TSTP Solution File: GRP049-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP049-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:45:00 EDT 2022
% Result : Unsatisfiable 256.71s 256.89s
% Output : Refutation 257.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of clauses : 99 ( 94 unt; 0 nHn; 99 RR)
% Number of literals : 107 ( 0 equ; 14 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 : 16 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),inverse(multiply(v,multiply(inverse(v),v)))))),w),
file('GRP049-1.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('GRP049-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(v),w)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),inverse(multiply(x,multiply(inverse(x),x))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),inverse(multiply(x,multiply(inverse(x),x)))))),inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),inverse(multiply(x,multiply(inverse(x),x))))))))))),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,inverse(multiply(inverse(v),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),v)),inverse(multiply(x,multiply(inverse(x),x)))))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(21,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(w),inverse(multiply(v,multiply(inverse(v),v))))))),w),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(28,plain,
equal(multiply(u,inverse(multiply(inverse(v),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),inverse(multiply(w,multiply(inverse(w),w))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),inverse(multiply(w,multiply(inverse(w),w))))))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(x),y)),v)),inverse(multiply(y,multiply(inverse(y),y)))))),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(30,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),x)),y)),inverse(multiply(x,multiply(inverse(x),x)))))),inverse(multiply(v,multiply(inverse(v),v)))))),inverse(multiply(inverse(y),inverse(multiply(w,multiply(inverse(w),w)))))),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(41,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,inverse(multiply(inverse(x),inverse(multiply(y,multiply(inverse(y),y)))))))),multiply(inverse(multiply(inverse(multiply(w,y)),v)),x)),
inference(spr,[status(thm),theory(equality)],[4,21]),
[iquote('0:SpR:4.0,21.0')] ).
cnf(56,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),inverse(multiply(v,multiply(inverse(v),v))))))),x)),multiply(inverse(w),y))),inverse(multiply(x,multiply(inverse(x),x))))),y),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(100,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(u),w))),inverse(multiply(v,multiply(inverse(v),v))))),w),
inference(rew,[status(thm),theory(equality)],[1,56]),
[iquote('0:Rew:1.0,56.0')] ).
cnf(127,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(inverse(x),v)),multiply(inverse(x),w))),
inference(spr,[status(thm),theory(equality)],[100,21]),
[iquote('0:SpR:100.0,21.0')] ).
cnf(136,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),inverse(multiply(v,multiply(inverse(v),v))))),w),
inference(spr,[status(thm),theory(equality)],[100]),
[iquote('0:SpR:100.0,100.0')] ).
cnf(185,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[127]),
[iquote('0:SpR:127.0,127.0')] ).
cnf(210,plain,
equal(multiply(inverse(multiply(u,multiply(v,inverse(multiply(inverse(w),inverse(multiply(x,multiply(inverse(x),x)))))))),multiply(u,y)),multiply(inverse(w),multiply(inverse(multiply(v,x)),y))),
inference(spr,[status(thm),theory(equality)],[21,127]),
[iquote('0:SpR:21.0,127.0')] ).
cnf(244,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,multiply(v,w))),x)),inverse(multiply(multiply(v,w),multiply(inverse(multiply(y,w)),multiply(y,w))))))),x),
inference(spr,[status(thm),theory(equality)],[185,1]),
[iquote('0:SpR:185.0,1.0')] ).
cnf(245,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,inverse(multiply(inverse(x),inverse(multiply(multiply(v,w),multiply(inverse(multiply(y,w)),multiply(y,w)))))))),x),
inference(spr,[status(thm),theory(equality)],[185,21]),
[iquote('0:SpR:185.0,21.0')] ).
cnf(249,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,x)),multiply(inverse(multiply(inverse(multiply(y,z)),multiply(y,w))),multiply(inverse(multiply(v,z)),x))),
inference(spr,[status(thm),theory(equality)],[185]),
[iquote('0:SpR:185.0,185.0')] ).
