TSTP Solution File: GRP668-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP668-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:48:53 EDT 2022
% Result : Unsatisfiable 141.35s 141.68s
% Output : Refutation 142.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 9
% Syntax : Number of clauses : 127 ( 127 unt; 0 nHn; 127 RR)
% Number of literals : 127 ( 0 equ; 3 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; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP668-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP668-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP668-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP668-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP668-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP668-1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(mult(u,v),v),w),mult(u,mult(v,mult(v,w)))),
file('GRP668-1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(mult(u,v),u),mult(u,mult(v,u))),
file('GRP668-1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(mult(mult(a,mult(mult(b,c),b)),c),mult(mult(a,b),mult(mult(c,b),c))),
file('GRP668-1.p',unknown),
[] ).
cnf(10,plain,
~ equal(mult(mult(a,mult(b,mult(c,b))),c),mult(mult(a,b),mult(c,mult(b,c)))),
inference(rew,[status(thm),theory(equality)],[8,9]),
[iquote('0:Rew:8.0,9.0,8.0,9.0')] ).
cnf(15,plain,
equal(rd(u,u),unit),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(30,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(36,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(56,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(73,plain,
equal(rd(mult(u,v),u),mult(u,rd(v,u))),
inference(spr,[status(thm),theory(equality)],[3,56]),
[iquote('0:SpR:3.0,56.0')] ).
cnf(85,plain,
equal(mult(u,mult(v,mult(v,unit))),mult(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(86,plain,
equal(rd(mult(u,mult(v,mult(v,w))),w),mult(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(87,plain,
equal(ld(mult(mult(u,v),v),mult(u,mult(v,mult(v,w)))),w),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(90,plain,
equal(mult(u,mult(v,mult(v,ld(mult(mult(u,v),v),w)))),w),
inference(spr,[status(thm),theory(equality)],[7,1]),
[iquote('0:SpR:7.0,1.0')] ).
cnf(93,plain,
equal(mult(unit,mult(u,mult(u,v))),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(96,plain,
equal(mult(u,mult(ld(u,v),mult(ld(u,v),w))),mult(mult(v,ld(u,v)),w)),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(97,plain,
equal(mult(rd(u,v),mult(v,mult(v,w))),mult(mult(u,v),w)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(100,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[5,85]),
[iquote('0:Rew:5.0,85.0')] ).
cnf(101,plain,
equal(mult(mult(u,mult(v,v)),w),mult(u,mult(v,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[100,7]),
[iquote('0:Rew:100.0,7.0')] ).
cnf(102,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[6,93]),
[iquote('0:Rew:6.0,93.0')] ).
cnf(105,plain,
equal(rd(mult(u,mult(v,mult(v,w))),w),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[100,86]),
[iquote('0:Rew:100.0,86.0')] ).
cnf(106,plain,
equal(ld(mult(u,mult(v,v)),mult(u,mult(v,mult(v,w)))),w),
inference(rew,[status(thm),theory(equality)],[100,87]),
[iquote('0:Rew:100.0,87.0')] ).
cnf(107,plain,
equal(mult(u,mult(v,mult(v,ld(mult(u,mult(v,v)),w)))),w),
inference(rew,[status(thm),theory(equality)],[100,90]),
[iquote('0:Rew:100.0,90.0')] ).
cnf(166,plain,
equal(mult(u,rd(unit,u)),rd(u,u)),
inference(spr,[status(thm),theory(equality)],[5,73]),
[iquote('0:SpR:5.0,73.0')] ).
cnf(167,plain,
equal(mult(u,rd(ld(u,v),u)),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[1,73]),
[iquote('0:SpR:1.0,73.0')] ).
cnf(171,plain,
equal(mult(u,rd(unit,u)),unit),
inference(rew,[status(thm),theory(equality)],[15,166]),
[iquote('0:Rew:15.0,166.0')] ).
cnf(176,plain,
equal(rd(unit,u),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[171,2]),
[iquote('0:SpR:171.0,2.0')] ).
