TSTP Solution File: GRP667+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP667+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:48:51 EDT 2022
% Result : Theorem 34.41s 34.60s
% Output : Refutation 34.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 12
% Syntax : Number of clauses : 184 ( 169 unt; 0 nHn; 184 RR)
% Number of literals : 199 ( 0 equ; 18 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 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,unit),u),
file('GRP667+1.p',unknown),
[] ).
cnf(2,axiom,
equal(mult(unit,u),u),
file('GRP667+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP667+1.p',unknown),
[] ).
cnf(4,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP667+1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(rd(u,v),v),u),
file('GRP667+1.p',unknown),
[] ).
cnf(6,axiom,
equal(rd(mult(u,v),v),u),
file('GRP667+1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(f(u),f(u)),u),
file('GRP667+1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(mult(u,v),u),mult(u,mult(v,u))),
file('GRP667+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(mult(mult(mult(a,b),a),c),mult(a,mult(b,mult(a,c)))),
file('GRP667+1.p',unknown),
[] ).
cnf(10,axiom,
equal(mult(mult(u,mult(mult(v,w),v)),w),mult(mult(u,v),mult(mult(w,v),w))),
file('GRP667+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(mult(mult(u,v),mult(w,u)),mult(u,mult(mult(v,w),u)))
| equal(mult(mult(mult(u,v),u),w),mult(u,mult(v,mult(u,w)))) ),
file('GRP667+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ equal(mult(mult(mult(u,v),w),v),mult(u,mult(v,mult(w,v))))
| equal(mult(mult(mult(v,u),v),w),mult(v,mult(u,mult(v,w)))) ),
file('GRP667+1.p',unknown),
[] ).
cnf(14,plain,
~ equal(mult(mult(a,mult(b,a)),c),mult(a,mult(b,mult(a,c)))),
inference(rew,[status(thm),theory(equality)],[8,9]),
[iquote('0:Rew:8.0,9.0')] ).
cnf(15,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)],[8,10]),
[iquote('0:Rew:8.0,10.0,8.0,10.0')] ).
cnf(16,plain,
( ~ equal(mult(mult(u,v),mult(w,u)),mult(u,mult(mult(v,w),u)))
| equal(mult(mult(u,mult(v,u)),w),mult(u,mult(v,mult(u,w)))) ),
inference(rew,[status(thm),theory(equality)],[8,11]),
[iquote('0:Rew:8.0,11.1')] ).
cnf(18,plain,
( ~ equal(mult(mult(mult(u,v),w),v),mult(u,mult(v,mult(w,v))))
| equal(mult(mult(v,mult(u,v)),w),mult(v,mult(u,mult(v,w)))) ),
inference(rew,[status(thm),theory(equality)],[8,13]),
[iquote('0:Rew:8.0,13.1')] ).
cnf(20,plain,
~ equal(mult(mult(mult(b,a),c),a),mult(b,mult(a,mult(c,a)))),
inference(res,[status(thm),theory(equality)],[18,14]),
[iquote('0:Res:18.1,14.0')] ).
cnf(26,plain,
equal(rd(u,u),unit),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(42,plain,
equal(ld(unit,u),u),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(43,plain,
equal(ld(u,u),unit),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(45,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(47,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(67,plain,
equal(rd(mult(u,mult(v,u)),u),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[8,6]),
[iquote('0:SpR:8.0,6.0')] ).
cnf(72,plain,
equal(mult(u,mult(ld(u,v),u)),mult(v,u)),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(73,plain,
equal(mult(f(u),mult(f(u),f(u))),mult(u,f(u))),
inference(spr,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpR:7.0,8.0')] ).
cnf(74,plain,
equal(mult(rd(u,v),mult(v,rd(u,v))),mult(u,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[5,8]),
[iquote('0:SpR:5.0,8.0')] ).
cnf(77,plain,
equal(mult(f(u),u),mult(u,f(u))),
inference(rew,[status(thm),theory(equality)],[7,73]),
[iquote('0:Rew:7.0,73.0')] ).
cnf(88,plain,
equal(rd(mult(u,f(u)),u),f(u)),
inference(spr,[status(thm),theory(equality)],[77,6]),
[iquote('0:SpR:77.0,6.0')] ).
cnf(110,plain,
equal(rd(mult(u,v),u),mult(u,rd(v,u))),
inference(spr,[status(thm),theory(equality)],[5,67]),
[iquote('0:SpR:5.0,67.0')] ).
cnf(116,plain,
equal(mult(u,rd(f(u),u)),f(u)),
inference(rew,[status(thm),theory(equality)],[110,88]),
[iquote('0:Rew:110.0,88.0')] ).
cnf(126,plain,
equal(rd(f(u),u),ld(u,f(u))),
inference(spr,[status(thm),theory(equality)],[116,4]),
[iquote('0:SpR:116.0,4.0')] ).
cnf(133,plain,
equal(mult(ld(u,f(u)),u),f(u)),
inference(spr,[status(thm),theory(equality)],[126,5]),
[iquote('0:SpR:126.0,5.0')] ).
cnf(134,plain,
equal(ld(ld(u,f(u)),f(u)),u),
inference(spr,[status(thm),theory(equality)],[126,45]),
[iquote('0:SpR:126.0,45.0')] ).
