TSTP Solution File: GRP056-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP056-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:45:04 EDT 2022
% Result : Unsatisfiable 1.31s 1.50s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 2
% Syntax : Number of clauses : 137 ( 132 unt; 0 nHn; 137 RR)
% Number of literals : 145 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w)))),inverse(multiply(inverse(w),w))),v),
file('GRP056-1.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('GRP056-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),multiply(inverse(multiply(x,inverse(multiply(inverse(v),w)))),multiply(x,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(5,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w)))),inverse(multiply(inverse(x),multiply(inverse(w),w))))),v)),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),x),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(33,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),w)))),multiply(x,inverse(w)))),inverse(multiply(inverse(v),multiply(inverse(w),w))))),y)),
inference(spr,[status(thm),theory(equality)],[5,1]),
[iquote('0:SpR:5.0,1.0')] ).
cnf(49,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(x),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))),multiply(inverse(multiply(y,inverse(multiply(inverse(v),w)))),multiply(y,inverse(w))))),inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),x),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(59,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(w),w)))),w)))),multiply(u,inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(68,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w))),multiply(inverse(multiply(x,inverse(multiply(inverse(v),w)))),multiply(x,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(75,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,inverse(multiply(inverse(w),x)))))),multiply(u,inverse(inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x)))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x))))),inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x))))))),multiply(inverse(multiply(y,inverse(multiply(inverse(multiply(inverse(multiply(z,inverse(w))),multiply(z,inverse(inverse(multiply(inverse(x),x)))))),inverse(multiply(inverse(inverse(multiply(inverse(x),x))),inverse(multiply(inverse(x),x)))))))),multiply(y,inverse(multiply(v,inverse(x)))))),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(77,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(w),w))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(101,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x)))))),inverse(multiply(inverse(multiply(w,inverse(x))),multiply(w,inverse(x))))),multiply(w,inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(x),x)))),x)))),
inference(spr,[status(thm),theory(equality)],[59,1]),
[iquote('0:SpR:59.0,1.0')] ).
cnf(102,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x)))))),inverse(multiply(inverse(y),multiply(inverse(multiply(w,inverse(x))),multiply(w,inverse(x))))))),multiply(w,inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(x),x)))),x))))),inverse(multiply(inverse(multiply(inverse(multiply(w,inverse(x))),multiply(w,inverse(x)))),multiply(inverse(multiply(w,inverse(x))),multiply(w,inverse(x)))))),y),
inference(spr,[status(thm),theory(equality)],[59,5]),
[iquote('0:SpR:59.0,5.0')] ).
cnf(103,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(w),inverse(multiply(inverse(x),x)))),x)))))),multiply(u,inverse(inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x)))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x))))),inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x))))))),multiply(inverse(multiply(y,inverse(w))),multiply(y,inverse(multiply(v,inverse(x)))))),
inference(spr,[status(thm),theory(equality)],[59,3]),
[iquote('0:SpR:59.0,3.0')] ).
cnf(124,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))))),multiply(inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))))),w)))),multiply(x,inverse(w)))),inverse(multiply(inverse(v),multiply(inverse(w),w))))),
inference(spr,[status(thm),theory(equality)],[5,59]),
[iquote('0:SpR:5.0,59.0')] ).
cnf(183,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,inverse(x))))),multiply(inverse(multiply(y,inverse(v))),multiply(y,inverse(multiply(w,inverse(x)))))),
inference(spr,[status(thm),theory(equality)],[59,68]),
[iquote('0:SpR:59.0,68.0')] ).
cnf(270,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[5,183]),
[iquote('0:SpR:5.0,183.0')] ).
cnf(351,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(x)))))),multiply(u,inverse(multiply(y,inverse(x)))))),inverse(multiply(inverse(multiply(y,inverse(x))),multiply(y,inverse(x))))),multiply(y,inverse(w))),
inference(spr,[status(thm),theory(equality)],[270,1]),
[iquote('0:SpR:270.0,1.0')] ).
cnf(366,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(w),inverse(x))),multiply(inverse(w),inverse(x)))))),multiply(v,inverse(x)))))),multiply(u,inverse(multiply(inverse(w),inverse(x))))),w),
inference(spr,[status(thm),theory(equality)],[270,59]),
[iquote('0:SpR:270.0,59.0')] ).
cnf(388,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(w))),multiply(inverse(x),multiply(inverse(multiply(inverse(multiply(y,inverse(multiply(inverse(x),v)))),multiply(y,inverse(v)))),inverse(w)))),
inference(spr,[status(thm),theory(equality)],[1,270]),
[iquote('0:SpR:1.0,270.0')] ).
cnf(391,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(u,inverse(w))),multiply(inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),v)))),multiply(x,inverse(v)))),multiply(inverse(multiply(inverse(multiply(z,inverse(y))),multiply(z,inverse(inverse(multiply(inverse(v),v)))))),inverse(w)))),
inference(spr,[status(thm),theory(equality)],[3,270]),
[iquote('0:SpR:3.0,270.0')] ).
cnf(394,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(x)))),inverse(multiply(inverse(x),x)))),x))),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[101,351]),
[iquote('0:Rew:101.0,351.0')] ).