cnf(224,plain,
equal(ld(ld(u,unit),unit),u),
inference(spr,[status(thm),theory(equality)],[176,30]),
[iquote('0:SpR:176.0,30.0')] ).
cnf(242,plain,
equal(rd(mult(u,mult(v,v)),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[100,4]),
[iquote('0:SpR:100.0,4.0')] ).
cnf(255,plain,
equal(mult(rd(u,v),mult(v,v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[3,100]),
[iquote('0:SpR:3.0,100.0')] ).
cnf(277,plain,
equal(mult(u,mult(u,ld(mult(u,u),v))),v),
inference(spr,[status(thm),theory(equality)],[102,1]),
[iquote('0:SpR:102.0,1.0')] ).
cnf(403,plain,
equal(rd(ld(u,v),u),ld(u,rd(v,u))),
inference(spr,[status(thm),theory(equality)],[167,2]),
[iquote('0:SpR:167.0,2.0')] ).
cnf(421,plain,
equal(mult(ld(u,unit),rd(u,ld(u,unit))),rd(unit,ld(u,unit))),
inference(spr,[status(thm),theory(equality)],[224,167]),
[iquote('0:SpR:224.0,167.0')] ).
cnf(436,plain,
equal(mult(ld(u,unit),rd(u,ld(u,unit))),u),
inference(rew,[status(thm),theory(equality)],[224,421,176]),
[iquote('0:Rew:224.0,421.0,176.0,421.0')] ).
cnf(486,plain,
equal(rd(u,ld(u,unit)),ld(ld(u,unit),u)),
inference(spr,[status(thm),theory(equality)],[436,2]),
[iquote('0:SpR:436.0,2.0')] ).
cnf(602,plain,
equal(rd(mult(u,mult(v,w)),ld(v,w)),mult(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[1,105]),
[iquote('0:SpR:1.0,105.0')] ).
cnf(644,plain,
equal(mult(rd(u,mult(v,v)),v),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[3,242]),
[iquote('0:SpR:3.0,242.0')] ).
cnf(658,plain,
equal(rd(mult(u,v),mult(v,v)),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[255,4]),
[iquote('0:SpR:255.0,4.0')] ).
cnf(659,plain,
equal(ld(rd(u,v),mult(u,v)),mult(v,v)),
inference(spr,[status(thm),theory(equality)],[255,2]),
[iquote('0:SpR:255.0,2.0')] ).
cnf(790,plain,
equal(ld(mult(u,mult(v,v)),mult(u,mult(v,w))),ld(v,w)),
inference(spr,[status(thm),theory(equality)],[1,106]),
[iquote('0:SpR:1.0,106.0')] ).
cnf(863,plain,
equal(rd(mult(u,v),ld(mult(w,w),v)),mult(u,mult(w,w))),
inference(spr,[status(thm),theory(equality)],[277,105]),
[iquote('0:SpR:277.0,105.0')] ).
cnf(1016,plain,
equal(mult(ld(mult(u,u),unit),u),rd(unit,u)),
inference(spr,[status(thm),theory(equality)],[176,644]),
[iquote('0:SpR:176.0,644.0')] ).
cnf(1020,plain,
equal(mult(ld(mult(u,u),unit),u),ld(u,unit)),
inference(rew,[status(thm),theory(equality)],[176,1016]),
[iquote('0:Rew:176.0,1016.0')] ).
cnf(1037,plain,
equal(mult(u,mult(u,ld(mult(v,mult(u,u)),w))),ld(v,w)),
inference(spr,[status(thm),theory(equality)],[107,2]),
[iquote('0:SpR:107.0,2.0')] ).
cnf(1123,plain,
equal(rd(ld(u,unit),u),ld(mult(u,u),unit)),
inference(spr,[status(thm),theory(equality)],[1020,4]),
[iquote('0:SpR:1020.0,4.0')] ).
cnf(1142,plain,
equal(ld(mult(u,u),unit),ld(u,ld(u,unit))),
inference(rew,[status(thm),theory(equality)],[176,1123,403]),
[iquote('0:Rew:176.0,1123.0,403.0,1123.0')] ).