cnf(141,plain,
equal(mult(ld(u,f(u)),mult(u,ld(u,f(u)))),mult(f(u),ld(u,f(u)))),
inference(spr,[status(thm),theory(equality)],[133,8]),
[iquote('0:SpR:133.0,8.0')] ).
cnf(143,plain,
equal(mult(ld(u,f(u)),f(u)),mult(f(u),ld(u,f(u)))),
inference(rew,[status(thm),theory(equality)],[3,141]),
[iquote('0:Rew:3.0,141.0')] ).
cnf(144,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)],[15,8]),
[iquote('0:SpR:15.0,8.0')] ).
cnf(145,plain,
equal(mult(mult(u,v),mult(unit,mult(v,unit))),mult(u,mult(v,mult(unit,v)))),
inference(spr,[status(thm),theory(equality)],[15,1]),
[iquote('0:SpR:15.0,1.0')] ).
cnf(146,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)],[15,6]),
[iquote('0:SpR:15.0,6.0')] ).
cnf(155,plain,
equal(mult(mult(u,v),mult(ld(v,f(v)),mult(v,ld(v,f(v))))),mult(mult(u,mult(v,f(v))),ld(v,f(v)))),
inference(spr,[status(thm),theory(equality)],[133,15]),
[iquote('0:SpR:133.0,15.0')] ).
cnf(157,plain,
equal(mult(mult(u,ld(v,w)),mult(v,mult(ld(v,w),v))),mult(mult(u,mult(ld(v,w),w)),v)),
inference(spr,[status(thm),theory(equality)],[3,15]),
[iquote('0:SpR:3.0,15.0')] ).
cnf(159,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)],[5,15]),
[iquote('0:SpR:5.0,15.0')] ).
cnf(161,plain,
equal(mult(mult(unit,u),mult(v,mult(u,v))),mult(mult(u,mult(v,u)),v)),
inference(spr,[status(thm),theory(equality)],[2,15]),
[iquote('0:SpR:2.0,15.0')] ).
cnf(165,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)],[5,15]),
[iquote('0:SpR:5.0,15.0')] ).
cnf(166,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[2,145,1]),
[iquote('0:Rew:2.0,145.0,1.0,145.0,2.0,145.0')] ).
cnf(172,plain,
equal(mult(mult(u,mult(v,u)),v),mult(u,mult(v,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[2,161]),
[iquote('0:Rew:2.0,161.0')] ).
cnf(173,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)],[172,144]),
[iquote('0:Rew:172.0,144.0')] ).
cnf(174,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)],[74,159]),
[iquote('0:Rew:74.0,159.0')] ).
cnf(176,plain,
equal(mult(mult(u,mult(ld(v,w),w)),v),mult(mult(u,ld(v,w)),mult(w,v))),
inference(rew,[status(thm),theory(equality)],[72,157]),
[iquote('0:Rew:72.0,157.0')] ).
cnf(178,plain,
equal(mult(mult(u,mult(v,f(v))),ld(v,f(v))),mult(mult(u,v),mult(ld(v,f(v)),f(v)))),
inference(rew,[status(thm),theory(equality)],[3,155]),
[iquote('0:Rew:3.0,155.0')] ).
cnf(179,plain,
equal(mult(mult(u,mult(v,f(v))),ld(v,f(v))),mult(mult(u,v),mult(f(v),ld(v,f(v))))),
inference(rew,[status(thm),theory(equality)],[143,178]),
[iquote('0:Rew:143.0,178.0')] ).
cnf(216,plain,
( ~ equal(mult(unit,mult(u,mult(v,u))),mult(mult(u,v),u))
| equal(mult(mult(u,mult(unit,u)),v),mult(u,mult(unit,mult(u,v)))) ),
inference(spl,[status(thm),theory(equality)],[2,18]),
[iquote('0:SpL:2.0,18.0')] ).
cnf(235,plain,
( ~ equal(mult(u,mult(v,u)),mult(u,mult(v,u)))
| equal(mult(mult(u,u),v),mult(u,mult(u,v))) ),
inference(rew,[status(thm),theory(equality)],[2,216,8]),
[iquote('0:Rew:2.0,216.1,2.0,216.1,2.0,216.0,8.0,216.0')] ).
cnf(236,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(obv,[status(thm),theory(equality)],[235]),
[iquote('0:Obv:235.0')] ).
cnf(355,plain,
( ~ equal(mult(mult(f(u),f(u)),mult(v,f(u))),mult(f(u),mult(mult(f(u),v),f(u))))
| equal(mult(f(u),mult(f(u),mult(f(u),v))),mult(mult(f(u),u),v)) ),
inference(spr,[status(thm),theory(equality)],[7,16]),
[iquote('0:SpR:7.0,16.1')] ).
cnf(375,plain,
( ~ equal(mult(f(u),mult(f(u),mult(v,f(u)))),mult(u,mult(v,f(u))))
| equal(mult(f(u),mult(f(u),mult(f(u),v))),mult(mult(u,f(u)),v)) ),
inference(rew,[status(thm),theory(equality)],[77,355,7,8]),
[iquote('0:Rew:77.0,355.1,7.0,355.0,8.0,355.0')] ).
cnf(453,plain,
equal(mult(ld(u,v),u),ld(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[72,4]),
[iquote('0:SpR:72.0,4.0')] ).
cnf(556,plain,
equal(rd(mult(u,mult(v,v)),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[166,6]),
[iquote('0:SpR:166.0,6.0')] ).
