Z),Z),rd(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[587,638,theory(equality)]),640,theory(equality)]) ).
cnf(690,plain,
ld(ld(X,mult(X,rd(Y,Z))),rd(Y,Z)) = ld(ld(X,mult(X,Z)),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[127,638,theory(equality)]),127,theory(equality)]) ).
cnf(695,plain,
mult(ld(ld(X,mult(X,Y)),Y),rd(Z,Y)) = mult(rd(ld(X,mult(X,rd(Z,Y))),Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[638,238,theory(equality)]),690,theory(equality)]) ).
cnf(698,plain,
mult(ld(ld(X,mult(X,Y)),Y),rd(ld(Z,Z),Y)) = rd(ld(X,X),Y),
inference('REWRITE',[status(thm)],[610,695,theory(equality)]) ).
cnf(701,plain,
rd(X,ld(Y,Y)) = mult(rd(rd(X,ld(Y,Y)),Y),Y),
inference('PARAMODULATE',[status(thm)],[587,636,theory(equality)]) ).
cnf(722,plain,
mult(rd(X,Y),Y) = mult(rd(X,ld(Z,mult(Z,Y))),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[636,290,theory(equality)]),324,642,339,theory(equality)]) ).
cnf(726,plain,
mult(rd(X,Y),Y) = rd(mult(X,Y),ld(Z,mult(Z,Y))),
inference('REWRITE',[status(thm)],[344,722,theory(equality)]) ).
cnf(730,plain,
mult(mult(rd(X,Y),Y),ld(Y,Y)) = mult(X,ld(Y,Y)),
inference('PARAMODULATE',[status(thm)],[637,14,theory(equality)]) ).
cnf(733,plain,
ld(rd(X,Y),mult(rd(X,Y),mult(X,Y))) = mult(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[637,400,theory(equality)]),472,636,theory(equality)]) ).
cnf(734,plain,
mult(X,Y) = mult(mult(rd(X,Y),Y),Y),
inference('REWRITE',[status(thm)],[472,733,theory(equality)]) ).
cnf(738,plain,
mult(ld(ld(X,mult(X,Y)),Y),rd(Z,Y)) = mult(ld(X,X),rd(Z,Y)),
inference('PARAMODULATE',[status(thm)],[637,127,theory(equality)]) ).
cnf(739,plain,
mult(ld(X,X),rd(ld(Y,Y),Z)) = rd(ld(X,X),Z),
inference('REWRITE',[status(thm)],[698,738,theory(equality)]) ).
cnf(745,plain,
ld(mult(rd(X,Y),Y),mult(X,rd(Z,Y))) = ld(rd(X,Y),mult(rd(X,Y),rd(Z,Y))),
inference('PARAMODULATE',[status(thm)],[84,637,theory(equality)]) ).
cnf(756,plain,
ld(X,mult(X,Y)) = ld(rd(X,Z),mult(rd(X,Z),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[84,637,theory(equality)]),84,theory(equality)]) ).
cnf(761,plain,
X = mult(rd(X,mult(Y,X)),mult(Y,X)),
inference('REWRITE',[status(thm)],[175,114,756,theory(equality)]) ).
cnf(763,plain,
ld(mult(rd(X,Y),Y),mult(X,rd(Z,Y))) = ld(X,mult(X,rd(Z,Y))),
inference('REWRITE',[status(thm)],[745,756,theory(equality)]) ).
cnf(774,plain,
ld(ld(mult(X,Y),mult(X,Y)),mult(X,mult(rd(Y,Z),Z))) = mult(rd(mult(X,Y),Z),Z),
inference('REWRITE',[status(thm)],[160,53,84,756,theory(equality)]) ).
cnf(781,plain,
ld(X,mult(X,rd(Y,Z))) = mult(ld(X,X),rd(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,637,theory(equality)]),738,690,763,theory(equality)]) ).
cnf(783,plain,
ld(X,mult(X,rd(ld(Y,Y),Z))) = rd(ld(X,X),Z),
inference('REWRITE',[status(thm)],[739,781,theory(equality)]) ).
cnf(785,plain,
ld(ld(ld(X,mult(X,Y)),Y),rd(Z,Y)) = ld(X,mult(X,rd(Z,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[135,637,theory(equality)]),690,763,theory(equality)]) ).
cnf(811,plain,
ld(ld(ld(X,mult(X,Y)),Y),rd(ld(Z,Z),Y)) = rd(ld(X,X),Y),
inference('REWRITE',[status(thm)],[783,785,theory(equality)]) ).
cnf(832,plain,
ld(X,Y) = mult(rd(ld(X,Y),Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[761,3,theory(equality)]),722,324,theory(equality)]) ).
