TSTP Solution File: GRP687-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP687-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:48:59 EDT 2022
% Result : Unsatisfiable 3.57s 3.82s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 8
% Syntax : Number of clauses : 124 ( 124 unt; 0 nHn; 124 RR)
% Number of literals : 124 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP687-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP687-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP687-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP687-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP687-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP687-1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(u,mult(u,v)),w),mult(mult(u,u),mult(v,w))),
file('GRP687-1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(mult(mult(a,mult(b,b)),c),mult(a,mult(b,mult(b,c)))),
file('GRP687-1.p',unknown),
[] ).
cnf(27,plain,
equal(ld(u,u),unit),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(28,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(34,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(52,plain,
equal(mult(mult(u,u),mult(v,unit)),mult(u,mult(u,v))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(53,plain,
equal(rd(mult(mult(u,u),mult(v,w)),w),mult(u,mult(u,v))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(54,plain,
equal(ld(mult(u,mult(u,v)),mult(mult(u,u),mult(v,w))),w),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(61,plain,
equal(mult(mult(u,u),mult(ld(u,v),w)),mult(mult(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(62,plain,
equal(mult(mult(rd(u,v),rd(u,v)),mult(v,w)),mult(mult(rd(u,v),u),w)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(64,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[5,52]),
[iquote('0:Rew:5.0,52.0')] ).
cnf(65,plain,
equal(mult(mult(u,mult(u,v)),w),mult(u,mult(u,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[64,7]),
[iquote('0:Rew:64.0,7.0')] ).
cnf(69,plain,
equal(rd(mult(u,mult(u,mult(v,w))),w),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[64,53]),
[iquote('0:Rew:64.0,53.0')] ).
cnf(70,plain,
equal(ld(mult(u,mult(u,v)),mult(u,mult(u,mult(v,w)))),w),
inference(rew,[status(thm),theory(equality)],[64,54]),
[iquote('0:Rew:64.0,54.0')] ).
cnf(72,plain,
equal(mult(u,mult(u,mult(ld(u,v),w))),mult(mult(u,v),w)),
inference(rew,[status(thm),theory(equality)],[64,61]),
[iquote('0:Rew:64.0,61.0')] ).
cnf(73,plain,
equal(mult(rd(u,v),mult(rd(u,v),mult(v,w))),mult(mult(rd(u,v),u),w)),
inference(rew,[status(thm),theory(equality)],[64,62]),
[iquote('0:Rew:64.0,62.0')] ).
cnf(77,plain,
equal(rd(mult(u,mult(u,v)),v),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[64,4]),
[iquote('0:SpR:64.0,4.0')] ).
cnf(78,plain,
equal(ld(mult(u,u),mult(u,mult(u,v))),v),
inference(spr,[status(thm),theory(equality)],[64,2]),
[iquote('0:SpR:64.0,2.0')] ).
cnf(119,plain,
equal(rd(mult(u,v),ld(u,v)),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[1,77]),
[iquote('0:SpR:1.0,77.0')] ).
cnf(138,plain,
equal(ld(mult(u,u),mult(u,v)),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[1,78]),
[iquote('0:SpR:1.0,78.0')] ).
cnf(203,plain,
equal(rd(u,ld(u,unit)),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[5,119]),
[iquote('0:SpR:5.0,119.0')] ).
cnf(205,plain,
equal(rd(u,ld(rd(u,v),v)),mult(rd(u,v),rd(u,v))),
inference(spr,[status(thm),theory(equality)],[3,119]),
[iquote('0:SpR:3.0,119.0')] ).
cnf(219,plain,
equal(mult(rd(unit,u),rd(unit,u)),rd(rd(unit,u),u)),
inference(spr,[status(thm),theory(equality)],[28,203]),
[iquote('0:SpR:28.0,203.0')] ).
cnf(242,plain,
equal(ld(mult(u,u),v),ld(u,ld(u,v))),
inference(spr,[status(thm),theory(equality)],[1,138]),
[iquote('0:SpR:1.0,138.0')] ).
