TSTP Solution File: GRP106-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP106-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 11:45:20 EDT 2022
% Result : Unsatisfiable 0.47s 0.69s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 3
% Syntax : Number of clauses : 159 ( 153 unt; 0 nHn; 159 RR)
% Number of literals : 171 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(double_divide(double_divide(u,v),inverse(double_divide(u,inverse(double_divide(w,v)))))),w),
file('GRP106-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP106-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ 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('GRP106-1.p',unknown),
[] ).
cnf(4,plain,
equal(multiply(multiply(multiply(u,v),w),double_divide(w,u)),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,v),double_divide(v,multiply(multiply(w,u),x))),double_divide(x,w)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(7,plain,
equal(multiply(u,double_divide(double_divide(v,w),multiply(w,u))),v),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(multiply(double_divide(double_divide(u,v),multiply(v,w)),double_divide(double_divide(x,w),u)),x),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(10,plain,
equal(multiply(multiply(u,v),double_divide(v,w)),double_divide(double_divide(u,x),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(18,plain,
equal(double_divide(multiply(u,double_divide(v,multiply(w,u))),w),v),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(21,plain,
equal(multiply(multiply(u,v),double_divide(v,double_divide(w,x))),double_divide(double_divide(u,multiply(multiply(x,y),w)),y)),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(24,plain,
equal(multiply(multiply(u,v),double_divide(v,w)),double_divide(double_divide(double_divide(w,x),multiply(x,multiply(y,u))),y)),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(32,plain,
equal(multiply(u,multiply(v,double_divide(w,multiply(u,v)))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[18,2]),
[iquote('0:SpR:18.0,2.0')] ).
cnf(37,plain,
equal(multiply(u,double_divide(v,multiply(multiply(w,x),u))),double_divide(multiply(x,v),w)),
inference(spr,[status(thm),theory(equality)],[18]),
[iquote('0:SpR:18.0,18.0')] ).
cnf(42,plain,
equal(double_divide(double_divide(multiply(u,v),w),multiply(w,u)),v),
inference(spr,[status(thm),theory(equality)],[6,18]),
[iquote('0:SpR:6.0,18.0')] ).
cnf(44,plain,
equal(multiply(multiply(u,v),double_divide(multiply(v,w),u)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[42,2]),
[iquote('0:SpR:42.0,2.0')] ).
cnf(55,plain,
equal(double_divide(double_divide(u,v),multiply(v,multiply(multiply(w,u),x))),double_divide(x,w)),
inference(spr,[status(thm),theory(equality)],[4,42]),
[iquote('0:SpR:4.0,42.0')] ).
cnf(59,plain,
equal(multiply(multiply(multiply(u,double_divide(v,multiply(w,u))),x),double_divide(x,multiply(inverse(v),y))),double_divide(y,w)),
inference(spr,[status(thm),theory(equality)],[32,6]),
[iquote('0:SpR:32.0,6.0')] ).
cnf(62,plain,
equal(multiply(multiply(inverse(u),v),double_divide(v,w)),multiply(x,double_divide(u,multiply(w,x)))),
inference(spr,[status(thm),theory(equality)],[32,4]),
[iquote('0:SpR:32.0,4.0')] ).
cnf(67,plain,
equal(multiply(inverse(u),double_divide(multiply(v,double_divide(u,multiply(multiply(w,x),v))),w)),x),
inference(spr,[status(thm),theory(equality)],[32,4]),
[iquote('0:SpR:32.0,4.0')] ).
cnf(68,plain,
equal(multiply(multiply(u,v),double_divide(v,inverse(w))),double_divide(multiply(x,double_divide(w,multiply(multiply(y,u),x))),y)),
inference(spr,[status(thm),theory(equality)],[32,6]),
[iquote('0:SpR:32.0,6.0')] ).
cnf(76,plain,
equal(multiply(inverse(u),double_divide(double_divide(multiply(v,u),w),w)),v),
inference(rew,[status(thm),theory(equality)],[37,67]),
[iquote('0:Rew:37.0,67.0')] ).
cnf(78,plain,
equal(multiply(multiply(u,v),double_divide(v,inverse(w))),double_divide(double_divide(multiply(u,w),x),x)),
inference(rew,[status(thm),theory(equality)],[37,68]),
[iquote('0:Rew:37.0,68.0')] ).
cnf(94,plain,
equal(multiply(multiply(u,multiply(multiply(v,w),x)),double_divide(w,u)),inverse(double_divide(x,v))),
inference(spr,[status(thm),theory(equality)],[4,44]),
[iquote('0:SpR:4.0,44.0')] ).
