TSTP Solution File: GRP667-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP667-3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 11:48:52 EDT 2022
% Result : Unsatisfiable 112.31s 112.47s
% Output : Refutation 112.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 10
% Syntax : Number of clauses : 200 ( 200 unt; 0 nHn; 200 RR)
% Number of literals : 200 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP667-3.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP667-3.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP667-3.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP667-3.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP667-3.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP667-3.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(u,mult(mult(v,w),v)),w),mult(mult(u,v),mult(mult(w,v),w))),
file('GRP667-3.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(mult(u,v),u),mult(u,mult(v,u))),
file('GRP667-3.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(f(u),f(u)),u),
file('GRP667-3.p',unknown),
[] ).
cnf(10,axiom,
~ equal(mult(mult(mult(a,b),c),b),mult(a,mult(b,mult(c,b)))),
file('GRP667-3.p',unknown),
[] ).
cnf(11,plain,
equal(mult(mult(u,mult(v,mult(w,v))),w),mult(mult(u,v),mult(w,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[8,7]),
[iquote('0:Rew:8.0,7.0,8.0,7.0')] ).
cnf(17,plain,
equal(rd(u,u),unit),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(33,plain,
equal(ld(unit,u),u),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(34,plain,
equal(ld(u,u),unit),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(36,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(38,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(58,plain,
equal(rd(mult(u,mult(v,u)),u),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(59,plain,
equal(ld(mult(u,v),mult(u,mult(v,u))),u),
inference(spr,[status(thm),theory(equality)],[8,2]),
[iquote('0:SpR:8.0,2.0')] ).
cnf(63,plain,
equal(mult(u,mult(ld(u,v),u)),mult(v,u)),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(64,plain,
equal(mult(f(u),mult(f(u),f(u))),mult(u,f(u))),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.0,8.0')] ).
cnf(65,plain,
equal(mult(rd(u,v),mult(v,rd(u,v))),mult(u,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(68,plain,
equal(mult(f(u),u),mult(u,f(u))),
inference(rew,[status(thm),theory(equality)],[9,64]),
[iquote('0:Rew:9.0,64.0')] ).
cnf(79,plain,
equal(rd(mult(u,f(u)),u),f(u)),
inference(spr,[status(thm),theory(equality)],[68,4]),
[iquote('0:SpR:68.0,4.0')] ).
cnf(81,plain,
equal(mult(mult(u,f(u)),f(u)),mult(f(u),mult(u,f(u)))),
inference(spr,[status(thm),theory(equality)],[68,8]),
[iquote('0:SpR:68.0,8.0')] ).
cnf(101,plain,
equal(rd(mult(u,v),u),mult(u,rd(v,u))),
inference(spr,[status(thm),theory(equality)],[3,58]),
[iquote('0:SpR:3.0,58.0')] ).
cnf(107,plain,
equal(mult(u,rd(f(u),u)),f(u)),
inference(rew,[status(thm),theory(equality)],[101,79]),
[iquote('0:Rew:101.0,79.0')] ).
cnf(117,plain,
equal(rd(f(u),u),ld(u,f(u))),
inference(spr,[status(thm),theory(equality)],[107,2]),
[iquote('0:SpR:107.0,2.0')] ).
cnf(135,plain,
equal(mult(mult(u,v),mult(u,mult(v,u))),mult(u,mult(mult(v,mult(u,v)),u))),
inference(spr,[status(thm),theory(equality)],[11,8]),
[iquote('0:SpR:11.0,8.0')] ).
cnf(136,plain,
equal(mult(mult(u,v),mult(unit,mult(v,unit))),mult(u,mult(v,mult(unit,v)))),
inference(spr,[status(thm),theory(equality)],[11,5]),
[iquote('0:SpR:11.0,5.0')] ).
cnf(137,plain,
equal(rd(mult(mult(u,v),mult(w,mult(v,w))),w),mult(u,mult(v,mult(w,v)))),
inference(spr,[status(thm),theory(equality)],[11,4]),
[iquote('0:SpR:11.0,4.0')] ).
cnf(145,plain,
equal(mult(mult(u,mult(v,mult(v,f(v)))),f(v)),mult(mult(u,v),mult(f(v),mult(v,f(v))))),
inference(spr,[status(thm),theory(equality)],[68,11]),
[iquote('0:SpR:68.0,11.0')] ).
cnf(149,plain,
equal(mult(mult(u,f(v)),mult(f(v),mult(f(v),f(v)))),mult(mult(u,mult(f(v),v)),f(v))),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(150,plain,
equal(mult(mult(u,v),mult(rd(w,v),mult(v,rd(w,v)))),mult(mult(u,mult(v,w)),rd(w,v))),
inference(spr,[status(thm),theory(equality)],[3,11]),
[iquote('0:SpR:3.0,11.0')] ).
cnf(152,plain,
equal(mult(mult(unit,u),mult(v,mult(u,v))),mult(mult(u,mult(v,u)),v)),
inference(spr,[status(thm),theory(equality)],[6,11]),
[iquote('0:SpR:6.0,11.0')] ).
cnf(156,plain,
equal(mult(mult(rd(u,mult(v,mult(w,v))),v),mult(w,mult(v,w))),mult(u,w)),
inference(spr,[status(thm),theory(equality)],[3,11]),
[iquote('0:SpR:3.0,11.0')] ).
cnf(157,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[6,136,5]),
[iquote('0:Rew:6.0,136.0,5.0,136.0,6.0,136.0')] ).
cnf(158,plain,
equal(mult(f(u),mult(u,f(u))),mult(u,mult(f(u),f(u)))),
inference(rew,[status(thm),theory(equality)],[157,81]),
[iquote('0:Rew:157.0,81.0')] ).
cnf(159,plain,
equal(mult(f(u),mult(u,f(u))),mult(u,u)),
inference(rew,[status(thm),theory(equality)],[9,158]),
[iquote('0:Rew:9.0,158.0')] ).
