%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP594-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:48:12 EDT 2022
% Result : Unsatisfiable 0.48s 0.69s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of clauses : 103 ( 103 unt; 0 nHn; 103 RR)
% Number of literals : 103 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 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('GRP594-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP594-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP594-1.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(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(8,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(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)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(10,plain,
equal(multiply(u,double_divide(double_divide(double_divide(u,v),multiply(v,multiply(w,x))),w)),x),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(21,plain,
equal(double_divide(multiply(u,double_divide(v,multiply(w,u))),w),v),
inference(spr,[status(thm),theory(equality)],[8,6]),
[iquote('0:SpR:8.0,6.0')] ).
cnf(32,plain,
equal(multiply(u,multiply(v,double_divide(w,multiply(u,v)))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[21,2]),
[iquote('0:SpR:21.0,2.0')] ).
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)],[21]),
[iquote('0:SpR:21.0,21.0')] ).
cnf(41,plain,
equal(double_divide(double_divide(multiply(u,v),w),multiply(w,u)),v),
inference(spr,[status(thm),theory(equality)],[8,21]),
[iquote('0:SpR:8.0,21.0')] ).
cnf(44,plain,
equal(multiply(multiply(u,v),double_divide(multiply(v,w),u)),inverse(w)),
inference(spr,[status(thm),theory(equality)],[41,2]),
[iquote('0:SpR:41.0,2.0')] ).
cnf(54,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)],[4,41]),
[iquote('0:SpR:4.0,41.0')] ).
cnf(62,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(76,plain,
equal(multiply(inverse(u),double_divide(double_divide(multiply(v,u),w),w)),v),
inference(rew,[status(thm),theory(equality)],[37,62]),
[iquote('0:Rew:37.0,62.0')] ).
cnf(92,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(95,plain,
equal(multiply(multiply(u,v),double_divide(inverse(w),u)),inverse(multiply(x,double_divide(w,multiply(v,x))))),
inference(spr,[status(thm),theory(equality)],[32,44]),
[iquote('0:SpR:32.0,44.0')] ).
cnf(101,plain,
equal(multiply(multiply(u,multiply(multiply(v,w),x)),double_divide(w,u)),multiply(v,x)),
inference(rew,[status(thm),theory(equality)],[2,92]),
[iquote('0:Rew:2.0,92.0')] ).
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)],[76,21]),
[iquote('0:SpR:76.0,21.0')] ).
cnf(142,plain,
equal(double_divide(multiply(u,v),multiply(w,inverse(v))),double_divide(u,w)),
inference(spr,[status(thm),theory(equality)],[76,21]),
[iquote('0:SpR:76.0,21.0')] ).
cnf(143,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(145,plain,
equal(multiply(double_divide(double_divide(u,inverse(v)),w),double_divide(double_divide(x,double_divide(double_divide(multiply(w,v),y),y)),u)),x),
inference(spr,[status(thm),theory(equality)],[76,9]),
[iquote('0:SpR:76.0,9.0')] ).
cnf(147,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)],[2,143]),
[iquote('0:Rew:2.0,143.0')] ).
cnf(158,plain,
equal(multiply(multiply(u,v),double_divide(double_divide(w,x),x)),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[2,147]),
[iquote('0:Rew:2.0,147.0')] ).
cnf(159,plain,
equal(multiply(multiply(u,multiply(v,double_divide(w,u))),w),v),
inference(rew,[status(thm),theory(equality)],[158,154]),
[iquote('0:Rew:158.0,154.0')] ).
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)],[159,76]),
[iquote('0:SpR:159.0,76.0')] ).
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)],[159,8]),
[iquote('0:SpR:159.0,8.0')] ).
cnf(183,plain,
equal(multiply(u,double_divide(v,multiply(multiply(w,multiply(x,multiply(u,double_divide(v,x)))),y))),double_divide(y,w)),
inference(spr,[status(thm),theory(equality)],[159,8]),
[iquote('0:SpR:159.0,8.0')] ).