cnf(294,plain,
equal(rd(mult(u,mult(u,v)),w),mult(u,mult(u,rd(v,w)))),
inference(spr,[status(thm),theory(equality)],[3,69]),
[iquote('0:SpR:3.0,69.0')] ).
cnf(378,plain,
equal(mult(rd(unit,u),mult(rd(unit,u),v)),mult(rd(rd(unit,u),u),v)),
inference(spr,[status(thm),theory(equality)],[219,64]),
[iquote('0:SpR:219.0,64.0')] ).
cnf(379,plain,
equal(ld(rd(unit,u),ld(rd(unit,u),v)),ld(rd(rd(unit,u),u),v)),
inference(spr,[status(thm),theory(equality)],[219,242]),
[iquote('0:SpR:219.0,242.0')] ).
cnf(468,plain,
equal(ld(mult(u,mult(u,v)),mult(u,mult(u,w))),ld(v,w)),
inference(spr,[status(thm),theory(equality)],[1,70]),
[iquote('0:SpR:1.0,70.0')] ).
cnf(598,plain,
equal(mult(mult(u,v),ld(ld(u,v),w)),mult(u,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[1,72]),
[iquote('0:SpR:1.0,72.0')] ).
cnf(703,plain,
equal(mult(rd(u,v),mult(rd(u,v),mult(mult(v,w),x))),mult(mult(mult(rd(u,v),u),w),x)),
inference(spr,[status(thm),theory(equality)],[73,65]),
[iquote('0:SpR:73.0,65.0')] ).
cnf(704,plain,
equal(mult(rd(u,rd(v,w)),mult(rd(u,rd(v,w)),mult(mult(rd(v,w),v),x))),mult(mult(rd(u,rd(v,w)),u),mult(rd(v,w),mult(w,x)))),
inference(spr,[status(thm),theory(equality)],[73]),
[iquote('0:SpR:73.0,73.0')] ).
cnf(770,plain,
equal(mult(mult(rd(u,rd(v,w)),u),mult(rd(v,w),mult(w,x))),mult(mult(mult(rd(u,rd(v,w)),u),v),x)),
inference(rew,[status(thm),theory(equality)],[703,704]),
[iquote('0:Rew:703.0,704.0')] ).
cnf(771,plain,
equal(mult(u,mult(u,rd(v,mult(u,v)))),u),
inference(spr,[status(thm),theory(equality)],[294,4]),
[iquote('0:SpR:294.0,4.0')] ).
cnf(786,plain,
equal(mult(u,mult(u,rd(unit,v))),rd(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[5,294]),
[iquote('0:SpR:5.0,294.0')] ).
cnf(822,plain,
equal(mult(u,rd(v,mult(u,v))),ld(u,u)),
inference(spr,[status(thm),theory(equality)],[771,2]),
[iquote('0:SpR:771.0,2.0')] ).
cnf(849,plain,
equal(mult(u,rd(v,mult(u,v))),unit),
inference(rew,[status(thm),theory(equality)],[27,822]),
[iquote('0:Rew:27.0,822.0')] ).
cnf(878,plain,
equal(rd(u,mult(v,u)),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[849,2]),
[iquote('0:SpR:849.0,2.0')] ).
cnf(888,plain,
equal(mult(u,rd(unit,u)),unit),
inference(spr,[status(thm),theory(equality)],[5,849]),
[iquote('0:SpR:5.0,849.0')] ).
cnf(928,plain,
equal(rd(unit,u),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[888,2]),
[iquote('0:SpR:888.0,2.0')] ).
cnf(938,plain,
equal(mult(ld(u,unit),u),unit),
inference(spr,[status(thm),theory(equality)],[34,888]),
[iquote('0:SpR:34.0,888.0')] ).
cnf(942,plain,
equal(mult(ld(u,unit),ld(u,unit)),rd(ld(u,unit),u)),
inference(rew,[status(thm),theory(equality)],[928,219]),
[iquote('0:Rew:928.0,219.0')] ).
cnf(947,plain,
equal(mult(ld(u,unit),mult(ld(u,unit),v)),mult(rd(ld(u,unit),u),v)),
inference(rew,[status(thm),theory(equality)],[928,378]),
[iquote('0:Rew:928.0,378.0')] ).
