TSTP Solution File: GRP060-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP060-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:45:06 EDT 2022
% Result : Unsatisfiable 65.13s 65.28s
% Output : Refutation 65.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 2
% Syntax : Number of clauses : 115 ( 111 unt; 0 nHn; 115 RR)
% Number of literals : 121 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 16 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),u))))),x),
file('GRP060-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP060-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),y)))),multiply(z,multiply(multiply(inverse(z),inverse(x)),u))))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,x))),inverse(y))),multiply(y,multiply(w,u))))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(multiply(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,u))),multiply(inverse(x),inverse(multiply(y,z))))))),inverse(multiply(z,multiply(x,w)))),y),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(15,plain,
equal(multiply(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,u))),x)))),inverse(multiply(multiply(y,multiply(multiply(inverse(y),inverse(multiply(x,z))),inverse(x1))),multiply(x1,w)))),z),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(17,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(w,inverse(x))),multiply(x,multiply(y,u))))),multiply(z,multiply(multiply(inverse(z),inverse(multiply(w,y))),inverse(v)))),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(24,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,x))),w))),inverse(v))),x),
inference(spr,[status(thm),theory(equality)],[17,4]),
[iquote('0:SpR:17.0,4.0')] ).
cnf(38,plain,
equal(multiply(inverse(u),inverse(multiply(v,multiply(w,inverse(multiply(multiply(u,multiply(x,inverse(y))),multiply(y,multiply(v,w)))))))),x),
inference(spr,[status(thm),theory(equality)],[17,1]),
[iquote('0:SpR:17.0,1.0')] ).
cnf(73,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(multiply(multiply(x,multiply(y,inverse(z))),multiply(z,multiply(x1,w))))))),x2))),inverse(v))),multiply(multiply(inverse(x2),inverse(multiply(y,x1))),inverse(x))),
inference(spr,[status(thm),theory(equality)],[17,24]),
[iquote('0:SpR:17.0,24.0')] ).
cnf(103,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(u,multiply(x,inverse(v)))))),w))),x),
inference(spr,[status(thm),theory(equality)],[1,38]),
[iquote('0:SpR:1.0,38.0')] ).
cnf(108,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u))))),multiply(inverse(y),inverse(multiply(v,multiply(w,multiply(x,inverse(y))))))),
inference(spr,[status(thm),theory(equality)],[103,1]),
[iquote('0:SpR:103.0,1.0')] ).
cnf(129,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,x))),w))),multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(y,x))),y)))),
inference(spr,[status(thm),theory(equality)],[24,103]),
[iquote('0:SpR:24.0,103.0')] ).
cnf(182,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(v,inverse(multiply(w,multiply(u,multiply(x,v))))),w))),x),
inference(spr,[status(thm),theory(equality)],[108,103]),
[iquote('0:SpR:108.0,103.0')] ).
cnf(183,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u))))),multiply(y,inverse(multiply(v,multiply(w,multiply(x,y)))))),
inference(spr,[status(thm),theory(equality)],[108]),
[iquote('0:SpR:108.0,108.0')] ).
cnf(206,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,inverse(multiply(x,multiply(y,multiply(v,w)))))))),inverse(y))),x),
inference(spr,[status(thm),theory(equality)],[182,24]),
[iquote('0:SpR:182.0,24.0')] ).
cnf(215,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(inverse(w),inverse(x))),multiply(x,multiply(inverse(multiply(multiply(y,inverse(multiply(z,multiply(w,multiply(x1,y))))),z)),u))))),multiply(x2,multiply(multiply(inverse(x2),inverse(x1)),inverse(v)))),
inference(spr,[status(thm),theory(equality)],[182,17]),
[iquote('0:SpR:182.0,17.0')] ).
cnf(230,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,x))),multiply(y,multiply(multiply(inverse(y),inverse(z)),u))))),inverse(multiply(x1,multiply(x2,multiply(multiply(inverse(x2),inverse(multiply(x,x1))),multiply(inverse(w),inverse(multiply(z,v)))))))),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(251,plain,
equal(multiply(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(inverse(multiply(w,multiply(x,multiply(multiply(inverse(x),inverse(multiply(y,w))),z)))),u))),multiply(inverse(z),inverse(multiply(x1,x2))))))),inverse(multiply(x2,y))),x1),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
cnf(340,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(multiply(x,multiply(y,multiply(z,w))))))),x1))),inverse(v))),inverse(multiply(x,multiply(y,multiply(z,x1))))),
inference(spr,[status(thm),theory(equality)],[183,24]),
[iquote('0:SpR:183.0,24.0')] ).
