TSTP Solution File: GRP583-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP583-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:48:09 EDT 2022
% Result : Unsatisfiable 0.39s 0.58s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 117 RR)
% Number of literals : 117 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(identity,identity)),w),
file('GRP583-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP583-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP583-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP583-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP583-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(49,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,u),double_divide(v,identity))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(50,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,u),double_divide(v,inverse(u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(52,plain,
equal(double_divide(double_divide(u,double_divide(identity,double_divide(v,double_divide(inverse(identity),u)))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(54,plain,
equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),inverse(identity)),v),
inference(rew,[status(thm),theory(equality)],[3,49]),
[iquote('0:Rew:3.0,49.0')] ).
cnf(64,plain,
equal(double_divide(double_divide(inverse(inverse(identity)),double_divide(identity,inverse(u))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,54]),
[iquote('0:SpR:4.0,54.0')] ).
cnf(65,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(inverse(identity),inverse(u))),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[3,54]),
[iquote('0:SpR:3.0,54.0')] ).
cnf(66,plain,
equal(double_divide(double_divide(inverse(u),identity),inverse(identity)),double_divide(identity,u)),
inference(spr,[status(thm),theory(equality)],[4,54]),
[iquote('0:SpR:4.0,54.0')] ).
cnf(67,plain,
equal(double_divide(double_divide(inverse(double_divide(double_divide(identity,u),double_divide(v,double_divide(u,identity)))),v),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[7,54]),
[iquote('0:SpR:7.0,54.0')] ).
cnf(69,plain,
equal(double_divide(inverse(inverse(u)),inverse(identity)),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[3,66]),
[iquote('0:Rew:3.0,66.0')] ).
cnf(72,plain,
equal(double_divide(double_divide(multiply(double_divide(u,inverse(v)),double_divide(identity,v)),u),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,67,3]),
[iquote('0:Rew:6.0,67.0,3.0,67.0')] ).
cnf(73,plain,
equal(multiply(inverse(identity),inverse(inverse(u))),inverse(double_divide(identity,u))),
inference(spr,[status(thm),theory(equality)],[69,6]),
[iquote('0:SpR:69.0,6.0')] ).
cnf(78,plain,
equal(double_divide(inverse(multiply(u,v)),inverse(identity)),double_divide(identity,double_divide(v,u))),
inference(spr,[status(thm),theory(equality)],[6,69]),
[iquote('0:SpR:6.0,69.0')] ).
cnf(79,plain,
equal(multiply(inverse(identity),inverse(inverse(u))),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[6,73]),
[iquote('0:Rew:6.0,73.0')] ).
cnf(85,plain,
equal(multiply(inverse(identity),inverse(multiply(u,v))),multiply(double_divide(v,u),identity)),
inference(spr,[status(thm),theory(equality)],[6,79]),
[iquote('0:SpR:6.0,79.0')] ).
cnf(102,plain,
equal(double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),double_divide(v,u))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[65,7]),
[iquote('0:SpR:65.0,7.0')] ).
cnf(116,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,u),identity)),inverse(identity)),u),
inference(spr,[status(thm),theory(equality)],[4,50]),
[iquote('0:SpR:4.0,50.0')] ).
cnf(117,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(double_divide(identity,double_divide(double_divide(identity,identity),w)),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[7,50]),
[iquote('0:SpR:7.0,50.0')] ).
cnf(118,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),u)),inverse(identity)),double_divide(inverse(v),double_divide(double_divide(identity,v),inverse(u)))),
inference(spr,[status(thm),theory(equality)],[54,50]),
[iquote('0:SpR:54.0,50.0')] ).
cnf(119,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),u)),inverse(identity)),double_divide(inverse(inverse(identity)),double_divide(identity,inverse(u)))),
inference(spr,[status(thm),theory(equality)],[64,50]),
[iquote('0:SpR:64.0,50.0')] ).
cnf(120,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),u)),inverse(identity)),double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),
inference(spr,[status(thm),theory(equality)],[65,50]),
[iquote('0:SpR:65.0,50.0')] ).
cnf(121,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(identity,u))),inverse(identity)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[69,50]),
[iquote('0:SpR:69.0,50.0')] ).
cnf(124,plain,
equal(double_divide(double_divide(identity,multiply(u,identity)),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[6,116,3]),
[iquote('0:Rew:6.0,116.0,3.0,116.0')] ).
cnf(126,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),double_divide(identity,u))),inverse(identity)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,121]),
[iquote('0:Rew:3.0,121.0')] ).