cnf(163,plain,
equal(mult(mult(u,mult(v,u)),v),mult(u,mult(v,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[6,152]),
[iquote('0:Rew:6.0,152.0')] ).
cnf(164,plain,
equal(mult(mult(u,v),mult(u,mult(v,u))),mult(u,mult(v,mult(u,mult(v,u))))),
inference(rew,[status(thm),theory(equality)],[163,135]),
[iquote('0:Rew:163.0,135.0')] ).
cnf(165,plain,
equal(mult(mult(u,mult(v,w)),rd(w,v)),mult(mult(u,v),mult(w,rd(w,v)))),
inference(rew,[status(thm),theory(equality)],[65,150]),
[iquote('0:Rew:65.0,150.0')] ).
cnf(166,plain,
equal(mult(mult(u,mult(v,f(v))),f(v)),mult(mult(u,f(v)),mult(v,f(v)))),
inference(rew,[status(thm),theory(equality)],[68,149,9]),
[iquote('0:Rew:68.0,149.0,9.0,149.0,68.0,149.0')] ).
cnf(168,plain,
equal(mult(mult(u,mult(v,mult(v,f(v)))),f(v)),mult(mult(u,v),mult(v,v))),
inference(rew,[status(thm),theory(equality)],[159,145]),
[iquote('0:Rew:159.0,145.0')] ).
cnf(286,plain,
equal(mult(ld(u,v),u),ld(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[63,2]),
[iquote('0:SpR:63.0,2.0')] ).
cnf(288,plain,
equal(ld(mult(u,v),mult(v,mult(mult(ld(v,u),v),v))),v),
inference(spr,[status(thm),theory(equality)],[63,59]),
[iquote('0:SpR:63.0,59.0')] ).
cnf(321,plain,
equal(ld(mult(u,v),mult(v,ld(v,mult(u,mult(v,v))))),v),
inference(rew,[status(thm),theory(equality)],[157,288,286]),
[iquote('0:Rew:157.0,288.0,286.0,288.0,286.0,288.0')] ).
cnf(322,plain,
equal(ld(mult(u,v),mult(u,mult(v,v))),v),
inference(rew,[status(thm),theory(equality)],[1,321]),
[iquote('0:Rew:1.0,321.0')] ).
cnf(384,plain,
equal(rd(mult(u,mult(v,v)),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[157,4]),
[iquote('0:SpR:157.0,4.0')] ).
cnf(388,plain,
equal(mult(mult(u,mult(v,v)),v),mult(mult(u,v),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[157]),
[iquote('0:SpR:157.0,157.0')] ).
cnf(399,plain,
equal(mult(rd(u,v),mult(v,v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[3,157]),
[iquote('0:SpR:3.0,157.0')] ).
cnf(441,plain,
equal(mult(u,rd(unit,u)),rd(u,u)),
inference(spr,[status(thm),theory(equality)],[5,101]),
[iquote('0:SpR:5.0,101.0')] ).
cnf(442,plain,
equal(mult(u,rd(ld(u,v),u)),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[1,101]),
[iquote('0:SpR:1.0,101.0')] ).
cnf(450,plain,
equal(mult(u,rd(unit,u)),unit),
inference(rew,[status(thm),theory(equality)],[17,441]),
[iquote('0:Rew:17.0,441.0')] ).
cnf(459,plain,
equal(rd(unit,u),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[450,2]),
[iquote('0:SpR:450.0,2.0')] ).
cnf(548,plain,
equal(ld(ld(u,unit),unit),u),
inference(spr,[status(thm),theory(equality)],[459,36]),
[iquote('0:SpR:459.0,36.0')] ).
cnf(672,plain,
equal(rd(mult(u,mult(v,mult(u,v))),v),mult(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[163,4]),
[iquote('0:SpR:163.0,4.0')] ).
cnf(689,plain,
equal(mult(ld(u,v),mult(u,mult(ld(u,v),u))),mult(mult(ld(u,v),v),u)),
inference(spr,[status(thm),theory(equality)],[1,163]),
[iquote('0:SpR:1.0,163.0')] ).
cnf(708,plain,
equal(mult(mult(ld(u,v),v),u),mult(ld(u,v),mult(v,u))),
inference(rew,[status(thm),theory(equality)],[1,689,286]),
[iquote('0:Rew:1.0,689.0,286.0,689.0')] ).
cnf(726,plain,
equal(ld(mult(u,f(v)),mult(u,v)),f(v)),
inference(spr,[status(thm),theory(equality)],[9,322]),
[iquote('0:SpR:9.0,322.0')] ).
cnf(766,plain,
equal(rd(mult(u,v),f(v)),mult(u,f(v))),
inference(spr,[status(thm),theory(equality)],[726,38]),
[iquote('0:SpR:726.0,38.0')] ).
cnf(788,plain,
equal(ld(u,mult(rd(u,f(v)),v)),f(v)),
inference(spr,[status(thm),theory(equality)],[3,726]),
[iquote('0:SpR:3.0,726.0')] ).
cnf(846,plain,
equal(rd(mult(mult(u,f(v)),mult(v,f(v))),f(v)),mult(u,mult(v,f(v)))),
inference(spr,[status(thm),theory(equality)],[166,4]),
[iquote('0:SpR:166.0,4.0')] ).
cnf(850,plain,
equal(mult(mult(mult(u,f(v)),mult(v,f(v))),f(v)),mult(mult(u,mult(v,f(v))),mult(f(v),f(v)))),
inference(spr,[status(thm),theory(equality)],[166,157]),
[iquote('0:SpR:166.0,157.0')] ).
cnf(875,plain,
equal(mult(mult(u,mult(v,f(v))),v),mult(mult(u,v),mult(v,f(v)))),
inference(rew,[status(thm),theory(equality)],[9,850,157,166]),
[iquote('0:Rew:9.0,850.0,157.0,850.0,166.0,850.0,9.0,850.0')] ).