cnf(98,plain,
equal(multiply(inverse(u),double_divide(multiply(multiply(v,double_divide(u,multiply(w,v))),x),w)),inverse(x)),
inference(spr,[status(thm),theory(equality)],[32,44]),
[iquote('0:SpR:32.0,44.0')] ).
cnf(102,plain,
equal(multiply(multiply(u,multiply(multiply(v,w),x)),double_divide(w,u)),multiply(v,x)),
inference(rew,[status(thm),theory(equality)],[2,94]),
[iquote('0:Rew:2.0,94.0')] ).
cnf(110,plain,
equal(multiply(multiply(u,v),double_divide(v,double_divide(double_divide(w,x),multiply(x,y)))),double_divide(double_divide(u,y),w)),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(135,plain,
equal(double_divide(multiply(double_divide(double_divide(multiply(u,v),w),w),double_divide(x,u)),inverse(v)),x),
inference(spr,[status(thm),theory(equality)],[76,18]),
[iquote('0:SpR:76.0,18.0')] ).
cnf(142,plain,
equal(double_divide(multiply(u,v),multiply(w,inverse(v))),double_divide(u,w)),
inference(spr,[status(thm),theory(equality)],[76,18]),
[iquote('0:SpR:76.0,18.0')] ).
cnf(144,plain,
equal(inverse(double_divide(multiply(u,v),multiply(w,inverse(v)))),multiply(w,u)),
inference(spr,[status(thm),theory(equality)],[76,32]),
[iquote('0:SpR:76.0,32.0')] ).
cnf(148,plain,
equal(multiply(inverse(multiply(u,double_divide(v,multiply(w,u)))),double_divide(double_divide(inverse(v),x),x)),w),
inference(spr,[status(thm),theory(equality)],[32,76]),
[iquote('0:SpR:32.0,76.0')] ).
cnf(149,plain,
equal(multiply(inverse(double_divide(u,v)),double_divide(double_divide(w,x),x)),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[4,76]),
[iquote('0:SpR:4.0,76.0')] ).
cnf(154,plain,
equal(multiply(multiply(u,v),double_divide(double_divide(multiply(w,double_divide(v,u)),x),x)),w),
inference(spr,[status(thm),theory(equality)],[2,76]),
[iquote('0:SpR:2.0,76.0')] ).
cnf(156,plain,
equal(multiply(multiply(u,inverse(v)),multiply(w,v)),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[2,144]),
[iquote('0:Rew:2.0,144.0')] ).
cnf(159,plain,
equal(multiply(multiply(u,v),double_divide(double_divide(w,x),x)),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[2,149]),
[iquote('0:Rew:2.0,149.0')] ).
cnf(161,plain,
equal(multiply(multiply(u,multiply(v,double_divide(w,u))),w),v),
inference(rew,[status(thm),theory(equality)],[159,154]),
[iquote('0:Rew:159.0,154.0')] ).
cnf(174,plain,
equal(multiply(inverse(u),double_divide(double_divide(v,w),w)),multiply(x,multiply(v,double_divide(u,x)))),
inference(spr,[status(thm),theory(equality)],[161,76]),
[iquote('0:SpR:161.0,76.0')] ).
cnf(176,plain,
equal(multiply(multiply(u,v),double_divide(v,multiply(w,x))),double_divide(x,multiply(y,multiply(w,double_divide(u,y))))),
inference(spr,[status(thm),theory(equality)],[161,6]),
[iquote('0:SpR:161.0,6.0')] ).
cnf(190,plain,
equal(multiply(multiply(u,multiply(v,w)),multiply(x,double_divide(w,multiply(u,x)))),v),
inference(spr,[status(thm),theory(equality)],[18,161]),
[iquote('0:SpR:18.0,161.0')] ).
cnf(210,plain,
equal(multiply(u,multiply(inverse(v),double_divide(w,u))),inverse(multiply(w,v))),
inference(spr,[status(thm),theory(equality)],[142,32]),
[iquote('0:SpR:142.0,32.0')] ).
cnf(217,plain,
equal(double_divide(u,multiply(v,inverse(double_divide(w,x)))),double_divide(multiply(multiply(x,u),w),v)),
inference(spr,[status(thm),theory(equality)],[4,142]),
[iquote('0:SpR:4.0,142.0')] ).
cnf(220,plain,
equal(double_divide(u,multiply(v,inverse(double_divide(double_divide(multiply(u,w),x),x)))),double_divide(inverse(w),v)),
inference(spr,[status(thm),theory(equality)],[76,142]),
[iquote('0:SpR:76.0,142.0')] ).