cnf(264,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,x))),multiply(inverse(multiply(inverse(multiply(w,y)),v)),multiply(inverse(multiply(z,y)),multiply(z,x)))),
inference(spr,[status(thm),theory(equality)],[185]),
[iquote('0:SpR:185.0,185.0')] ).
cnf(279,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,w)),x)),inverse(multiply(w,multiply(inverse(w),w))))))),multiply(u,y)),multiply(inverse(x),multiply(v,y))),
inference(spr,[status(thm),theory(equality)],[1,185]),
[iquote('0:SpR:1.0,185.0')] ).
cnf(313,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(v,multiply(inverse(v),v))))),multiply(u,w)),multiply(x,multiply(inverse(multiply(inverse(multiply(y,v)),multiply(y,x))),w))),
inference(spr,[status(thm),theory(equality)],[136,185]),
[iquote('0:SpR:136.0,185.0')] ).
cnf(320,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,x))),inverse(multiply(multiply(v,w),multiply(inverse(multiply(y,w)),multiply(y,w)))))),x),
inference(spr,[status(thm),theory(equality)],[185,136]),
[iquote('0:SpR:185.0,136.0')] ).
cnf(567,plain,
equal(multiply(inverse(multiply(u,multiply(v,inverse(multiply(inverse(w),inverse(multiply(x,multiply(inverse(x),x)))))))),multiply(u,multiply(v,y))),multiply(inverse(w),multiply(inverse(multiply(z,x)),multiply(z,y)))),
inference(spr,[status(thm),theory(equality)],[21,264]),
[iquote('0:SpR:21.0,264.0')] ).
cnf(577,plain,
equal(multiply(inverse(u),multiply(inverse(multiply(v,w)),multiply(v,x))),multiply(inverse(u),multiply(inverse(multiply(y,w)),multiply(y,x)))),
inference(rew,[status(thm),theory(equality)],[210,567]),
[iquote('0:Rew:210.0,567.0')] ).
cnf(751,plain,
equal(multiply(u,multiply(inverse(multiply(v,w)),multiply(v,x))),multiply(u,multiply(inverse(multiply(y,w)),multiply(y,x)))),
inference(spr,[status(thm),theory(equality)],[136,577]),
[iquote('0:SpR:136.0,577.0')] ).
cnf(1120,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,multiply(v,inverse(multiply(inverse(x),inverse(multiply(y,multiply(inverse(y),y)))))))),multiply(inverse(multiply(inverse(multiply(z,y)),multiply(z,w))),x)),
inference(spr,[status(thm),theory(equality)],[21,249]),
[iquote('0:SpR:21.0,249.0')] ).
cnf(1163,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),x),multiply(inverse(multiply(inverse(multiply(y,v)),multiply(y,w))),x)),
inference(rew,[status(thm),theory(equality)],[41,1120]),
[iquote('0:Rew:41.0,1120.0')] ).
cnf(2578,plain,
equal(multiply(inverse(multiply(u,v)),inverse(multiply(w,inverse(multiply(multiply(u,w),multiply(inverse(multiply(x,w)),multiply(x,w))))))),inverse(multiply(v,multiply(inverse(v),v)))),
inference(spr,[status(thm),theory(equality)],[136,244]),
[iquote('0:SpR:136.0,244.0')] ).
cnf(3986,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,multiply(inverse(v),v))))),w)),multiply(x,multiply(inverse(multiply(inverse(multiply(y,v)),multiply(y,x))),z)))),inverse(multiply(w,multiply(inverse(w),w))))),multiply(u,z)),
inference(spr,[status(thm),theory(equality)],[313,136]),
[iquote('0:SpR:313.0,136.0')] ).
cnf(4165,plain,
equal(multiply(u,multiply(inverse(multiply(inverse(multiply(v,w)),multiply(v,u))),x)),multiply(y,multiply(inverse(multiply(inverse(multiply(z,w)),multiply(z,y))),x))),
inference(spr,[status(thm),theory(equality)],[136,313]),
[iquote('0:SpR:136.0,313.0')] ).