cnf(572,plain,
equal(mult(rd(u,v),mult(v,v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[5,166]),
[iquote('0:SpR:5.0,166.0')] ).
cnf(602,plain,
equal(mult(u,rd(unit,u)),rd(u,u)),
inference(spr,[status(thm),theory(equality)],[1,110]),
[iquote('0:SpR:1.0,110.0')] ).
cnf(603,plain,
equal(mult(u,rd(ld(u,v),u)),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[3,110]),
[iquote('0:SpR:3.0,110.0')] ).
cnf(612,plain,
equal(mult(u,rd(unit,u)),unit),
inference(rew,[status(thm),theory(equality)],[26,602]),
[iquote('0:Rew:26.0,602.0')] ).
cnf(622,plain,
equal(rd(unit,u),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[612,4]),
[iquote('0:SpR:612.0,4.0')] ).
cnf(657,plain,
equal(ld(ld(u,unit),unit),u),
inference(spr,[status(thm),theory(equality)],[622,45]),
[iquote('0:SpR:622.0,45.0')] ).
cnf(682,plain,
equal(rd(mult(u,mult(u,v)),v),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[236,6]),
[iquote('0:SpR:236.0,6.0')] ).
cnf(683,plain,
equal(ld(mult(u,u),mult(u,mult(u,v))),v),
inference(spr,[status(thm),theory(equality)],[236,4]),
[iquote('0:SpR:236.0,4.0')] ).
cnf(709,plain,
equal(mult(f(u),mult(f(u),v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[7,236]),
[iquote('0:SpR:7.0,236.0')] ).
cnf(715,plain,
( ~ equal(mult(f(u),mult(f(u),mult(v,f(u)))),mult(u,mult(v,f(u))))
| equal(mult(mult(u,f(u)),v),mult(f(u),mult(u,v))) ),
inference(rew,[status(thm),theory(equality)],[709,375]),
[iquote('0:Rew:709.0,375.1')] ).
cnf(739,plain,
( ~ equal(mult(u,mult(v,f(u))),mult(u,mult(v,f(u))))
| equal(mult(mult(u,f(u)),v),mult(f(u),mult(u,v))) ),
inference(rew,[status(thm),theory(equality)],[709,715]),
[iquote('0:Rew:709.0,715.0')] ).
cnf(740,plain,
equal(mult(mult(u,f(u)),v),mult(f(u),mult(u,v))),
inference(obv,[status(thm),theory(equality)],[739]),
[iquote('0:Obv:739.0')] ).
cnf(760,plain,
equal(ld(f(u),mult(u,v)),mult(f(u),v)),
inference(spr,[status(thm),theory(equality)],[709,4]),
[iquote('0:SpR:709.0,4.0')] ).
cnf(768,plain,
equal(mult(f(u),mult(u,v)),mult(u,mult(f(u),v))),
inference(spr,[status(thm),theory(equality)],[709]),
[iquote('0:SpR:709.0,709.0')] ).
cnf(775,plain,
equal(mult(u,ld(f(u),v)),mult(f(u),v)),
inference(spr,[status(thm),theory(equality)],[3,709]),
[iquote('0:SpR:3.0,709.0')] ).
cnf(784,plain,
equal(mult(mult(u,f(u)),v),mult(u,mult(f(u),v))),
inference(rew,[status(thm),theory(equality)],[768,740]),
[iquote('0:Rew:768.0,740.0')] ).
cnf(1004,plain,
equal(mult(f(u),ld(u,v)),ld(f(u),v)),
inference(spr,[status(thm),theory(equality)],[3,760]),
[iquote('0:SpR:3.0,760.0')] ).
cnf(1017,plain,
equal(mult(mult(u,mult(v,f(v))),ld(v,f(v))),mult(mult(u,v),ld(f(v),f(v)))),
inference(rew,[status(thm),theory(equality)],[1004,179]),
[iquote('0:Rew:1004.0,179.0')] ).
cnf(1018,plain,
equal(mult(ld(u,f(u)),f(u)),ld(f(u),f(u))),
inference(rew,[status(thm),theory(equality)],[1004,143]),
[iquote('0:Rew:1004.0,143.0')] ).
cnf(1020,plain,
equal(mult(ld(u,f(u)),f(u)),unit),
inference(rew,[status(thm),theory(equality)],[43,1018]),
[iquote('0:Rew:43.0,1018.0')] ).
cnf(1027,plain,
equal(mult(mult(u,mult(v,f(v))),ld(v,f(v))),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[1,1017,43]),
[iquote('0:Rew:1.0,1017.0,43.0,1017.0')] ).
cnf(1031,plain,
equal(rd(unit,f(u)),ld(u,f(u))),
inference(spr,[status(thm),theory(equality)],[1020,6]),
[iquote('0:SpR:1020.0,6.0')] ).
cnf(1043,plain,
equal(ld(f(u),unit),ld(u,f(u))),
inference(rew,[status(thm),theory(equality)],[622,1031]),
[iquote('0:Rew:622.0,1031.0')] ).
cnf(1165,plain,
equal(ld(ld(f(u),unit),f(u)),u),
inference(spr,[status(thm),theory(equality)],[1043,134]),
[iquote('0:SpR:1043.0,134.0')] ).
cnf(1170,plain,
equal(rd(f(u),ld(f(u),unit)),u),
inference(spr,[status(thm),theory(equality)],[1043,47]),
[iquote('0:SpR:1043.0,47.0')] ).