cnf(225,plain,
equal(double_divide(multiply(multiply(u,v),w),x),double_divide(v,multiply(x,multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[2,217]),
[iquote('0:Rew:2.0,217.0')] ).
cnf(226,plain,
equal(multiply(inverse(u),double_divide(double_divide(u,multiply(v,w)),multiply(v,multiply(w,x)))),inverse(x)),
inference(rew,[status(thm),theory(equality)],[225,98]),
[iquote('0:Rew:225.0,98.0')] ).
cnf(230,plain,
equal(double_divide(u,multiply(v,multiply(w,double_divide(multiply(u,x),w)))),double_divide(inverse(x),v)),
inference(rew,[status(thm),theory(equality)],[2,220]),
[iquote('0:Rew:2.0,220.0')] ).
cnf(254,plain,
equal(multiply(multiply(u,inverse(double_divide(v,w))),x),multiply(u,multiply(multiply(w,x),v))),
inference(spr,[status(thm),theory(equality)],[4,156]),
[iquote('0:SpR:4.0,156.0')] ).
cnf(258,plain,
equal(multiply(multiply(u,inverse(double_divide(double_divide(v,w),x))),v),multiply(u,double_divide(double_divide(x,y),multiply(y,w)))),
inference(spr,[status(thm),theory(equality)],[9,156]),
[iquote('0:SpR:9.0,156.0')] ).
cnf(267,plain,
equal(multiply(multiply(u,multiply(v,w)),x),multiply(u,multiply(multiply(v,x),w))),
inference(rew,[status(thm),theory(equality)],[2,254]),
[iquote('0:Rew:2.0,254.0')] ).
cnf(268,plain,
equal(multiply(u,multiply(multiply(v,w),double_divide(w,u))),v),
inference(rew,[status(thm),theory(equality)],[267,161]),
[iquote('0:Rew:267.0,161.0')] ).
cnf(273,plain,
equal(multiply(u,multiply(multiply(multiply(v,w),double_divide(w,u)),x)),multiply(v,x)),
inference(rew,[status(thm),theory(equality)],[267,102]),
[iquote('0:Rew:267.0,102.0')] ).
cnf(276,plain,
equal(multiply(u,multiply(multiply(v,multiply(w,double_divide(x,multiply(u,w)))),x)),v),
inference(rew,[status(thm),theory(equality)],[267,190]),
[iquote('0:Rew:267.0,190.0')] ).
cnf(285,plain,
equal(multiply(u,multiply(v,multiply(multiply(w,x),double_divide(x,multiply(u,w))))),v),
inference(rew,[status(thm),theory(equality)],[267,276]),
[iquote('0:Rew:267.0,276.0')] ).
cnf(298,plain,
equal(multiply(multiply(u,multiply(v,double_divide(w,x))),w),multiply(u,double_divide(double_divide(v,y),multiply(y,x)))),
inference(rew,[status(thm),theory(equality)],[2,258]),
[iquote('0:Rew:2.0,258.0')] ).
cnf(299,plain,
equal(multiply(u,multiply(multiply(v,w),double_divide(w,x))),multiply(u,double_divide(double_divide(v,y),multiply(y,x)))),
inference(rew,[status(thm),theory(equality)],[267,298]),
[iquote('0:Rew:267.0,298.0')] ).
cnf(328,plain,
equal(inverse(multiply(multiply(u,v),double_divide(v,w))),multiply(multiply(x,w),double_divide(u,x))),
inference(spr,[status(thm),theory(equality)],[10,2]),
[iquote('0:SpR:10.0,2.0')] ).
cnf(344,plain,
equal(multiply(multiply(u,double_divide(multiply(v,w),x)),w),double_divide(double_divide(u,y),multiply(y,multiply(x,v)))),
inference(spr,[status(thm),theory(equality)],[42,10]),
[iquote('0:SpR:42.0,10.0')] ).
cnf(349,plain,
equal(double_divide(double_divide(multiply(multiply(u,v),w),x),multiply(x,y)),multiply(v,double_divide(double_divide(w,u),y))),
inference(spr,[status(thm),theory(equality)],[4,10]),
[iquote('0:SpR:4.0,10.0')] ).
cnf(355,plain,
equal(multiply(multiply(u,v),double_divide(v,multiply(w,double_divide(x,multiply(y,w))))),double_divide(double_divide(u,y),inverse(x))),
inference(spr,[status(thm),theory(equality)],[32,10]),
[iquote('0:SpR:32.0,10.0')] ).