cnf(854,plain,
mult(ld(X,X),Y) = ld(X,mult(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[734,127,theory(equality)]),129,theory(equality)]) ).
cnf(869,plain,
X = mult(rd(X,ld(Y,X)),ld(Y,X)),
inference('PARAMODULATE',[status(thm)],[761,832,theory(equality)]) ).
cnf(901,plain,
ld(ld(X,X),Y) = ld(X,mult(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[55,854,theory(equality)]),290,theory(equality)]) ).
cnf(913,plain,
ld(ld(X,X),mult(X,Y)) = mult(X,Y),
inference('REWRITE',[status(thm)],[53,901,theory(equality)]) ).
cnf(939,plain,
ld(X,Y) = ld(X,ld(ld(Z,Z),Y)),
inference('REWRITE',[status(thm)],[290,901,theory(equality)]) ).
cnf(941,plain,
mult(rd(X,Y),Y) = rd(mult(X,Y),ld(ld(Z,Z),Y)),
inference('REWRITE',[status(thm)],[726,901,theory(equality)]) ).
cnf(943,plain,
ld(X,ld(Y,Z)) = ld(X,ld(ld(ld(U,U),Y),Z)),
inference('REWRITE',[status(thm)],[313,901,theory(equality)]) ).
cnf(956,plain,
mult(X,ld(ld(Y,Y),Z)) = mult(X,Z),
inference('REWRITE',[status(thm)],[324,901,theory(equality)]) ).
cnf(958,plain,
mult(X,ld(ld(ld(Y,Y),Z),U)) = mult(X,ld(Z,U)),
inference('REWRITE',[status(thm)],[339,901,theory(equality)]) ).
cnf(978,plain,
ld(ld(ld(X,Y),ld(X,Y)),Z) = ld(ld(X,X),Z),
inference('REWRITE',[status(thm)],[55,901,theory(equality)]) ).
cnf(979,plain,
ld(ld(mult(X,Y),mult(X,Y)),Z) = ld(ld(X,X),Z),
inference('REWRITE',[status(thm)],[84,901,theory(equality)]) ).
cnf(983,plain,
mult(X,mult(rd(Y,Z),Z)) = mult(rd(mult(X,Y),Z),Z),
inference('REWRITE',[status(thm)],[774,913,979,theory(equality)]) ).
cnf(1007,plain,
mult(X,ld(X,Y)) = ld(ld(X,X),Y),
inference('REWRITE',[status(thm)],[3,901,theory(equality)]) ).
cnf(1012,plain,
ld(ld(ld(X,X),Y),Y) = mult(rd(ld(X,X),Y),Y),
inference('REWRITE',[status(thm)],[127,901,theory(equality)]) ).
cnf(1025,plain,
ld(ld(X,X),mult(ld(Y,Z),U)) = mult(ld(ld(ld(X,X),Y),Z),U),
inference('REWRITE',[status(thm)],[318,901,theory(equality)]) ).
cnf(1032,plain,
ld(ld(X,X),mult(ld(Y,Y),ld(Z,Z))) = mult(rd(ld(X,X),Y),mult(rd(Y,Z),Z)),
inference('REWRITE',[status(thm)],[341,1025,901,theory(equality)]) ).
cnf(1068,plain,
ld(ld(X,X),Y) = ld(ld(rd(X,Z),rd(X,Z)),Y),
inference('REWRITE',[status(thm)],[756,901,theory(equality)]) ).
cnf(1078,plain,
ld(ld(ld(ld(X,X),Y),Y),rd(Z,Y)) = ld(ld(X,X),rd(Z,Y)),
inference('REWRITE',[status(thm)],[785,901,theory(equality)]) ).
cnf(1092,plain,
ld(ld(X,X),rd(ld(Y,Y),Z)) = rd(ld(X,X),Z),
inference('REWRITE',[status(thm)],[811,1078,901,theory(equality)]) ).
cnf(1096,plain,
mult(ld(X,X),Y) = ld(ld(X,X),Y),
inference('REWRITE',[status(thm)],[854,901,theory(equality)]) ).
cnf(1101,plain,
ld(ld(X,X),ld(Y,Y)) = mult(rd(ld(X,X),Z),mult(rd(Z,Y),Y)),
inference('REWRITE',[status(thm)],[1032,939,1096,theory(equality)]) ).
cnf(1107,plain,
ld(ld(X,X),ld(X,Y)) = ld(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[913,832,theory(equality)]),978,1068,theory(equality)]) ).
cnf(1129,plain,
ld(ld(X,X),ld(Y,Y)) = rd(ld(X,X),ld(Y,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1092,14,theory(equality)]),1107,theory(equality)]) ).