cnf(1185,plain,
equal(mult(ld(f(u),unit),u),f(u)),
inference(spr,[status(thm),theory(equality)],[1165,3]),
[iquote('0:SpR:1165.0,3.0')] ).
cnf(1239,plain,
equal(mult(rd(u,v),mult(v,mult(rd(u,v),v))),mult(mult(u,rd(u,v)),v)),
inference(spr,[status(thm),theory(equality)],[74,172]),
[iquote('0:SpR:74.0,172.0')] ).
cnf(1267,plain,
equal(mult(mult(u,rd(u,v)),v),mult(rd(u,v),mult(v,u))),
inference(rew,[status(thm),theory(equality)],[5,1239]),
[iquote('0:Rew:5.0,1239.0')] ).
cnf(1297,plain,
equal(mult(ld(f(u),unit),mult(u,u)),mult(f(u),u)),
inference(spr,[status(thm),theory(equality)],[1185,166]),
[iquote('0:SpR:1185.0,166.0')] ).
cnf(1298,plain,
equal(mult(ld(f(u),unit),rd(u,ld(f(u),unit))),rd(f(u),ld(f(u),unit))),
inference(spr,[status(thm),theory(equality)],[1185,110]),
[iquote('0:SpR:1185.0,110.0')] ).
cnf(1311,plain,
equal(mult(ld(f(u),unit),mult(u,u)),mult(u,f(u))),
inference(rew,[status(thm),theory(equality)],[77,1297]),
[iquote('0:Rew:77.0,1297.0')] ).
cnf(1321,plain,
equal(mult(ld(f(u),unit),rd(u,ld(f(u),unit))),u),
inference(rew,[status(thm),theory(equality)],[1170,1298]),
[iquote('0:Rew:1170.0,1298.0')] ).
cnf(1388,plain,
equal(ld(f(u),ld(f(u),v)),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[1004,4]),
[iquote('0:SpR:1004.0,4.0')] ).
cnf(1727,plain,
equal(ld(f(u),mult(ld(f(u),v),f(u))),mult(ld(u,v),f(u))),
inference(spr,[status(thm),theory(equality)],[1388,453]),
[iquote('0:SpR:1388.0,453.0')] ).
cnf(1739,plain,
equal(mult(ld(u,v),f(u)),ld(u,mult(v,f(u)))),
inference(rew,[status(thm),theory(equality)],[1388,1727,453]),
[iquote('0:Rew:1388.0,1727.0,453.0,1727.0')] ).
cnf(2898,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)],[5,146]),
[iquote('0:SpR:5.0,146.0')] ).
cnf(3123,plain,
equal(mult(rd(u,mult(v,v)),v),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[5,556]),
[iquote('0:SpR:5.0,556.0')] ).
cnf(3164,plain,
equal(rd(mult(u,v),mult(v,v)),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[572,6]),
[iquote('0:SpR:572.0,6.0')] ).
cnf(3165,plain,
equal(ld(rd(u,v),mult(u,v)),mult(v,v)),
inference(spr,[status(thm),theory(equality)],[572,4]),
[iquote('0:SpR:572.0,4.0')] ).
cnf(3491,plain,
equal(rd(ld(u,v),u),ld(u,rd(v,u))),
inference(spr,[status(thm),theory(equality)],[603,4]),
[iquote('0:SpR:603.0,4.0')] ).
cnf(3504,plain,
equal(mult(u,mult(rd(ld(u,v),u),mult(u,mult(rd(ld(u,v),u),u)))),mult(rd(v,u),mult(u,mult(rd(ld(u,v),u),u)))),
inference(spr,[status(thm),theory(equality)],[603,173]),
[iquote('0:SpR:603.0,173.0')] ).
cnf(3537,plain,
equal(mult(ld(u,unit),rd(u,ld(u,unit))),rd(unit,ld(u,unit))),
inference(spr,[status(thm),theory(equality)],[657,603]),
[iquote('0:SpR:657.0,603.0')] ).
cnf(3583,plain,
equal(mult(ld(u,unit),rd(u,ld(u,unit))),u),
inference(rew,[status(thm),theory(equality)],[657,3537,622]),
[iquote('0:Rew:657.0,3537.0,622.0,3537.0')] ).
cnf(3626,plain,
equal(mult(u,mult(rd(ld(u,v),u),v)),mult(rd(v,u),v)),
inference(rew,[status(thm),theory(equality)],[3,3504,5]),
[iquote('0:Rew:3.0,3504.0,5.0,3504.0')] ).
cnf(3627,plain,
equal(mult(u,mult(ld(u,rd(v,u)),v)),mult(rd(v,u),v)),
inference(rew,[status(thm),theory(equality)],[3491,3626]),
[iquote('0:Rew:3491.0,3626.0')] ).
cnf(3643,plain,
equal(rd(u,ld(u,unit)),ld(ld(u,unit),u)),
inference(spr,[status(thm),theory(equality)],[3583,4]),
[iquote('0:SpR:3583.0,4.0')] ).
cnf(3849,plain,
equal(mult(mult(mult(rd(u,mult(v,mult(w,v))),v),w),mult(v,mult(w,v))),mult(mult(u,w),v)),
inference(spr,[status(thm),theory(equality)],[165,15]),
[iquote('0:SpR:165.0,15.0')] ).