cnf(370,plain,
equal(inverse(multiply(multiply(u,multiply(v,inverse(w))),multiply(w,multiply(x,y)))),multiply(multiply(inverse(y),inverse(multiply(v,x))),inverse(u))),
inference(rew,[status(thm),theory(equality)],[340,73]),
[iquote('0:Rew:340.0,73.0')] ).
cnf(392,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(inverse(v),inverse(multiply(multiply(w,inverse(multiply(x,multiply(v,multiply(y,w))))),x))))),inverse(z))),multiply(x1,multiply(multiply(inverse(x1),inverse(y)),inverse(z)))),
inference(rew,[status(thm),theory(equality)],[370,215]),
[iquote('0:Rew:370.0,215.0')] ).
cnf(480,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(v)),inverse(w))),multiply(x,multiply(multiply(inverse(x),inverse(v)),inverse(w)))),
inference(rew,[status(thm),theory(equality)],[182,392]),
[iquote('0:Rew:182.0,392.0')] ).
cnf(827,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(inverse(w),inverse(multiply(multiply(inverse(x),inverse(multiply(y,z))),y))))),inverse(w)))),inverse(v))),inverse(multiply(multiply(inverse(x),inverse(multiply(x1,z))),x1))),
inference(spr,[status(thm),theory(equality)],[129,24]),
[iquote('0:SpR:129.0,24.0')] ).
cnf(883,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,w))),v)),inverse(multiply(multiply(inverse(u),inverse(multiply(x,w))),x))),
inference(rew,[status(thm),theory(equality)],[24,827]),
[iquote('0:Rew:24.0,827.0')] ).
cnf(937,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,inverse(multiply(multiply(inverse(x),inverse(multiply(y,z))),y)))))),inverse(x1))),multiply(inverse(x),inverse(multiply(multiply(x1,multiply(v,w)),z)))),
inference(spr,[status(thm),theory(equality)],[883,206]),
[iquote('0:SpR:883.0,206.0')] ).
cnf(1009,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),inverse(u)))))),v)),inverse(multiply(y,inverse(multiply(z,multiply(x1,multiply(multiply(inverse(x1),inverse(multiply(x,z))),y))))))),
inference(spr,[status(thm),theory(equality)],[3,883]),
[iquote('0:SpR:3.0,883.0')] ).
cnf(1023,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),inverse(u)))))),v)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[1,1009]),
[iquote('0:Rew:1.0,1009.0')] ).
cnf(1109,plain,
equal(inverse(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),u))))),v)),inverse(x)),
inference(spr,[status(thm),theory(equality)],[183,1023]),
[iquote('0:SpR:183.0,1023.0')] ).
cnf(1190,plain,
equal(inverse(multiply(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,multiply(inverse(w),inverse(x))))),inverse(y))),multiply(y,multiply(v,inverse(w))))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[370,1109]),
[iquote('0:SpR:370.0,1109.0')] ).
cnf(1202,plain,
equal(multiply(multiply(inverse(inverse(u)),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(inverse(u),inverse(x))))),w))),inverse(v)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[370,1190]),
[iquote('0:Rew:370.0,1190.0')] ).
cnf(1488,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(inverse(w))),multiply(inverse(inverse(x)),inverse(multiply(multiply(inverse(y),inverse(multiply(z,multiply(inverse(x),inverse(w))))),z)))))),inverse(v))),inverse(y)),
inference(spr,[status(thm),theory(equality)],[1202,24]),
[iquote('0:SpR:1202.0,24.0')] ).
cnf(1559,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(inverse(w))),inverse(inverse(x)))),multiply(inverse(x),inverse(w))))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[937,1488]),
[iquote('0:Rew:937.0,1488.0')] ).