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(213,plain,
equal(double_divide(u,multiply(v,multiply(w,double_divide(inverse(x),v)))),double_divide(multiply(u,x),w)),
inference(spr,[status(thm),theory(equality)],[159,142]),
[iquote('0:SpR:159.0,142.0')] ).
cnf(215,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(224,plain,
equal(double_divide(multiply(multiply(u,v),w),x),double_divide(v,multiply(x,multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[2,215]),
[iquote('0:Rew:2.0,215.0')] ).
cnf(251,plain,
equal(multiply(u,multiply(v,multiply(w,double_divide(x,v)))),multiply(multiply(u,inverse(x)),w)),
inference(spr,[status(thm),theory(equality)],[159,156]),
[iquote('0:SpR:159.0,156.0')] ).
cnf(252,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(265,plain,
equal(multiply(u,double_divide(v,multiply(multiply(multiply(w,inverse(v)),u),x))),double_divide(x,w)),
inference(rew,[status(thm),theory(equality)],[251,183]),
[iquote('0:Rew:251.0,183.0')] ).
cnf(266,plain,
equal(multiply(multiply(u,multiply(v,w)),x),multiply(u,multiply(multiply(v,x),w))),
inference(rew,[status(thm),theory(equality)],[2,252]),
[iquote('0:Rew:2.0,252.0')] ).
cnf(267,plain,
equal(multiply(u,multiply(multiply(v,w),double_divide(w,u))),v),
inference(rew,[status(thm),theory(equality)],[266,159]),
[iquote('0:Rew:266.0,159.0')] ).
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)],[266,101]),
[iquote('0:Rew:266.0,101.0')] ).
cnf(313,plain,
equal(double_divide(double_divide(u,v),multiply(v,w)),double_divide(double_divide(double_divide(w,x),multiply(x,multiply(y,u))),y)),
inference(spr,[status(thm),theory(equality)],[10,41]),
[iquote('0:SpR:10.0,41.0')] ).
cnf(324,plain,
equal(multiply(u,double_divide(double_divide(double_divide(u,v),multiply(v,w)),x)),double_divide(double_divide(double_divide(x,y),multiply(y,multiply(z,w))),z)),
inference(spr,[status(thm),theory(equality)],[10]),
[iquote('0:SpR:10.0,10.0')] ).
cnf(327,plain,
equal(multiply(u,double_divide(double_divide(double_divide(u,v),multiply(v,double_divide(w,x))),multiply(y,z))),double_divide(z,multiply(multiply(x,y),w))),
inference(spr,[status(thm),theory(equality)],[8,10]),
[iquote('0:SpR:8.0,10.0')] ).
cnf(353,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)],[267,21]),
[iquote('0:SpR:267.0,21.0')] ).
cnf(360,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)],[267,32]),
[iquote('0:SpR:267.0,32.0')] ).
cnf(376,plain,
equal(multiply(u,multiply(inverse(v),double_divide(double_divide(multiply(w,v),x),u))),multiply(x,w)),
inference(spr,[status(thm),theory(equality)],[44,267]),
[iquote('0:SpR:44.0,267.0')] ).
cnf(386,plain,
equal(double_divide(double_divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[54,353,224]),
[iquote('0:Rew:54.0,353.0,224.0,353.0')] ).
cnf(387,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(rew,[status(thm),theory(equality)],[386,76]),
[iquote('0:Rew:386.0,76.0')] ).
cnf(389,plain,
equal(multiply(double_divide(double_divide(u,inverse(v)),w),double_divide(double_divide(x,multiply(w,v)),u)),x),
inference(rew,[status(thm),theory(equality)],[386,145]),
[iquote('0:Rew:386.0,145.0')] ).
cnf(395,plain,
equal(multiply(u,multiply(v,double_divide(w,u))),multiply(inverse(w),v)),
inference(rew,[status(thm),theory(equality)],[386,174]),
[iquote('0:Rew:386.0,174.0')] ).