cnf(4106,plain,
equal(rd(mult(u,v),ld(u,v)),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[3,682]),
[iquote('0:SpR:3.0,682.0')] ).
cnf(4213,plain,
equal(ld(mult(u,u),mult(u,v)),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[3,683]),
[iquote('0:SpR:3.0,683.0')] ).
cnf(4733,plain,
equal(rd(rd(u,v),v),rd(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[3123,6]),
[iquote('0:SpR:3123.0,6.0')] ).
cnf(5245,plain,
equal(rd(u,mult(u,u)),rd(unit,u)),
inference(spr,[status(thm),theory(equality)],[2,3164]),
[iquote('0:SpR:2.0,3164.0')] ).
cnf(5277,plain,
equal(rd(u,mult(u,u)),ld(u,unit)),
inference(rew,[status(thm),theory(equality)],[622,5245]),
[iquote('0:Rew:622.0,5245.0')] ).
cnf(5313,plain,
equal(ld(ld(u,unit),u),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[5277,45]),
[iquote('0:SpR:5277.0,45.0')] ).
cnf(5333,plain,
equal(rd(u,ld(u,unit)),mult(u,u)),
inference(rew,[status(thm),theory(equality)],[5313,3643]),
[iquote('0:Rew:5313.0,3643.0')] ).
cnf(5805,plain,
equal(mult(ld(u,v),ld(u,v)),ld(rd(u,ld(u,v)),v)),
inference(spr,[status(thm),theory(equality)],[3,3165]),
[iquote('0:SpR:3.0,3165.0')] ).
cnf(5834,plain,
equal(mult(ld(u,v),ld(u,v)),ld(u,mult(v,ld(u,v)))),
inference(spr,[status(thm),theory(equality)],[47,3165]),
[iquote('0:SpR:47.0,3165.0')] ).
cnf(5889,plain,
equal(ld(rd(u,ld(u,v)),v),ld(u,mult(v,ld(u,v)))),
inference(rew,[status(thm),theory(equality)],[5805,5834]),
[iquote('0:Rew:5805.0,5834.0')] ).
cnf(5891,plain,
equal(mult(ld(u,v),ld(u,v)),ld(u,mult(v,ld(u,v)))),
inference(rew,[status(thm),theory(equality)],[5889,5805]),
[iquote('0:Rew:5889.0,5805.0')] ).
cnf(6396,plain,
equal(rd(u,ld(v,ld(v,u))),mult(v,v)),
inference(spr,[status(thm),theory(equality)],[3,4106]),
[iquote('0:SpR:3.0,4106.0')] ).
cnf(6528,plain,
equal(ld(mult(ld(f(u),unit),ld(f(u),unit)),f(u)),ld(ld(f(u),unit),u)),
inference(spr,[status(thm),theory(equality)],[1185,4213]),
[iquote('0:SpR:1185.0,4213.0')] ).
cnf(6622,plain,
equal(ld(ld(f(u),mult(unit,ld(f(u),unit))),f(u)),ld(ld(f(u),unit),u)),
inference(rew,[status(thm),theory(equality)],[5891,6528]),
[iquote('0:Rew:5891.0,6528.0')] ).
cnf(6623,plain,
equal(ld(ld(f(u),unit),u),ld(ld(u,unit),f(u))),
inference(rew,[status(thm),theory(equality)],[1388,6622,2]),
[iquote('0:Rew:1388.0,6622.0,2.0,6622.0')] ).
cnf(8981,plain,
equal(rd(u,ld(f(u),unit)),ld(ld(f(u),unit),u)),
inference(spr,[status(thm),theory(equality)],[1321,4]),
[iquote('0:SpR:1321.0,4.0')] ).
cnf(8987,plain,
equal(mult(ld(f(u),unit),rd(rd(u,ld(f(u),unit)),ld(f(u),unit))),rd(u,ld(f(u),unit))),
inference(spr,[status(thm),theory(equality)],[1321,110]),
[iquote('0:SpR:1321.0,110.0')] ).
cnf(9025,plain,
equal(rd(u,ld(f(u),unit)),ld(ld(u,unit),f(u))),
inference(rew,[status(thm),theory(equality)],[6623,8981]),
[iquote('0:Rew:6623.0,8981.0')] ).
cnf(9046,plain,
equal(mult(ld(f(u),unit),rd(u,mult(ld(f(u),unit),ld(f(u),unit)))),rd(u,ld(f(u),unit))),
inference(rew,[status(thm),theory(equality)],[4733,8987]),
[iquote('0:Rew:4733.0,8987.0')] ).
cnf(9047,plain,
equal(mult(ld(f(u),unit),rd(u,ld(f(u),mult(unit,ld(f(u),unit))))),ld(ld(u,unit),f(u))),
inference(rew,[status(thm),theory(equality)],[5891,9046,9025]),
[iquote('0:Rew:5891.0,9046.0,9025.0,9046.0')] ).
cnf(9048,plain,
equal(mult(ld(f(u),unit),mult(u,u)),ld(ld(u,unit),f(u))),
inference(rew,[status(thm),theory(equality)],[5333,9047,1388,2]),
[iquote('0:Rew:5333.0,9047.0,1388.0,9047.0,2.0,9047.0')] ).
cnf(9049,plain,
equal(ld(ld(u,unit),f(u)),mult(u,f(u))),
inference(rew,[status(thm),theory(equality)],[1311,9048]),
[iquote('0:Rew:1311.0,9048.0')] ).