cnf(894,plain,
equal(mult(rd(u,v),f(v)),rd(u,f(v))),
inference(spr,[status(thm),theory(equality)],[3,766]),
[iquote('0:SpR:3.0,766.0')] ).
cnf(913,plain,
equal(mult(rd(u,f(v)),v),mult(u,f(v))),
inference(spr,[status(thm),theory(equality)],[788,1]),
[iquote('0:SpR:788.0,1.0')] ).
cnf(915,plain,
equal(mult(rd(unit,f(u)),u),f(u)),
inference(spr,[status(thm),theory(equality)],[788,33]),
[iquote('0:SpR:788.0,33.0')] ).
cnf(928,plain,
equal(mult(ld(f(u),unit),u),f(u)),
inference(rew,[status(thm),theory(equality)],[459,915]),
[iquote('0:Rew:459.0,915.0')] ).
cnf(939,plain,
equal(mult(u,mult(ld(f(u),unit),mult(u,ld(f(u),unit)))),mult(mult(u,f(u)),ld(f(u),unit))),
inference(spr,[status(thm),theory(equality)],[928,163]),
[iquote('0:SpR:928.0,163.0')] ).
cnf(942,plain,
equal(rd(f(u),u),ld(f(u),unit)),
inference(spr,[status(thm),theory(equality)],[928,4]),
[iquote('0:SpR:928.0,4.0')] ).
cnf(943,plain,
equal(ld(ld(f(u),unit),f(u)),u),
inference(spr,[status(thm),theory(equality)],[928,2]),
[iquote('0:SpR:928.0,2.0')] ).
cnf(944,plain,
equal(mult(ld(f(u),unit),mult(u,ld(f(u),unit))),mult(f(u),ld(f(u),unit))),
inference(spr,[status(thm),theory(equality)],[928,8]),
[iquote('0:SpR:928.0,8.0')] ).
cnf(954,plain,
equal(mult(mult(u,v),mult(ld(f(v),unit),mult(v,ld(f(v),unit)))),mult(mult(u,mult(v,f(v))),ld(f(v),unit))),
inference(spr,[status(thm),theory(equality)],[928,11]),
[iquote('0:SpR:928.0,11.0')] ).
cnf(959,plain,
equal(ld(u,f(u)),ld(f(u),unit)),
inference(rew,[status(thm),theory(equality)],[117,942]),
[iquote('0:Rew:117.0,942.0')] ).
cnf(966,plain,
equal(mult(ld(f(u),unit),mult(u,ld(f(u),unit))),unit),
inference(rew,[status(thm),theory(equality)],[1,944]),
[iquote('0:Rew:1.0,944.0')] ).
cnf(969,plain,
equal(mult(mult(u,f(u)),ld(f(u),unit)),mult(u,unit)),
inference(rew,[status(thm),theory(equality)],[966,939]),
[iquote('0:Rew:966.0,939.0')] ).
cnf(970,plain,
equal(mult(mult(u,f(u)),ld(f(u),unit)),u),
inference(rew,[status(thm),theory(equality)],[5,969]),
[iquote('0:Rew:5.0,969.0')] ).
cnf(971,plain,
equal(mult(mult(u,mult(v,f(v))),ld(f(v),unit)),mult(mult(u,v),unit)),
inference(rew,[status(thm),theory(equality)],[966,954]),
[iquote('0:Rew:966.0,954.0')] ).
cnf(972,plain,
equal(mult(mult(u,mult(v,f(v))),ld(f(v),unit)),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[5,971]),
[iquote('0:Rew:5.0,971.0')] ).
cnf(973,plain,
equal(mult(u,ld(f(u),unit)),f(u)),
inference(spr,[status(thm),theory(equality)],[959,1]),
[iquote('0:SpR:959.0,1.0')] ).
cnf(978,plain,
equal(mult(f(u),ld(u,f(u))),unit),
inference(spr,[status(thm),theory(equality)],[959,1]),
[iquote('0:SpR:959.0,1.0')] ).
cnf(1116,plain,
equal(mult(ld(f(u),unit),mult(u,mult(ld(f(u),unit),u))),mult(mult(ld(f(u),unit),f(u)),u)),
inference(spr,[status(thm),theory(equality)],[973,163]),
[iquote('0:SpR:973.0,163.0')] ).
cnf(1141,plain,
equal(mult(ld(f(u),unit),mult(u,f(u))),u),
inference(rew,[status(thm),theory(equality)],[928,1116,6,34,286]),
[iquote('0:Rew:928.0,1116.0,6.0,1116.0,34.0,1116.0,6.0,1116.0,286.0,1116.0')] ).
cnf(1161,plain,
equal(mult(f(u),rd(ld(u,f(u)),f(u))),rd(unit,f(u))),
inference(spr,[status(thm),theory(equality)],[978,101]),
[iquote('0:SpR:978.0,101.0')] ).
cnf(1176,plain,
equal(mult(f(u),rd(ld(u,f(u)),f(u))),ld(f(u),unit)),
inference(rew,[status(thm),theory(equality)],[459,1161]),
[iquote('0:Rew:459.0,1161.0')] ).
cnf(1229,plain,
equal(mult(mult(u,rd(v,u)),mult(u,v)),mult(u,mult(rd(v,u),mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[3,164]),
[iquote('0:SpR:3.0,164.0')] ).
cnf(1247,plain,
equal(mult(u,mult(ld(u,v),mult(u,mult(ld(u,v),u)))),mult(v,mult(u,mult(ld(u,v),u)))),
inference(spr,[status(thm),theory(equality)],[1,164]),
[iquote('0:SpR:1.0,164.0')] ).
cnf(1266,plain,
equal(mult(u,mult(ld(u,v),mult(v,u))),mult(v,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[1,1247,286]),
[iquote('0:Rew:1.0,1247.0,286.0,1247.0')] ).
cnf(1379,plain,
equal(mult(mult(u,f(u)),mult(ld(f(u),unit),ld(f(u),unit))),mult(u,ld(f(u),unit))),
inference(spr,[status(thm),theory(equality)],[970,157]),
[iquote('0:SpR:970.0,157.0')] ).