cnf(1790,plain,
equal(multiply(u,multiply(inverse(u),inverse(v))),multiply(w,multiply(multiply(inverse(w),inverse(multiply(multiply(x,multiply(multiply(inverse(x),inverse(inverse(y))),inverse(inverse(z)))),multiply(inverse(z),inverse(y))))),inverse(v)))),
inference(spr,[status(thm),theory(equality)],[1559,480]),
[iquote('0:SpR:1559.0,480.0')] ).
cnf(1799,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(inverse(v))),inverse(v))),inverse(multiply(multiply(inverse(u),inverse(multiply(w,inverse(multiply(multiply(x,multiply(multiply(inverse(x),inverse(inverse(y))),inverse(inverse(z)))),multiply(inverse(z),inverse(y))))))),w))),
inference(spr,[status(thm),theory(equality)],[1559,883]),
[iquote('0:SpR:1559.0,883.0')] ).
cnf(1857,plain,
equal(multiply(u,multiply(inverse(u),inverse(v))),multiply(w,multiply(inverse(w),inverse(v)))),
inference(rew,[status(thm),theory(equality)],[1559,1790]),
[iquote('0:Rew:1559.0,1790.0')] ).
cnf(2204,plain,
equal(multiply(u,multiply(inverse(u),inverse(multiply(multiply(v,inverse(multiply(w,multiply(x,multiply(y,v))))),w)))),multiply(x,y)),
inference(spr,[status(thm),theory(equality)],[182,1857]),
[iquote('0:SpR:182.0,1857.0')] ).
cnf(2208,plain,
equal(multiply(u,multiply(inverse(u),inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(inverse(w))),inverse(inverse(x)))),multiply(inverse(x),inverse(w)))))),multiply(y,inverse(y))),
inference(spr,[status(thm),theory(equality)],[1559,1857]),
[iquote('0:SpR:1559.0,1857.0')] ).
cnf(2211,plain,
equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[1559,2208]),
[iquote('0:Rew:1559.0,2208.0')] ).
cnf(2244,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(w,multiply(inverse(w),inverse(inverse(u))))),
inference(spr,[status(thm),theory(equality)],[2211,1857]),
[iquote('0:SpR:2211.0,1857.0')] ).
cnf(2266,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(u,multiply(x,inverse(x)))))),w))),v),
inference(spr,[status(thm),theory(equality)],[2211,182]),
[iquote('0:SpR:2211.0,182.0')] ).
cnf(2279,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(w)))),x))),inverse(v))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[2211,24]),
[iquote('0:SpR:2211.0,24.0')] ).
cnf(2294,plain,
equal(inverse(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(x,inverse(x)),u))))),v)),inverse(inverse(w))),
inference(spr,[status(thm),theory(equality)],[2211,1109]),
[iquote('0:SpR:2211.0,1109.0')] ).
cnf(2302,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,inverse(v)))),w)),inverse(multiply(multiply(inverse(u),inverse(multiply(x,inverse(w)))),x))),
inference(spr,[status(thm),theory(equality)],[2211,883]),
[iquote('0:SpR:2211.0,883.0')] ).
cnf(2417,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(u,multiply(w,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[2244]),
[iquote('0:SpR:2244.0,2244.0')] ).
cnf(3306,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(u,multiply(x,inverse(x)))))),w))),multiply(multiply(y,inverse(multiply(z,multiply(x1,multiply(multiply(inverse(x1),inverse(v)),y))))),z)),
inference(spr,[status(thm),theory(equality)],[1109,2266]),
[iquote('0:SpR:1109.0,2266.0')] ).
cnf(3307,plain,
equal(multiply(inverse(u),inverse(multiply(multiply(inverse(inverse(v)),inverse(multiply(w,multiply(u,multiply(x,inverse(x)))))),w))),multiply(multiply(y,inverse(multiply(z,multiply(v,multiply(multiply(x1,inverse(x1)),y))))),z)),
inference(spr,[status(thm),theory(equality)],[2294,2266]),
[iquote('0:SpR:2294.0,2266.0')] ).
cnf(3319,plain,
equal(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),inverse(u)))))),multiply(y,multiply(z,multiply(multiply(inverse(z),inverse(multiply(multiply(x1,inverse(x1)),y))),x)))),
inference(spr,[status(thm),theory(equality)],[15,2266]),
[iquote('0:SpR:15.0,2266.0')] ).