cnf(9221,plain,
equal(mult(ld(u,unit),mult(u,f(u))),f(u)),
inference(spr,[status(thm),theory(equality)],[9049,3]),
[iquote('0:SpR:9049.0,3.0')] ).
cnf(10273,plain,
equal(mult(mult(rd(u,mult(mult(v,f(v)),f(v))),mult(v,f(v))),mult(ld(v,unit),mult(mult(v,f(v)),ld(v,unit)))),mult(u,ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[9221,165]),
[iquote('0:SpR:9221.0,165.0')] ).
cnf(10386,plain,
equal(mult(mult(rd(u,mult(v,v)),mult(v,f(v))),mult(ld(v,unit),f(v))),mult(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[7,10273,784,1,775,1004]),
[iquote('0:Rew:7.0,10273.0,784.0,10273.0,1.0,10273.0,775.0,10273.0,1004.0,10273.0,784.0,10273.0')] ).
cnf(10387,plain,
equal(mult(mult(rd(u,mult(v,v)),mult(v,f(v))),ld(v,mult(unit,f(v)))),mult(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[1739,10386]),
[iquote('0:Rew:1739.0,10386.0')] ).
cnf(10388,plain,
equal(mult(mult(rd(u,mult(v,v)),mult(v,f(v))),ld(v,f(v))),mult(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[2,10387]),
[iquote('0:Rew:2.0,10387.0')] ).
cnf(10389,plain,
equal(mult(rd(u,mult(v,v)),v),mult(u,ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[1027,10388]),
[iquote('0:Rew:1027.0,10388.0')] ).
cnf(10390,plain,
equal(mult(u,ld(v,unit)),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[3123,10389]),
[iquote('0:Rew:3123.0,10389.0')] ).
cnf(11053,plain,
equal(ld(u,rd(u,v)),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[10390,4]),
[iquote('0:SpR:10390.0,4.0')] ).
cnf(11054,plain,
equal(mult(u,mult(ld(v,unit),u)),mult(rd(u,v),u)),
inference(spr,[status(thm),theory(equality)],[10390,8]),
[iquote('0:SpR:10390.0,8.0')] ).
cnf(11061,plain,
equal(rd(mult(u,rd(u,v)),ld(v,unit)),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[10390,682]),
[iquote('0:SpR:10390.0,682.0')] ).
cnf(11122,plain,
equal(rd(u,rd(unit,v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[45,10390]),
[iquote('0:SpR:45.0,10390.0')] ).
cnf(11137,plain,
( ~ equal(mult(u,mult(v,mult(ld(w,unit),v))),mult(rd(mult(u,v),w),v))
| equal(mult(mult(v,mult(u,v)),ld(w,unit)),mult(v,mult(u,mult(v,ld(w,unit))))) ),
inference(spl,[status(thm),theory(equality)],[10390,18]),
[iquote('0:SpL:10390.0,18.0')] ).
cnf(11142,plain,
equal(rd(u,ld(v,unit)),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[622,11122]),
[iquote('0:Rew:622.0,11122.0')] ).
cnf(11186,plain,
equal(mult(rd(u,v),mult(v,u)),mult(u,u)),
inference(rew,[status(thm),theory(equality)],[1267,11061,11142]),
[iquote('0:Rew:1267.0,11061.0,11142.0,11061.0')] ).
cnf(11324,plain,
( ~ equal(mult(u,mult(v,mult(ld(w,unit),v))),mult(rd(mult(u,v),w),v))
| equal(rd(mult(v,mult(u,v)),w),mult(v,mult(u,rd(v,w)))) ),
inference(rew,[status(thm),theory(equality)],[10390,11137]),
[iquote('0:Rew:10390.0,11137.1,10390.0,11137.1')] ).
cnf(11325,plain,
( ~ equal(mult(rd(mult(u,v),w),v),mult(u,mult(rd(v,w),v)))
| equal(rd(mult(v,mult(u,v)),w),mult(v,mult(u,rd(v,w)))) ),
inference(rew,[status(thm),theory(equality)],[11054,11324]),
[iquote('0:Rew:11054.0,11324.0')] ).
cnf(11368,plain,
equal(ld(u,mult(rd(u,v),u)),mult(ld(v,unit),u)),
inference(spr,[status(thm),theory(equality)],[11053,453]),
[iquote('0:SpR:11053.0,453.0')] ).
cnf(11395,plain,
equal(ld(ld(u,v),unit),ld(v,u)),
inference(spr,[status(thm),theory(equality)],[47,11053]),
[iquote('0:SpR:47.0,11053.0')] ).
cnf(11396,plain,
equal(ld(ld(u,ld(u,v)),unit),ld(v,mult(u,u))),
inference(spr,[status(thm),theory(equality)],[6396,11053]),
[iquote('0:SpR:6396.0,11053.0')] ).
cnf(11443,plain,
equal(ld(ld(u,v),u),ld(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[11395,11396]),
[iquote('0:Rew:11395.0,11396.0')] ).
cnf(11502,plain,
equal(mult(mult(u,mult(ld(v,unit),w)),mult(w,v)),mult(mult(u,ld(v,unit)),mult(w,mult(w,v)))),
inference(spr,[status(thm),theory(equality)],[11142,174]),
[iquote('0:SpR:11142.0,174.0')] ).