cnf(423,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(w),w))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(x,inverse(v))),multiply(x,inverse(y)))),inverse(multiply(inverse(y),y)))),y)),
inference(spr,[status(thm),theory(equality)],[394,77]),
[iquote('0:SpR:394.0,77.0')] ).
cnf(468,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w)))),inverse(multiply(inverse(w),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[77,423]),
[iquote('0:Rew:77.0,423.0')] ).
cnf(506,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(w))))),inverse(multiply(inverse(inverse(w)),inverse(w))))),inverse(multiply(inverse(multiply(inverse(x),inverse(multiply(inverse(w),w)))),w)))),v),x),
inference(spr,[status(thm),theory(equality)],[468,59]),
[iquote('0:SpR:468.0,59.0')] ).
cnf(522,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(x,inverse(y))),multiply(x,inverse(inverse(w))))),inverse(multiply(inverse(inverse(w)),inverse(w))))),inverse(v))),y)),
inference(spr,[status(thm),theory(equality)],[468,270]),
[iquote('0:SpR:468.0,270.0')] ).
cnf(566,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,inverse(multiply(inverse(w),w)))))),multiply(u,inverse(inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x)))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x))))),inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x))))))),multiply(inverse(multiply(y,inverse(multiply(inverse(z),multiply(inverse(multiply(inverse(multiply(x1,inverse(multiply(inverse(z),w)))),multiply(x1,inverse(w)))),inverse(x)))))),multiply(y,inverse(multiply(v,inverse(x)))))),
inference(spr,[status(thm),theory(equality)],[388,3]),
[iquote('0:SpR:388.0,3.0')] ).
cnf(588,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(w,inverse(multiply(inverse(v),x)))),multiply(w,inverse(x)))),inverse(y))),multiply(inverse(multiply(inverse(multiply(w,inverse(multiply(inverse(v),x)))),multiply(w,inverse(x)))),inverse(y)))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(w,inverse(multiply(inverse(v),x)))),multiply(w,inverse(x)))),inverse(y))),multiply(inverse(multiply(inverse(multiply(w,inverse(multiply(inverse(v),x)))),multiply(w,inverse(x)))),inverse(y))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(w,inverse(multiply(inverse(v),x)))),multiply(w,inverse(x)))),inverse(y))),multiply(inverse(multiply(inverse(multiply(w,inverse(multiply(inverse(v),x)))),multiply(w,inverse(x)))),inverse(y))))))),multiply(inverse(multiply(z,inverse(multiply(inverse(multiply(x1,inverse(multiply(inverse(x),x)))),multiply(x1,inverse(y)))))),multiply(z,inverse(multiply(inverse(multiply(inverse(multiply(w,inverse(multiply(inverse(v),x)))),multiply(w,inverse(x)))),inverse(y)))))),
inference(spr,[status(thm),theory(equality)],[388,3]),
[iquote('0:SpR:388.0,3.0')] ).
cnf(635,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(multiply(inverse(v),v)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[1,388]),
[iquote('0:SpR:1.0,388.0')] ).
cnf(730,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[635]),
[iquote('0:SpR:635.0,635.0')] ).
cnf(743,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w)))),inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),y)))),multiply(x,inverse(multiply(inverse(y),y)))))),v),
inference(spr,[status(thm),theory(equality)],[635,1]),
[iquote('0:SpR:635.0,1.0')] ).
cnf(767,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w)))),inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),y)))),multiply(x,inverse(multiply(inverse(y),y))))))),v)),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(w),w)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[635,5]),
[iquote('0:SpR:635.0,5.0')] ).
cnf(820,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[743,767]),
[iquote('0:Rew:743.0,767.0')] ).
cnf(837,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),v)))),v),v),
inference(spr,[status(thm),theory(equality)],[730,468]),
[iquote('0:SpR:730.0,468.0')] ).
cnf(875,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),w)))),multiply(u,inverse(w)))),inverse(multiply(inverse(x),x))),v),
inference(spr,[status(thm),theory(equality)],[730,1]),
[iquote('0:SpR:730.0,1.0')] ).
cnf(878,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(w),w)))),x)))),multiply(u,inverse(x))),v),
inference(spr,[status(thm),theory(equality)],[730,59]),
[iquote('0:SpR:730.0,59.0')] ).
cnf(879,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w)))),inverse(multiply(inverse(x),x)))),w),v),
inference(spr,[status(thm),theory(equality)],[730,468]),
[iquote('0:SpR:730.0,468.0')] ).
cnf(881,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(w)))),inverse(multiply(inverse(w),w))),w),
inference(spr,[status(thm),theory(equality)],[730,1]),
[iquote('0:SpR:730.0,1.0')] ).
cnf(899,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(w))),multiply(inverse(v),multiply(inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),y)))),multiply(x,inverse(v)))),inverse(w)))),
inference(spr,[status(thm),theory(equality)],[730,388]),
[iquote('0:SpR:730.0,388.0')] ).
cnf(902,plain,
equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(u),u)))),u)))),multiply(inverse(w),w)),v),
inference(spr,[status(thm),theory(equality)],[730,59]),
[iquote('0:SpR:730.0,59.0')] ).