cnf(3354,plain,
equal(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(multiply(w,inverse(w)),u))),x))),x),
inference(rew,[status(thm),theory(equality)],[1,3319]),
[iquote('0:Rew:1.0,3319.0')] ).
cnf(3358,plain,
equal(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(x,inverse(x)),u))))),v),inverse(w)),
inference(rew,[status(thm),theory(equality)],[2266,3307]),
[iquote('0:Rew:2266.0,3307.0')] ).
cnf(3396,plain,
equal(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),u))))),v),x),
inference(rew,[status(thm),theory(equality)],[2266,3306]),
[iquote('0:Rew:2266.0,3306.0')] ).
cnf(3587,plain,
equal(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,u))),multiply(inverse(x),inverse(multiply(multiply(y,inverse(y)),z))))))),multiply(z,multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[1,3354]),
[iquote('0:SpR:1.0,3354.0')] ).
cnf(4097,plain,
equal(multiply(u,inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(w)),inverse(x))),multiply(x,w)))),u),
inference(spr,[status(thm),theory(equality)],[3396,1]),
[iquote('0:SpR:3396.0,1.0')] ).
cnf(4229,plain,
equal(multiply(multiply(u,inverse(u)),v),multiply(multiply(w,inverse(w)),v)),
inference(spr,[status(thm),theory(equality)],[3354,3396]),
[iquote('0:SpR:3354.0,3396.0')] ).
cnf(4247,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(inverse(v))),inverse(v))),inverse(multiply(multiply(inverse(u),inverse(w)),w))),
inference(rew,[status(thm),theory(equality)],[4097,1799]),
[iquote('0:Rew:4097.0,1799.0')] ).
cnf(4508,plain,
equal(multiply(multiply(u,inverse(multiply(v,multiply(multiply(w,inverse(w)),multiply(multiply(x,inverse(x)),u))))),v),inverse(multiply(y,inverse(y)))),
inference(spr,[status(thm),theory(equality)],[4229,3358]),
[iquote('0:SpR:4229.0,3358.0')] ).
cnf(4512,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(w,inverse(w)),multiply(inverse(multiply(x,inverse(x))),inverse(inverse(u))))),
inference(spr,[status(thm),theory(equality)],[4229,2244]),
[iquote('0:SpR:4229.0,2244.0')] ).
cnf(4556,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(v,inverse(v)))),
inference(rew,[status(thm),theory(equality)],[3358,4508]),
[iquote('0:Rew:3358.0,4508.0')] ).
cnf(4634,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w)))))),
inference(spr,[status(thm),theory(equality)],[4556]),
[iquote('0:SpR:4556.0,4556.0')] ).
cnf(5381,plain,
equal(multiply(multiply(u,inverse(multiply(v,multiply(multiply(w,inverse(w)),multiply(multiply(inverse(multiply(multiply(x,inverse(x)),inverse(multiply(y,inverse(y))))),inverse(z)),u))))),v),z),
inference(spr,[status(thm),theory(equality)],[4634,3396]),
[iquote('0:SpR:4634.0,3396.0')] ).
cnf(5610,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(w,multiply(multiply(inverse(w),inverse(multiply(multiply(inverse(x),inverse(y)),y))),u))))),multiply(inverse(x),inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[4247,1]),
[iquote('0:SpR:4247.0,1.0')] ).
cnf(5632,plain,
equal(inverse(multiply(u,inverse(u))),inverse(multiply(multiply(inverse(multiply(v,inverse(v))),inverse(w)),w))),
inference(spr,[status(thm),theory(equality)],[4247,4634]),
[iquote('0:SpR:4247.0,4634.0')] ).
cnf(5901,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(w,multiply(multiply(inverse(w),inverse(multiply(multiply(inverse(multiply(x,inverse(x))),inverse(y)),y))),u))))),v),
inference(spr,[status(thm),theory(equality)],[5632,1]),
[iquote('0:SpR:5632.0,1.0')] ).
cnf(5928,plain,
equal(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),inverse(v)),v)),inverse(multiply(multiply(inverse(multiply(w,inverse(w))),inverse(x)),x))),
inference(spr,[status(thm),theory(equality)],[5632]),
[iquote('0:SpR:5632.0,5632.0')] ).