cnf(11580,plain,
equal(mult(mult(u,mult(ld(v,unit),w)),mult(w,v)),mult(rd(u,v),mult(w,mult(w,v)))),
inference(rew,[status(thm),theory(equality)],[10390,11502]),
[iquote('0:Rew:10390.0,11502.0')] ).
cnf(12033,plain,
equal(rd(u,ld(v,w)),mult(u,ld(w,v))),
inference(spr,[status(thm),theory(equality)],[11395,10390]),
[iquote('0:SpR:11395.0,10390.0')] ).
cnf(14315,plain,
equal(mult(rd(ld(u,v),u),v),mult(ld(u,v),ld(u,v))),
inference(spr,[status(thm),theory(equality)],[3,11186]),
[iquote('0:SpR:3.0,11186.0')] ).
cnf(14439,plain,
equal(mult(ld(u,rd(v,u)),v),mult(ld(u,v),ld(u,v))),
inference(rew,[status(thm),theory(equality)],[3491,14315]),
[iquote('0:Rew:3491.0,14315.0')] ).
cnf(14440,plain,
equal(mult(ld(u,rd(v,u)),v),ld(u,mult(v,ld(u,v)))),
inference(rew,[status(thm),theory(equality)],[5891,14439]),
[iquote('0:Rew:5891.0,14439.0')] ).
cnf(14442,plain,
equal(mult(u,ld(u,mult(v,ld(u,v)))),mult(rd(v,u),v)),
inference(rew,[status(thm),theory(equality)],[14440,3627]),
[iquote('0:Rew:14440.0,3627.0')] ).
cnf(14448,plain,
equal(mult(rd(u,v),u),mult(u,ld(v,u))),
inference(rew,[status(thm),theory(equality)],[3,14442]),
[iquote('0:Rew:3.0,14442.0')] ).
cnf(14485,plain,
( ~ equal(mult(rd(mult(u,v),w),v),mult(u,mult(v,ld(w,v))))
| equal(rd(mult(v,mult(u,v)),w),mult(v,mult(u,rd(v,w)))) ),
inference(rew,[status(thm),theory(equality)],[14448,11325]),
[iquote('0:Rew:14448.0,11325.0')] ).
cnf(14501,plain,
equal(ld(u,mult(u,ld(v,u))),mult(ld(v,unit),u)),
inference(rew,[status(thm),theory(equality)],[14448,11368]),
[iquote('0:Rew:14448.0,11368.0')] ).
cnf(14503,plain,
equal(mult(ld(u,unit),v),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[4,14501]),
[iquote('0:Rew:4.0,14501.0')] ).
cnf(14546,plain,
equal(mult(mult(u,ld(v,w)),mult(w,v)),mult(rd(u,v),mult(w,mult(w,v)))),
inference(rew,[status(thm),theory(equality)],[14503,11580]),
[iquote('0:Rew:14503.0,11580.0')] ).
cnf(14721,plain,
equal(mult(mult(u,mult(ld(v,w),w)),v),mult(rd(u,v),mult(w,mult(w,v)))),
inference(rew,[status(thm),theory(equality)],[14546,176]),
[iquote('0:Rew:14546.0,176.0')] ).
cnf(15217,plain,
equal(rd(ld(u,v),v),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[14503,6]),
[iquote('0:SpR:14503.0,6.0')] ).
cnf(15276,plain,
equal(rd(mult(mult(u,v),ld(w,mult(v,ld(w,unit)))),ld(w,unit)),mult(u,mult(v,mult(ld(w,unit),v)))),
inference(spr,[status(thm),theory(equality)],[14503,146]),
[iquote('0:SpR:14503.0,146.0')] ).
cnf(15322,plain,
equal(ld(rd(unit,u),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[45,14503]),
[iquote('0:SpR:45.0,14503.0')] ).
cnf(15325,plain,
equal(mult(ld(u,v),w),ld(ld(v,u),w)),
inference(spr,[status(thm),theory(equality)],[11395,14503]),
[iquote('0:SpR:11395.0,14503.0')] ).
cnf(15342,plain,
equal(ld(ld(u,unit),v),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[622,15322]),
[iquote('0:Rew:622.0,15322.0')] ).
cnf(15703,plain,
equal(mult(mult(u,ld(ld(v,w),v)),w),mult(rd(u,w),mult(v,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[15325,14721]),
[iquote('0:Rew:15325.0,14721.0')] ).
cnf(16237,plain,
equal(mult(mult(u,ld(v,mult(w,w))),v),mult(rd(u,v),mult(w,mult(w,v)))),
inference(rew,[status(thm),theory(equality)],[11443,15703]),
[iquote('0:Rew:11443.0,15703.0')] ).
cnf(16361,plain,
equal(rd(mult(mult(u,v),ld(w,rd(v,w))),ld(w,unit)),mult(u,mult(v,mult(ld(w,unit),v)))),
inference(rew,[status(thm),theory(equality)],[10390,15276]),
[iquote('0:Rew:10390.0,15276.0')] ).
cnf(16362,plain,
equal(mult(mult(mult(u,v),ld(w,rd(v,w))),ld(unit,w)),mult(u,mult(v,ld(ld(unit,w),v)))),
inference(rew,[status(thm),theory(equality)],[12033,16361,15325]),
[iquote('0:Rew:12033.0,16361.0,15325.0,16361.0')] ).