cnf(1140,plain,
rd(X,ld(ld(Y,Y),ld(Z,Z))) = rd(mult(rd(X,Z),Z),ld(ld(Y,Y),ld(Z,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[687,1129,theory(equality)]),636,theory(equality)]) ).
cnf(1181,plain,
rd(X,mult(Y,X)) = rd(X,ld(ld(Z,Z),mult(Y,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[941,761,theory(equality)]),587,theory(equality)]) ).
cnf(1197,plain,
rd(X,ld(Y,Y)) = rd(X,ld(ld(Z,Z),ld(Y,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[941,636,theory(equality)]),1140,587,theory(equality)]) ).
cnf(1216,plain,
mult(rd(X,ld(Y,X)),mult(rd(ld(Y,X),Z),Z)) = mult(rd(X,Z),Z),
inference('PARAMODULATE',[status(thm)],[983,869,theory(equality)]) ).
cnf(1224,plain,
mult(rd(X,ld(Y,Y)),ld(Z,Z)) = mult(rd(X,Y),mult(rd(Y,Z),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[983,636,theory(equality)]),983,958,1012,theory(equality)]) ).
cnf(1227,plain,
mult(mult(rd(X,Y),Y),ld(Z,Z)) = mult(X,ld(Z,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[983,730,theory(equality)]),983,958,1012,theory(equality)]) ).
cnf(1284,plain,
ld(ld(X,X),ld(Y,Y)) = ld(ld(ld(X,X),mult(Z,Y)),mult(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1101,4,theory(equality)]),1012,734,theory(equality)]) ).
cnf(1339,plain,
rd(X,ld(ld(ld(Y,Y),X),X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1181,1012,theory(equality)]),400,1197,943,theory(equality)]) ).
cnf(1347,plain,
mult(X,Y) = mult(mult(X,Y),ld(Y,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[983,1339,theory(equality)]),77,1007,956,400,1197,1284,theory(equality)]) ).
cnf(1354,plain,
rd(X,ld(Y,Y)) = mult(rd(X,Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1347,701,theory(equality)]),77,1096,14,1224,theory(equality)]) ).
cnf(1362,plain,
mult(X,ld(Y,Y)) = mult(rd(X,Z),mult(rd(Z,Y),Y)),
inference('REWRITE',[status(thm)],[1224,1227,1354,theory(equality)]) ).
cnf(1371,plain,
mult(X,ld(Y,Y)) = mult(rd(X,Y),Y),
inference('REWRITE',[status(thm)],[1216,1362,theory(equality)]) ).
cnf(1447,plain,
mult(X,Y) = mult(mult(X,ld(Y,Y)),Y),
inference('REWRITE',[status(thm)],[734,1371,theory(equality)]) ).
cnf(1459,plain,
mult(mult(X,ld(Y,Y)),ld(Z,Z)) = mult(X,ld(Z,Z)),
inference('REWRITE',[status(thm)],[1227,1371,theory(equality)]) ).
cnf(1462,plain,
mult(mult('SKOLEMAAAS1',ld('SKOLEMAAAS2','SKOLEMAAAS2')),'SKOLEMAAAS3') != mult('SKOLEMAAAS1','SKOLEMAAAS3'),
inference('REWRITE',[status(thm)],[328,1371,theory(equality)]) ).
cnf(1542,plain,
mult(mult(X,ld(Y,Y)),Z) = mult(X,Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1447,1459,theory(equality)]),1447,theory(equality)]) ).
cnf(1543,plain,
$false,
inference('REWRITE',[status(thm)],[1462,1542,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : GRP683+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n024.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 07:37:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 *
% 0.18/0.43 *
% 0.18/0.44 #<PACKAGE "SNARK-USER">
% 0.18/0.44 *
% 0.18/0.44 SNARK-TPTP-OPTIONS
% 0.18/0.44 *
% 0.18/0.44 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.44 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.44 (USE-FACTORING :POS)
% 0.18/0.44 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.44 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.44 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.44 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.44 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.44 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.44 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.44 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.44 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.44 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.44 *
% 0.18/0.44 "."
% 0.18/0.44 *
% 0.18/0.44 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T07:37:19
% 0.18/0.44 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n024.cluster.edu at 2022-06-13T07:37:19
% 1.46/1.63
% 1.46/1.63
% 1.46/1.63 #||
% 1.46/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.46/1.63 % SZS output start Refutation
% See solution above
% 1.46/1.69 ||#
% 1.46/1.69
% 1.46/1.69 ; Summary of computation:
% 1.46/1.69 ; 5721 formulas have been input or derived (from 131 formulas).