cnf(5022,plain,
equal(multiply(u,multiply(inverse(multiply(inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(multiply(w,x)),y)),inverse(multiply(x,multiply(inverse(x),x))))))),multiply(v,u))),z)),multiply(x1,multiply(inverse(multiply(inverse(y),multiply(w,x1))),z))),
inference(spr,[status(thm),theory(equality)],[1,4165]),
[iquote('0:SpR:1.0,4165.0')] ).
cnf(5078,plain,
equal(multiply(u,multiply(inverse(multiply(inverse(v),multiply(w,u))),x)),multiply(y,multiply(inverse(multiply(inverse(v),multiply(w,y))),x))),
inference(rew,[status(thm),theory(equality)],[279,5022]),
[iquote('0:Rew:279.0,5022.0')] ).
cnf(5234,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(w,multiply(inverse(multiply(inverse(x),multiply(y,w))),z)))),inverse(multiply(v,multiply(inverse(v),v))))),multiply(inverse(multiply(inverse(x),multiply(y,u))),z)),
inference(spr,[status(thm),theory(equality)],[5078,136]),
[iquote('0:SpR:5078.0,136.0')] ).
cnf(5404,plain,
equal(multiply(u,multiply(inverse(multiply(v,multiply(w,u))),x)),multiply(y,multiply(inverse(multiply(v,multiply(w,y))),x))),
inference(spr,[status(thm),theory(equality)],[320,5078]),
[iquote('0:SpR:320.0,5078.0')] ).
cnf(5454,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(w,inverse(multiply(v,multiply(inverse(v),v)))))))),x),multiply(w,x)),
inference(rew,[status(thm),theory(equality)],[5234,3986]),
[iquote('0:Rew:5234.0,3986.0')] ).
cnf(5946,plain,
equal(multiply(u,inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(x,y))),inverse(multiply(w,multiply(inverse(w),w))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(x,y))),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(x,y))),inverse(multiply(w,multiply(inverse(w),w))))))))))),multiply(x,inverse(multiply(v,inverse(multiply(y,multiply(inverse(y),y))))))),
inference(spr,[status(thm),theory(equality)],[5454,3]),
[iquote('0:SpR:5454.0,3.0')] ).
cnf(8183,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(v,multiply(inverse(v),v)))),w),
inference(spr,[status(thm),theory(equality)],[2578,245]),
[iquote('0:SpR:2578.0,245.0')] ).
cnf(9308,plain,
equal(multiply(inverse(u),u),multiply(v,multiply(inverse(multiply(inverse(multiply(w,x)),multiply(w,v))),inverse(multiply(x,multiply(inverse(x),x)))))),
inference(spr,[status(thm),theory(equality)],[8183,5404]),
[iquote('0:SpR:8183.0,5404.0')] ).
cnf(9755,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),w)),x)),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(y,multiply(inverse(y),y)))))),inverse(multiply(inverse(x),inverse(multiply(multiply(inverse(multiply(inverse(multiply(z,x1)),multiply(z,inverse(multiply(u,y))))),inverse(multiply(x1,multiply(inverse(x1),x1)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(z,x1)),multiply(z,inverse(multiply(u,y))))),inverse(multiply(x1,multiply(inverse(x1),x1))))),multiply(inverse(multiply(inverse(multiply(z,x1)),multiply(z,inverse(multiply(u,y))))),inverse(multiply(x1,multiply(inverse(x1),x1)))))))))),
inference(spr,[status(thm),theory(equality)],[9308,30]),
[iquote('0:SpR:9308.0,30.0')] ).