cnf(6015,plain,
equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(w)))),multiply(inverse(multiply(x,inverse(x))),inverse(y))))),inverse(v))),y),
inference(spr,[status(thm),theory(equality)],[5632,24]),
[iquote('0:SpR:5632.0,24.0')] ).
cnf(6174,plain,
equal(multiply(inverse(multiply(u,inverse(u))),inverse(inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[5610,5901]),
[iquote('0:Rew:5610.0,5901.0')] ).
cnf(6176,plain,
equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(w,inverse(w)),u)),
inference(rew,[status(thm),theory(equality)],[6174,4512]),
[iquote('0:Rew:6174.0,4512.0')] ).
cnf(6180,plain,
equal(inverse(multiply(inverse(multiply(u,inverse(u))),inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[2279,6015]),
[iquote('0:Rew:2279.0,6015.0')] ).
cnf(6677,plain,
equal(multiply(multiply(u,inverse(u)),v),multiply(w,multiply(inverse(w),inverse(inverse(v))))),
inference(spr,[status(thm),theory(equality)],[6174,1857]),
[iquote('0:SpR:6174.0,1857.0')] ).
cnf(6681,plain,
equal(multiply(multiply(u,inverse(multiply(v,multiply(multiply(w,inverse(w)),multiply(x,u))))),v),inverse(x)),
inference(spr,[status(thm),theory(equality)],[6174,3396]),
[iquote('0:SpR:6174.0,3396.0')] ).
cnf(6746,plain,
equal(inverse(multiply(inverse(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v))))),inverse(w))),w),
inference(rew,[status(thm),theory(equality)],[6681,5381]),
[iquote('0:Rew:6681.0,5381.0')] ).
cnf(6803,plain,
equal(multiply(multiply(u,inverse(u)),v),multiply(multiply(multiply(inverse(multiply(w,inverse(w))),inverse(x)),x),v)),
inference(spr,[status(thm),theory(equality)],[6180,4229]),
[iquote('0:SpR:6180.0,4229.0')] ).
cnf(6915,plain,
equal(inverse(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u)))))),multiply(v,multiply(w,multiply(x,inverse(multiply(y,inverse(y))))))),
inference(spr,[status(thm),theory(equality)],[183,6180]),
[iquote('0:SpR:183.0,6180.0')] ).
cnf(6989,plain,
equal(multiply(inverse(u),inverse(multiply(v,multiply(multiply(w,inverse(w)),x)))),multiply(y,inverse(multiply(v,multiply(x,multiply(u,y)))))),
inference(spr,[status(thm),theory(equality)],[6176,183]),
[iquote('0:SpR:6176.0,183.0')] ).
cnf(7036,plain,
equal(multiply(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(inverse(multiply(w,multiply(x,multiply(multiply(inverse(x),inverse(multiply(y,w))),z)))),u))),multiply(inverse(z),inverse(multiply(multiply(x1,inverse(x1)),x2))))))),inverse(multiply(multiply(x3,inverse(x3)),y))),x2),
inference(spr,[status(thm),theory(equality)],[6176,251]),
[iquote('0:SpR:6176.0,251.0')] ).
cnf(7257,plain,
equal(multiply(multiply(u,multiply(v,inverse(multiply(w,multiply(x,multiply(multiply(inverse(x),inverse(multiply(y,w))),v)))))),inverse(multiply(multiply(z,inverse(z)),y))),u),
inference(rew,[status(thm),theory(equality)],[3587,7036]),
[iquote('0:Rew:3587.0,7036.0')] ).
cnf(7258,plain,
equal(multiply(multiply(u,v),inverse(multiply(multiply(w,inverse(w)),v))),u),
inference(rew,[status(thm),theory(equality)],[1,7257]),
[iquote('0:Rew:1.0,7257.0')] ).
cnf(7862,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(multiply(v,inverse(v)),w)),multiply(x,multiply(multiply(inverse(x),inverse(y)),u))))),inverse(multiply(z,multiply(x1,multiply(multiply(inverse(x1),inverse(multiply(inverse(x2),z))),multiply(inverse(x2),inverse(multiply(y,w)))))))),
inference(spr,[status(thm),theory(equality)],[6176,230]),
[iquote('0:SpR:6176.0,230.0')] ).