% 1.46/1.69 ; 1543 (27%) were retained. Of these,
% 1.46/1.69 ; 1353 (88%) were simplified or subsumed later,
% 1.46/1.69 ; 190 (12%) are still being kept.
% 1.46/1.69 ;
% 1.46/1.69 ; Run time in seconds excluding printing time:
% 1.46/1.69 ; 0.002 0% Read assertion file (1 call)
% 1.46/1.69 ; 0.001 0% Assert (8 calls)
% 1.46/1.69 ; 0.247 21% Process new row (5,643 calls)
% 1.46/1.69 ; 0.008 1% Resolution (260 calls)
% 1.46/1.69 ; 0.117 10% Paramodulation (130 calls)
% 1.46/1.69 ; 0.000 0% Condensing (2 calls)
% 1.46/1.69 ; 0.000 0% Forward subsumption (2 calls)
% 1.46/1.69 ; 0.001 0% Backward subsumption (2 calls)
% 1.46/1.69 ; 0.410 34% Forward simplification (5,361 calls)
% 1.46/1.69 ; 0.176 15% Backward simplification (1,540 calls)
% 1.46/1.69 ; 0.173 15% Ordering (17,437 calls)
% 1.46/1.69 ; 0.000 0% Sortal reasoning (32 calls)
% 1.46/1.69 ; 0.000 0% Purity testing (1 call)
% 1.46/1.69 ; 0.054 5% Other
% 1.46/1.69 ; 1.189 Total
% 1.46/1.69 ; 1.247 Real time
% 1.46/1.69 ;
% 1.46/1.69 ; Term-hash-array has 4,685 terms in all.
% 1.46/1.69 ; Feature-vector-row-index has 0 entries (2 at peak, 2 added, 2 deleted).
% 1.46/1.69 ; Feature-vector-row-index has 1 node (38 at peak, 38 added, 37 deleted).
% 1.46/1.69 ; Retrieved 0 possibly forward subsuming rows in 2 calls.
% 1.46/1.69 ; Retrieved 0 possibly backward subsumed rows in 2 calls.
% 1.46/1.69 ; Path-index has 634 entries (1,260 at peak, 5,546 added, 4,912 deleted).
% 1.46/1.69 ; Path-index has 7,349 nodes (7,549 at peak, 14,189 added, 6,840 deleted).
% 1.46/1.69 ; Trie-index has 634 entries (1,260 at peak, 5,546 added, 4,912 deleted).
% 1.46/1.69 ; Trie-index has 3,465 nodes (8,431 at peak, 38,138 added, 34,673 deleted).
% 1.46/1.69 ; Retrieved 63,281 generalization terms in 66,064 calls.
% 1.46/1.69 ; Retrieved 5,601 instance terms in 1,823 calls.
% 1.46/1.69 ; Retrieved 12,662 unifiable terms in 869 calls.
% 1.46/1.69 ;
% 1.46/1.69 ; The agenda of rows to process has 43 entries:
% 1.46/1.69 ; 2 with value 25 4 with value 30 2 with value 36
% 1.46/1.69 ; 3 with value 26 4 with value 31 3 with value 38
% 1.46/1.69 ; 3 with value 27 2 with value 33 1 with value 40
% 1.46/1.69 ; 1 with value 28 6 with value 34 4 with value 42
% 1.46/1.69 ; 4 with value 29 3 with value 35 1 with value 43
% 1.46/1.69 ; The agenda of rows to give has 154 entries:
% 1.46/1.69 ; 1 with value (4 21) 22 with value (4 29) 8 with value (4 35)
% 1.46/1.69 ; 1 with value (4 24) 14 with value (4 30) 1 with value (4 37)
% 1.46/1.69 ; 19 with value (4 25) 12 with value (4 31) 2 with value (4 38)
% 1.46/1.69 ; 6 with value (4 26) 8 with value (4 32) 2 with value (4 39)
% 1.46/1.69 ; 15 with value (4 27) 13 with value (4 33) 1 with value (4 42)
% 1.46/1.69 ; 14 with value (4 28) 12 with value (4 34) 3 with value (4 43)
% 1.46/1.69 Evaluation took:
% 1.46/1.69 1.248 seconds of real time
% 1.46/1.69 1.155925 seconds of user run time
% 1.46/1.69 0.092282 seconds of system run time
% 1.46/1.69 [Run times include 0.09 seconds GC run time.]
% 1.46/1.69 0 calls to %EVAL
% 1.46/1.69 0 page faults and
% 1.46/1.69 75,738,168 bytes consed.
% 1.46/1.69 :PROOF-FOUND
% 1.46/1.69 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T07:37:20
% 1.46/1.69 :PROOF-FOUND
% 1.46/1.69 *
%------------------------------------------------------------------------------