cnf(360,plain,
equal(multiply(multiply(u,v),double_divide(v,double_divide(double_divide(multiply(w,x),y),y))),double_divide(double_divide(u,inverse(x)),w)),
inference(spr,[status(thm),theory(equality)],[76,10]),
[iquote('0:SpR:76.0,10.0')] ).
cnf(361,plain,
equal(multiply(multiply(u,v),double_divide(v,double_divide(double_divide(w,x),y))),double_divide(double_divide(u,double_divide(double_divide(y,z),multiply(z,x))),w)),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(362,plain,
equal(multiply(multiply(multiply(u,double_divide(v,multiply(w,u))),x),double_divide(x,y)),double_divide(v,multiply(w,y))),
inference(spr,[status(thm),theory(equality)],[18,10]),
[iquote('0:SpR:18.0,10.0')] ).
cnf(376,plain,
equal(double_divide(double_divide(u,multiply(v,multiply(w,x))),multiply(v,y)),multiply(u,double_divide(double_divide(x,w),y))),
inference(rew,[status(thm),theory(equality)],[225,349]),
[iquote('0:Rew:225.0,349.0')] ).
cnf(377,plain,
equal(double_divide(u,multiply(v,multiply(inverse(u),w))),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[362,59]),
[iquote('0:Rew:362.0,59.0')] ).
cnf(395,plain,
equal(multiply(inverse(multiply(multiply(u,v),double_divide(v,w))),double_divide(double_divide(u,x),x)),w),
inference(spr,[status(thm),theory(equality)],[268,76]),
[iquote('0:SpR:268.0,76.0')] ).
cnf(398,plain,
equal(double_divide(multiply(multiply(multiply(u,v),double_divide(v,w)),double_divide(x,u)),w),x),
inference(spr,[status(thm),theory(equality)],[268,18]),
[iquote('0:SpR:268.0,18.0')] ).
cnf(403,plain,
equal(multiply(u,multiply(multiply(multiply(v,w),double_divide(w,u)),double_divide(x,v))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[268,32]),
[iquote('0:SpR:268.0,32.0')] ).
cnf(409,plain,
equal(multiply(multiply(u,v),double_divide(v,w)),double_divide(multiply(multiply(w,x),double_divide(x,multiply(y,u))),y)),
inference(spr,[status(thm),theory(equality)],[268,6]),
[iquote('0:SpR:268.0,6.0')] ).
cnf(424,plain,
equal(multiply(u,multiply(double_divide(double_divide(v,w),multiply(w,x)),double_divide(double_divide(y,x),u))),multiply(v,y)),
inference(spr,[status(thm),theory(equality)],[10,268]),
[iquote('0:SpR:10.0,268.0')] ).
cnf(433,plain,
equal(double_divide(double_divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[55,398,225]),
[iquote('0:Rew:55.0,398.0,225.0,398.0')] ).
cnf(435,plain,
equal(multiply(multiply(u,v),double_divide(v,multiply(w,x))),double_divide(double_divide(u,inverse(x)),w)),
inference(rew,[status(thm),theory(equality)],[433,360]),
[iquote('0:Rew:433.0,360.0')] ).
cnf(438,plain,
equal(multiply(inverse(multiply(u,double_divide(v,multiply(w,u)))),inverse(v)),w),
inference(rew,[status(thm),theory(equality)],[433,148]),
[iquote('0:Rew:433.0,148.0')] ).
cnf(439,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[433,159]),
[iquote('0:Rew:433.0,159.0')] ).
cnf(440,plain,
equal(multiply(multiply(u,v),double_divide(v,inverse(w))),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[433,78]),
[iquote('0:Rew:433.0,78.0')] ).
cnf(442,plain,
equal(multiply(u,multiply(v,double_divide(w,u))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[433,174]),
[iquote('0:Rew:433.0,174.0')] ).
cnf(445,plain,
equal(double_divide(multiply(multiply(u,v),double_divide(w,u)),inverse(v)),w),
inference(rew,[status(thm),theory(equality)],[433,135]),
[iquote('0:Rew:433.0,135.0')] ).
cnf(450,plain,
equal(multiply(multiply(u,v),double_divide(multiply(w,v),x)),double_divide(double_divide(u,y),multiply(y,multiply(x,w)))),
inference(rew,[status(thm),theory(equality)],[439,344]),
[iquote('0:Rew:439.0,344.0')] ).
cnf(459,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[442,210]),
[iquote('0:Rew:442.0,210.0')] ).
cnf(460,plain,
equal(multiply(multiply(u,v),double_divide(v,multiply(w,x))),double_divide(x,multiply(inverse(u),w))),
inference(rew,[status(thm),theory(equality)],[442,176]),
[iquote('0:Rew:442.0,176.0')] ).