cnf(7865,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,inverse(w)))),multiply(x,multiply(multiply(inverse(x),inverse(y)),u))))),inverse(multiply(z,multiply(x1,multiply(multiply(inverse(x1),inverse(multiply(inverse(x2),z))),multiply(inverse(x2),inverse(multiply(y,v)))))))),
inference(spr,[status(thm),theory(equality)],[2417,230]),
[iquote('0:SpR:2417.0,230.0')] ).
cnf(8180,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(multiply(v,inverse(v)),w)),multiply(x,multiply(multiply(inverse(x),inverse(y)),u))))),multiply(y,w)),
inference(spr,[status(thm),theory(equality)],[7258,1]),
[iquote('0:SpR:7258.0,1.0')] ).
cnf(8223,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,inverse(w)))),multiply(x,multiply(multiply(inverse(x),inverse(y)),u))))),inverse(multiply(multiply(z,inverse(z)),inverse(multiply(y,v))))),
inference(spr,[status(thm),theory(equality)],[7258,3]),
[iquote('0:SpR:7258.0,3.0')] ).
cnf(8231,plain,
equal(multiply(inverse(multiply(multiply(u,inverse(u)),inverse(v))),multiply(w,inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[7258,6176]),
[iquote('0:SpR:7258.0,6176.0')] ).
cnf(8235,plain,
equal(multiply(multiply(u,inverse(u)),inverse(multiply(multiply(v,inverse(v)),inverse(w)))),w),
inference(spr,[status(thm),theory(equality)],[7258,4229]),
[iquote('0:SpR:7258.0,4229.0')] ).
cnf(8314,plain,
equal(multiply(multiply(u,inverse(multiply(v,inverse(v)))),inverse(multiply(multiply(w,inverse(w)),inverse(multiply(x,inverse(x)))))),u),
inference(spr,[status(thm),theory(equality)],[4634,7258]),
[iquote('0:SpR:4634.0,7258.0')] ).
cnf(8377,plain,
equal(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(inverse(w),u))),multiply(inverse(w),inverse(multiply(x,y))))))),multiply(x,y)),
inference(rew,[status(thm),theory(equality)],[8180,7862]),
[iquote('0:Rew:8180.0,7862.0')] ).
cnf(8385,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,inverse(w)))),multiply(x,multiply(multiply(inverse(x),inverse(y)),u))))),multiply(y,v)),
inference(rew,[status(thm),theory(equality)],[8377,7865]),
[iquote('0:Rew:8377.0,7865.0')] ).
cnf(8392,plain,
equal(inverse(multiply(multiply(u,inverse(u)),inverse(multiply(v,w)))),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[8385,8223]),
[iquote('0:Rew:8385.0,8223.0')] ).
cnf(8424,plain,
equal(inverse(multiply(multiply(u,inverse(u)),inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[8392,6746]),
[iquote('0:Rew:8392.0,6746.0')] ).
cnf(8478,plain,
equal(multiply(multiply(u,inverse(multiply(v,inverse(v)))),multiply(w,inverse(w))),u),
inference(rew,[status(thm),theory(equality)],[8392,8314]),
[iquote('0:Rew:8392.0,8314.0')] ).
cnf(8495,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[8424,8235]),
[iquote('0:Rew:8424.0,8235.0')] ).
cnf(8498,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[8424,8231]),
[iquote('0:Rew:8424.0,8231.0')] ).
cnf(8741,plain,
equal(multiply(u,multiply(inverse(u),inverse(inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[8495,6677]),
[iquote('0:Rew:8495.0,6677.0')] ).
cnf(8742,plain,
equal(multiply(multiply(multiply(inverse(multiply(u,inverse(u))),inverse(v)),v),w),w),
inference(rew,[status(thm),theory(equality)],[8495,6803]),
[iquote('0:Rew:8495.0,6803.0')] ).
cnf(8878,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u))))),multiply(inverse(x),inverse(multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[8495,6989]),
[iquote('0:Rew:8495.0,6989.0')] ).
cnf(8900,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[8495,8424]),
[iquote('0:Rew:8495.0,8424.0')] ).
cnf(9092,plain,
equal(multiply(inverse(multiply(u,inverse(u))),v),v),
inference(rew,[status(thm),theory(equality)],[8900,6174]),
[iquote('0:Rew:8900.0,6174.0')] ).