cnf(398,plain,
equal(double_divide(multiply(multiply(u,v),double_divide(w,u)),inverse(v)),w),
inference(rew,[status(thm),theory(equality)],[386,135]),
[iquote('0:Rew:386.0,135.0')] ).
cnf(409,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)],[395,176]),
[iquote('0:Rew:395.0,176.0')] ).
cnf(412,plain,
equal(double_divide(u,multiply(inverse(inverse(v)),w)),double_divide(multiply(u,v),w)),
inference(rew,[status(thm),theory(equality)],[395,213]),
[iquote('0:Rew:395.0,213.0')] ).
cnf(414,plain,
equal(multiply(multiply(u,inverse(v)),w),multiply(u,multiply(inverse(v),w))),
inference(rew,[status(thm),theory(equality)],[395,251]),
[iquote('0:Rew:395.0,251.0')] ).
cnf(418,plain,
equal(multiply(inverse(u),inverse(v)),inverse(multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[395,210]),
[iquote('0:Rew:395.0,210.0')] ).
cnf(422,plain,
equal(double_divide(u,multiply(inverse(u),multiply(v,double_divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[224,398]),
[iquote('0:Rew:224.0,398.0')] ).
cnf(430,plain,
equal(multiply(u,double_divide(v,multiply(multiply(w,multiply(inverse(v),u)),x))),double_divide(x,w)),
inference(rew,[status(thm),theory(equality)],[414,265]),
[iquote('0:Rew:414.0,265.0')] ).
cnf(454,plain,
equal(multiply(u,double_divide(v,u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[273,360]),
[iquote('0:Rew:273.0,360.0')] ).
cnf(455,plain,
equal(double_divide(u,multiply(inverse(u),inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[454,422]),
[iquote('0:Rew:454.0,422.0')] ).
cnf(457,plain,
equal(double_divide(u,inverse(multiply(u,v))),v),
inference(rew,[status(thm),theory(equality)],[418,455]),
[iquote('0:Rew:418.0,455.0')] ).
cnf(462,plain,
equal(inverse(multiply(double_divide(multiply(u,v),w),v)),multiply(w,u)),
inference(rew,[status(thm),theory(equality)],[418,376,395]),
[iquote('0:Rew:418.0,376.0,395.0,376.0')] ).
cnf(481,plain,
equal(multiply(u,double_divide(v,multiply(w,multiply(multiply(inverse(v),x),u)))),double_divide(x,w)),
inference(rew,[status(thm),theory(equality)],[266,430]),
[iquote('0:Rew:266.0,430.0')] ).
cnf(508,plain,
equal(multiply(u,double_divide(v,multiply(w,u))),double_divide(v,w)),
inference(spr,[status(thm),theory(equality)],[386,6]),
[iquote('0:SpR:386.0,6.0')] ).
cnf(509,plain,
equal(multiply(double_divide(double_divide(u,v),multiply(v,w)),double_divide(x,u)),double_divide(x,w)),
inference(spr,[status(thm),theory(equality)],[386,9]),
[iquote('0:SpR:386.0,9.0')] ).
cnf(510,plain,
equal(double_divide(multiply(u,v),w),double_divide(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[386,21]),
[iquote('0:SpR:386.0,21.0')] ).
cnf(511,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[386,32]),
[iquote('0:SpR:386.0,32.0')] ).
cnf(523,plain,
equal(multiply(multiply(u,v),double_divide(inverse(w),u)),inverse(double_divide(w,v))),
inference(rew,[status(thm),theory(equality)],[508,95]),
[iquote('0:Rew:508.0,95.0')] ).
cnf(537,plain,
equal(double_divide(u,multiply(multiply(v,inverse(u)),w)),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[510,142]),
[iquote('0:Rew:510.0,142.0')] ).
cnf(569,plain,
equal(double_divide(u,multiply(inverse(inverse(v)),w)),double_divide(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[510,412]),
[iquote('0:Rew:510.0,412.0')] ).