cnf(1396,plain,
equal(mult(mult(u,f(u)),mult(ld(f(u),unit),ld(f(u),unit))),f(u)),
inference(rew,[status(thm),theory(equality)],[973,1379]),
[iquote('0:Rew:973.0,1379.0')] ).
cnf(1490,plain,
equal(rd(mult(mult(u,mult(v,f(v))),mult(ld(f(v),unit),v)),ld(f(v),unit)),mult(u,mult(mult(v,f(v)),mult(ld(f(v),unit),mult(v,f(v)))))),
inference(spr,[status(thm),theory(equality)],[970,137]),
[iquote('0:SpR:970.0,137.0')] ).
cnf(1508,plain,
equal(rd(mult(u,mult(v,mult(w,v))),v),mult(rd(u,w),mult(w,mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[3,137]),
[iquote('0:SpR:3.0,137.0')] ).
cnf(1559,plain,
equal(rd(mult(mult(u,f(v)),mult(v,f(v))),ld(f(v),unit)),mult(u,mult(v,mult(v,f(v))))),
inference(rew,[status(thm),theory(equality)],[166,1490,928,68,8,1141]),
[iquote('0:Rew:166.0,1490.0,928.0,1490.0,68.0,1490.0,8.0,1490.0,1141.0,1490.0')] ).
cnf(1804,plain,
equal(mult(ld(u,unit),f(u)),rd(unit,f(u))),
inference(spr,[status(thm),theory(equality)],[459,894]),
[iquote('0:SpR:459.0,894.0')] ).
cnf(1811,plain,
equal(mult(ld(u,unit),f(u)),ld(f(u),unit)),
inference(rew,[status(thm),theory(equality)],[459,1804]),
[iquote('0:Rew:459.0,1804.0')] ).
cnf(1833,plain,
equal(rd(ld(f(u),unit),f(u)),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[1811,4]),
[iquote('0:SpR:1811.0,4.0')] ).
cnf(1840,plain,
equal(mult(ld(u,unit),rd(f(u),ld(u,unit))),rd(ld(f(u),unit),ld(u,unit))),
inference(spr,[status(thm),theory(equality)],[1811,101]),
[iquote('0:SpR:1811.0,101.0')] ).
cnf(1906,plain,
equal(rd(ld(u,f(u)),f(u)),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[959,1833]),
[iquote('0:SpR:959.0,1833.0')] ).
cnf(1909,plain,
equal(mult(f(u),ld(u,unit)),ld(f(u),unit)),
inference(rew,[status(thm),theory(equality)],[1906,1176]),
[iquote('0:Rew:1906.0,1176.0')] ).
cnf(2133,plain,
equal(rd(ld(f(u),unit),ld(u,unit)),f(u)),
inference(spr,[status(thm),theory(equality)],[1909,4]),
[iquote('0:SpR:1909.0,4.0')] ).
cnf(2167,plain,
equal(mult(ld(u,unit),rd(f(u),ld(u,unit))),f(u)),
inference(rew,[status(thm),theory(equality)],[2133,1840]),
[iquote('0:Rew:2133.0,1840.0')] ).
cnf(2316,plain,
equal(mult(mult(u,mult(mult(v,f(w)),mult(w,f(w)))),rd(f(w),mult(v,mult(w,f(w))))),mult(mult(u,mult(v,mult(w,f(w)))),mult(f(w),rd(f(w),mult(v,mult(w,f(w))))))),
inference(spr,[status(thm),theory(equality)],[166,165]),
[iquote('0:SpR:166.0,165.0')] ).
cnf(2507,plain,
equal(mult(mult(u,f(v)),v),mult(mult(u,v),f(v))),
inference(spr,[status(thm),theory(equality)],[766,913]),
[iquote('0:SpR:766.0,913.0')] ).
cnf(3563,plain,
equal(mult(rd(u,mult(v,v)),v),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[3,384]),
[iquote('0:SpR:3.0,384.0')] ).
cnf(3598,plain,
equal(ld(rd(u,v),mult(u,v)),mult(v,v)),
inference(spr,[status(thm),theory(equality)],[399,2]),
[iquote('0:SpR:399.0,2.0')] ).
cnf(3707,plain,
equal(rd(ld(u,v),u),ld(u,rd(v,u))),
inference(spr,[status(thm),theory(equality)],[442,2]),
[iquote('0:SpR:442.0,2.0')] ).
cnf(4950,plain,
equal(mult(ld(mult(u,u),unit),u),rd(unit,u)),
inference(spr,[status(thm),theory(equality)],[459,3563]),
[iquote('0:SpR:459.0,3563.0')] ).
cnf(4958,plain,
equal(mult(ld(mult(u,u),unit),u),ld(u,unit)),
inference(rew,[status(thm),theory(equality)],[459,4950]),
[iquote('0:Rew:459.0,4950.0')] ).
cnf(5001,plain,
equal(rd(ld(u,unit),u),ld(mult(u,u),unit)),
inference(spr,[status(thm),theory(equality)],[4958,4]),
[iquote('0:SpR:4958.0,4.0')] ).
cnf(5048,plain,
equal(ld(mult(u,u),unit),ld(u,rd(unit,u))),
inference(rew,[status(thm),theory(equality)],[3707,5001]),
[iquote('0:Rew:3707.0,5001.0')] ).
cnf(5049,plain,
equal(ld(mult(u,u),unit),ld(u,ld(u,unit))),
inference(rew,[status(thm),theory(equality)],[459,5048]),
[iquote('0:Rew:459.0,5048.0')] ).
cnf(5170,plain,
equal(ld(ld(u,ld(u,unit)),unit),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[5049,548]),
[iquote('0:SpR:5049.0,548.0')] ).