cnf(1248,plain,
equal(rd(u,mult(u,u)),rd(unit,u)),
inference(spr,[status(thm),theory(equality)],[6,658]),
[iquote('0:SpR:6.0,658.0')] ).
cnf(1262,plain,
equal(rd(u,mult(u,u)),ld(u,unit)),
inference(rew,[status(thm),theory(equality)],[176,1248]),
[iquote('0:Rew:176.0,1248.0')] ).
cnf(1296,plain,
equal(mult(rd(u,v),mult(v,w)),mult(mult(u,v),ld(v,w))),
inference(spr,[status(thm),theory(equality)],[1,97]),
[iquote('0:SpR:1.0,97.0')] ).
cnf(1305,plain,
equal(mult(rd(u,mult(v,mult(w,w))),mult(v,mult(w,mult(w,mult(mult(v,mult(w,w)),x))))),mult(mult(u,mult(v,mult(w,w))),x)),
inference(spr,[status(thm),theory(equality)],[101,97]),
[iquote('0:SpR:101.0,97.0')] ).
cnf(1315,plain,
equal(mult(ld(ld(u,unit),u),mult(ld(u,unit),mult(ld(u,unit),v))),mult(mult(u,ld(u,unit)),v)),
inference(spr,[status(thm),theory(equality)],[486,97]),
[iquote('0:SpR:486.0,97.0')] ).
cnf(1341,plain,
equal(mult(ld(ld(u,unit),u),mult(ld(u,unit),mult(ld(u,unit),v))),v),
inference(rew,[status(thm),theory(equality)],[6,1315,1]),
[iquote('0:Rew:6.0,1315.0,1.0,1315.0')] ).
cnf(1362,plain,
equal(mult(rd(u,mult(v,mult(w,w))),mult(v,mult(w,mult(w,mult(v,mult(w,mult(w,x))))))),mult(mult(u,mult(v,mult(w,w))),x)),
inference(rew,[status(thm),theory(equality)],[101,1305]),
[iquote('0:Rew:101.0,1305.0')] ).
cnf(1365,plain,
equal(ld(ld(u,unit),u),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[1262,30]),
[iquote('0:SpR:1262.0,30.0')] ).
cnf(1382,plain,
equal(mult(mult(u,u),mult(ld(u,unit),mult(ld(u,unit),v))),v),
inference(rew,[status(thm),theory(equality)],[1365,1341]),
[iquote('0:Rew:1365.0,1341.0')] ).
cnf(1387,plain,
equal(mult(u,mult(u,mult(ld(u,unit),mult(ld(u,unit),v)))),v),
inference(rew,[status(thm),theory(equality)],[102,1382]),
[iquote('0:Rew:102.0,1382.0')] ).
cnf(1388,plain,
equal(mult(u,mult(mult(unit,ld(u,unit)),v)),v),
inference(rew,[status(thm),theory(equality)],[96,1387]),
[iquote('0:Rew:96.0,1387.0')] ).
cnf(1389,plain,
equal(mult(u,mult(ld(u,unit),v)),v),
inference(rew,[status(thm),theory(equality)],[6,1388]),
[iquote('0:Rew:6.0,1388.0')] ).
cnf(1574,plain,
equal(mult(ld(u,unit),v),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[1389,2]),
[iquote('0:SpR:1389.0,2.0')] ).
cnf(1603,plain,
equal(ld(ld(u,unit),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[1,1389]),
[iquote('0:SpR:1.0,1389.0')] ).
cnf(1665,plain,
equal(rd(ld(u,v),v),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[1574,4]),
[iquote('0:SpR:1574.0,4.0')] ).
cnf(1683,plain,
equal(mult(ld(u,unit),mult(ld(u,unit),v)),mult(ld(u,ld(u,unit)),v)),
inference(spr,[status(thm),theory(equality)],[1574,102]),
[iquote('0:SpR:1574.0,102.0')] ).