cnf(16363,plain,
equal(mult(mult(mult(u,v),ld(w,rd(v,w))),w),mult(u,mult(v,ld(w,v)))),
inference(rew,[status(thm),theory(equality)],[42,16362]),
[iquote('0:Rew:42.0,16362.0')] ).
cnf(16922,plain,
equal(mult(rd(u,v),mult(f(w),mult(f(w),v))),mult(mult(u,ld(v,w)),v)),
inference(spr,[status(thm),theory(equality)],[7,16237]),
[iquote('0:SpR:7.0,16237.0')] ).
cnf(16980,plain,
equal(mult(mult(u,ld(v,w)),v),mult(rd(u,v),mult(w,v))),
inference(rew,[status(thm),theory(equality)],[709,16922]),
[iquote('0:Rew:709.0,16922.0')] ).
cnf(16999,plain,
equal(mult(rd(mult(u,v),w),mult(rd(v,w),w)),mult(u,mult(v,ld(w,v)))),
inference(rew,[status(thm),theory(equality)],[16980,16363]),
[iquote('0:Rew:16980.0,16363.0')] ).
cnf(17023,plain,
equal(mult(rd(mult(u,v),w),v),mult(u,mult(v,ld(w,v)))),
inference(rew,[status(thm),theory(equality)],[5,16999]),
[iquote('0:Rew:5.0,16999.0')] ).
cnf(17024,plain,
( ~ equal(mult(u,mult(v,ld(w,v))),mult(u,mult(v,ld(w,v))))
| equal(rd(mult(v,mult(u,v)),w),mult(v,mult(u,rd(v,w)))) ),
inference(rew,[status(thm),theory(equality)],[17023,14485]),
[iquote('0:Rew:17023.0,14485.0')] ).
cnf(17129,plain,
equal(rd(mult(u,mult(v,u)),w),mult(u,mult(v,rd(u,w)))),
inference(obv,[status(thm),theory(equality)],[17024]),
[iquote('0:Obv:17024.0')] ).
cnf(17312,plain,
equal(ld(rd(u,v),unit),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[45,15217]),
[iquote('0:SpR:45.0,15217.0')] ).
cnf(18120,plain,
equal(mult(rd(u,v),w),ld(rd(v,u),w)),
inference(spr,[status(thm),theory(equality)],[17312,15342]),
[iquote('0:SpR:17312.0,15342.0')] ).
cnf(18625,plain,
equal(rd(mult(u,mult(v,mult(w,v))),v),ld(rd(w,u),mult(w,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[18120,2898]),
[iquote('0:Rew:18120.0,2898.0')] ).
cnf(18724,plain,
equal(mult(mult(ld(rd(mult(u,mult(v,u)),w),u),v),mult(u,mult(v,u))),mult(mult(w,v),u)),
inference(rew,[status(thm),theory(equality)],[18120,3849]),
[iquote('0:Rew:18120.0,3849.0')] ).
cnf(19058,plain,
equal(ld(ld(u,ld(v,mult(v,mult(u,rd(v,w))))),mult(v,mult(u,v))),mult(mult(w,u),v)),
inference(rew,[status(thm),theory(equality)],[15325,18724,17129]),
[iquote('0:Rew:15325.0,18724.0,15325.0,18724.0,17129.0,18724.0')] ).
cnf(19059,plain,
equal(ld(rd(u,v),mult(u,mult(w,u))),mult(mult(v,w),u)),
inference(rew,[status(thm),theory(equality)],[4,19058]),
[iquote('0:Rew:4.0,19058.0,4.0,19058.0')] ).
cnf(19060,plain,
equal(rd(mult(u,mult(v,mult(w,v))),v),mult(mult(u,v),w)),
inference(rew,[status(thm),theory(equality)],[19059,18625]),
[iquote('0:Rew:19059.0,18625.0')] ).
cnf(19063,plain,
equal(mult(mult(mult(u,v),w),v),mult(u,mult(v,mult(w,v)))),
inference(rew,[status(thm),theory(equality)],[19060,146]),
[iquote('0:Rew:19060.0,146.0')] ).
cnf(19098,plain,
$false,
inference(unc,[status(thm)],[19063,20]),
[iquote('0:UnC:19063.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP667+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 14:04:48 EDT 2022
% 0.14/0.36 % CPUTime :
% 34.41/34.60
% 34.41/34.60 SPASS V 3.9
% 34.41/34.60 SPASS beiseite: Proof found.
% 34.41/34.60 % SZS status Theorem
% 34.41/34.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.41/34.60 SPASS derived 11083 clauses, backtracked 0 clauses, performed 0 splits and kept 6178 clauses.
% 34.41/34.60 SPASS allocated 135011 KBytes.
% 34.41/34.60 SPASS spent 0:0:34.21 on the problem.
% 34.41/34.60 0:00:00.03 for the input.
% 34.41/34.60 0:00:00.02 for the FLOTTER CNF translation.
% 34.41/34.60 0:00:00.09 for inferences.
% 34.41/34.60 0:00:00.00 for the backtracking.
% 34.41/34.60 0:0:34.03 for the reduction.
% 34.41/34.60
% 34.41/34.60
% 34.41/34.60 Here is a proof with depth 17, length 184 :
% 34.41/34.60 % SZS output start Refutation
% See solution above
% 34.74/34.92 Formulae used in the proof : f05 f06 f01 f02 f03 f04 f09 f08 goals f07 f12 f10
% 34.74/34.92
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