cnf(5761,plain,
equal(mult(rd(unit,u),rd(unit,u)),ld(ld(rd(unit,u),u),unit)),
inference(spr,[status(thm),theory(equality)],[36,5170]),
[iquote('0:SpR:36.0,5170.0')] ).
cnf(5782,plain,
equal(mult(ld(u,unit),ld(u,unit)),ld(ld(ld(u,unit),u),unit)),
inference(rew,[status(thm),theory(equality)],[459,5761]),
[iquote('0:Rew:459.0,5761.0')] ).
cnf(5790,plain,
equal(mult(mult(u,f(u)),ld(ld(ld(f(u),unit),f(u)),unit)),f(u)),
inference(rew,[status(thm),theory(equality)],[5782,1396]),
[iquote('0:Rew:5782.0,1396.0')] ).
cnf(5794,plain,
equal(mult(mult(u,f(u)),ld(u,unit)),f(u)),
inference(rew,[status(thm),theory(equality)],[943,5790]),
[iquote('0:Rew:943.0,5790.0')] ).
cnf(5827,plain,
equal(rd(f(u),ld(u,unit)),mult(u,f(u))),
inference(spr,[status(thm),theory(equality)],[5794,4]),
[iquote('0:SpR:5794.0,4.0')] ).
cnf(5853,plain,
equal(mult(mult(rd(u,mult(mult(v,f(v)),mult(ld(v,unit),mult(v,f(v))))),mult(v,f(v))),mult(ld(v,unit),f(v))),mult(u,ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[5794,156]),
[iquote('0:SpR:5794.0,156.0')] ).
cnf(5878,plain,
equal(mult(ld(u,unit),mult(u,f(u))),f(u)),
inference(rew,[status(thm),theory(equality)],[5827,2167]),
[iquote('0:Rew:5827.0,2167.0')] ).
cnf(5919,plain,
equal(mult(mult(rd(u,mult(mult(v,f(v)),mult(ld(v,unit),mult(v,f(v))))),mult(v,f(v))),ld(f(v),unit)),mult(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[1811,5853]),
[iquote('0:Rew:1811.0,5853.0')] ).
cnf(5920,plain,
equal(mult(rd(u,mult(mult(v,f(v)),f(v))),v),mult(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[972,5919,5878]),
[iquote('0:Rew:972.0,5919.0,5878.0,5919.0')] ).
cnf(5921,plain,
equal(mult(u,ld(v,unit)),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[3563,5920,9,157]),
[iquote('0:Rew:3563.0,5920.0,9.0,5920.0,157.0,5920.0')] ).
cnf(5971,plain,
equal(rd(mult(u,mult(v,f(v))),f(v)),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[5921,972]),
[iquote('0:Rew:5921.0,972.0')] ).
cnf(6013,plain,
equal(mult(mult(u,f(v)),v),mult(u,mult(v,f(v)))),
inference(rew,[status(thm),theory(equality)],[5971,846]),
[iquote('0:Rew:5971.0,846.0')] ).
cnf(6014,plain,
equal(mult(mult(u,v),f(v)),mult(u,mult(v,f(v)))),
inference(rew,[status(thm),theory(equality)],[2507,6013]),
[iquote('0:Rew:2507.0,6013.0')] ).
cnf(6018,plain,
equal(mult(mult(u,f(v)),v),mult(u,mult(v,f(v)))),
inference(rew,[status(thm),theory(equality)],[6014,2507]),
[iquote('0:Rew:6014.0,2507.0')] ).
cnf(6138,plain,
equal(ld(u,rd(u,v)),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[5921,2]),
[iquote('0:SpR:5921.0,2.0')] ).
cnf(6139,plain,
equal(mult(u,mult(ld(v,unit),u)),mult(rd(u,v),u)),
inference(spr,[status(thm),theory(equality)],[5921,8]),
[iquote('0:SpR:5921.0,8.0')] ).
cnf(6191,plain,
equal(rd(u,rd(unit,v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[36,5921]),
[iquote('0:SpR:36.0,5921.0')] ).
cnf(6205,plain,
equal(rd(u,ld(v,unit)),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[459,6191]),
[iquote('0:Rew:459.0,6191.0')] ).
cnf(6213,plain,
equal(mult(mult(mult(u,f(v)),mult(v,f(v))),f(v)),mult(u,mult(v,mult(v,f(v))))),
inference(rew,[status(thm),theory(equality)],[6205,1559]),
[iquote('0:Rew:6205.0,1559.0')] ).
cnf(6351,plain,
equal(mult(mult(u,v),mult(v,f(v))),mult(u,mult(v,mult(v,f(v))))),
inference(rew,[status(thm),theory(equality)],[9,6213,157,166]),
[iquote('0:Rew:9.0,6213.0,157.0,6213.0,166.0,6213.0')] ).
cnf(6357,plain,
equal(mult(mult(u,mult(v,f(v))),v),mult(u,mult(v,mult(v,f(v))))),
inference(rew,[status(thm),theory(equality)],[6351,875]),
[iquote('0:Rew:6351.0,875.0')] ).
cnf(6445,plain,
equal(ld(mult(u,v),u),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[4,6138]),
[iquote('0:SpR:4.0,6138.0')] ).
cnf(6451,plain,
equal(ld(ld(u,v),unit),ld(v,u)),
inference(spr,[status(thm),theory(equality)],[38,6138]),
[iquote('0:SpR:38.0,6138.0')] ).
cnf(6455,plain,
equal(ld(mult(u,v),mult(u,rd(v,u))),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[101,6138]),
[iquote('0:SpR:101.0,6138.0')] ).
cnf(6770,plain,
equal(rd(u,ld(v,w)),mult(u,ld(w,v))),
inference(spr,[status(thm),theory(equality)],[6451,5921]),
[iquote('0:SpR:6451.0,5921.0')] ).
cnf(6852,plain,
equal(mult(mult(u,mult(v,f(v))),f(v)),mult(mult(u,v),mult(f(v),f(v)))),
inference(spr,[status(thm),theory(equality)],[6014,157]),
[iquote('0:SpR:6014.0,157.0')] ).