cnf(908,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),inverse(multiply(inverse(w),w)))),w))),inverse(w))),v),
inference(spr,[status(thm),theory(equality)],[730,59]),
[iquote('0:SpR:730.0,59.0')] ).
cnf(916,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(x),x))),multiply(inverse(multiply(y,inverse(multiply(inverse(v),w)))),multiply(y,inverse(w)))),
inference(spr,[status(thm),theory(equality)],[730,3]),
[iquote('0:SpR:730.0,3.0')] ).
cnf(922,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(multiply(inverse(inverse(w)),inverse(v))),multiply(inverse(x),x))),
inference(spr,[status(thm),theory(equality)],[730,270]),
[iquote('0:SpR:730.0,270.0')] ).
cnf(926,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(w))),multiply(inverse(x),multiply(inverse(multiply(inverse(multiply(inverse(y),y)),multiply(inverse(inverse(multiply(inverse(x),v))),inverse(v)))),inverse(w)))),
inference(spr,[status(thm),theory(equality)],[730,388]),
[iquote('0:SpR:730.0,388.0')] ).
cnf(928,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(u),u),a2),a2) ),
inference(spl,[status(thm),theory(equality)],[730,2]),
[iquote('0:SpL:730.0,2.2')] ).
cnf(964,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(inverse(v)),multiply(inverse(multiply(inverse(multiply(inverse(x),x)),inverse(multiply(inverse(inverse(v)),inverse(v))))),inverse(w)))),
inference(spr,[status(thm),theory(equality)],[837,270]),
[iquote('0:SpR:837.0,270.0')] ).
cnf(967,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),v)))),w),w),
inference(spr,[status(thm),theory(equality)],[730,837]),
[iquote('0:SpR:730.0,837.0')] ).
cnf(973,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(inverse(v)),inverse(w))),
inference(rew,[status(thm),theory(equality)],[967,964]),
[iquote('0:Rew:967.0,964.0')] ).
cnf(978,plain,
equal(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),inverse(multiply(inverse(v),v)))),w))),inverse(w)),u),
inference(rew,[status(thm),theory(equality)],[973,878]),
[iquote('0:Rew:973.0,878.0')] ).
cnf(986,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(inverse(w)),inverse(w))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(w)),inverse(w)))),inverse(multiply(inverse(inverse(w)),inverse(w)))))),multiply(inverse(multiply(x,inverse(multiply(inverse(multiply(y,inverse(multiply(inverse(z),z)))),multiply(y,inverse(w)))))),multiply(x,inverse(multiply(inverse(multiply(inverse(multiply(x1,inverse(multiply(inverse(v),z)))),multiply(x1,inverse(z)))),inverse(w)))))),
inference(rew,[status(thm),theory(equality)],[973,588]),
[iquote('0:Rew:973.0,588.0')] ).
cnf(1000,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(u,inverse(multiply(inverse(v),v))))),inverse(inverse(multiply(inverse(multiply(u,inverse(w))),multiply(u,inverse(w))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(u,inverse(w))),multiply(u,inverse(w))))),inverse(multiply(inverse(multiply(u,inverse(w))),multiply(u,inverse(w))))))),multiply(inverse(multiply(x,inverse(multiply(inverse(y),multiply(inverse(multiply(inverse(multiply(z,inverse(multiply(inverse(y),v)))),multiply(z,inverse(v)))),inverse(w)))))),multiply(x,inverse(multiply(u,inverse(w)))))),
inference(rew,[status(thm),theory(equality)],[973,566]),
[iquote('0:Rew:973.0,566.0')] ).
cnf(1016,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(u)),inverse(inverse(v)))),inverse(multiply(inverse(inverse(v)),inverse(v))))),inverse(multiply(inverse(multiply(inverse(w),inverse(multiply(inverse(v),v)))),v)))),u),w),
inference(rew,[status(thm),theory(equality)],[973,506]),
[iquote('0:Rew:973.0,506.0')] ).
cnf(1021,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(x)),inverse(inverse(w)))),inverse(multiply(inverse(inverse(w)),inverse(w))))),inverse(v))),x)),
inference(rew,[status(thm),theory(equality)],[973,522]),
[iquote('0:Rew:973.0,522.0')] ).
cnf(1023,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(v),v)))))),multiply(u,inverse(w))),multiply(inverse(multiply(inverse(multiply(x,inverse(multiply(inverse(y),v)))),multiply(x,inverse(v)))),multiply(inverse(multiply(inverse(inverse(y)),inverse(inverse(multiply(inverse(v),v))))),inverse(w)))),
inference(rew,[status(thm),theory(equality)],[973,391]),
[iquote('0:Rew:973.0,391.0')] ).
cnf(1028,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(inverse(u)),inverse(v))),inverse(multiply(inverse(w),w)))),v),u),
inference(rew,[status(thm),theory(equality)],[973,879]),
[iquote('0:Rew:973.0,879.0')] ).
cnf(1030,plain,
equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(v))),multiply(inverse(w),w)),multiply(inverse(inverse(v)),inverse(u))),
inference(rew,[status(thm),theory(equality)],[973,922]),
[iquote('0:Rew:973.0,922.0')] ).