cnf(129,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),u)),inverse(identity)),double_divide(inverse(inverse(identity)),double_divide(identity,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[3,119]),
[iquote('0:Rew:3.0,119.0')] ).
cnf(130,plain,
equal(double_divide(inverse(inverse(identity)),double_divide(identity,inverse(double_divide(identity,u)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[129,126]),
[iquote('0:Rew:129.0,126.0')] ).
cnf(133,plain,
equal(double_divide(inverse(inverse(identity)),double_divide(identity,multiply(u,identity))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,130]),
[iquote('0:Rew:6.0,130.0')] ).
cnf(134,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),u)),inverse(identity)),double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),
inference(rew,[status(thm),theory(equality)],[3,120]),
[iquote('0:Rew:3.0,120.0')] ).
cnf(135,plain,
equal(double_divide(inverse(inverse(identity)),double_divide(identity,inverse(u))),double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),
inference(rew,[status(thm),theory(equality)],[129,134]),
[iquote('0:Rew:129.0,134.0')] ).
cnf(139,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),u)),inverse(identity)),double_divide(inverse(identity),double_divide(inverse(identity),inverse(u)))),
inference(rew,[status(thm),theory(equality)],[135,129]),
[iquote('0:Rew:135.0,129.0')] ).
cnf(140,plain,
equal(double_divide(double_divide(identity,double_divide(inverse(identity),u)),inverse(identity)),double_divide(inverse(v),double_divide(double_divide(identity,v),inverse(u)))),
inference(rew,[status(thm),theory(equality)],[3,118]),
[iquote('0:Rew:3.0,118.0')] ).
cnf(141,plain,
equal(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),double_divide(inverse(identity),double_divide(inverse(identity),inverse(v)))),
inference(rew,[status(thm),theory(equality)],[139,140]),
[iquote('0:Rew:139.0,140.0')] ).
cnf(149,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(double_divide(identity,double_divide(inverse(identity),w)),inverse(identity))),
inference(rew,[status(thm),theory(equality)],[3,117]),
[iquote('0:Rew:3.0,117.0')] ).
cnf(150,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(inverse(identity),double_divide(inverse(identity),inverse(w)))),
inference(rew,[status(thm),theory(equality)],[139,149]),
[iquote('0:Rew:139.0,149.0')] ).
cnf(159,plain,
equal(double_divide(double_divide(identity,inverse(identity)),inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[12,124]),
[iquote('0:SpR:12.0,124.0')] ).
cnf(161,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,159]),
[iquote('0:Rew:4.0,159.0,4.0,159.0')] ).
cnf(164,plain,
equal(double_divide(inverse(inverse(u)),identity),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[161,69]),
[iquote('0:Rew:161.0,69.0')] ).
cnf(167,plain,
equal(double_divide(double_divide(identity,multiply(u,identity)),identity),u),
inference(rew,[status(thm),theory(equality)],[161,124]),
[iquote('0:Rew:161.0,124.0')] ).
cnf(168,plain,
equal(double_divide(double_divide(u,double_divide(identity,double_divide(v,double_divide(identity,u)))),identity),v),
inference(rew,[status(thm),theory(equality)],[161,52]),
[iquote('0:Rew:161.0,52.0')] ).
cnf(172,plain,
equal(double_divide(double_divide(multiply(double_divide(u,inverse(v)),double_divide(identity,v)),u),identity),identity),
inference(rew,[status(thm),theory(equality)],[161,72]),
[iquote('0:Rew:161.0,72.0')] ).
cnf(173,plain,
equal(double_divide(inverse(multiply(u,v)),identity),double_divide(identity,double_divide(v,u))),
inference(rew,[status(thm),theory(equality)],[161,78]),
[iquote('0:Rew:161.0,78.0')] ).
cnf(175,plain,
equal(multiply(identity,inverse(multiply(u,v))),multiply(double_divide(v,u),identity)),
inference(rew,[status(thm),theory(equality)],[161,85]),
[iquote('0:Rew:161.0,85.0')] ).
cnf(176,plain,
equal(double_divide(inverse(identity),double_divide(identity,multiply(u,identity))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[161,133]),
[iquote('0:Rew:161.0,133.0')] ).
cnf(181,plain,
equal(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,inverse(u)))),double_divide(v,u))),identity),v),
inference(rew,[status(thm),theory(equality)],[161,102]),
[iquote('0:Rew:161.0,102.0')] ).