cnf(10123,plain,
equal(inverse(multiply(multiply(inverse(multiply(u,inverse(u))),inverse(v)),v)),inverse(multiply(inverse(w),w))),
inference(rew,[status(thm),theory(equality)],[9092,5928]),
[iquote('0:Rew:9092.0,5928.0')] ).
cnf(10203,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[8900,8741]),
[iquote('0:Rew:8900.0,8741.0')] ).
cnf(10272,plain,
equal(inverse(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u))))),v)),multiply(w,x)),
inference(rew,[status(thm),theory(equality)],[10203,2204]),
[iquote('0:Rew:10203.0,2204.0')] ).
cnf(10310,plain,
equal(multiply(u,inverse(multiply(v,inverse(v)))),u),
inference(rew,[status(thm),theory(equality)],[8498,8478]),
[iquote('0:Rew:8498.0,8478.0')] ).
cnf(10315,plain,
equal(inverse(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u)))))),multiply(v,multiply(w,x))),
inference(rew,[status(thm),theory(equality)],[10310,6915]),
[iquote('0:Rew:10310.0,6915.0')] ).
cnf(10329,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,inverse(w)))),v)),inverse(multiply(inverse(u),w))),
inference(rew,[status(thm),theory(equality)],[10310,2302]),
[iquote('0:Rew:10310.0,2302.0')] ).
cnf(10368,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[9092,8742]),
[iquote('0:Rew:9092.0,8742.0')] ).
cnf(10369,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[10368,2]),
[iquote('0:Rew:10368.0,2.2')] ).
cnf(11570,plain,
equal(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[9092,10123]),
[iquote('0:Rew:9092.0,10123.0')] ).
cnf(11662,plain,
equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,w))),v)),multiply(w,u)),
inference(rew,[status(thm),theory(equality)],[8878,10272]),
[iquote('0:Rew:8878.0,10272.0')] ).
cnf(11664,plain,
equal(inverse(multiply(inverse(u),inverse(multiply(v,w)))),multiply(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[8878,10315]),
[iquote('0:Rew:8878.0,10315.0')] ).
cnf(11681,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[11662,10329]),
[iquote('0:Rew:11662.0,10329.0')] ).
cnf(11703,plain,
equal(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[11681,11570]),
[iquote('0:Rew:11681.0,11570.0')] ).
cnf(11710,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[11681,11703]),
[iquote('0:Rew:11681.0,11703.0')] ).
cnf(11711,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[8900,11664,11681]),
[iquote('0:Rew:8900.0,11664.0,11681.0,11664.0')] ).
cnf(12332,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[10369]),
[iquote('0:Obv:10369.2')] ).
cnf(12333,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[11711,12332]),
[iquote('0:Rew:11711.0,12332.1')] ).
cnf(12334,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[12333]),
[iquote('0:Obv:12333.1')] ).
cnf(12335,plain,
$false,
inference(unc,[status(thm)],[12334,11710]),
[iquote('0:UnC:12334.0,11710.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP060-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n020.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 13:23:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 65.13/65.28
% 65.13/65.28 SPASS V 3.9
% 65.13/65.28 SPASS beiseite: Proof found.
% 65.13/65.28 % SZS status Theorem
% 65.13/65.28 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.13/65.28 SPASS derived 10834 clauses, backtracked 0 clauses, performed 0 splits and kept 4008 clauses.
% 65.13/65.28 SPASS allocated 123596 KBytes.
% 65.13/65.28 SPASS spent 0:01:04.91 on the problem.
% 65.13/65.28 0:00:00.04 for the input.
% 65.13/65.28 0:00:00.00 for the FLOTTER CNF translation.
% 65.13/65.28 0:00:00.12 for inferences.
% 65.13/65.28 0:00:00.00 for the backtracking.
% 65.13/65.28 0:01:04.72 for the reduction.
% 65.13/65.28
% 65.13/65.28
% 65.13/65.28 Here is a proof with depth 20, length 115 :
% 65.13/65.28 % SZS output start Refutation
% See solution above
% 65.61/65.81 Formulae used in the proof : single_axiom prove_these_axioms
% 65.61/65.81
%------------------------------------------------------------------------------