cnf(1037,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(v,inverse(multiply(inverse(inverse(w)),inverse(w))))),multiply(v,inverse(w)))))),multiply(u,inverse(multiply(inverse(x),inverse(w))))),x),
inference(rew,[status(thm),theory(equality)],[973,366]),
[iquote('0:Rew:973.0,366.0')] ).
cnf(1057,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(v),v)))),multiply(u,inverse(w))),multiply(inverse(v),multiply(inverse(multiply(inverse(inverse(multiply(inverse(x),x))),inverse(v))),inverse(w)))),
inference(rew,[status(thm),theory(equality)],[973,899]),
[iquote('0:Rew:973.0,899.0')] ).
cnf(1072,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(v))),inverse(multiply(inverse(v),v))),v),
inference(rew,[status(thm),theory(equality)],[973,881]),
[iquote('0:Rew:973.0,881.0')] ).
cnf(1074,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(inverse(multiply(inverse(u),w))),inverse(w)))),inverse(x))),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(x))),
inference(rew,[status(thm),theory(equality)],[973,926]),
[iquote('0:Rew:973.0,926.0')] ).
cnf(1086,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(x),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))))),multiply(inverse(multiply(y,inverse(multiply(inverse(v),w)))),multiply(y,inverse(w))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w))))),x),
inference(rew,[status(thm),theory(equality)],[973,49]),
[iquote('0:Rew:973.0,49.0')] ).
cnf(1092,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(w),inverse(multiply(inverse(x),x)))),x)))))),multiply(u,inverse(inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x)))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x))))),inverse(multiply(inverse(multiply(v,inverse(x))),multiply(v,inverse(x))))))),multiply(inverse(inverse(w)),inverse(multiply(v,inverse(x))))),
inference(rew,[status(thm),theory(equality)],[973,103]),
[iquote('0:Rew:973.0,103.0')] ).
cnf(1096,plain,
equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(multiply(v,inverse(w))))),inverse(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(w))))),multiply(v,inverse(multiply(inverse(multiply(inverse(u),inverse(multiply(inverse(w),w)))),w)))),
inference(rew,[status(thm),theory(equality)],[973,101]),
[iquote('0:Rew:973.0,101.0')] ).
cnf(1097,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(u)),inverse(multiply(v,inverse(w))))),inverse(multiply(inverse(x),multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(w))))))),multiply(v,inverse(multiply(inverse(multiply(inverse(u),inverse(multiply(inverse(w),w)))),w))))),inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(w)))),multiply(inverse(multiply(v,inverse(w))),multiply(v,inverse(w)))))),x),
inference(rew,[status(thm),theory(equality)],[973,102]),
[iquote('0:Rew:973.0,102.0')] ).
cnf(1100,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(u,inverse(multiply(inverse(v),w))))),inverse(inverse(multiply(inverse(multiply(u,inverse(w))),multiply(u,inverse(w))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(u,inverse(w))),multiply(u,inverse(w))))),inverse(multiply(inverse(multiply(u,inverse(w))),multiply(u,inverse(w))))))),multiply(inverse(multiply(x,inverse(multiply(inverse(multiply(inverse(multiply(y,inverse(v))),multiply(y,inverse(inverse(multiply(inverse(w),w)))))),inverse(multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))))),multiply(x,inverse(multiply(u,inverse(w)))))),
inference(rew,[status(thm),theory(equality)],[973,75]),
[iquote('0:Rew:973.0,75.0')] ).
cnf(1130,plain,
equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))),inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(w,inverse(multiply(inverse(x),v)))),multiply(w,inverse(v)))),inverse(multiply(inverse(u),multiply(inverse(v),v))))),x)),
inference(rew,[status(thm),theory(equality)],[973,33]),
[iquote('0:Rew:973.0,33.0')] ).
cnf(1134,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))),inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))))),v)))),multiply(u,inverse(v)))),inverse(multiply(inverse(w),multiply(inverse(v),v)))),multiply(inverse(inverse(w)),inverse(inverse(multiply(inverse(multiply(inverse(v),v)),multiply(inverse(v),v)))))),
inference(rew,[status(thm),theory(equality)],[973,124]),
[iquote('0:Rew:973.0,124.0')] ).
cnf(1140,plain,
equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(w),w))),multiply(inverse(multiply(x,inverse(multiply(inverse(u),v)))),multiply(x,inverse(v)))),
inference(rew,[status(thm),theory(equality)],[973,916]),
[iquote('0:Rew:973.0,916.0')] ).
cnf(1194,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),v))),inverse(v))),inverse(multiply(inverse(w),w))),u),
inference(rew,[status(thm),theory(equality)],[973,875]),
[iquote('0:Rew:973.0,875.0')] ).
cnf(1196,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(rew,[status(thm),theory(equality)],[978,908]),
[iquote('0:Rew:978.0,908.0')] ).
cnf(1202,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(u),u))),multiply(inverse(u),u)),
inference(rew,[status(thm),theory(equality)],[1196,820]),
[iquote('0:Rew:1196.0,820.0')] ).
cnf(1212,plain,
equal(inverse(multiply(inverse(u),u)),multiply(inverse(u),u)),
inference(rew,[status(thm),theory(equality)],[1196,1202]),
[iquote('0:Rew:1196.0,1202.0')] ).