cnf(469,plain,
equal(double_divide(u,multiply(inverse(u),multiply(v,double_divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[225,445]),
[iquote('0:Rew:225.0,445.0')] ).
cnf(472,plain,
equal(inverse(multiply(multiply(u,v),double_divide(v,multiply(w,u)))),w),
inference(rew,[status(thm),theory(equality)],[439,438,459]),
[iquote('0:Rew:439.0,438.0,459.0,438.0')] ).
cnf(500,plain,
equal(multiply(inverse(multiply(multiply(u,v),double_divide(v,w))),u),w),
inference(rew,[status(thm),theory(equality)],[433,395]),
[iquote('0:Rew:433.0,395.0')] ).
cnf(501,plain,
equal(multiply(u,double_divide(v,u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[273,403]),
[iquote('0:Rew:273.0,403.0')] ).
cnf(502,plain,
equal(double_divide(u,multiply(inverse(u),inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[501,469]),
[iquote('0:Rew:501.0,469.0')] ).
cnf(503,plain,
equal(double_divide(u,multiply(v,inverse(multiply(u,w)))),double_divide(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[501,230]),
[iquote('0:Rew:501.0,230.0')] ).
cnf(504,plain,
equal(double_divide(u,inverse(multiply(u,v))),v),
inference(rew,[status(thm),theory(equality)],[459,502]),
[iquote('0:Rew:459.0,502.0')] ).
cnf(513,plain,
equal(multiply(u,multiply(v,double_divide(double_divide(w,inverse(w)),u))),v),
inference(rew,[status(thm),theory(equality)],[435,285]),
[iquote('0:Rew:435.0,285.0')] ).
cnf(516,plain,
equal(inverse(double_divide(double_divide(u,inverse(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[435,472]),
[iquote('0:Rew:435.0,472.0')] ).
cnf(517,plain,
equal(double_divide(double_divide(u,inverse(double_divide(v,multiply(w,x)))),x),double_divide(double_divide(u,w),inverse(v))),
inference(rew,[status(thm),theory(equality)],[435,355]),
[iquote('0:Rew:435.0,355.0')] ).
cnf(524,plain,
equal(multiply(u,double_divide(v,inverse(v))),u),
inference(rew,[status(thm),theory(equality)],[2,516]),
[iquote('0:Rew:2.0,516.0')] ).
cnf(525,plain,
equal(multiply(inverse(double_divide(u,inverse(u))),v),v),
inference(rew,[status(thm),theory(equality)],[442,513]),
[iquote('0:Rew:442.0,513.0')] ).
cnf(526,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[2,525]),
[iquote('0:Rew:2.0,525.0')] ).
cnf(527,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ 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)],[526,3]),
[iquote('0:Rew:526.0,3.3')] ).
cnf(529,plain,
equal(double_divide(double_divide(u,inverse(v)),w),double_divide(v,multiply(inverse(u),w))),
inference(rew,[status(thm),theory(equality)],[435,460]),
[iquote('0:Rew:435.0,460.0')] ).
cnf(537,plain,
equal(multiply(multiply(u,v),double_divide(v,multiply(w,x))),double_divide(x,multiply(inverse(u),w))),
inference(rew,[status(thm),theory(equality)],[529,435]),
[iquote('0:Rew:529.0,435.0')] ).
cnf(554,plain,
equal(double_divide(double_divide(u,multiply(multiply(v,w),x)),w),double_divide(double_divide(u,v),inverse(x))),
inference(rew,[status(thm),theory(equality)],[2,517]),
[iquote('0:Rew:2.0,517.0')] ).
cnf(556,plain,
equal(multiply(multiply(u,v),double_divide(v,double_divide(w,x))),double_divide(double_divide(u,x),inverse(w))),
inference(rew,[status(thm),theory(equality)],[554,21]),
[iquote('0:Rew:554.0,21.0')] ).
cnf(561,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,w),multiply(w,x))),y),double_divide(double_divide(u,v),inverse(double_divide(y,x)))),
inference(rew,[status(thm),theory(equality)],[556,361]),
[iquote('0:Rew:556.0,361.0')] ).
cnf(562,plain,
equal(double_divide(double_divide(u,multiply(v,w)),inverse(double_divide(x,v))),double_divide(double_divide(u,w),x)),
inference(rew,[status(thm),theory(equality)],[556,110]),
[iquote('0:Rew:556.0,110.0')] ).
