TSTP Solution File: GRP684-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP684-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n029.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 : Unsatisfiable 0.92s 1.13s
% Output : Refutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 8
% Syntax : Number of clauses : 154 ( 154 unt; 0 nHn; 4 RR)
% Number of literals : 154 ( 153 equ; 3 neg)
% Maximal clause size : 1 ( 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 : 393 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c01,axiom,
ld(X,mult(X,X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c02,axiom,
rd(mult(X,X),X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c03,axiom,
mult(X,ld(X,Y)) = ld(X,mult(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c04,axiom,
mult(rd(X,Y),Y) = rd(mult(X,Y),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c05,axiom,
ld(ld(X,Y),mult(ld(X,Y),mult(Z,U))) = mult(ld(X,mult(X,Z)),U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c06,axiom,
rd(mult(mult(X,Y),rd(Z,U)),rd(Z,U)) = mult(X,rd(mult(Y,U),U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
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)],[c06,c04,theory(equality)]) ).
cnf(c07,axiom,
ld(X,mult(X,ld(Y,Y))) = rd(mult(rd(X,X),Y),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(9,plain,
ld(X,mult(X,ld(Y,Y))) = mult(rd(rd(X,X),Y),Y),
inference('REWRITE',[status(thm)],[c07,c04,theory(equality)]) ).
cnf(goals,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(11,plain,
mult(rd(a,mult(b,c)),mult(b,c)) != mult(rd(a,c),c),
inference('REWRITE',[status(thm)],[goals,c04,theory(equality)]) ).
cnf(12,plain,
mult(rd(X,X),X) = X,
inference('REWRITE',[status(thm)],[c02,c04,theory(equality)]) ).
cnf(14,plain,
ld(X,X) = rd(X,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[c04,12,theory(equality)]),c01,c03,9,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)],[c04,c03,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)],[c04,15,theory(equality)]) ).
cnf(19,plain,
ld(X,mult(X,mult(Y,Z))) = mult(ld(X,mult(X,Y)),Z),
inference('PARAMODULATE',[status(thm)],[c05,c01,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)],[c05,16,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)],[c04,c05,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)],[c05,c03,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,c04,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,c03,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,c01,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)],[c01,55,theory(equality)]),c03,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)],[c03,55,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,c03,theory(equality)]),55,theory(equality)]) ).
cnf(91,plain,
ld(ld(X,X),ld(X,X)) = ld(X,X),
inference('REWRITE',[status(thm)],[47,c01,c03,90,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)],[c01,95,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,c03,theory(equality)]) ).
cnf(127,plain,
ld(ld(X,mult(X,Y)),Y) = mult(rd(ld(X,X),Y),Y),
inference('REWRITE',[status(thm)],[15,c01,120,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,c01,120,theory(equality)]) ).
cnf(129,plain,
ld(X,mult(X,Y)) = mult(ld(ld(X,mult(X,Y)),Y),Y),
inference('REWRITE',[status(thm)],[54,c01,120,theory(equality)]) ).
cnf(135,plain,
ld(ld(ld(X,mult(X,Y)),Y),Y) = ld(X,mult(X,Y)),
inference('REWRITE',[status(thm)],[117,c01,120,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)],[c03,95,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)]),c01,120,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(159,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(174,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(207,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(212,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)]),207,theory(equality)]) ).
cnf(237,plain,
ld(ld(X,mult(X,Y)),Y) = rd(ld(X,mult(X,Y)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[c04,129,theory(equality)]),95,212,theory(equality)]) ).
cnf(246,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(247,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,c01,120,246,theory(equality)]) ).
cnf(289,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(303,plain,
ld(ld(X,mult(X,Y)),Z) = ld(X,mult(X,ld(Y,Z))),
inference('REWRITE',[status(thm)],[120,289,theory(equality)]) ).
cnf(312,plain,
ld(X,ld(Y,Z)) = ld(X,ld(ld(U,mult(U,Y)),Z)),
inference('PARAMODULATE',[status(thm)],[289,303,theory(equality)]) ).