cnf(185,plain,
equal(double_divide(double_divide(identity,double_divide(identity,u)),identity),double_divide(identity,double_divide(identity,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[161,139]),
[iquote('0:Rew:161.0,139.0')] ).
cnf(186,plain,
equal(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),double_divide(identity,double_divide(identity,inverse(v)))),
inference(rew,[status(thm),theory(equality)],[161,141]),
[iquote('0:Rew:161.0,141.0')] ).
cnf(188,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),double_divide(identity,double_divide(identity,inverse(w)))),
inference(rew,[status(thm),theory(equality)],[161,150]),
[iquote('0:Rew:161.0,150.0')] ).
cnf(189,plain,
equal(inverse(inverse(inverse(u))),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[3,164]),
[iquote('0:Rew:3.0,164.0')] ).
cnf(192,plain,
equal(multiply(multiply(u,identity),identity),u),
inference(rew,[status(thm),theory(equality)],[6,167,3]),
[iquote('0:Rew:6.0,167.0,3.0,167.0')] ).
cnf(207,plain,
equal(double_divide(identity,double_divide(u,v)),inverse(inverse(multiply(v,u)))),
inference(rew,[status(thm),theory(equality)],[3,173]),
[iquote('0:Rew:3.0,173.0')] ).
cnf(209,plain,
equal(inverse(inverse(inverse(multiply(u,v)))),multiply(double_divide(v,u),identity)),
inference(rew,[status(thm),theory(equality)],[13,175]),
[iquote('0:Rew:13.0,175.0')] ).
cnf(210,plain,
equal(double_divide(identity,multiply(u,v)),multiply(double_divide(v,u),identity)),
inference(rew,[status(thm),theory(equality)],[189,209]),
[iquote('0:Rew:189.0,209.0')] ).
cnf(211,plain,
equal(multiply(inverse(inverse(multiply(u,identity))),identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[207,176,210,161]),
[iquote('0:Rew:207.0,176.0,210.0,176.0,161.0,176.0,210.0,176.0')] ).
cnf(219,plain,
equal(multiply(double_divide(identity,double_divide(u,double_divide(identity,v))),v),u),
inference(rew,[status(thm),theory(equality)],[6,168,3]),
[iquote('0:Rew:6.0,168.0,3.0,168.0')] ).
cnf(220,plain,
equal(multiply(inverse(inverse(multiply(double_divide(identity,u),v))),u),v),
inference(rew,[status(thm),theory(equality)],[207,219]),
[iquote('0:Rew:207.0,219.0')] ).
cnf(225,plain,
equal(multiply(u,multiply(double_divide(u,inverse(v)),double_divide(identity,v))),identity),
inference(rew,[status(thm),theory(equality)],[6,172,3]),
[iquote('0:Rew:6.0,172.0,3.0,172.0')] ).
cnf(229,plain,
equal(double_divide(identity,double_divide(identity,inverse(u))),multiply(double_divide(identity,u),identity)),
inference(rew,[status(thm),theory(equality)],[6,185,3]),
[iquote('0:Rew:6.0,185.0,3.0,185.0')] ).
cnf(230,plain,
equal(inverse(inverse(multiply(inverse(u),identity))),multiply(double_divide(identity,u),identity)),
inference(rew,[status(thm),theory(equality)],[207,229]),
[iquote('0:Rew:207.0,229.0')] ).
cnf(235,plain,
equal(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),multiply(double_divide(identity,v),identity)),
inference(rew,[status(thm),theory(equality)],[230,186,207]),
[iquote('0:Rew:230.0,186.0,207.0,186.0')] ).
cnf(240,plain,
equal(multiply(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,inverse(u)))),double_divide(v,u)),identity),v),
inference(rew,[status(thm),theory(equality)],[6,181,3]),
[iquote('0:Rew:6.0,181.0,3.0,181.0')] ).
cnf(241,plain,
equal(multiply(double_divide(inverse(inverse(u)),double_divide(v,u)),identity),v),
inference(rew,[status(thm),theory(equality)],[211,240,207,210,230]),
[iquote('0:Rew:211.0,240.0,207.0,240.0,210.0,240.0,230.0,240.0,207.0,240.0')] ).
cnf(242,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),multiply(double_divide(identity,w),identity)),
inference(rew,[status(thm),theory(equality)],[230,188,207]),
[iquote('0:Rew:230.0,188.0,207.0,188.0')] ).
cnf(274,plain,
equal(double_divide(identity,inverse(inverse(u))),inverse(inverse(double_divide(identity,u)))),
inference(spr,[status(thm),theory(equality)],[189]),
[iquote('0:SpR:189.0,189.0')] ).