cnf(9763,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(v,w)),multiply(v,inverse(multiply(inverse(multiply(u,x)),y))))),inverse(multiply(w,multiply(inverse(w),w))))),inverse(multiply(x,multiply(inverse(x),x)))))),inverse(multiply(inverse(multiply(inverse(z),z)),inverse(multiply(y,multiply(inverse(y),y)))))),
inference(spr,[status(thm),theory(equality)],[9308,4]),
[iquote('0:SpR:9308.0,4.0')] ).
cnf(9776,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(multiply(x,multiply(y,w))),multiply(inverse(multiply(inverse(multiply(z,x1)),multiply(z,inverse(multiply(x,multiply(y,u)))))),inverse(multiply(x1,multiply(inverse(x1),x1))))))),
inference(spr,[status(thm),theory(equality)],[9308,5404]),
[iquote('0:SpR:9308.0,5404.0')] ).
cnf(9859,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[9308]),
[iquote('0:SpR:9308.0,9308.0')] ).
cnf(10024,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(multiply(x,multiply(y,w))),multiply(x,multiply(y,u))))),
inference(rew,[status(thm),theory(equality)],[8183,9776]),
[iquote('0:Rew:8183.0,9776.0')] ).
cnf(10048,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(v,multiply(inverse(v),v))))),v),
inference(rew,[status(thm),theory(equality)],[1,9763,8183]),
[iquote('0:Rew:1.0,9763.0,8183.0,9763.0')] ).
cnf(10091,plain,
equal(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),w)),x)),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(y,multiply(inverse(y),y)))))),inverse(multiply(inverse(x),inverse(multiply(multiply(u,y),multiply(inverse(multiply(u,y)),multiply(u,y))))))),
inference(rew,[status(thm),theory(equality)],[8183,9755]),
[iquote('0:Rew:8183.0,9755.0')] ).
cnf(10120,plain,
equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[9859,185]),
[iquote('0:SpR:9859.0,185.0')] ).
cnf(10138,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),multiply(inverse(multiply(inverse(multiply(w,x)),multiply(w,x))),v)),
inference(spr,[status(thm),theory(equality)],[9859,1163]),
[iquote('0:SpR:9859.0,1163.0')] ).
cnf(10160,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),multiply(inverse(inverse(v)),inverse(v))))),v),
inference(spr,[status(thm),theory(equality)],[9859,8183]),
[iquote('0:SpR:9859.0,8183.0')] ).
cnf(10162,plain,
equal(multiply(u,multiply(inverse(multiply(v,w)),multiply(v,w))),multiply(u,multiply(inverse(x),x))),
inference(spr,[status(thm),theory(equality)],[9859,751]),
[iquote('0:SpR:9859.0,751.0')] ).
cnf(10239,plain,
equal(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w)),multiply(inverse(multiply(x,v)),multiply(x,u))),
inference(spr,[status(thm),theory(equality)],[9859,185]),
[iquote('0:SpR:9859.0,185.0')] ).
cnf(10316,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),inverse(multiply(v,multiply(inverse(x),x))))),w),
inference(spr,[status(thm),theory(equality)],[9859,136]),
[iquote('0:SpR:9859.0,136.0')] ).
cnf(10325,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),w)),inverse(multiply(u,multiply(inverse(u),u)))))),w),
inference(spr,[status(thm),theory(equality)],[9859,1]),
[iquote('0:SpR:9859.0,1.0')] ).
cnf(10428,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(w),w)))),inverse(multiply(v,multiply(inverse(v),v)))),
inference(spr,[status(thm),theory(equality)],[9859,21]),
[iquote('0:SpR:9859.0,21.0')] ).
cnf(10449,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(v),inverse(multiply(u,multiply(inverse(u),u)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(w),w)),x)),v)),inverse(multiply(x,multiply(inverse(x),x)))))),
inference(spr,[status(thm),theory(equality)],[9859,4]),
[iquote('0:SpR:9859.0,4.0')] ).
cnf(10548,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)],[9859,2]),
[iquote('0:SpL:9859.0,2.2')] ).