cnf(564,plain,
equal(double_divide(double_divide(u,multiply(v,w)),multiply(v,x)),double_divide(double_divide(u,w),x)),
inference(rew,[status(thm),theory(equality)],[2,562]),
[iquote('0:Rew:2.0,562.0')] ).
cnf(565,plain,
equal(multiply(u,double_divide(double_divide(v,w),x)),double_divide(double_divide(u,multiply(w,v)),x)),
inference(rew,[status(thm),theory(equality)],[564,376]),
[iquote('0:Rew:564.0,376.0')] ).
cnf(569,plain,
equal(multiply(inverse(u),double_divide(double_divide(u,v),multiply(v,w))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[564,226]),
[iquote('0:Rew:564.0,226.0')] ).
cnf(573,plain,
equal(double_divide(double_divide(u,multiply(v,w)),multiply(v,u)),w),
inference(rew,[status(thm),theory(equality)],[565,7]),
[iquote('0:Rew:565.0,7.0')] ).
cnf(574,plain,
equal(double_divide(double_divide(inverse(u),multiply(v,u)),multiply(v,w)),inverse(w)),
inference(rew,[status(thm),theory(equality)],[565,569]),
[iquote('0:Rew:565.0,569.0')] ).
cnf(578,plain,
equal(multiply(u,multiply(multiply(v,w),double_divide(w,x))),double_divide(double_divide(u,multiply(y,v)),multiply(y,x))),
inference(rew,[status(thm),theory(equality)],[565,299]),
[iquote('0:Rew:565.0,299.0')] ).
cnf(611,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[564,573]),
[iquote('0:Rew:564.0,573.0')] ).
cnf(613,plain,
equal(double_divide(double_divide(inverse(u),u),v),inverse(v)),
inference(rew,[status(thm),theory(equality)],[564,574]),
[iquote('0:Rew:564.0,574.0')] ).
cnf(632,plain,
equal(multiply(multiply(u,v),double_divide(v,w)),double_divide(double_divide(u,multiply(inverse(w),x)),x)),
inference(rew,[status(thm),theory(equality)],[537,409]),
[iquote('0:Rew:537.0,409.0')] ).
cnf(636,plain,
equal(double_divide(double_divide(multiply(u,v),w),u),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[611,424,564,565]),
[iquote('0:Rew:611.0,424.0,564.0,424.0,565.0,424.0,565.0,424.0,565.0,424.0')] ).
cnf(638,plain,
equal(multiply(u,multiply(multiply(v,w),double_divide(w,x))),double_divide(double_divide(u,v),x)),
inference(rew,[status(thm),theory(equality)],[564,578]),
[iquote('0:Rew:564.0,578.0')] ).
cnf(655,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(v,w),multiply(w,x))),y),double_divide(double_divide(u,v),multiply(x,y))),
inference(rew,[status(thm),theory(equality)],[2,561]),
[iquote('0:Rew:2.0,561.0')] ).
cnf(669,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ 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)],[527]),
[iquote('0:Obv:527.3')] ).
cnf(674,plain,
equal(multiply(multiply(u,double_divide(v,w)),v),double_divide(double_divide(u,x),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[433,10]),
[iquote('0:SpR:433.0,10.0')] ).
cnf(675,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[433,18]),
[iquote('0:SpR:433.0,18.0')] ).
cnf(676,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[433,32]),
[iquote('0:SpR:433.0,32.0')] ).
cnf(678,plain,
equal(multiply(u,double_divide(v,multiply(w,u))),double_divide(v,w)),
inference(spr,[status(thm),theory(equality)],[18,433]),
[iquote('0:SpR:18.0,433.0')] ).
cnf(702,plain,
equal(multiply(multiply(u,v),double_divide(v,multiply(w,x))),double_divide(double_divide(u,y),multiply(y,multiply(w,x)))),
inference(rew,[status(thm),theory(equality)],[675,450]),
[iquote('0:Rew:675.0,450.0')] ).
cnf(736,plain,
equal(double_divide(double_divide(u,multiply(v,w)),w),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[675,636]),
[iquote('0:Rew:675.0,636.0')] ).
cnf(743,plain,
equal(multiply(multiply(inverse(u),v),double_divide(v,w)),double_divide(u,w)),
inference(rew,[status(thm),theory(equality)],[678,62]),
[iquote('0:Rew:678.0,62.0')] ).
cnf(752,plain,
equal(multiply(multiply(u,v),double_divide(v,w)),multiply(inverse(w),u)),
inference(rew,[status(thm),theory(equality)],[736,632]),
[iquote('0:Rew:736.0,632.0')] ).
cnf(756,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2,676]),
[iquote('0:Rew:2.0,676.0')] ).