cnf(276,plain,
equal(double_divide(identity,inverse(u)),inverse(double_divide(identity,u))),
inference(spr,[status(thm),theory(equality)],[189]),
[iquote('0:SpR:189.0,189.0')] ).
cnf(281,plain,
equal(double_divide(identity,inverse(u)),multiply(u,identity)),
inference(rew,[status(thm),theory(equality)],[6,276]),
[iquote('0:Rew:6.0,276.0')] ).
cnf(284,plain,
equal(double_divide(identity,inverse(inverse(u))),inverse(multiply(u,identity))),
inference(rew,[status(thm),theory(equality)],[6,274]),
[iquote('0:Rew:6.0,274.0')] ).
cnf(285,plain,
equal(multiply(inverse(u),identity),inverse(multiply(u,identity))),
inference(rew,[status(thm),theory(equality)],[281,284]),
[iquote('0:Rew:281.0,284.0')] ).
cnf(393,plain,
equal(inverse(multiply(double_divide(u,v),identity)),multiply(multiply(v,u),identity)),
inference(spr,[status(thm),theory(equality)],[6,285]),
[iquote('0:SpR:6.0,285.0')] ).
cnf(462,plain,
equal(multiply(u,multiply(identity,double_divide(identity,u))),identity),
inference(spr,[status(thm),theory(equality)],[4,225]),
[iquote('0:SpR:4.0,225.0')] ).
cnf(465,plain,
equal(multiply(u,inverse(multiply(u,identity))),identity),
inference(rew,[status(thm),theory(equality)],[6,462,13]),
[iquote('0:Rew:6.0,462.0,13.0,462.0')] ).
cnf(480,plain,
equal(inverse(multiply(double_divide(identity,u),identity)),multiply(inverse(inverse(identity)),u)),
inference(spr,[status(thm),theory(equality)],[465,220]),
[iquote('0:SpR:465.0,220.0')] ).
cnf(493,plain,
equal(inverse(multiply(double_divide(identity,u),identity)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[13,480,161]),
[iquote('0:Rew:13.0,480.0,161.0,480.0,161.0,480.0')] ).
cnf(494,plain,
equal(multiply(multiply(u,identity),identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[393,493]),
[iquote('0:Rew:393.0,493.0')] ).
cnf(495,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[192,494]),
[iquote('0:Rew:192.0,494.0')] ).
cnf(496,plain,
equal(double_divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[495,189]),
[iquote('0:Rew:495.0,189.0')] ).
cnf(498,plain,
equal(multiply(multiply(double_divide(identity,u),v),u),v),
inference(rew,[status(thm),theory(equality)],[495,220]),
[iquote('0:Rew:495.0,220.0')] ).
cnf(515,plain,
equal(multiply(double_divide(u,double_divide(v,u)),identity),v),
inference(rew,[status(thm),theory(equality)],[495,241]),
[iquote('0:Rew:495.0,241.0')] ).
cnf(518,plain,
equal(multiply(u,identity),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[496,281]),
[iquote('0:Rew:496.0,281.0')] ).
cnf(521,plain,
equal(double_divide(u,double_divide(double_divide(identity,v),double_divide(w,double_divide(v,u)))),multiply(inverse(w),identity)),
inference(rew,[status(thm),theory(equality)],[496,242]),
[iquote('0:Rew:496.0,242.0')] ).
cnf(522,plain,
equal(double_divide(inverse(u),double_divide(double_divide(identity,u),inverse(v))),multiply(inverse(v),identity)),
inference(rew,[status(thm),theory(equality)],[496,235]),
[iquote('0:Rew:496.0,235.0')] ).
cnf(524,plain,
equal(multiply(double_divide(u,v),identity),inverse(multiply(v,u))),
inference(rew,[status(thm),theory(equality)],[496,210]),
[iquote('0:Rew:496.0,210.0')] ).
cnf(529,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[495,518]),
[iquote('0:Rew:495.0,518.0')] ).
cnf(540,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(rew,[status(thm),theory(equality)],[496,498]),
[iquote('0:Rew:496.0,498.0')] ).
cnf(541,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[529,515]),
[iquote('0:Rew:529.0,515.0')] ).
cnf(543,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[529,524]),
[iquote('0:Rew:529.0,524.0')] ).
cnf(560,plain,
equal(double_divide(inverse(u),double_divide(inverse(u),inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[496,522,529]),
[iquote('0:Rew:496.0,522.0,529.0,522.0')] ).