cnf(6875,plain,
equal(mult(mult(u,mult(v,mult(w,f(w)))),rd(f(w),mult(v,w))),mult(mult(u,mult(v,w)),mult(f(w),rd(f(w),mult(v,w))))),
inference(spr,[status(thm),theory(equality)],[6014,165]),
[iquote('0:SpR:6014.0,165.0')] ).
cnf(6932,plain,
equal(mult(mult(u,f(v)),mult(v,f(v))),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[166,6852,157,9]),
[iquote('0:Rew:166.0,6852.0,157.0,6852.0,9.0,6852.0')] ).
cnf(6940,plain,
equal(mult(mult(u,mult(v,mult(w,f(w)))),mult(f(w),rd(f(w),mult(v,mult(w,f(w)))))),mult(mult(u,mult(v,mult(w,w))),rd(f(w),mult(v,mult(w,f(w)))))),
inference(rew,[status(thm),theory(equality)],[6932,2316]),
[iquote('0:Rew:6932.0,2316.0')] ).
cnf(12262,plain,
equal(rd(mult(rd(u,v),mult(v,u)),v),mult(rd(u,v),mult(v,rd(u,v)))),
inference(spr,[status(thm),theory(equality)],[3,672]),
[iquote('0:SpR:3.0,672.0')] ).
cnf(12320,plain,
equal(rd(mult(rd(u,v),mult(v,u)),v),mult(u,rd(u,v))),
inference(rew,[status(thm),theory(equality)],[65,12262]),
[iquote('0:Rew:65.0,12262.0')] ).
cnf(15022,plain,
equal(mult(ld(u,v),mult(v,u)),ld(u,mult(v,mult(v,u)))),
inference(spr,[status(thm),theory(equality)],[1266,2]),
[iquote('0:SpR:1266.0,2.0')] ).
cnf(15197,plain,
equal(mult(mult(ld(u,v),v),u),ld(u,mult(v,mult(v,u)))),
inference(rew,[status(thm),theory(equality)],[15022,708]),
[iquote('0:Rew:15022.0,708.0')] ).
cnf(17909,plain,
equal(mult(mult(u,mult(v,mult(v,f(v)))),f(v)),mult(mult(u,mult(v,f(v))),mult(v,f(v)))),
inference(spr,[status(thm),theory(equality)],[6357,6014]),
[iquote('0:SpR:6357.0,6014.0')] ).
cnf(18002,plain,
equal(mult(mult(u,mult(v,mult(v,f(v)))),f(v)),mult(u,mult(mult(v,f(v)),mult(v,f(v))))),
inference(rew,[status(thm),theory(equality)],[157,17909]),
[iquote('0:Rew:157.0,17909.0')] ).
cnf(18003,plain,
equal(mult(mult(u,v),mult(v,v)),mult(u,mult(v,mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[168,18002,6932]),
[iquote('0:Rew:168.0,18002.0,6932.0,18002.0')] ).
cnf(18004,plain,
equal(mult(mult(u,mult(v,v)),v),mult(u,mult(v,mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[18003,388]),
[iquote('0:Rew:18003.0,388.0')] ).
cnf(18752,plain,
equal(ld(rd(mult(u,mult(v,v)),v),mult(u,mult(v,mult(v,v)))),mult(v,v)),
inference(spr,[status(thm),theory(equality)],[18004,3598]),
[iquote('0:SpR:18004.0,3598.0')] ).
cnf(18859,plain,
equal(ld(mult(u,v),mult(u,mult(v,mult(v,v)))),mult(v,v)),
inference(rew,[status(thm),theory(equality)],[384,18752]),
[iquote('0:Rew:384.0,18752.0')] ).
cnf(21884,plain,
equal(ld(mult(u,v),mult(mult(u,rd(v,u)),mult(mult(u,rd(v,u)),mult(u,v)))),mult(mult(ld(u,unit),mult(u,rd(v,u))),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[6455,15197]),
[iquote('0:SpR:6455.0,15197.0')] ).
cnf(22114,plain,
equal(ld(mult(u,v),mult(mult(u,rd(v,u)),mult(u,mult(rd(v,u),mult(u,v))))),mult(mult(ld(u,unit),mult(u,rd(v,u))),mult(u,v))),
inference(rew,[status(thm),theory(equality)],[1229,21884]),
[iquote('0:Rew:1229.0,21884.0')] ).
cnf(33555,plain,
equal(rd(mult(u,mult(v,u)),u),mult(rd(unit,v),mult(v,mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[6,1508]),
[iquote('0:SpR:6.0,1508.0')] ).
cnf(33670,plain,
equal(mult(ld(u,unit),mult(u,mult(v,u))),mult(v,u)),
inference(rew,[status(thm),theory(equality)],[4,33555,101,459]),
[iquote('0:Rew:4.0,33555.0,101.0,33555.0,459.0,33555.0')] ).
cnf(33932,plain,
equal(mult(ld(u,unit),mult(u,v)),v),
inference(spr,[status(thm),theory(equality)],[3,33670]),
[iquote('0:SpR:3.0,33670.0')] ).
cnf(34025,plain,
equal(ld(mult(u,v),mult(mult(u,rd(v,u)),mult(u,mult(rd(v,u),mult(u,v))))),mult(rd(v,u),mult(u,v))),
inference(rew,[status(thm),theory(equality)],[33932,22114]),
[iquote('0:Rew:33932.0,22114.0')] ).
cnf(34328,plain,
equal(mult(mult(mult(u,v),ld(u,unit)),mult(mult(u,v),v)),mult(mult(u,v),mult(ld(u,unit),mult(mult(u,v),v)))),
inference(spr,[status(thm),theory(equality)],[33932,164]),
[iquote('0:SpR:33932.0,164.0')] ).
cnf(34342,plain,
equal(mult(rd(mult(u,v),u),mult(u,v)),mult(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[33932,6139]),
[iquote('0:SpR:33932.0,6139.0')] ).