cnf(317,plain,
ld(X,mult(X,mult(ld(Y,Z),U))) = mult(ld(ld(X,mult(X,Y)),Z),U),
inference('PARAMODULATE',[status(thm)],[19,303,theory(equality)]) ).
cnf(322,plain,
mult(X,ld(ld(X,mult(X,Y)),Z)) = mult(X,ld(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[c03,303,theory(equality)]),53,theory(equality)]) ).
cnf(323,plain,
mult(X,ld(Y,mult(Y,Z))) = mult(X,Z),
inference('REWRITE',[status(thm)],[140,322,theory(equality)]) ).
cnf(337,plain,
mult(X,ld(ld(Y,mult(Y,Z)),U)) = mult(X,ld(Z,U)),
inference('PARAMODULATE',[status(thm)],[323,303,theory(equality)]) ).
cnf(339,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)],[247,337,theory(equality)]) ).
cnf(342,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)],[c04,323,theory(equality)]),323,theory(equality)]) ).
cnf(345,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)],[323,37,theory(equality)]) ).
cnf(365,plain,
mult(rd(X,ld(X,X)),ld(X,X)) = rd(X,ld(X,X)),
inference('PARAMODULATE',[status(thm)],[17,c01,theory(equality)]) ).
cnf(396,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(398,plain,
X = rd(X,ld(X,X)),
inference('REWRITE',[status(thm)],[365,16,14,396,theory(equality)]) ).
cnf(401,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)],[c04,36,theory(equality)]),36,theory(equality)]) ).
cnf(404,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(407,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)],[36,237,theory(equality)]),337,theory(equality)]) ).
cnf(412,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,c04,theory(equality)]),53,84,55,c03,345,36,theory(equality)]) ).
cnf(426,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)],[36,398,theory(equality)]),396,theory(equality)]) ).
cnf(469,plain,
mult(X,mult(Y,Z)) = mult(X,mult(mult(rd(Y,Z),Z),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[323,38,theory(equality)]),77,theory(equality)]) ).
cnf(470,plain,
ld(rd(X,Y),mult(rd(X,Y),mult(X,Y))) = mult(mult(rd(X,Y),Y),Y),
inference('PARAMODULATE',[status(thm)],[78,469,theory(equality)]) ).
cnf(519,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)]),303,337,theory(equality)]) ).
cnf(579,plain,
mult(ld(X,X),mult(rd(X,Y),Y)) = mult(rd(X,Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[396,91,theory(equality)]),426,396,theory(equality)]) ).
cnf(585,plain,
rd(X,Y) = mult(rd(rd(X,Y),Y),Y),
inference('REWRITE',[status(thm)],[404,579,theory(equality)]) ).
cnf(591,plain,
rd(ld(X,X),Y) = rd(ld(ld(X,mult(X,Y)),Y),Y),
inference('REWRITE',[status(thm)],[128,585,theory(equality)]) ).
cnf(608,plain,
mult(rd(ld(X,mult(X,rd(ld(Y,Y),Z))),Z),Z) = rd(ld(X,X),Z),
inference('REWRITE',[status(thm)],[519,591,theory(equality)]) ).
cnf(634,plain,
mult(rd(X,ld(Y,Y)),ld(Y,Y)) = mult(rd(X,Y),Y),
inference('REWRITE',[status(thm)],[396,579,theory(equality)]) ).
cnf(635,plain,
mult(mult(rd(X,Y),Y),rd(Z,Y)) = mult(X,rd(Z,Y)),
inference('REWRITE',[status(thm)],[412,585,579,theory(equality)]) ).
cnf(636,plain,
mult(rd(X,rd(Y,Z)),rd(Y,Z)) = mult(rd(X,Z),Z),
inference('REWRITE',[status(thm)],[36,579,theory(equality)]) ).
cnf(638,plain,
mult(rd(rd(X,rd(Y,Z)),Z),Z) = rd(mult(rd(X,Z),Z),rd(Y,Z)),
inference('REWRITE',[status(thm)],[401,579,theory(equality)]) ).