cnf(10617,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(v,multiply(inverse(w),w))))),v),
inference(spr,[status(thm),theory(equality)],[9859,10048]),
[iquote('0:SpR:9859.0,10048.0')] ).
cnf(11075,plain,
equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),v)))),inverse(multiply(inverse(w),w))),
inference(spr,[status(thm),theory(equality)],[9859,10617]),
[iquote('0:SpR:9859.0,10617.0')] ).
cnf(11175,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(u,multiply(inverse(w),w))),
inference(spr,[status(thm),theory(equality)],[10162]),
[iquote('0:SpR:10162.0,10162.0')] ).
cnf(11403,plain,
equal(multiply(inverse(u),u),multiply(inverse(multiply(inverse(v),v)),multiply(inverse(w),w))),
inference(spr,[status(thm),theory(equality)],[11175,9859]),
[iquote('0:SpR:11175.0,9859.0')] ).
cnf(11533,plain,
equal(multiply(inverse(multiply(u,multiply(inverse(v),v))),multiply(u,multiply(w,x))),multiply(inverse(multiply(inverse(multiply(w,y)),multiply(inverse(z),z))),multiply(inverse(multiply(x1,y)),multiply(x1,x)))),
inference(spr,[status(thm),theory(equality)],[11175,264]),
[iquote('0:SpR:11175.0,264.0')] ).
cnf(12622,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),multiply(inverse(w),w)))),v),
inference(spr,[status(thm),theory(equality)],[9859,10160]),
[iquote('0:SpR:9859.0,10160.0')] ).
cnf(12632,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),v))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[11403,10160]),
[iquote('0:SpR:11403.0,10160.0')] ).
cnf(12767,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(multiply(v,w)),multiply(v,x)))),multiply(inverse(x),w)),
inference(spr,[status(thm),theory(equality)],[185,12622]),
[iquote('0:SpR:185.0,12622.0')] ).
cnf(14298,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),multiply(inverse(multiply(inverse(w),w)),v)),
inference(spr,[status(thm),theory(equality)],[10138]),
[iquote('0:SpR:10138.0,10138.0')] ).
cnf(15649,plain,
equal(multiply(inverse(multiply(u,v)),multiply(inverse(w),w)),multiply(inverse(multiply(x,v)),multiply(x,multiply(inverse(multiply(inverse(y),y)),inverse(multiply(u,multiply(inverse(z),z))))))),
inference(spr,[status(thm),theory(equality)],[10617,10239]),
[iquote('0:SpR:10617.0,10239.0')] ).
cnf(15758,plain,
equal(multiply(inverse(multiply(inverse(u),multiply(inverse(v),v))),multiply(inverse(w),w)),multiply(inverse(multiply(x,multiply(inverse(y),y))),multiply(x,u))),
inference(spr,[status(thm),theory(equality)],[11175,10239]),
[iquote('0:SpR:11175.0,10239.0')] ).
cnf(17408,plain,
equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))))),v),
inference(spr,[status(thm),theory(equality)],[10428,12622]),
[iquote('0:SpR:10428.0,12622.0')] ).
cnf(18119,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),v)),multiply(inverse(w),w))),inverse(multiply(v,multiply(inverse(x),x))))),inverse(multiply(inverse(y),y))),
inference(spr,[status(thm),theory(equality)],[12632,10316]),
[iquote('0:SpR:12632.0,10316.0')] ).
cnf(18226,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w))),inverse(multiply(v,multiply(inverse(x),x))))),u),
inference(spr,[status(thm),theory(equality)],[11175,10316]),
[iquote('0:SpR:11175.0,10316.0')] ).
cnf(18248,plain,
equal(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),
inference(rew,[status(thm),theory(equality)],[18226,18119]),
[iquote('0:Rew:18226.0,18119.0')] ).