cnf(34344,plain,
equal(rd(u,mult(v,u)),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[33932,4]),
[iquote('0:SpR:33932.0,4.0')] ).
cnf(34345,plain,
equal(ld(ld(u,unit),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[33932,2]),
[iquote('0:SpR:33932.0,2.0')] ).
cnf(34365,plain,
equal(ld(mult(u,v),unit),ld(v,ld(u,unit))),
inference(spr,[status(thm),theory(equality)],[33932,6445]),
[iquote('0:SpR:33932.0,6445.0')] ).
cnf(34401,plain,
equal(rd(mult(u,mult(mult(v,w),w)),mult(v,w)),mult(rd(u,ld(v,unit)),mult(ld(v,unit),mult(mult(v,w),ld(v,unit))))),
inference(spr,[status(thm),theory(equality)],[33932,1508]),
[iquote('0:SpR:33932.0,1508.0')] ).
cnf(34486,plain,
equal(mult(ld(u,unit),v),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[1,33932]),
[iquote('0:SpR:1.0,33932.0')] ).
cnf(35334,plain,
equal(mult(u,mult(rd(v,u),mult(u,v))),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1229,34342,101,157]),
[iquote('0:Rew:1229.0,34342.0,101.0,34342.0,157.0,34342.0')] ).
cnf(35379,plain,
equal(ld(mult(u,v),mult(mult(u,rd(v,u)),mult(u,mult(v,v)))),mult(rd(v,u),mult(u,v))),
inference(rew,[status(thm),theory(equality)],[35334,34025]),
[iquote('0:Rew:35334.0,34025.0')] ).
cnf(36357,plain,
equal(mult(mult(u,v),mult(ld(u,unit),mult(u,mult(v,v)))),mult(mult(u,rd(v,u)),mult(u,mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[101,34328,5921,157]),
[iquote('0:Rew:101.0,34328.0,5921.0,34328.0,157.0,34328.0')] ).
cnf(36358,plain,
equal(mult(mult(u,rd(v,u)),mult(u,mult(v,v))),mult(mult(u,v),ld(u,mult(u,mult(v,v))))),
inference(rew,[status(thm),theory(equality)],[34486,36357]),
[iquote('0:Rew:34486.0,36357.0')] ).
cnf(36359,plain,
equal(mult(mult(u,rd(v,u)),mult(u,mult(v,v))),mult(mult(u,v),mult(v,v))),
inference(rew,[status(thm),theory(equality)],[2,36358]),
[iquote('0:Rew:2.0,36358.0')] ).
cnf(36360,plain,
equal(mult(mult(u,rd(v,u)),mult(u,mult(v,v))),mult(u,mult(v,mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[18003,36359]),
[iquote('0:Rew:18003.0,36359.0')] ).
cnf(36361,plain,
equal(ld(mult(u,v),mult(u,mult(v,mult(v,v)))),mult(rd(v,u),mult(u,v))),
inference(rew,[status(thm),theory(equality)],[36360,35379]),
[iquote('0:Rew:36360.0,35379.0')] ).
cnf(36362,plain,
equal(mult(rd(u,v),mult(v,u)),mult(u,u)),
inference(rew,[status(thm),theory(equality)],[18859,36361]),
[iquote('0:Rew:18859.0,36361.0')] ).
cnf(36423,plain,
equal(rd(mult(u,u),v),mult(u,rd(u,v))),
inference(rew,[status(thm),theory(equality)],[36362,12320]),
[iquote('0:Rew:36362.0,12320.0')] ).
cnf(36614,plain,
equal(rd(mult(u,mult(v,mult(w,w))),mult(v,w)),mult(mult(u,v),mult(ld(v,unit),mult(v,rd(w,v))))),
inference(rew,[status(thm),theory(equality)],[157,34401,33,6770,101,5921]),
[iquote('0:Rew:157.0,34401.0,33.0,34401.0,6770.0,34401.0,101.0,34401.0,5921.0,34401.0')] ).
cnf(36615,plain,
equal(rd(mult(u,mult(v,mult(w,w))),mult(v,w)),mult(mult(u,v),ld(v,mult(v,rd(w,v))))),
inference(rew,[status(thm),theory(equality)],[34486,36614]),
[iquote('0:Rew:34486.0,36614.0')] ).
cnf(36616,plain,
equal(rd(mult(u,mult(v,mult(w,w))),mult(v,w)),mult(mult(u,v),rd(w,v))),
inference(rew,[status(thm),theory(equality)],[2,36615]),
[iquote('0:Rew:2.0,36615.0')] ).
cnf(39633,plain,
equal(rd(ld(u,v),v),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[1,34344]),
[iquote('0:SpR:1.0,34344.0')] ).
cnf(39639,plain,
equal(ld(rd(u,v),unit),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[3,34344]),
[iquote('0:SpR:3.0,34344.0')] ).
cnf(39640,plain,
equal(ld(rd(u,mult(v,v)),unit),rd(v,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[3563,34344]),
[iquote('0:SpR:3563.0,34344.0')] ).
cnf(39668,plain,
equal(rd(u,mult(v,mult(u,f(u)))),ld(mult(v,f(u)),unit)),
inference(spr,[status(thm),theory(equality)],[6018,34344]),
[iquote('0:SpR:6018.0,34344.0')] ).
cnf(39680,plain,
equal(rd(f(u),rd(v,f(u))),ld(rd(v,u),unit)),
inference(spr,[status(thm),theory(equality)],[894,34344]),
[iquote('0:SpR:894.0,34344.0')] ).
cnf(39682,plain,
equal(rd(f(u),mult(v,mult(u,f(u)))),ld(mult(v,u),unit)),
inference(spr,[status(thm),theory(equality)],[6014,34344]),
[iquote('0:SpR:6014.0,34344.0')] ).
cnf(39734,plain,
equal(rd(u,rd(v,u)),mult(u,rd(u,v))),
inference(rew,[status(thm),theory(equality)],[36423,39640,39639]),
[iquote('0:Rew:36423.0,39640.0,39639.0,39640.0')] ).