cnf(640,plain,
mult(rd(X,ld(ld(Y,mult(Y,Z)),Z)),ld(Z,Z)) = mult(rd(X,Z),Z),
inference('REWRITE',[status(thm)],[407,579,theory(equality)]) ).
cnf(685,plain,
rd(X,rd(Y,Z)) = rd(mult(rd(X,Z),Z),rd(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[585,636,theory(equality)]),638,theory(equality)]) ).
cnf(688,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)],[127,636,theory(equality)]),127,theory(equality)]) ).
cnf(693,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)],[636,237,theory(equality)]),688,theory(equality)]) ).
cnf(696,plain,
mult(ld(ld(X,mult(X,Y)),Y),rd(ld(Z,Z),Y)) = rd(ld(X,X),Y),
inference('REWRITE',[status(thm)],[608,693,theory(equality)]) ).
cnf(699,plain,
rd(X,ld(Y,Y)) = mult(rd(rd(X,ld(Y,Y)),Y),Y),
inference('PARAMODULATE',[status(thm)],[585,634,theory(equality)]) ).
cnf(720,plain,
mult(rd(X,Y),Y) = mult(rd(X,ld(Z,mult(Z,Y))),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[634,289,theory(equality)]),323,640,337,theory(equality)]) ).
cnf(724,plain,
mult(rd(X,Y),Y) = rd(mult(X,Y),ld(Z,mult(Z,Y))),
inference('REWRITE',[status(thm)],[342,720,theory(equality)]) ).
cnf(728,plain,
mult(mult(rd(X,Y),Y),ld(Y,Y)) = mult(X,ld(Y,Y)),
inference('PARAMODULATE',[status(thm)],[635,14,theory(equality)]) ).
cnf(731,plain,
ld(rd(X,Y),mult(rd(X,Y),mult(X,Y))) = mult(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[635,398,theory(equality)]),470,634,theory(equality)]) ).
cnf(732,plain,
mult(X,Y) = mult(mult(rd(X,Y),Y),Y),
inference('REWRITE',[status(thm)],[470,731,theory(equality)]) ).
cnf(736,plain,
mult(ld(ld(X,mult(X,Y)),Y),rd(Z,Y)) = mult(ld(X,X),rd(Z,Y)),
inference('PARAMODULATE',[status(thm)],[635,127,theory(equality)]) ).
cnf(737,plain,
mult(ld(X,X),rd(ld(Y,Y),Z)) = rd(ld(X,X),Z),
inference('REWRITE',[status(thm)],[696,736,theory(equality)]) ).
cnf(743,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)],[84,635,theory(equality)]) ).
cnf(754,plain,
ld(X,mult(X,Y)) = ld(rd(X,Z),mult(rd(X,Z),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[84,635,theory(equality)]),84,theory(equality)]) ).
cnf(759,plain,
X = mult(rd(X,mult(Y,X)),mult(Y,X)),
inference('REWRITE',[status(thm)],[174,114,754,theory(equality)]) ).
cnf(761,plain,
ld(mult(rd(X,Y),Y),mult(X,rd(Z,Y))) = ld(X,mult(X,rd(Z,Y))),
inference('REWRITE',[status(thm)],[743,754,theory(equality)]) ).
cnf(772,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)],[159,53,84,754,theory(equality)]) ).
cnf(779,plain,
ld(X,mult(X,rd(Y,Z))) = mult(ld(X,X),rd(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[129,635,theory(equality)]),736,688,761,theory(equality)]) ).
cnf(781,plain,
ld(X,mult(X,rd(ld(Y,Y),Z))) = rd(ld(X,X),Z),
inference('REWRITE',[status(thm)],[737,779,theory(equality)]) ).
cnf(783,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)],[135,635,theory(equality)]),688,761,theory(equality)]) ).
cnf(809,plain,
ld(ld(ld(X,mult(X,Y)),Y),rd(ld(Z,Z),Y)) = rd(ld(X,X),Y),
inference('REWRITE',[status(thm)],[781,783,theory(equality)]) ).