cnf(948,plain,
equal(ld(ld(u,unit),ld(ld(u,unit),v)),ld(rd(ld(u,unit),u),v)),
inference(rew,[status(thm),theory(equality)],[928,379]),
[iquote('0:Rew:928.0,379.0')] ).
cnf(956,plain,
equal(mult(u,mult(u,ld(v,unit))),rd(mult(u,u),v)),
inference(rew,[status(thm),theory(equality)],[928,786]),
[iquote('0:Rew:928.0,786.0')] ).
cnf(1065,plain,
equal(rd(unit,ld(ld(u,unit),u)),mult(ld(u,unit),ld(u,unit))),
inference(spr,[status(thm),theory(equality)],[928,205]),
[iquote('0:SpR:928.0,205.0')] ).
cnf(1075,plain,
equal(mult(ld(u,unit),ld(u,unit)),ld(ld(ld(u,unit),u),unit)),
inference(rew,[status(thm),theory(equality)],[928,1065]),
[iquote('0:Rew:928.0,1065.0')] ).
cnf(1076,plain,
equal(ld(ld(ld(u,unit),u),unit),rd(ld(u,unit),u)),
inference(rew,[status(thm),theory(equality)],[942,1075]),
[iquote('0:Rew:942.0,1075.0')] ).
cnf(1086,plain,
equal(mult(ld(u,unit),mult(ld(u,unit),rd(u,v))),rd(mult(ld(u,unit),unit),v)),
inference(spr,[status(thm),theory(equality)],[938,294]),
[iquote('0:SpR:938.0,294.0')] ).
cnf(1098,plain,
equal(mult(ld(u,unit),mult(ld(u,unit),rd(u,v))),rd(ld(u,unit),v)),
inference(rew,[status(thm),theory(equality)],[5,1086]),
[iquote('0:Rew:5.0,1086.0')] ).
cnf(1099,plain,
equal(mult(rd(ld(u,unit),u),rd(u,v)),rd(ld(u,unit),v)),
inference(rew,[status(thm),theory(equality)],[947,1098]),
[iquote('0:Rew:947.0,1098.0')] ).
cnf(1118,plain,
equal(ld(ld(u,unit),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[878,28]),
[iquote('0:SpR:878.0,28.0')] ).
cnf(1127,plain,
equal(rd(ld(u,v),v),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[1,878]),
[iquote('0:SpR:1.0,878.0')] ).
cnf(1128,plain,
equal(ld(rd(u,v),unit),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[3,878]),
[iquote('0:SpR:3.0,878.0')] ).
cnf(1134,plain,
equal(mult(u,ld(ld(u,unit),v)),ld(rd(ld(u,unit),u),v)),
inference(rew,[status(thm),theory(equality)],[1118,948]),
[iquote('0:Rew:1118.0,948.0')] ).
cnf(1137,plain,
equal(rd(ld(u,unit),u),ld(mult(u,u),unit)),
inference(rew,[status(thm),theory(equality)],[1118,1076]),
[iquote('0:Rew:1118.0,1076.0')] ).
cnf(1146,plain,
equal(rd(ld(u,unit),u),ld(u,ld(u,unit))),
inference(rew,[status(thm),theory(equality)],[242,1137]),
[iquote('0:Rew:242.0,1137.0')] ).
cnf(1150,plain,
equal(mult(ld(u,unit),mult(ld(u,unit),v)),mult(ld(u,ld(u,unit)),v)),
inference(rew,[status(thm),theory(equality)],[1146,947]),
[iquote('0:Rew:1146.0,947.0')] ).
cnf(1157,plain,
equal(mult(ld(u,ld(u,unit)),rd(u,v)),rd(ld(u,unit),v)),
inference(rew,[status(thm),theory(equality)],[1146,1099]),
[iquote('0:Rew:1146.0,1099.0')] ).
cnf(1162,plain,
equal(ld(ld(u,ld(u,unit)),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[1118,1134,1146]),
[iquote('0:Rew:1118.0,1134.0,1146.0,1134.0')] ).