cnf(570,plain,
equal(inverse(multiply(double_divide(u,multiply(v,w)),u)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[510,462]),
[iquote('0:Rew:510.0,462.0')] ).
cnf(587,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2,511]),
[iquote('0:Rew:2.0,511.0')] ).
cnf(589,plain,
~ equal(multiply(inverse(b2),multiply(b2,a2)),a2),
inference(rew,[status(thm),theory(equality)],[587,3]),
[iquote('0:Rew:587.0,3.0')] ).
cnf(594,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)],[587,409]),
[iquote('0:Rew:587.0,409.0')] ).
cnf(615,plain,
equal(multiply(u,double_divide(v,multiply(w,multiply(inverse(v),multiply(x,u))))),double_divide(x,w)),
inference(rew,[status(thm),theory(equality)],[587,481]),
[iquote('0:Rew:587.0,481.0')] ).
cnf(629,plain,
equal(multiply(u,double_divide(double_divide(double_divide(u,v),multiply(v,double_divide(w,x))),multiply(y,z))),double_divide(z,multiply(x,multiply(y,w)))),
inference(rew,[status(thm),theory(equality)],[587,327]),
[iquote('0:Rew:587.0,327.0')] ).
cnf(649,plain,
equal(double_divide(u,multiply(v,multiply(inverse(u),w))),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[587,537]),
[iquote('0:Rew:587.0,537.0')] ).
cnf(659,plain,
equal(multiply(multiply(u,v),double_divide(inverse(w),u)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[2,523]),
[iquote('0:Rew:2.0,523.0')] ).
cnf(660,plain,
equal(multiply(inverse(inverse(u)),v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[395,659,587]),
[iquote('0:Rew:395.0,659.0,587.0,659.0')] ).
cnf(663,plain,
equal(double_divide(u,multiply(v,w)),double_divide(w,multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[660,569]),
[iquote('0:Rew:660.0,569.0')] ).
cnf(704,plain,
equal(multiply(u,double_divide(u,multiply(v,w))),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[510,615,649]),
[iquote('0:Rew:510.0,615.0,649.0,615.0')] ).
cnf(705,plain,
equal(double_divide(u,multiply(inverse(v),w)),multiply(v,double_divide(u,w))),
inference(rew,[status(thm),theory(equality)],[704,594]),
[iquote('0:Rew:704.0,594.0')] ).
cnf(748,plain,
equal(multiply(u,double_divide(double_divide(double_divide(u,inverse(v)),w),w)),v),
inference(spr,[status(thm),theory(equality)],[387,10]),
[iquote('0:SpR:387.0,10.0')] ).
cnf(754,plain,
equal(multiply(u,double_divide(u,inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[386,748]),
[iquote('0:Rew:386.0,748.0')] ).
cnf(774,plain,
equal(double_divide(double_divide(double_divide(u,v),multiply(v,multiply(w,x))),w),double_divide(u,inverse(x))),
inference(spr,[status(thm),theory(equality)],[10,457]),
[iquote('0:SpR:10.0,457.0')] ).
cnf(781,plain,
equal(multiply(u,double_divide(double_divide(double_divide(u,v),multiply(v,w)),x)),double_divide(x,inverse(w))),
inference(rew,[status(thm),theory(equality)],[774,324]),
[iquote('0:Rew:774.0,324.0')] ).
cnf(784,plain,
equal(double_divide(double_divide(u,v),multiply(v,w)),double_divide(w,inverse(u))),
inference(rew,[status(thm),theory(equality)],[774,313]),
[iquote('0:Rew:774.0,313.0')] ).
cnf(790,plain,
equal(multiply(u,double_divide(double_divide(double_divide(v,w),inverse(u)),multiply(x,y))),double_divide(y,multiply(w,multiply(x,v)))),
inference(rew,[status(thm),theory(equality)],[784,629]),
[iquote('0:Rew:784.0,629.0')] ).