cnf(830,plain,
ld(X,Y) = mult(rd(ld(X,Y),Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[759,c03,theory(equality)]),720,323,theory(equality)]) ).
cnf(852,plain,
mult(ld(X,X),Y) = ld(X,mult(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[732,127,theory(equality)]),129,theory(equality)]) ).
cnf(867,plain,
X = mult(rd(X,ld(Y,X)),ld(Y,X)),
inference('PARAMODULATE',[status(thm)],[759,830,theory(equality)]) ).
cnf(899,plain,
ld(ld(X,X),Y) = ld(X,mult(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[55,852,theory(equality)]),289,theory(equality)]) ).
cnf(911,plain,
ld(ld(X,X),mult(X,Y)) = mult(X,Y),
inference('REWRITE',[status(thm)],[53,899,theory(equality)]) ).
cnf(937,plain,
ld(X,Y) = ld(X,ld(ld(Z,Z),Y)),
inference('REWRITE',[status(thm)],[289,899,theory(equality)]) ).
cnf(939,plain,
mult(rd(X,Y),Y) = rd(mult(X,Y),ld(ld(Z,Z),Y)),
inference('REWRITE',[status(thm)],[724,899,theory(equality)]) ).
cnf(941,plain,
ld(X,ld(Y,Z)) = ld(X,ld(ld(ld(U,U),Y),Z)),
inference('REWRITE',[status(thm)],[312,899,theory(equality)]) ).
cnf(954,plain,
mult(X,ld(ld(Y,Y),Z)) = mult(X,Z),
inference('REWRITE',[status(thm)],[323,899,theory(equality)]) ).
cnf(956,plain,
mult(X,ld(ld(ld(Y,Y),Z),U)) = mult(X,ld(Z,U)),
inference('REWRITE',[status(thm)],[337,899,theory(equality)]) ).
cnf(976,plain,
ld(ld(ld(X,Y),ld(X,Y)),Z) = ld(ld(X,X),Z),
inference('REWRITE',[status(thm)],[55,899,theory(equality)]) ).
cnf(977,plain,
ld(ld(mult(X,Y),mult(X,Y)),Z) = ld(ld(X,X),Z),
inference('REWRITE',[status(thm)],[84,899,theory(equality)]) ).
cnf(981,plain,
mult(X,mult(rd(Y,Z),Z)) = mult(rd(mult(X,Y),Z),Z),
inference('REWRITE',[status(thm)],[772,911,977,theory(equality)]) ).
cnf(1005,plain,
mult(X,ld(X,Y)) = ld(ld(X,X),Y),
inference('REWRITE',[status(thm)],[c03,899,theory(equality)]) ).
cnf(1010,plain,
ld(ld(ld(X,X),Y),Y) = mult(rd(ld(X,X),Y),Y),
inference('REWRITE',[status(thm)],[127,899,theory(equality)]) ).
cnf(1023,plain,
ld(ld(X,X),mult(ld(Y,Z),U)) = mult(ld(ld(ld(X,X),Y),Z),U),
inference('REWRITE',[status(thm)],[317,899,theory(equality)]) ).
cnf(1030,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)],[339,1023,899,theory(equality)]) ).
cnf(1066,plain,
ld(ld(X,X),Y) = ld(ld(rd(X,Z),rd(X,Z)),Y),
inference('REWRITE',[status(thm)],[754,899,theory(equality)]) ).
cnf(1076,plain,
ld(ld(ld(ld(X,X),Y),Y),rd(Z,Y)) = ld(ld(X,X),rd(Z,Y)),
inference('REWRITE',[status(thm)],[783,899,theory(equality)]) ).
cnf(1090,plain,
ld(ld(X,X),rd(ld(Y,Y),Z)) = rd(ld(X,X),Z),
inference('REWRITE',[status(thm)],[809,1076,899,theory(equality)]) ).
cnf(1094,plain,
mult(ld(X,X),Y) = ld(ld(X,X),Y),
inference('REWRITE',[status(thm)],[852,899,theory(equality)]) ).