cnf(1214,plain,
equal(multiply(inverse(inverse(multiply(inverse(multiply(inverse(u),multiply(inverse(v),v))),w))),inverse(w)),u),
inference(rew,[status(thm),theory(equality)],[1212,978]),
[iquote('0:Rew:1212.0,978.0')] ).
cnf(1217,plain,
equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(multiply(inverse(multiply(inverse(v),multiply(inverse(u),u))),u)))),multiply(inverse(w),w)),v),
inference(rew,[status(thm),theory(equality)],[1212,902]),
[iquote('0:Rew:1212.0,902.0')] ).
cnf(1221,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[1212,1196]),
[iquote('0:Rew:1212.0,1196.0')] ).
cnf(1223,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)],[1221,928]),
[iquote('0:Rew:1221.0,928.2')] ).
cnf(1225,plain,
equal(multiply(inverse(multiply(inverse(multiply(inverse(inverse(u)),inverse(v))),multiply(inverse(w),w))),v),u),
inference(rew,[status(thm),theory(equality)],[1212,1028]),
[iquote('0:Rew:1212.0,1028.0')] ).
cnf(1227,plain,
equal(multiply(inverse(inverse(u)),multiply(inverse(u),u)),u),
inference(rew,[status(thm),theory(equality)],[1221,1072,1212]),
[iquote('0:Rew:1221.0,1072.0,1212.0,1072.0,1212.0,1072.0,1212.0,1072.0')] ).
cnf(1228,plain,
equal(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),v))),inverse(v))),multiply(inverse(w),w)),u),
inference(rew,[status(thm),theory(equality)],[1212,1194]),
[iquote('0:Rew:1212.0,1194.0')] ).
cnf(1232,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(inverse(v),u))),v),
inference(rew,[status(thm),theory(equality)],[1030,1228]),
[iquote('0:Rew:1030.0,1228.0')] ).
cnf(1233,plain,
equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(v))),u),v),
inference(rew,[status(thm),theory(equality)],[1030,1225]),
[iquote('0:Rew:1030.0,1225.0')] ).
cnf(1235,plain,
equal(multiply(inverse(multiply(inverse(u),multiply(inverse(v),v))),multiply(inverse(w),w)),u),
inference(rew,[status(thm),theory(equality)],[1232,1217]),
[iquote('0:Rew:1232.0,1217.0')] ).
cnf(1240,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)],[1223]),
[iquote('0:Obv:1223.2')] ).
cnf(1242,plain,
equal(multiply(inverse(inverse(multiply(inverse(multiply(u,multiply(inverse(inverse(v)),inverse(v)))),multiply(u,inverse(v))))),inverse(multiply(inverse(w),inverse(v)))),w),
inference(rew,[status(thm),theory(equality)],[973,1037,1212]),
[iquote('0:Rew:973.0,1037.0,1212.0,1037.0')] ).
cnf(1245,plain,
equal(multiply(inverse(multiply(u,multiply(inverse(v),v))),multiply(u,inverse(w))),multiply(inverse(v),multiply(inverse(inverse(v)),inverse(w)))),
inference(rew,[status(thm),theory(equality)],[1212,1057,1221]),
[iquote('0:Rew:1212.0,1057.0,1221.0,1057.0,1212.0,1057.0,1212.0,1057.0')] ).
cnf(1247,plain,
equal(multiply(inverse(inverse(multiply(inverse(inverse(u)),multiply(inverse(inverse(inverse(u))),inverse(u))))),inverse(multiply(inverse(v),inverse(u)))),v),
inference(rew,[status(thm),theory(equality)],[1245,1242]),
[iquote('0:Rew:1245.0,1242.0')] ).
cnf(1251,plain,
equal(multiply(inverse(inverse(multiply(inverse(u),v))),inverse(v)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1235,1140,1212,973]),
[iquote('0:Rew:1235.0,1140.0,1212.0,1140.0,1212.0,1140.0,1212.0,1140.0,973.0,1140.0')] ).
cnf(1255,plain,
equal(inverse(multiply(inverse(u),multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[1251,1214]),
[iquote('0:Rew:1251.0,1214.0')] ).
cnf(1256,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[1255,1235]),
[iquote('0:Rew:1255.0,1235.0')] ).
cnf(1259,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[1256,1227]),
[iquote('0:Rew:1256.0,1227.0')] ).
cnf(1261,plain,
equal(inverse(multiply(inverse(inverse(u)),inverse(v))),multiply(inverse(inverse(v)),inverse(u))),
inference(rew,[status(thm),theory(equality)],[1256,1030]),
[iquote('0:Rew:1256.0,1030.0')] ).
cnf(1262,plain,
equal(multiply(inverse(inverse(multiply(inverse(inverse(u)),multiply(inverse(u),inverse(u))))),inverse(multiply(inverse(v),inverse(u)))),v),
inference(rew,[status(thm),theory(equality)],[1259,1247]),
[iquote('0:Rew:1259.0,1247.0')] ).