cnf(18460,plain,
equal(multiply(multiply(inverse(u),u),v),multiply(inverse(multiply(inverse(w),w)),v)),
inference(spr,[status(thm),theory(equality)],[18248,14298]),
[iquote('0:SpR:18248.0,14298.0')] ).
cnf(21381,plain,
equal(multiply(u,inverse(multiply(inverse(v),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(inverse(multiply(inverse(x),x)),inverse(multiply(inverse(y),y))))),inverse(multiply(w,multiply(inverse(w),w))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(inverse(multiply(inverse(x),x)),inverse(multiply(inverse(y),y))))),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(inverse(multiply(inverse(x),x)),inverse(multiply(inverse(y),y))))),inverse(multiply(w,multiply(inverse(w),w))))))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(z),z)),x1)),v)),inverse(multiply(x1,multiply(inverse(x1),x1)))))),
inference(spr,[status(thm),theory(equality)],[11075,28]),
[iquote('0:SpR:11075.0,28.0')] ).
cnf(21758,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),v)),w)),inverse(multiply(v,multiply(inverse(v),v))))),w),
inference(rew,[status(thm),theory(equality)],[17408,21381,5946]),
[iquote('0:Rew:17408.0,21381.0,5946.0,21381.0')] ).
cnf(21765,plain,
equal(multiply(inverse(u),inverse(multiply(inverse(v),inverse(multiply(u,multiply(inverse(u),u)))))),v),
inference(rew,[status(thm),theory(equality)],[21758,10449]),
[iquote('0:Rew:21758.0,10449.0')] ).
cnf(21771,plain,
equal(inverse(multiply(inverse(u),inverse(multiply(multiply(v,w),multiply(inverse(multiply(v,w)),multiply(v,w)))))),multiply(v,inverse(multiply(inverse(u),inverse(multiply(w,multiply(inverse(w),w))))))),
inference(rew,[status(thm),theory(equality)],[21758,10091]),
[iquote('0:Rew:21758.0,10091.0')] ).
cnf(21787,plain,
equal(multiply(inverse(multiply(inverse(u),u)),v),v),
inference(rew,[status(thm),theory(equality)],[21765,10325]),
[iquote('0:Rew:21765.0,10325.0')] ).
cnf(21819,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
inference(rew,[status(thm),theory(equality)],[21787,10120]),
[iquote('0:Rew:21787.0,10120.0')] ).
cnf(21826,plain,
equal(inverse(multiply(inverse(u),multiply(inverse(v),v))),u),
inference(rew,[status(thm),theory(equality)],[21787,12622]),
[iquote('0:Rew:21787.0,12622.0')] ).
cnf(21827,plain,
equal(inverse(inverse(multiply(u,multiply(inverse(v),v)))),u),
inference(rew,[status(thm),theory(equality)],[21787,10617]),
[iquote('0:Rew:21787.0,10617.0')] ).
cnf(22578,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[21787,18460]),
[iquote('0:Rew:21787.0,18460.0')] ).
cnf(22925,plain,
equal(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[21787,12767]),
[iquote('0:Rew:21787.0,12767.0')] ).
cnf(22958,plain,
equal(multiply(inverse(multiply(u,v)),multiply(inverse(w),w)),multiply(inverse(multiply(x,v)),multiply(x,inverse(multiply(u,multiply(inverse(y),y)))))),
inference(rew,[status(thm),theory(equality)],[21787,15649]),
[iquote('0:Rew:21787.0,15649.0')] ).
cnf(23182,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)],[22578,10548]),
[iquote('0:Rew:22578.0,10548.2')] ).
cnf(23413,plain,
equal(multiply(inverse(multiply(u,multiply(inverse(v),v))),multiply(u,multiply(w,x))),multiply(multiply(w,y),multiply(inverse(multiply(z,y)),multiply(z,x)))),
inference(rew,[status(thm),theory(equality)],[21826,11533]),
[iquote('0:Rew:21826.0,11533.0')] ).