cnf(1099,plain,
ld(ld(X,X),ld(Y,Y)) = mult(rd(ld(X,X),Z),mult(rd(Z,Y),Y)),
inference('REWRITE',[status(thm)],[1030,937,1094,theory(equality)]) ).
cnf(1105,plain,
ld(ld(X,X),ld(X,Y)) = ld(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[911,830,theory(equality)]),976,1066,theory(equality)]) ).
cnf(1127,plain,
ld(ld(X,X),ld(Y,Y)) = rd(ld(X,X),ld(Y,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1090,14,theory(equality)]),1105,theory(equality)]) ).
cnf(1138,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)],[685,1127,theory(equality)]),634,theory(equality)]) ).
cnf(1179,plain,
rd(X,mult(Y,X)) = rd(X,ld(ld(Z,Z),mult(Y,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[939,759,theory(equality)]),585,theory(equality)]) ).
cnf(1195,plain,
rd(X,ld(Y,Y)) = rd(X,ld(ld(Z,Z),ld(Y,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[939,634,theory(equality)]),1138,585,theory(equality)]) ).
cnf(1214,plain,
mult(rd(X,ld(Y,X)),mult(rd(ld(Y,X),Z),Z)) = mult(rd(X,Z),Z),
inference('PARAMODULATE',[status(thm)],[981,867,theory(equality)]) ).
cnf(1222,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)],[981,634,theory(equality)]),981,956,1010,theory(equality)]) ).
cnf(1225,plain,
mult(mult(rd(X,Y),Y),ld(Z,Z)) = mult(X,ld(Z,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[981,728,theory(equality)]),981,956,1010,theory(equality)]) ).
cnf(1282,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)],[1099,c04,theory(equality)]),1010,732,theory(equality)]) ).
cnf(1337,plain,
rd(X,ld(ld(ld(Y,Y),X),X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1179,1010,theory(equality)]),398,1195,941,theory(equality)]) ).
cnf(1345,plain,
mult(X,Y) = mult(mult(X,Y),ld(Y,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[981,1337,theory(equality)]),77,1005,954,398,1195,1282,theory(equality)]) ).
cnf(1352,plain,
rd(X,ld(Y,Y)) = mult(rd(X,Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1345,699,theory(equality)]),77,1094,14,1222,theory(equality)]) ).
cnf(1360,plain,
mult(X,ld(Y,Y)) = mult(rd(X,Z),mult(rd(Z,Y),Y)),
inference('REWRITE',[status(thm)],[1222,1225,1352,theory(equality)]) ).
cnf(1369,plain,
mult(X,ld(Y,Y)) = mult(rd(X,Y),Y),
inference('REWRITE',[status(thm)],[1214,1360,theory(equality)]) ).
cnf(1460,plain,
mult(a,ld(mult(b,c),mult(b,c))) != mult(a,ld(c,c)),
inference('REWRITE',[status(thm)],[11,1369,theory(equality)]) ).
cnf(1462,plain,
ld(ld(X,X),ld(Y,Y)) = ld(mult(X,Y),mult(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[899,1345,theory(equality)]),977,theory(equality)]) ).
cnf(1464,plain,
$false,
inference('REWRITE',[status(thm)],[1460,954,1462,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP684-1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n029.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 12:18:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 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)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T12:18:40
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n029.cluster.edu at 2022-06-13T12:18:40
% 0.92/1.13
% 0.92/1.13
% 0.92/1.13 #||
% 0.92/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.13 % SZS output start Refutation
% See solution above
% 0.92/1.16 ||#
% 0.92/1.16
% 0.92/1.16 ; Summary of computation:
% 0.92/1.16 ; 4888 formulas have been input or derived (from 109 formulas).
% 0.92/1.16 ; 1464 (30%) were retained. Of these,
% 0.92/1.16 ; 1234 (84%) were simplified or subsumed later,
% 0.92/1.16 ; 230 (16%) are still being kept.