cnf(1263,plain,
equal(multiply(inverse(multiply(u,inverse(v))),u),v),
inference(rew,[status(thm),theory(equality)],[1259,1233]),
[iquote('0:Rew:1259.0,1233.0')] ).
cnf(1265,plain,
equal(multiply(multiply(inverse(u),v),inverse(v)),inverse(u)),
inference(rew,[status(thm),theory(equality)],[1259,1251]),
[iquote('0:Rew:1259.0,1251.0')] ).
cnf(1266,plain,
equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(w))),multiply(v,inverse(w))),
inference(rew,[status(thm),theory(equality)],[1259,973]),
[iquote('0:Rew:1259.0,973.0')] ).
cnf(1267,plain,
equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[1259,1261]),
[iquote('0:Rew:1259.0,1261.0,1259.0,1261.0')] ).
cnf(1268,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(rew,[status(thm),theory(equality)],[1267,1263]),
[iquote('0:Rew:1267.0,1263.0')] ).
cnf(1270,plain,
equal(multiply(multiply(u,inverse(v)),multiply(v,inverse(w))),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[1267,1266]),
[iquote('0:Rew:1267.0,1266.0')] ).
cnf(1275,plain,
equal(multiply(multiply(u,multiply(inverse(u),inverse(u))),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[1259,1262,1267]),
[iquote('0:Rew:1259.0,1262.0,1259.0,1262.0,1259.0,1262.0,1267.0,1262.0')] ).
cnf(1282,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1259,1074,1221,1212,1265]),
[iquote('0:Rew:1259.0,1074.0,1221.0,1074.0,1212.0,1074.0,1265.0,1074.0,1259.0,1074.0,1221.0,1074.0,1212.0,1074.0,1212.0,1074.0')] ).
cnf(1292,plain,
equal(multiply(multiply(u,multiply(inverse(multiply(v,w)),multiply(w,inverse(w)))),v),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[1270,1021,1267,1259]),
[iquote('0:Rew:1270.0,1021.0,1267.0,1021.0,1259.0,1021.0,1267.0,1021.0,1259.0,1021.0,1267.0,1021.0,1259.0,1021.0')] ).
cnf(1294,plain,
equal(multiply(multiply(u,v),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[1292,1016,1259,1267,1256,1212]),
[iquote('0:Rew:1292.0,1016.0,1259.0,1016.0,1267.0,1016.0,1259.0,1016.0,1267.0,1016.0,1259.0,1016.0,1259.0,1016.0,1256.0,1016.0,1212.0,1016.0')] ).
cnf(1302,plain,
equal(multiply(inverse(multiply(u,multiply(v,inverse(w)))),multiply(v,inverse(v))),multiply(w,inverse(multiply(u,v)))),
inference(rew,[status(thm),theory(equality)],[1267,1096,1270,1259,1256,1212]),
[iquote('0:Rew:1267.0,1096.0,1270.0,1096.0,1267.0,1096.0,1259.0,1096.0,1256.0,1096.0,1212.0,1096.0')] ).
cnf(1354,plain,
equal(multiply(u,multiply(inverse(u),inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1282,1023,1256,1212,1259,1294,1270,1267]),
[iquote('0:Rew:1282.0,1023.0,1256.0,1023.0,1212.0,1023.0,1256.0,1023.0,1259.0,1023.0,1294.0,1023.0,1270.0,1023.0,1267.0,1023.0,1256.0,1023.0,1259.0,1023.0,1212.0,1023.0,1212.0,1023.0')] ).
cnf(1355,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[1354,1275]),
[iquote('0:Rew:1354.0,1275.0')] ).
cnf(1406,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[1256,1086,1259,1267,1268,1294,1270,1212]),
[iquote('0:Rew:1256.0,1086.0,1259.0,1086.0,1267.0,1086.0,1268.0,1086.0,1267.0,1086.0,1256.0,1086.0,1259.0,1086.0,1256.0,1086.0,1294.0,1086.0,1270.0,1086.0,1267.0,1086.0,1212.0,1086.0,1256.0,1086.0,1212.0,1086.0,1212.0,1086.0')] ).
cnf(1409,plain,
equal(multiply(multiply(u,inverse(u)),v),v),
inference(rew,[status(thm),theory(equality)],[1267,1134,1270,1221,1212,1256,1259]),
[iquote('0:Rew:1267.0,1134.0,1270.0,1134.0,1267.0,1134.0,1221.0,1134.0,1212.0,1134.0,1212.0,1134.0,1256.0,1134.0,1259.0,1134.0,1256.0,1134.0,1256.0,1134.0,1259.0,1134.0,1212.0,1134.0,1212.0,1134.0,1256.0,1134.0,1212.0,1134.0')] ).
cnf(1422,plain,
equal(multiply(inverse(multiply(multiply(multiply(inverse(u),multiply(v,inverse(v))),multiply(w,multiply(v,inverse(x)))),multiply(x,inverse(multiply(w,v))))),multiply(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[1259,1097,1267,1256,1212,1409,1270]),
[iquote('0:Rew:1259.0,1097.0,1267.0,1097.0,1259.0,1097.0,1256.0,1097.0,1212.0,1097.0,1267.0,1097.0,1409.0,1097.0,1267.0,1097.0,1270.0,1097.0,1267.0,1097.0')] ).