cnf(1690,plain,
equal(mult(u,mult(ld(v,unit),mult(ld(v,unit),w))),mult(mult(u,ld(v,ld(v,unit))),w)),
inference(spr,[status(thm),theory(equality)],[1574,101]),
[iquote('0:SpR:1574.0,101.0')] ).
cnf(1692,plain,
equal(rd(mult(u,ld(v,ld(v,unit))),ld(v,unit)),mult(u,ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[1574,242]),
[iquote('0:SpR:1574.0,242.0')] ).
cnf(1693,plain,
equal(mult(rd(u,ld(v,ld(v,unit))),ld(v,unit)),rd(u,ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[1574,644]),
[iquote('0:SpR:1574.0,644.0')] ).
cnf(1698,plain,
equal(mult(ld(u,ld(u,unit)),v),ld(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[1142,1574]),
[iquote('0:SpR:1142.0,1574.0')] ).
cnf(1747,plain,
equal(mult(ld(u,ld(u,unit)),v),ld(u,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1574,1683]),
[iquote('0:Rew:1574.0,1683.0,1574.0,1683.0')] ).
cnf(1748,plain,
equal(ld(mult(u,u),v),ld(u,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1698,1747]),
[iquote('0:Rew:1698.0,1747.0')] ).
cnf(1757,plain,
equal(rd(mult(u,v),ld(w,ld(w,v))),mult(u,mult(w,w))),
inference(rew,[status(thm),theory(equality)],[1748,863]),
[iquote('0:Rew:1748.0,863.0')] ).
cnf(1764,plain,
equal(mult(ld(u,ld(u,unit)),v),ld(u,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1748,1698]),
[iquote('0:Rew:1748.0,1698.0')] ).
cnf(1782,plain,
equal(mult(mult(u,ld(v,ld(v,unit))),w),mult(u,ld(v,ld(v,w)))),
inference(rew,[status(thm),theory(equality)],[1574,1690]),
[iquote('0:Rew:1574.0,1690.0,1574.0,1690.0')] ).
cnf(1801,plain,
equal(rd(u,mult(v,u)),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[1603,36]),
[iquote('0:SpR:1603.0,36.0')] ).
cnf(1837,plain,
equal(ld(rd(u,v),unit),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[30,1665]),
[iquote('0:SpR:30.0,1665.0')] ).
cnf(1942,plain,
equal(ld(rd(u,mult(v,v)),unit),rd(v,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[644,1801]),
[iquote('0:SpR:644.0,1801.0')] ).
cnf(1953,plain,
equal(rd(mult(u,u),v),rd(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[1837,1942]),
[iquote('0:Rew:1837.0,1942.0')] ).
cnf(1969,plain,
equal(mult(rd(u,v),w),ld(rd(v,u),w)),
inference(spr,[status(thm),theory(equality)],[1837,1574]),
[iquote('0:SpR:1837.0,1574.0')] ).
cnf(2003,plain,
equal(ld(rd(ld(u,ld(u,unit)),v),ld(u,unit)),rd(v,ld(u,unit))),
inference(rew,[status(thm),theory(equality)],[1969,1693]),
[iquote('0:Rew:1969.0,1693.0')] ).
cnf(2018,plain,
equal(ld(rd(mult(u,mult(v,v)),w),mult(u,mult(v,mult(v,mult(u,mult(v,mult(v,x))))))),mult(mult(w,mult(u,mult(v,v))),x)),
inference(rew,[status(thm),theory(equality)],[1969,1362]),
[iquote('0:Rew:1969.0,1362.0')] ).
cnf(2023,plain,
equal(mult(mult(u,v),ld(v,w)),ld(rd(v,u),mult(v,w))),
inference(rew,[status(thm),theory(equality)],[1969,1296]),
[iquote('0:Rew:1969.0,1296.0')] ).
cnf(2103,plain,
equal(ld(ld(u,unit),mult(v,mult(u,v))),mult(mult(u,v),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[1801,659]),
[iquote('0:SpR:1801.0,659.0')] ).