cnf(24066,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(inverse(multiply(w,multiply(inverse(x),x))),multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[21826,15758]),
[iquote('0:Rew:21826.0,15758.0')] ).
cnf(25201,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(multiply(x,w)),multiply(x,u)))),
inference(rew,[status(thm),theory(equality)],[21819,10024]),
[iquote('0:Rew:21819.0,10024.0')] ).
cnf(26903,plain,
equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[21819,22925]),
[iquote('0:Rew:21819.0,22925.0')] ).
cnf(27441,plain,
equal(multiply(inverse(u),multiply(inverse(inverse(multiply(u,multiply(inverse(u),u)))),v)),v),
inference(rew,[status(thm),theory(equality)],[26903,21765]),
[iquote('0:Rew:26903.0,21765.0')] ).
cnf(27536,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[21827,27441]),
[iquote('0:Rew:21827.0,27441.0')] ).
cnf(27659,plain,
equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(w),u))),
inference(rew,[status(thm),theory(equality)],[21819,25201]),
[iquote('0:Rew:21819.0,25201.0')] ).
cnf(27711,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(rew,[status(thm),theory(equality)],[22578,24066,26903,21819]),
[iquote('0:Rew:22578.0,24066.0,26903.0,24066.0,21819.0,24066.0')] ).
cnf(27722,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[27711,21827]),
[iquote('0:Rew:27711.0,21827.0')] ).
cnf(27724,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[27711,27659]),
[iquote('0:Rew:27711.0,27659.0')] ).
cnf(28218,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[27711,22958,21819]),
[iquote('0:Rew:27711.0,22958.0,21819.0,22958.0,27711.0,22958.0')] ).
cnf(28433,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)],[23182]),
[iquote('0:Obv:23182.2')] ).
cnf(28436,plain,
equal(multiply(multiply(u,v),multiply(inverse(v),w)),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[27536,23413,27711,21819]),
[iquote('0:Rew:27536.0,23413.0,27711.0,23413.0,21819.0,23413.0')] ).
cnf(28840,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[27722,21771,28218,28436,21819,27724]),
[iquote('0:Rew:27722.0,21771.0,28218.0,21771.0,28436.0,21771.0,21819.0,21771.0,27722.0,21771.0,28218.0,21771.0,27724.0,21771.0')] ).
cnf(28846,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)],[28840,28433]),
[iquote('0:Rew:28840.0,28433.1')] ).
cnf(28867,plain,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
inference(obv,[status(thm),theory(equality)],[28846]),
[iquote('0:Obv:28846.1')] ).
cnf(28868,plain,
$false,
inference(unc,[status(thm)],[28867,9859]),
[iquote('0:UnC:28867.0,9859.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP049-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 12:57:16 EDT 2022
% 0.14/0.35 % CPUTime :
% 256.71/256.89
% 256.71/256.89 SPASS V 3.9
% 256.71/256.89 SPASS beiseite: Proof found.
% 256.71/256.89 % SZS status Theorem
% 256.71/256.89 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 256.71/256.89 SPASS derived 25362 clauses, backtracked 0 clauses, performed 0 splits and kept 6866 clauses.
% 256.71/256.89 SPASS allocated 209783 KBytes.
% 256.71/256.89 SPASS spent 0:4:16.46 on the problem.
% 256.71/256.89 0:00:00.04 for the input.
% 256.71/256.89 0:00:00.00 for the FLOTTER CNF translation.
% 256.71/256.89 0:00:00.45 for inferences.
% 256.71/256.89 0:00:00.00 for the backtracking.
% 256.71/256.89 0:4:15.94 for the reduction.
% 256.71/256.89
% 256.71/256.89
% 256.71/256.89 Here is a proof with depth 16, length 99 :
% 256.71/256.89 % SZS output start Refutation
% See solution above
% 257.75/257.95 Formulae used in the proof : single_axiom prove_these_axioms
% 257.75/257.95
%------------------------------------------------------------------------------