cnf(1431,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,multiply(multiply(v,w),inverse(x)))),multiply(u,multiply(w,inverse(w))))),multiply(w,inverse(w))),multiply(v,multiply(w,inverse(x)))),
inference(rew,[status(thm),theory(equality)],[1267,1092,1259,1256,1212,1409,1270]),
[iquote('0:Rew:1267.0,1092.0,1259.0,1092.0,1256.0,1092.0,1212.0,1092.0,1267.0,1092.0,1409.0,1092.0,1267.0,1092.0,1267.0,1092.0,1270.0,1092.0,1259.0,1092.0,1267.0,1092.0')] ).
cnf(1432,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1256,1130,1212,1259,1294,1270,1267]),
[iquote('0:Rew:1256.0,1130.0,1256.0,1130.0,1212.0,1130.0,1256.0,1130.0,1212.0,1130.0,1212.0,1130.0,1256.0,1130.0,1212.0,1130.0,1259.0,1130.0,1294.0,1130.0,1270.0,1130.0,1267.0,1130.0,1259.0,1130.0,1256.0,1130.0')] ).
cnf(1440,plain,
equal(multiply(inverse(multiply(multiply(u,inverse(v)),multiply(v,multiply(w,inverse(w))))),multiply(w,inverse(w))),multiply(inverse(multiply(x,w)),multiply(x,multiply(w,inverse(u))))),
inference(rew,[status(thm),theory(equality)],[1267,986,1409,1259,1355,1256,1212,1294,1270]),
[iquote('0:Rew:1267.0,986.0,1267.0,986.0,1409.0,986.0,1267.0,986.0,1267.0,986.0,1259.0,986.0,1355.0,986.0,1256.0,986.0,1212.0,986.0,1267.0,986.0,1259.0,986.0,1294.0,986.0,1270.0,986.0,1267.0,986.0')] ).
cnf(1454,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(v,inverse(w)))),multiply(v,inverse(multiply(w,v)))),
inference(rew,[status(thm),theory(equality)],[1302,1000,1259,1256,1212,1267,1409,1270,1355,1294]),
[iquote('0:Rew:1302.0,1000.0,1259.0,1000.0,1256.0,1000.0,1212.0,1000.0,1267.0,1000.0,1409.0,1000.0,1267.0,1000.0,1267.0,1000.0,1270.0,1000.0,1259.0,1000.0,1355.0,1000.0,1259.0,1000.0,1294.0,1000.0,1270.0,1000.0,1267.0,1000.0,1267.0,1000.0')] ).
cnf(1456,plain,
equal(multiply(inverse(multiply(multiply(u,inverse(v)),multiply(v,multiply(w,inverse(w))))),multiply(w,inverse(w))),multiply(w,inverse(multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[1454,1440]),
[iquote('0:Rew:1454.0,1440.0')] ).
cnf(1479,plain,
equal(multiply(u,inverse(multiply(multiply(v,inverse(multiply(inverse(w),u))),u))),multiply(inverse(multiply(x,w)),multiply(x,multiply(u,inverse(v))))),
inference(rew,[status(thm),theory(equality)],[1302,1100,1267,1409,1270,1259,1256,1268,1212]),
[iquote('0:Rew:1302.0,1100.0,1267.0,1100.0,1267.0,1100.0,1267.0,1100.0,1409.0,1100.0,1267.0,1100.0,1267.0,1100.0,1270.0,1100.0,1259.0,1100.0,1256.0,1100.0,1268.0,1100.0,1267.0,1100.0,1256.0,1100.0,1212.0,1100.0,1256.0,1100.0,1212.0,1100.0,1212.0,1100.0,1267.0,1100.0')] ).
cnf(1536,plain,
equal(multiply(u,multiply(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[1259,1256]),
[iquote('0:SpR:1259.0,1256.0')] ).
cnf(1540,plain,
equal(multiply(inverse(multiply(multiply(inverse(u),multiply(v,multiply(w,inverse(x)))),multiply(x,inverse(multiply(v,w))))),multiply(w,inverse(w))),u),
inference(rew,[status(thm),theory(equality)],[1536,1422]),
[iquote('0:Rew:1536.0,1422.0')] ).
cnf(1544,plain,
equal(inverse(multiply(multiply(u,inverse(v)),multiply(v,multiply(w,inverse(w))))),multiply(w,inverse(multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[1536,1456]),
[iquote('0:Rew:1536.0,1456.0')] ).
cnf(1546,plain,
equal(inverse(multiply(inverse(multiply(u,multiply(multiply(v,w),inverse(x)))),multiply(u,multiply(w,inverse(w))))),multiply(v,multiply(w,inverse(x)))),
inference(rew,[status(thm),theory(equality)],[1536,1431]),
[iquote('0:Rew:1536.0,1431.0')] ).
cnf(1556,plain,
equal(multiply(multiply(u,inverse(multiply(v,w))),v),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[1536,1292]),
[iquote('0:Rew:1536.0,1292.0')] ).
cnf(1557,plain,
equal(inverse(multiply(u,multiply(v,inverse(w)))),multiply(w,inverse(multiply(u,v)))),
inference(rew,[status(thm),theory(equality)],[1536,1302]),
[iquote('0:Rew:1536.0,1302.0')] ).