cnf(1184,plain,
equal(ld(mult(ld(u,unit),mult(ld(u,unit),v)),mult(ld(u,unit),unit)),ld(v,u)),
inference(spr,[status(thm),theory(equality)],[938,468]),
[iquote('0:SpR:938.0,468.0')] ).
cnf(1186,plain,
equal(ld(mult(u,mult(u,v)),mult(u,w)),ld(v,ld(u,w))),
inference(spr,[status(thm),theory(equality)],[1,468]),
[iquote('0:SpR:1.0,468.0')] ).
cnf(1196,plain,
equal(ld(mult(ld(u,unit),unit),mult(ld(u,unit),mult(ld(u,unit),v))),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[938,468]),
[iquote('0:SpR:938.0,468.0')] ).
cnf(1218,plain,
equal(ld(mult(ld(u,unit),mult(ld(u,unit),v)),ld(u,unit)),ld(v,u)),
inference(rew,[status(thm),theory(equality)],[5,1184]),
[iquote('0:Rew:5.0,1184.0')] ).
cnf(1219,plain,
equal(ld(mult(ld(u,ld(u,unit)),v),ld(u,unit)),ld(v,u)),
inference(rew,[status(thm),theory(equality)],[1150,1218]),
[iquote('0:Rew:1150.0,1218.0')] ).
cnf(1222,plain,
equal(mult(ld(u,unit),v),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[2,1196,5]),
[iquote('0:Rew:2.0,1196.0,5.0,1196.0')] ).
cnf(1226,plain,
equal(mult(ld(u,ld(u,unit)),v),mult(ld(u,unit),ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1222,1150]),
[iquote('0:Rew:1222.0,1150.0')] ).
cnf(1233,plain,
equal(mult(ld(u,ld(u,unit)),v),ld(u,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1222,1226]),
[iquote('0:Rew:1222.0,1226.0')] ).
cnf(1237,plain,
equal(ld(ld(u,ld(u,v)),ld(u,unit)),ld(v,u)),
inference(rew,[status(thm),theory(equality)],[1233,1219]),
[iquote('0:Rew:1233.0,1219.0')] ).
cnf(1238,plain,
equal(ld(u,ld(u,rd(u,v))),rd(ld(u,unit),v)),
inference(rew,[status(thm),theory(equality)],[1233,1157]),
[iquote('0:Rew:1233.0,1157.0')] ).
cnf(1392,plain,
equal(mult(ld(u,unit),mult(ld(u,unit),mult(v,w))),mult(mult(ld(u,unit),ld(u,v)),w)),
inference(spr,[status(thm),theory(equality)],[1127,73]),
[iquote('0:SpR:1127.0,73.0')] ).
cnf(1416,plain,
equal(mult(ld(u,ld(u,v)),w),ld(u,ld(u,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[1222,1392]),
[iquote('0:Rew:1222.0,1392.0,1222.0,1392.0,1222.0,1392.0')] ).
cnf(1425,plain,
equal(mult(rd(u,v),w),ld(rd(v,u),w)),
inference(spr,[status(thm),theory(equality)],[1128,1118]),
[iquote('0:SpR:1128.0,1118.0')] ).
cnf(1461,plain,
equal(mult(mult(rd(u,rd(v,w)),u),ld(rd(w,v),mult(w,x))),mult(mult(mult(rd(u,rd(v,w)),u),v),x)),
inference(rew,[status(thm),theory(equality)],[1425,770]),
[iquote('0:Rew:1425.0,770.0')] ).
cnf(1523,plain,
equal(mult(ld(rd(rd(u,v),w),w),ld(rd(v,u),mult(v,x))),mult(mult(ld(rd(rd(u,v),w),w),u),x)),
inference(rew,[status(thm),theory(equality)],[1425,1461]),
[iquote('0:Rew:1425.0,1461.0')] ).
cnf(1918,plain,
equal(rd(rd(mult(u,u),v),mult(u,ld(v,unit))),u),
inference(spr,[status(thm),theory(equality)],[956,4]),
[iquote('0:SpR:956.0,4.0')] ).