cnf(2139,plain,
equal(mult(mult(u,v),mult(u,v)),mult(u,mult(v,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[1603,2103]),
[iquote('0:Rew:1603.0,2103.0')] ).
cnf(4356,plain,
equal(rd(mult(u,ld(v,ld(v,unit))),ld(v,ld(v,ld(v,ld(v,unit))))),rd(u,ld(v,ld(v,unit)))),
inference(spr,[status(thm),theory(equality)],[1764,658]),
[iquote('0:SpR:1764.0,658.0')] ).
cnf(4403,plain,
equal(rd(u,ld(v,ld(v,unit))),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1757,4356]),
[iquote('0:Rew:1757.0,4356.0')] ).
cnf(6225,plain,
equal(rd(ld(u,ld(u,unit)),v),ld(mult(v,mult(u,u)),unit)),
inference(spr,[status(thm),theory(equality)],[4403,1837]),
[iquote('0:SpR:4403.0,1837.0')] ).
cnf(6253,plain,
equal(mult(u,mult(rd(unit,v),rd(unit,v))),rd(u,ld(rd(unit,v),v))),
inference(spr,[status(thm),theory(equality)],[30,4403]),
[iquote('0:SpR:30.0,4403.0')] ).
cnf(6276,plain,
equal(ld(ld(mult(u,mult(v,v)),unit),ld(v,unit)),rd(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[6225,2003]),
[iquote('0:Rew:6225.0,2003.0')] ).
cnf(6302,plain,
equal(mult(u,ld(v,ld(v,unit))),rd(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[1574,6253,1603,176]),
[iquote('0:Rew:1574.0,6253.0,1603.0,6253.0,176.0,6253.0')] ).
cnf(6317,plain,
equal(rd(rd(u,mult(v,v)),ld(v,unit)),mult(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[6302,1692]),
[iquote('0:Rew:6302.0,1692.0')] ).
cnf(6318,plain,
equal(mult(rd(u,mult(v,v)),w),mult(u,ld(v,ld(v,w)))),
inference(rew,[status(thm),theory(equality)],[6302,1782]),
[iquote('0:Rew:6302.0,1782.0')] ).
cnf(6328,plain,
equal(mult(u,ld(v,ld(v,w))),ld(rd(v,rd(u,v)),w)),
inference(rew,[status(thm),theory(equality)],[1953,6318,1969]),
[iquote('0:Rew:1953.0,6318.0,1969.0,6318.0')] ).
cnf(6361,plain,
equal(rd(u,ld(v,unit)),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[5,6276,1,101,1603]),
[iquote('0:Rew:5.0,6276.0,1.0,6276.0,101.0,6276.0,1603.0,6276.0')] ).
cnf(6362,plain,
equal(mult(rd(u,mult(v,v)),v),mult(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[6361,6317]),
[iquote('0:Rew:6361.0,6317.0')] ).
cnf(6384,plain,
equal(mult(u,ld(v,unit)),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[30,6362,1953,1969]),
[iquote('0:Rew:30.0,6362.0,1953.0,6362.0,1969.0,6362.0')] ).
cnf(6663,plain,
equal(ld(mult(u,v),u),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[6361,30]),
[iquote('0:SpR:6361.0,30.0')] ).
cnf(6664,plain,
equal(rd(ld(u,unit),v),ld(mult(v,u),unit)),
inference(spr,[status(thm),theory(equality)],[6361,1837]),
[iquote('0:SpR:6361.0,1837.0')] ).
cnf(6697,plain,
equal(rd(u,rd(v,w)),mult(u,rd(w,v))),
inference(spr,[status(thm),theory(equality)],[1837,6361]),
[iquote('0:SpR:1837.0,6361.0')] ).
cnf(6789,plain,
equal(mult(u,ld(v,ld(v,w))),ld(mult(v,rd(v,u)),w)),
inference(rew,[status(thm),theory(equality)],[6697,6328]),
[iquote('0:Rew:6697.0,6328.0')] ).