cnf(768,plain,
equal(multiply(u,multiply(v,double_divide(v,multiply(w,x)))),double_divide(x,multiply(inverse(u),w))),
inference(rew,[status(thm),theory(equality)],[756,537]),
[iquote('0:Rew:756.0,537.0')] ).
cnf(771,plain,
equal(multiply(u,multiply(v,double_divide(v,inverse(w)))),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[756,440]),
[iquote('0:Rew:756.0,440.0')] ).
cnf(773,plain,
equal(inverse(multiply(multiply(u,v),double_divide(v,w))),multiply(x,multiply(w,double_divide(u,x)))),
inference(rew,[status(thm),theory(equality)],[756,328]),
[iquote('0:Rew:756.0,328.0')] ).
cnf(779,plain,
equal(multiply(u,multiply(v,multiply(w,double_divide(w,x)))),double_divide(double_divide(u,v),x)),
inference(rew,[status(thm),theory(equality)],[756,638]),
[iquote('0:Rew:756.0,638.0')] ).
cnf(786,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[756,439]),
[iquote('0:Rew:756.0,439.0')] ).
cnf(789,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ 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)],[756,669]),
[iquote('0:Rew:756.0,669.2')] ).
cnf(811,plain,
equal(multiply(u,multiply(v,double_divide(v,w))),double_divide(double_divide(double_divide(w,x),multiply(x,multiply(y,u))),y)),
inference(rew,[status(thm),theory(equality)],[756,24]),
[iquote('0:Rew:756.0,24.0')] ).
cnf(812,plain,
equal(multiply(inverse(multiply(u,multiply(v,double_divide(v,w)))),u),w),
inference(rew,[status(thm),theory(equality)],[756,500]),
[iquote('0:Rew:756.0,500.0')] ).
cnf(814,plain,
equal(multiply(u,multiply(v,w)),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[756,786]),
[iquote('0:Rew:756.0,786.0')] ).
cnf(819,plain,
equal(multiply(inverse(u),multiply(v,double_divide(v,w))),double_divide(u,w)),
inference(rew,[status(thm),theory(equality)],[756,743]),
[iquote('0:Rew:756.0,743.0')] ).
cnf(820,plain,
equal(multiply(u,multiply(v,double_divide(v,w))),multiply(inverse(w),u)),
inference(rew,[status(thm),theory(equality)],[756,752]),
[iquote('0:Rew:756.0,752.0')] ).
cnf(821,plain,
equal(multiply(inverse(u),inverse(v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[820,819]),
[iquote('0:Rew:820.0,819.0')] ).
cnf(823,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[459,821]),
[iquote('0:Rew:459.0,821.0')] ).
cnf(828,plain,
equal(double_divide(u,multiply(v,double_divide(w,u))),double_divide(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[823,503]),
[iquote('0:Rew:823.0,503.0')] ).
cnf(831,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[823,504]),
[iquote('0:Rew:823.0,504.0')] ).
cnf(836,plain,
equal(multiply(inverse(inverse(u)),v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[820,771]),
[iquote('0:Rew:820.0,771.0')] ).
cnf(838,plain,
equal(multiply(double_divide(u,inverse(v)),u),v),
inference(rew,[status(thm),theory(equality)],[823,812,820]),
[iquote('0:Rew:823.0,812.0,820.0,812.0')] ).
cnf(849,plain,
equal(double_divide(double_divide(u,v),multiply(v,w)),multiply(inverse(w),u)),
inference(rew,[status(thm),theory(equality)],[820,674,814,756]),
[iquote('0:Rew:820.0,674.0,814.0,674.0,756.0,674.0')] ).
cnf(860,plain,
equal(double_divide(double_divide(u,multiply(inverse(v),w)),x),double_divide(double_divide(u,w),multiply(v,x))),
inference(rew,[status(thm),theory(equality)],[849,655]),
[iquote('0:Rew:849.0,655.0')] ).
cnf(896,plain,
equal(multiply(u,multiply(inverse(v),w)),double_divide(double_divide(u,w),v)),
inference(rew,[status(thm),theory(equality)],[820,779]),
[iquote('0:Rew:820.0,779.0')] ).
cnf(898,plain,
equal(double_divide(u,double_divide(double_divide(v,w),u)),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[896,377]),
[iquote('0:Rew:896.0,377.0')] ).
cnf(899,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[831,898]),
[iquote('0:Rew:831.0,898.0')] ).
cnf(904,plain,
equal(double_divide(double_divide(u,inverse(u)),v),inverse(v)),
inference(rew,[status(thm),theory(equality)],[899,613]),
[iquote('0:Rew:899.0,613.0')] ).