cnf(813,plain,
equal(multiply(double_divide(u,inverse(v)),double_divide(w,v)),double_divide(w,u)),
inference(rew,[status(thm),theory(equality)],[784,509]),
[iquote('0:Rew:784.0,509.0')] ).
cnf(828,plain,
equal(multiply(u,double_divide(double_divide(v,inverse(u)),w)),double_divide(w,inverse(v))),
inference(rew,[status(thm),theory(equality)],[784,781]),
[iquote('0:Rew:784.0,781.0')] ).
cnf(856,plain,
equal(multiply(double_divide(u,v),double_divide(w,x)),double_divide(w,multiply(v,multiply(x,u)))),
inference(rew,[status(thm),theory(equality)],[705,790,510,828]),
[iquote('0:Rew:705.0,790.0,510.0,790.0,828.0,790.0')] ).
cnf(859,plain,
equal(double_divide(u,multiply(inverse(v),multiply(v,w))),double_divide(u,w)),
inference(rew,[status(thm),theory(equality)],[856,813]),
[iquote('0:Rew:856.0,813.0')] ).
cnf(869,plain,
equal(double_divide(double_divide(u,multiply(v,w)),multiply(v,multiply(x,double_divide(x,inverse(w))))),u),
inference(rew,[status(thm),theory(equality)],[856,389]),
[iquote('0:Rew:856.0,389.0')] ).
cnf(871,plain,
equal(multiply(u,double_divide(v,multiply(u,w))),double_divide(v,w)),
inference(rew,[status(thm),theory(equality)],[705,859]),
[iquote('0:Rew:705.0,859.0')] ).
cnf(878,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[871,869,663,754]),
[iquote('0:Rew:871.0,869.0,663.0,869.0,754.0,869.0')] ).
cnf(890,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(spr,[status(thm),theory(equality)],[878,386]),
[iquote('0:SpR:878.0,386.0')] ).
cnf(891,plain,
equal(multiply(double_divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[878,454]),
[iquote('0:SpR:878.0,454.0')] ).
cnf(901,plain,
equal(inverse(inverse(multiply(u,v))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[891,570]),
[iquote('0:Rew:891.0,570.0')] ).
cnf(909,plain,
equal(inverse(multiply(u,v)),double_divide(u,v)),
inference(spr,[status(thm),theory(equality)],[457,890]),
[iquote('0:SpR:457.0,890.0')] ).
cnf(922,plain,
equal(inverse(double_divide(u,v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[909,901]),
[iquote('0:Rew:909.0,901.0')] ).
cnf(923,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[2,922]),
[iquote('0:Rew:2.0,922.0')] ).
cnf(995,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(spr,[status(thm),theory(equality)],[923,387]),
[iquote('0:SpR:923.0,387.0')] ).
cnf(1003,plain,
$false,
inference(unc,[status(thm)],[995,589]),
[iquote('0:UnC:995.0,589.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP594-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 07:31:38 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.48/0.69
% 0.48/0.69 SPASS V 3.9
% 0.48/0.69 SPASS beiseite: Proof found.
% 0.48/0.69 % SZS status Theorem
% 0.48/0.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.69 SPASS derived 710 clauses, backtracked 0 clauses, performed 0 splits and kept 418 clauses.
% 0.48/0.69 SPASS allocated 64795 KBytes.
% 0.48/0.69 SPASS spent 0:00:00.34 on the problem.
% 0.48/0.69 0:00:00.03 for the input.
% 0.48/0.69 0:00:00.00 for the FLOTTER CNF translation.
% 0.48/0.69 0:00:00.00 for inferences.
% 0.48/0.69 0:00:00.00 for the backtracking.
% 0.48/0.69 0:00:00.27 for the reduction.
% 0.48/0.69
% 0.48/0.69
% 0.48/0.69 Here is a proof with depth 8, length 103 :
% 0.48/0.69 % SZS output start Refutation
% See solution above
% 0.55/0.70 Formulae used in the proof : single_axiom multiply prove_these_axioms_2
% 0.55/0.70
%------------------------------------------------------------------------------