cnf(1923,plain,
equal(mult(u,mult(u,mult(ld(v,unit),w))),mult(rd(mult(u,u),v),w)),
inference(spr,[status(thm),theory(equality)],[956,65]),
[iquote('0:SpR:956.0,65.0')] ).
cnf(1951,plain,
equal(mult(u,mult(u,ld(v,w))),ld(rd(v,mult(u,u)),w)),
inference(rew,[status(thm),theory(equality)],[1222,1923,1425]),
[iquote('0:Rew:1222.0,1923.0,1425.0,1923.0')] ).
cnf(2198,plain,
equal(rd(ld(u,v),ld(v,unit)),ld(ld(v,ld(v,u)),unit)),
inference(spr,[status(thm),theory(equality)],[1237,1127]),
[iquote('0:SpR:1237.0,1127.0')] ).
cnf(2201,plain,
equal(rd(ld(u,unit),ld(v,u)),ld(u,ld(u,v))),
inference(spr,[status(thm),theory(equality)],[1237,34]),
[iquote('0:SpR:1237.0,34.0')] ).
cnf(2212,plain,
equal(ld(ld(u,v),ld(u,unit)),ld(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[2,1237]),
[iquote('0:SpR:2.0,1237.0')] ).
cnf(2223,plain,
equal(ld(ld(u,ld(u,ld(mult(u,u),v))),ld(mult(u,u),unit)),ld(v,mult(u,u))),
inference(spr,[status(thm),theory(equality)],[242,1237]),
[iquote('0:SpR:242.0,1237.0')] ).
cnf(2248,plain,
equal(ld(ld(u,ld(u,ld(u,ld(u,v)))),ld(u,ld(u,unit))),ld(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[242,2223]),
[iquote('0:Rew:242.0,2223.0,242.0,2223.0')] ).
cnf(2298,plain,
equal(rd(ld(u,unit),mult(v,u)),ld(u,ld(u,ld(v,unit)))),
inference(spr,[status(thm),theory(equality)],[878,1238]),
[iquote('0:SpR:878.0,1238.0')] ).
cnf(2718,plain,
equal(ld(rd(unit,u),ld(rd(unit,u),v)),rd(u,ld(v,rd(unit,u)))),
inference(spr,[status(thm),theory(equality)],[28,2201]),
[iquote('0:SpR:28.0,2201.0')] ).
cnf(2737,plain,
equal(rd(u,ld(v,ld(u,unit))),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[1118,2718,928]),
[iquote('0:Rew:1118.0,2718.0,1118.0,2718.0,928.0,2718.0')] ).
cnf(2775,plain,
equal(ld(ld(u,ld(u,v)),ld(mult(u,u),unit)),ld(mult(mult(u,u),v),mult(u,u))),
inference(spr,[status(thm),theory(equality)],[242,2212]),
[iquote('0:SpR:242.0,2212.0')] ).
cnf(2802,plain,
equal(ld(ld(u,ld(u,v)),ld(u,ld(u,unit))),ld(mult(u,mult(u,v)),mult(u,u))),
inference(rew,[status(thm),theory(equality)],[242,2775,64]),
[iquote('0:Rew:242.0,2775.0,64.0,2775.0')] ).
cnf(2803,plain,
equal(ld(ld(u,ld(u,v)),ld(u,ld(u,unit))),ld(v,ld(u,u))),
inference(rew,[status(thm),theory(equality)],[1186,2802]),
[iquote('0:Rew:1186.0,2802.0')] ).
cnf(2804,plain,
equal(ld(ld(u,ld(u,v)),ld(u,ld(u,unit))),ld(v,unit)),
inference(rew,[status(thm),theory(equality)],[27,2803]),
[iquote('0:Rew:27.0,2803.0')] ).
cnf(2805,plain,
equal(ld(ld(u,ld(u,v)),unit),ld(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[2804,2248]),
[iquote('0:Rew:2804.0,2248.0')] ).