cnf(7280,plain,
equal(rd(ld(u,unit),v),ld(u,ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[6384,1574]),
[iquote('0:SpR:6384.0,1574.0')] ).
cnf(7294,plain,
equal(mult(u,mult(v,mult(v,ld(w,unit)))),rd(mult(u,mult(v,v)),w)),
inference(spr,[status(thm),theory(equality)],[6384,101]),
[iquote('0:SpR:6384.0,101.0')] ).
cnf(7318,plain,
equal(ld(mult(u,v),unit),ld(v,ld(u,unit))),
inference(rew,[status(thm),theory(equality)],[6664,7280]),
[iquote('0:Rew:6664.0,7280.0')] ).
cnf(7531,plain,
equal(rd(mult(u,mult(v,v)),w),mult(u,mult(v,rd(v,w)))),
inference(rew,[status(thm),theory(equality)],[6384,7294]),
[iquote('0:Rew:6384.0,7294.0')] ).
cnf(7543,plain,
equal(ld(mult(u,mult(v,rd(v,w))),mult(u,mult(v,mult(v,mult(u,mult(v,mult(v,x))))))),mult(mult(w,mult(u,mult(v,v))),x)),
inference(rew,[status(thm),theory(equality)],[7531,2018]),
[iquote('0:Rew:7531.0,2018.0')] ).
cnf(7730,plain,
equal(ld(ld(u,v),unit),ld(v,u)),
inference(spr,[status(thm),theory(equality)],[1,6663]),
[iquote('0:SpR:1.0,6663.0')] ).
cnf(8213,plain,
equal(rd(u,ld(v,w)),mult(u,ld(w,v))),
inference(spr,[status(thm),theory(equality)],[7730,6361]),
[iquote('0:SpR:7730.0,6361.0')] ).
cnf(8378,plain,
equal(mult(mult(u,mult(v,w)),ld(w,v)),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[8213,602]),
[iquote('0:Rew:8213.0,602.0')] ).
cnf(8967,plain,
equal(ld(ld(u,ld(v,unit)),w),mult(mult(v,u),w)),
inference(spr,[status(thm),theory(equality)],[7318,1603]),
[iquote('0:SpR:7318.0,1603.0')] ).
cnf(8973,plain,
equal(mult(u,ld(v,ld(w,unit))),rd(u,mult(w,v))),
inference(spr,[status(thm),theory(equality)],[7318,6384]),
[iquote('0:SpR:7318.0,6384.0')] ).
cnf(14881,plain,
equal(ld(mult(u,mult(v,v)),mult(u,w)),ld(v,ld(v,w))),
inference(spr,[status(thm),theory(equality)],[1,790]),
[iquote('0:SpR:1.0,790.0')] ).
cnf(16214,plain,
equal(mult(u,rd(u,mult(v,mult(w,mult(u,u))))),ld(w,ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[8973,1037]),
[iquote('0:SpR:8973.0,1037.0')] ).
cnf(24464,plain,
equal(mult(mult(u,mult(mult(v,w),v)),w),mult(u,mult(mult(v,w),mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[2,8378]),
[iquote('0:SpR:2.0,8378.0')] ).
cnf(24533,plain,
equal(mult(mult(u,mult(v,mult(w,w))),ld(w,mult(v,w))),mult(u,mult(mult(v,w),mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[100,8378]),
[iquote('0:SpR:100.0,8378.0')] ).
cnf(24590,plain,
equal(mult(mult(u,mult(v,mult(w,v))),w),mult(u,mult(v,mult(w,mult(v,w))))),
inference(rew,[status(thm),theory(equality)],[8,24464,2139]),
[iquote('0:Rew:8.0,24464.0,2139.0,24464.0')] ).
cnf(24591,plain,
~ equal(mult(mult(a,b),mult(c,mult(b,c))),mult(a,mult(b,mult(c,mult(b,c))))),
inference(rew,[status(thm),theory(equality)],[24590,10]),
[iquote('0:Rew:24590.0,10.0')] ).