cnf(39828,plain,
equal(mult(f(u),rd(f(u),v)),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[39734,39680,39639]),
[iquote('0:Rew:39734.0,39680.0,39639.0,39680.0')] ).
cnf(39838,plain,
equal(mult(mult(u,mult(v,mult(w,f(w)))),rd(w,mult(v,mult(w,f(w))))),mult(mult(u,mult(v,mult(w,w))),rd(f(w),mult(v,mult(w,f(w)))))),
inference(rew,[status(thm),theory(equality)],[39828,6940]),
[iquote('0:Rew:39828.0,6940.0')] ).
cnf(39839,plain,
equal(mult(mult(u,mult(v,mult(w,f(w)))),rd(f(w),mult(v,w))),mult(mult(u,mult(v,w)),rd(w,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[39828,6875]),
[iquote('0:Rew:39828.0,6875.0')] ).
cnf(39883,plain,
equal(rd(u,mult(v,mult(u,f(u)))),ld(f(u),ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[34365,39668]),
[iquote('0:Rew:34365.0,39668.0')] ).
cnf(39904,plain,
equal(rd(f(u),mult(v,mult(u,f(u)))),ld(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[34365,39682]),
[iquote('0:Rew:34365.0,39682.0')] ).
cnf(40465,plain,
equal(mult(mult(u,mult(v,mult(w,f(w)))),rd(f(w),mult(v,w))),rd(mult(u,mult(v,w)),v)),
inference(rew,[status(thm),theory(equality)],[5921,39839,34344]),
[iquote('0:Rew:5921.0,39839.0,34344.0,39839.0')] ).
cnf(40515,plain,
equal(mult(mult(u,mult(v,mult(w,f(w)))),ld(f(w),ld(v,unit))),mult(mult(u,mult(v,mult(w,w))),ld(w,ld(v,unit)))),
inference(rew,[status(thm),theory(equality)],[39883,39838,39904]),
[iquote('0:Rew:39883.0,39838.0,39904.0,39838.0')] ).
cnf(40638,plain,
equal(mult(u,ld(v,ld(w,unit))),rd(u,mult(w,v))),
inference(spr,[status(thm),theory(equality)],[34345,6770]),
[iquote('0:SpR:34345.0,6770.0')] ).
cnf(41557,plain,
equal(rd(mult(u,mult(v,mult(w,f(w)))),mult(v,f(w))),mult(mult(u,mult(v,mult(w,w))),ld(w,ld(v,unit)))),
inference(rew,[status(thm),theory(equality)],[40638,40515]),
[iquote('0:Rew:40638.0,40515.0')] ).
cnf(42065,plain,
equal(rd(mult(u,mult(v,mult(w,f(w)))),mult(v,f(w))),mult(mult(u,v),rd(w,v))),
inference(rew,[status(thm),theory(equality)],[36616,41557,40638]),
[iquote('0:Rew:36616.0,41557.0,40638.0,41557.0')] ).
cnf(43001,plain,
equal(rd(f(u),mult(v,u)),ld(mult(v,f(u)),unit)),
inference(spr,[status(thm),theory(equality)],[726,39633]),
[iquote('0:SpR:726.0,39633.0')] ).
cnf(43238,plain,
equal(rd(f(u),mult(v,u)),ld(f(u),ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[34365,43001]),
[iquote('0:Rew:34365.0,43001.0')] ).
cnf(43240,plain,
equal(mult(mult(u,mult(v,mult(w,f(w)))),ld(f(w),ld(v,unit))),rd(mult(u,mult(v,w)),v)),
inference(rew,[status(thm),theory(equality)],[43238,40465]),
[iquote('0:Rew:43238.0,40465.0')] ).
cnf(43875,plain,
equal(rd(mult(u,mult(v,w)),v),mult(mult(u,v),rd(w,v))),
inference(rew,[status(thm),theory(equality)],[42065,43240,40638]),
[iquote('0:Rew:42065.0,43240.0,40638.0,43240.0')] ).
cnf(43876,plain,
equal(mult(mult(mult(u,v),w),rd(mult(v,w),w)),mult(u,mult(v,mult(w,v)))),
inference(rew,[status(thm),theory(equality)],[43875,137]),
[iquote('0:Rew:43875.0,137.0')] ).
cnf(44100,plain,
equal(mult(mult(mult(u,v),w),v),mult(u,mult(v,mult(w,v)))),
inference(rew,[status(thm),theory(equality)],[4,43876]),
[iquote('0:Rew:4.0,43876.0')] ).
cnf(44101,plain,
$false,
inference(unc,[status(thm)],[44100,10]),
[iquote('0:UnC:44100.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP667-3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 09:19:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 112.31/112.47
% 112.31/112.47 SPASS V 3.9
% 112.31/112.47 SPASS beiseite: Proof found.
% 112.31/112.47 % SZS status Theorem
% 112.31/112.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 112.31/112.47 SPASS derived 25074 clauses, backtracked 0 clauses, performed 0 splits and kept 12209 clauses.
% 112.31/112.47 SPASS allocated 161244 KBytes.
% 112.31/112.47 SPASS spent 0:1:52.08 on the problem.
% 112.31/112.47 0:00:00.04 for the input.
% 112.31/112.47 0:00:00.00 for the FLOTTER CNF translation.
% 112.31/112.47 0:00:00.22 for inferences.
% 112.31/112.47 0:00:00.00 for the backtracking.
% 112.31/112.47 0:1:51.77 for the reduction.
% 112.31/112.47
% 112.31/112.47
% 112.31/112.47 Here is a proof with depth 12, length 200 :
% 112.31/112.47 % SZS output start Refutation
% See solution above
% 112.94/113.10 Formulae used in the proof : c01 c02 c03 c04 c05 c06 c07 c08 c09 goals
% 112.94/113.10
%------------------------------------------------------------------------------