cnf(2808,plain,
equal(rd(ld(u,v),ld(v,unit)),ld(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[2805,2198]),
[iquote('0:Rew:2805.0,2198.0')] ).
cnf(3525,plain,
equal(rd(u,mult(v,ld(u,unit))),mult(u,mult(u,ld(v,unit)))),
inference(spr,[status(thm),theory(equality)],[1118,2737]),
[iquote('0:SpR:1118.0,2737.0')] ).
cnf(3536,plain,
equal(rd(u,mult(v,ld(u,unit))),ld(rd(v,mult(u,u)),unit)),
inference(rew,[status(thm),theory(equality)],[1951,3525]),
[iquote('0:Rew:1951.0,3525.0')] ).
cnf(3537,plain,
equal(rd(u,mult(v,ld(u,unit))),rd(mult(u,u),v)),
inference(rew,[status(thm),theory(equality)],[1128,3536]),
[iquote('0:Rew:1128.0,3536.0')] ).
cnf(3597,plain,
equal(mult(ld(u,mult(v,v)),w),ld(ld(v,ld(v,u)),w)),
inference(spr,[status(thm),theory(equality)],[2805,1222]),
[iquote('0:SpR:2805.0,1222.0')] ).
cnf(3744,plain,
equal(rd(mult(u,v),ld(v,unit)),ld(ld(u,unit),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[1118,2808]),
[iquote('0:SpR:1118.0,2808.0')] ).
cnf(3764,plain,
equal(rd(mult(u,v),ld(v,unit)),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1118,3744]),
[iquote('0:Rew:1118.0,3744.0')] ).
cnf(3995,plain,
equal(rd(mult(u,ld(v,unit)),v),ld(rd(mult(v,v),u),unit)),
inference(spr,[status(thm),theory(equality)],[3537,1128]),
[iquote('0:SpR:3537.0,1128.0')] ).
cnf(4033,plain,
equal(rd(mult(u,ld(v,unit)),v),rd(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1128,3995]),
[iquote('0:Rew:1128.0,3995.0')] ).
cnf(4283,plain,
equal(ld(rd(ld(u,unit),mult(v,u)),w),mult(mult(v,mult(u,u)),w)),
inference(spr,[status(thm),theory(equality)],[3764,1425]),
[iquote('0:SpR:3764.0,1425.0')] ).
cnf(4293,plain,
equal(mult(u,mult(rd(unit,v),rd(unit,v))),rd(mult(u,rd(unit,v)),v)),
inference(spr,[status(thm),theory(equality)],[28,3764]),
[iquote('0:SpR:28.0,3764.0')] ).
cnf(4322,plain,
equal(ld(ld(u,ld(u,ld(v,unit))),w),mult(mult(v,mult(u,u)),w)),
inference(rew,[status(thm),theory(equality)],[2298,4283]),
[iquote('0:Rew:2298.0,4283.0')] ).
cnf(4326,plain,
equal(rd(mult(u,ld(v,unit)),v),mult(u,ld(v,ld(v,unit)))),
inference(rew,[status(thm),theory(equality)],[1222,4293,928]),
[iquote('0:Rew:1222.0,4293.0,928.0,4293.0')] ).
cnf(4327,plain,
equal(mult(u,ld(v,ld(v,unit))),rd(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[4033,4326]),
[iquote('0:Rew:4033.0,4326.0')] ).
cnf(5261,plain,
equal(ld(u,rd(u,mult(v,v))),ld(v,ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[4327,2]),
[iquote('0:SpR:4327.0,2.0')] ).
cnf(5262,plain,
equal(mult(u,mult(u,mult(ld(v,ld(v,unit)),w))),mult(mult(u,rd(u,mult(v,v))),w)),
inference(spr,[status(thm),theory(equality)],[4327,65]),
[iquote('0:SpR:4327.0,65.0')] ).
cnf(5343,plain,
equal(ld(rd(u,mult(v,v)),ld(u,mult(unit,w))),mult(mult(v,rd(v,mult(u,u))),w)),
inference(rew,[status(thm),theory(equality)],[1951,5262,1416]),
[iquote('0:Rew:1951.0,5262.0,1416.0,5262.0')] ).