cnf(24634,plain,
equal(mult(mult(u,mult(v,mult(w,w))),ld(w,mult(v,w))),mult(u,mult(v,mult(w,mult(v,w))))),
inference(rew,[status(thm),theory(equality)],[2139,24533]),
[iquote('0:Rew:2139.0,24533.0')] ).
cnf(52861,plain,
equal(ld(rd(mult(u,mult(v,v)),w),mult(mult(u,mult(v,v)),mult(u,x))),mult(mult(w,mult(u,mult(v,v))),ld(v,ld(v,x)))),
inference(spr,[status(thm),theory(equality)],[14881,2023]),
[iquote('0:SpR:14881.0,2023.0')] ).
cnf(53304,plain,
equal(ld(mult(u,mult(v,rd(v,w))),mult(u,mult(v,mult(v,mult(u,x))))),ld(mult(v,rd(v,mult(w,mult(u,mult(v,v))))),x)),
inference(rew,[status(thm),theory(equality)],[7531,52861,101,6789]),
[iquote('0:Rew:7531.0,52861.0,101.0,52861.0,6789.0,52861.0')] ).
cnf(53305,plain,
equal(ld(mult(u,mult(v,rd(v,w))),mult(u,mult(v,mult(v,mult(u,x))))),ld(ld(u,ld(w,unit)),x)),
inference(rew,[status(thm),theory(equality)],[16214,53304]),
[iquote('0:Rew:16214.0,53304.0')] ).
cnf(53306,plain,
equal(ld(mult(u,mult(v,rd(v,w))),mult(u,mult(v,mult(v,mult(u,x))))),mult(mult(w,u),x)),
inference(rew,[status(thm),theory(equality)],[8967,53305]),
[iquote('0:Rew:8967.0,53305.0')] ).
cnf(53307,plain,
equal(mult(mult(u,mult(v,mult(w,w))),x),mult(mult(u,v),mult(w,mult(w,x)))),
inference(rew,[status(thm),theory(equality)],[53306,7543]),
[iquote('0:Rew:53306.0,7543.0')] ).
cnf(53321,plain,
equal(mult(mult(u,v),mult(w,mult(w,ld(w,mult(v,w))))),mult(u,mult(v,mult(w,mult(v,w))))),
inference(rew,[status(thm),theory(equality)],[53307,24634]),
[iquote('0:Rew:53307.0,24634.0')] ).
cnf(53327,plain,
equal(mult(mult(u,v),mult(w,mult(v,w))),mult(u,mult(v,mult(w,mult(v,w))))),
inference(rew,[status(thm),theory(equality)],[1,53321]),
[iquote('0:Rew:1.0,53321.0')] ).
cnf(53328,plain,
$false,
inference(unc,[status(thm)],[53327,24591]),
[iquote('0:UnC:53327.0,24591.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP668-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 17:36:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 141.35/141.68
% 141.35/141.68 SPASS V 3.9
% 141.35/141.68 SPASS beiseite: Proof found.
% 141.35/141.68 % SZS status Theorem
% 141.35/141.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 141.35/141.68 SPASS derived 22829 clauses, backtracked 0 clauses, performed 0 splits and kept 8507 clauses.
% 141.35/141.68 SPASS allocated 171682 KBytes.
% 141.35/141.68 SPASS spent 0:2:21.28 on the problem.
% 141.35/141.68 0:00:00.03 for the input.
% 141.35/141.68 0:00:00.00 for the FLOTTER CNF translation.
% 141.35/141.68 0:00:00.20 for inferences.
% 141.35/141.68 0:00:00.00 for the backtracking.
% 141.35/141.68 0:2:20.99 for the reduction.
% 141.35/141.68
% 141.35/141.68
% 141.35/141.68 Here is a proof with depth 13, length 127 :
% 141.35/141.68 % SZS output start Refutation
% See solution above
% 142.11/142.45 Formulae used in the proof : c01 c02 c03 c04 c05 c06 c07 c08 goals
% 142.11/142.45
%------------------------------------------------------------------------------