% 0.92/1.16 ;
% 0.92/1.16 ; Run time in seconds excluding printing time:
% 0.92/1.16 ; 0.002 0% Read assertion file (1 call)
% 0.92/1.16 ; 0.001 0% Assert (8 calls)
% 0.92/1.16 ; 0.185 28% Process new row (4,828 calls)
% 0.92/1.16 ; 0.014 2% Resolution (216 calls)
% 0.92/1.16 ; 0.066 10% Paramodulation (108 calls)
% 0.92/1.16 ; 0.181 27% Forward simplification (4,583 calls)
% 0.92/1.16 ; 0.089 13% Backward simplification (1,461 calls)
% 0.92/1.16 ; 0.071 11% Ordering (14,535 calls)
% 0.92/1.16 ; 0.000 0% Sortal reasoning (32 calls)
% 0.92/1.16 ; 0.000 0% Purity testing (1 call)
% 0.92/1.16 ; 0.052 8% Other
% 0.92/1.16 ; 0.661 Total
% 0.92/1.16 ; 0.691 Real time
% 0.92/1.16 ;
% 0.92/1.16 ; Term-hash-array has 4,492 terms in all.
% 0.92/1.16 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.92/1.16 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.92/1.16 ; Path-index has 775 entries (1,261 at peak, 5,322 added, 4,547 deleted).
% 0.92/1.16 ; Path-index has 7,467 nodes (7,556 at peak, 13,967 added, 6,500 deleted).
% 0.92/1.16 ; Trie-index has 775 entries (1,261 at peak, 5,322 added, 4,547 deleted).
% 0.92/1.16 ; Trie-index has 4,499 nodes (8,440 at peak, 36,825 added, 32,326 deleted).
% 0.92/1.16 ; Retrieved 52,883 generalization terms in 56,540 calls.
% 0.92/1.16 ; Retrieved 5,182 instance terms in 1,737 calls.
% 0.92/1.16 ; Retrieved 10,570 unifiable terms in 719 calls.
% 0.92/1.16 ;
% 0.92/1.16 ; The agenda of rows to process has 27 entries:
% 0.92/1.16 ; 7 with value 31 2 with value 36 2 with value 41
% 0.92/1.16 ; 5 with value 32 6 with value 40 3 with value 44
% 0.92/1.16 ; 2 with value 35
% 0.92/1.16 ; The agenda of input rows to give has 1 entry:
% 0.92/1.16 ; 1 with value 14
% 0.92/1.16 ; The agenda of rows to give has 200 entries:
% 0.92/1.16 ; 2 with value (4 20) 12 with value (4 28) 5 with value (4 36)
% 0.92/1.16 ; 2 with value (4 21) 23 with value (4 29) 1 with value (4 37)
% 0.92/1.16 ; 4 with value (4 22) 16 with value (4 30) 5 with value (4 38)
% 0.92/1.16 ; 3 with value (4 23) 10 with value (4 31) 2 with value (4 39)
% 0.92/1.16 ; 5 with value (4 24) 8 with value (4 32) 3 with value (4 40)
% 0.92/1.16 ; 24 with value (4 25) 10 with value (4 33) 2 with value (4 41)
% 0.92/1.16 ; 12 with value (4 26) 13 with value (4 34) 8 with value (4 42)
% 0.92/1.16 ; 12 with value (4 27) 12 with value (4 35) 6 with value (4 43)
% 0.92/1.16 Evaluation took:
% 0.92/1.16 0.691 seconds of real time
% 0.92/1.16 0.630936 seconds of user run time
% 0.92/1.16 0.059864 seconds of system run time
% 0.92/1.16 [Run times include 0.046 seconds GC run time.]
% 0.92/1.16 0 calls to %EVAL
% 0.92/1.16 0 page faults and
% 0.92/1.16 69,236,432 bytes consed.
% 0.92/1.16 :PROOF-FOUND
% 0.92/1.16 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T12:18:40
% 0.92/1.16 :PROOF-FOUND
% 0.92/1.16 *
%------------------------------------------------------------------------------