cnf(5344,plain,
equal(mult(mult(u,rd(u,mult(v,v))),w),ld(rd(v,mult(u,u)),ld(v,w))),
inference(rew,[status(thm),theory(equality)],[6,5343]),
[iquote('0:Rew:6.0,5343.0')] ).
cnf(6083,plain,
equal(mult(mult(u,rd(u,mult(v,v))),ld(ld(v,ld(v,unit)),w)),mult(u,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[5261,598]),
[iquote('0:SpR:5261.0,598.0')] ).
cnf(6154,plain,
equal(mult(mult(u,rd(u,mult(v,v))),mult(v,mult(v,w))),mult(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[1162,6083]),
[iquote('0:Rew:1162.0,6083.0')] ).
cnf(6155,plain,
equal(ld(rd(u,mult(v,v)),ld(u,mult(u,mult(u,w)))),mult(v,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[5344,6154]),
[iquote('0:Rew:5344.0,6154.0')] ).
cnf(6156,plain,
equal(ld(rd(u,mult(v,v)),mult(u,w)),mult(v,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[2,6155]),
[iquote('0:Rew:2.0,6155.0')] ).
cnf(9363,plain,
equal(mult(ld(u,mult(u,ld(v,unit))),ld(rd(v,mult(u,u)),mult(v,w))),mult(mult(ld(u,mult(u,ld(v,unit))),mult(u,u)),w)),
inference(spr,[status(thm),theory(equality)],[1918,1523]),
[iquote('0:SpR:1918.0,1523.0')] ).
cnf(9396,plain,
equal(ld(u,ld(rd(u,mult(v,v)),mult(u,w))),mult(ld(u,mult(v,v)),w)),
inference(rew,[status(thm),theory(equality)],[1222,9363,2]),
[iquote('0:Rew:1222.0,9363.0,1222.0,9363.0,2.0,9363.0')] ).
cnf(9397,plain,
equal(ld(ld(u,ld(u,v)),w),ld(v,mult(u,mult(u,w)))),
inference(rew,[status(thm),theory(equality)],[6156,9396,3597]),
[iquote('0:Rew:6156.0,9396.0,3597.0,9396.0')] ).
cnf(9406,plain,
equal(ld(ld(u,unit),mult(v,mult(v,w))),mult(mult(u,mult(v,v)),w)),
inference(rew,[status(thm),theory(equality)],[9397,4322]),
[iquote('0:Rew:9397.0,4322.0')] ).
cnf(9441,plain,
equal(mult(mult(u,mult(v,v)),w),mult(u,mult(v,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[1118,9406]),
[iquote('0:Rew:1118.0,9406.0')] ).
cnf(9442,plain,
$false,
inference(unc,[status(thm)],[9441,8]),
[iquote('0:UnC:9441.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP687-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.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 12:46:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.57/3.82
% 3.57/3.82 SPASS V 3.9
% 3.57/3.82 SPASS beiseite: Proof found.
% 3.57/3.82 % SZS status Theorem
% 3.57/3.82 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.57/3.82 SPASS derived 4511 clauses, backtracked 0 clauses, performed 0 splits and kept 1419 clauses.
% 3.57/3.82 SPASS allocated 79957 KBytes.
% 3.57/3.82 SPASS spent 0:00:03.47 on the problem.
% 3.57/3.82 0:00:00.04 for the input.
% 3.57/3.82 0:00:00.00 for the FLOTTER CNF translation.
% 3.57/3.82 0:00:00.04 for inferences.
% 3.57/3.82 0:00:00.00 for the backtracking.
% 3.57/3.82 0:00:03.37 for the reduction.
% 3.57/3.82
% 3.57/3.82
% 3.57/3.82 Here is a proof with depth 12, length 124 :
% 3.57/3.82 % SZS output start Refutation
% See solution above
% 3.71/3.89 Formulae used in the proof : c01 c02 c03 c04 c05 c06 c07 goals
% 3.71/3.89
%------------------------------------------------------------------------------