cnf(1567,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1268,1544,1536]),
[iquote('0:Rew:1268.0,1544.0,1536.0,1544.0')] ).
cnf(1568,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,inverse(x)))),inverse(multiply(x,inverse(multiply(inverse(v),w))))),
inference(rew,[status(thm),theory(equality)],[1567,1479]),
[iquote('0:Rew:1567.0,1479.0')] ).
cnf(1573,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,inverse(x)))),multiply(multiply(inverse(v),w),inverse(x))),
inference(rew,[status(thm),theory(equality)],[1267,1568]),
[iquote('0:Rew:1267.0,1568.0')] ).
cnf(1577,plain,
equal(multiply(multiply(u,v),inverse(multiply(multiply(inverse(w),multiply(u,multiply(v,inverse(x)))),x))),w),
inference(rew,[status(thm),theory(equality)],[1536,1540,1557]),
[iquote('0:Rew:1536.0,1540.0,1557.0,1540.0')] ).
cnf(1578,plain,
equal(multiply(multiply(u,v),inverse(w)),multiply(u,multiply(v,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[1267,1546,1556,1557,1536]),
[iquote('0:Rew:1267.0,1546.0,1556.0,1546.0,1557.0,1546.0,1536.0,1546.0')] ).
cnf(1579,plain,
equal(multiply(u,multiply(v,inverse(multiply(multiply(inverse(w),multiply(u,multiply(v,inverse(x)))),x)))),w),
inference(rew,[status(thm),theory(equality)],[1578,1577]),
[iquote('0:Rew:1578.0,1577.0')] ).
cnf(1583,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,inverse(x)))),multiply(inverse(v),multiply(w,inverse(x)))),
inference(rew,[status(thm),theory(equality)],[1578,1573]),
[iquote('0:Rew:1578.0,1573.0')] ).
cnf(1630,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[1432,1268]),
[iquote('0:SpR:1432.0,1268.0')] ).
cnf(1634,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[1355,1432]),
[iquote('0:SpR:1355.0,1432.0')] ).
cnf(1790,plain,
equal(multiply(inverse(u),multiply(inverse(v),inverse(w))),multiply(inverse(multiply(v,u)),inverse(w))),
inference(spr,[status(thm),theory(equality)],[1406,1583]),
[iquote('0:SpR:1406.0,1583.0')] ).
cnf(1813,plain,
equal(inverse(multiply(multiply(u,v),w)),inverse(multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[1634,1790]),
[iquote('0:Rew:1634.0,1790.0,1634.0,1790.0,1634.0,1790.0')] ).
cnf(1816,plain,
equal(multiply(u,multiply(v,inverse(multiply(inverse(w),multiply(multiply(u,multiply(v,inverse(x))),x))))),w),
inference(rew,[status(thm),theory(equality)],[1813,1579]),
[iquote('0:Rew:1813.0,1579.0')] ).
cnf(1823,plain,
equal(multiply(u,multiply(v,multiply(inverse(multiply(u,multiply(multiply(v,inverse(w)),w))),x))),x),
inference(rew,[status(thm),theory(equality)],[1813,1816,1630]),
[iquote('0:Rew:1813.0,1816.0,1630.0,1816.0')] ).
cnf(1824,plain,
equal(multiply(u,multiply(v,multiply(inverse(multiply(u,v)),w))),w),
inference(rew,[status(thm),theory(equality)],[1268,1823]),
[iquote('0:Rew:1268.0,1823.0')] ).
cnf(2120,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1355,1824]),
[iquote('0:SpR:1355.0,1824.0')] ).
cnf(2151,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)],[2120,1240]),
[iquote('0:Rew:2120.0,1240.1')] ).
cnf(2233,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[2151]),
[iquote('0:Obv:2151.1')] ).
cnf(2234,plain,
$false,
inference(unc,[status(thm)],[2233,730]),
[iquote('0:UnC:2233.0,730.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP056-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 21:00:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.31/1.50
% 1.31/1.50 SPASS V 3.9
% 1.31/1.50 SPASS beiseite: Proof found.
% 1.31/1.50 % SZS status Theorem
% 1.31/1.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.31/1.50 SPASS derived 1571 clauses, backtracked 0 clauses, performed 0 splits and kept 570 clauses.
% 1.31/1.50 SPASS allocated 72145 KBytes.
% 1.31/1.50 SPASS spent 0:00:01.15 on the problem.
% 1.31/1.50 0:00:00.03 for the input.
% 1.31/1.50 0:00:00.00 for the FLOTTER CNF translation.
% 1.31/1.50 0:00:00.03 for inferences.
% 1.31/1.50 0:00:00.00 for the backtracking.
% 1.31/1.50 0:00:01.06 for the reduction.
% 1.31/1.50
% 1.31/1.50
% 1.31/1.50 Here is a proof with depth 9, length 137 :
% 1.31/1.50 % SZS output start Refutation
% See solution above
% 1.36/1.54 Formulae used in the proof : single_axiom prove_these_axioms
% 1.36/1.54
%------------------------------------------------------------------------------