cnf(907,plain,
equal(double_divide(u,multiply(inverse(u),v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[529,904]),
[iquote('0:Rew:529.0,904.0')] ).
cnf(922,plain,
equal(double_divide(u,multiply(inverse(v),w)),multiply(double_divide(u,w),v)),
inference(rew,[status(thm),theory(equality)],[823,768,820]),
[iquote('0:Rew:823.0,768.0,820.0,768.0')] ).
cnf(923,plain,
equal(multiply(double_divide(u,v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[922,907]),
[iquote('0:Rew:922.0,907.0')] ).
cnf(925,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[923,838]),
[iquote('0:Rew:923.0,838.0')] ).
cnf(926,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[925,836]),
[iquote('0:Rew:925.0,836.0')] ).
cnf(928,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[926,923]),
[iquote('0:Rew:926.0,923.0')] ).
cnf(935,plain,
equal(multiply(inverse(u),v),double_divide(inverse(v),u)),
inference(rew,[status(thm),theory(equality)],[823,773,928,756,442]),
[iquote('0:Rew:823.0,773.0,928.0,773.0,756.0,773.0,442.0,773.0')] ).
cnf(937,plain,
equal(double_divide(u,double_divide(inverse(v),w)),multiply(double_divide(u,v),w)),
inference(rew,[status(thm),theory(equality)],[935,922]),
[iquote('0:Rew:935.0,922.0')] ).
cnf(980,plain,
equal(double_divide(u,multiply(v,double_divide(w,x))),double_divide(double_divide(w,x),multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[675,860,937,935]),
[iquote('0:Rew:675.0,860.0,937.0,860.0,935.0,860.0')] ).
cnf(998,plain,
equal(double_divide(u,multiply(v,multiply(w,double_divide(x,u)))),multiply(x,double_divide(w,v))),
inference(rew,[status(thm),theory(equality)],[823,702,928,756,980]),
[iquote('0:Rew:823.0,702.0,928.0,702.0,756.0,702.0,756.0,702.0,980.0,702.0')] ).
cnf(1023,plain,
equal(multiply(u,inverse(v)),double_divide(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[928,811,828,899,998,756,980]),
[iquote('0:Rew:928.0,811.0,828.0,811.0,899.0,811.0,998.0,811.0,756.0,811.0,980.0,811.0')] ).
cnf(1079,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)) ),
inference(obv,[status(thm),theory(equality)],[789]),
[iquote('0:Obv:789.2')] ).
cnf(1080,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))) ),
inference(rew,[status(thm),theory(equality)],[899,1079,1023,926]),
[iquote('0:Rew:899.0,1079.1,1023.0,1079.1,926.0,1079.1,899.0,1079.1,1023.0,1079.1,926.0,1079.1,926.0,1079.0')] ).
cnf(1081,plain,
~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
inference(obv,[status(thm),theory(equality)],[1080]),
[iquote('0:Obv:1080.0')] ).
cnf(1128,plain,
equal(multiply(double_divide(u,inverse(u)),v),v),
inference(spr,[status(thm),theory(equality)],[524,926]),
[iquote('0:SpR:524.0,926.0')] ).
cnf(1172,plain,
equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
inference(spr,[status(thm),theory(equality)],[1128,524]),
[iquote('0:SpR:1128.0,524.0')] ).
cnf(1180,plain,
$false,
inference(unc,[status(thm)],[1172,1081]),
[iquote('0:UnC:1172.0,1081.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : GRP106-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 07:22:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.47/0.69
% 0.47/0.69 SPASS V 3.9
% 0.47/0.69 SPASS beiseite: Proof found.
% 0.47/0.69 % SZS status Theorem
% 0.47/0.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.69 SPASS derived 790 clauses, backtracked 0 clauses, performed 0 splits and kept 485 clauses.
% 0.47/0.69 SPASS allocated 65059 KBytes.
% 0.47/0.69 SPASS spent 0:00:00.33 on the problem.
% 0.47/0.69 0:00:00.04 for the input.
% 0.47/0.69 0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.69 0:00:00.01 for inferences.
% 0.47/0.69 0:00:00.00 for the backtracking.
% 0.47/0.69 0:00:00.26 for the reduction.
% 0.47/0.69
% 0.47/0.69
% 0.47/0.69 Here is a proof with depth 7, length 159 :
% 0.47/0.69 % SZS output start Refutation
% See solution above
% 0.47/0.70 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 0.47/0.70
%------------------------------------------------------------------------------