cnf(561,plain,
equal(double_divide(u,double_divide(inverse(v),double_divide(w,double_divide(v,u)))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[496,521,529]),
[iquote('0:Rew:496.0,521.0,529.0,521.0')] ).
cnf(584,plain,
equal(multiply(multiply(multiply(u,v),w),double_divide(v,u)),w),
inference(spr,[status(thm),theory(equality)],[6,540]),
[iquote('0:SpR:6.0,540.0')] ).
cnf(626,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[541]),
[iquote('0:SpR:541.0,541.0')] ).
cnf(668,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[626,6]),
[iquote('0:SpR:626.0,6.0')] ).
cnf(747,plain,
equal(double_divide(inverse(u),inverse(v)),double_divide(inverse(v),inverse(u))),
inference(spr,[status(thm),theory(equality)],[560,626]),
[iquote('0:SpR:560.0,626.0')] ).
cnf(780,plain,
equal(double_divide(inverse(u),v),multiply(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[668,540]),
[iquote('0:SpR:668.0,540.0')] ).
cnf(793,plain,
equal(double_divide(u,multiply(inverse(double_divide(v,double_divide(w,u))),w)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[780,561]),
[iquote('0:Rew:780.0,561.0')] ).
cnf(794,plain,
equal(double_divide(inverse(u),inverse(v)),multiply(inverse(inverse(u)),v)),
inference(rew,[status(thm),theory(equality)],[780,747]),
[iquote('0:Rew:780.0,747.0')] ).
cnf(807,plain,
equal(double_divide(inverse(u),inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[495,794]),
[iquote('0:Rew:495.0,794.0')] ).
cnf(808,plain,
equal(multiply(inverse(inverse(u)),v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[780,807]),
[iquote('0:Rew:780.0,807.0')] ).
cnf(809,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[495,808]),
[iquote('0:Rew:495.0,808.0')] ).
cnf(812,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[809,5]),
[iquote('0:Rew:809.0,5.0')] ).
cnf(819,plain,
equal(multiply(double_divide(u,v),multiply(multiply(v,u),w)),w),
inference(rew,[status(thm),theory(equality)],[809,584]),
[iquote('0:Rew:809.0,584.0')] ).
cnf(823,plain,
equal(double_divide(u,multiply(multiply(double_divide(v,u),w),v)),inverse(w)),
inference(rew,[status(thm),theory(equality)],[6,793]),
[iquote('0:Rew:6.0,793.0')] ).
cnf(824,plain,
equal(double_divide(u,multiply(v,multiply(double_divide(v,u),w))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[809,823]),
[iquote('0:Rew:809.0,823.0')] ).
cnf(1279,plain,
equal(inverse(multiply(multiply(u,v),w)),double_divide(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[819,824]),
[iquote('0:SpR:819.0,824.0')] ).
cnf(1298,plain,
equal(double_divide(u,multiply(v,w)),double_divide(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[543,1279]),
[iquote('0:Rew:543.0,1279.0')] ).
cnf(1535,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1298,6]),
[iquote('0:SpR:1298.0,6.0')] ).
cnf(1606,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(w,u),v)),
inference(rew,[status(thm),theory(equality)],[6,1535]),
[iquote('0:Rew:6.0,1535.0')] ).
cnf(2098,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[1606,809]),
[iquote('0:SpR:1606.0,809.0')] ).
cnf(2113,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[1606]),
[iquote('0:SpR:1606.0,1606.0')] ).
cnf(2226,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(w,u))),
inference(rew,[status(thm),theory(equality)],[2098,2113]),
[iquote('0:Rew:2098.0,2113.0,2098.0,2113.0')] ).
cnf(2227,plain,
$false,
inference(unc,[status(thm)],[2226,812]),
[iquote('0:UnC:2226.0,812.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP583-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.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 : Mon Jun 13 21:27:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.39/0.58
% 0.39/0.58 SPASS V 3.9
% 0.39/0.58 SPASS beiseite: Proof found.
% 0.39/0.58 % SZS status Theorem
% 0.39/0.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.58 SPASS derived 1245 clauses, backtracked 0 clauses, performed 0 splits and kept 264 clauses.
% 0.39/0.58 SPASS allocated 65054 KBytes.
% 0.39/0.58 SPASS spent 0:00:00.22 on the problem.
% 0.39/0.58 0:00:00.03 for the input.
% 0.39/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.39/0.58 0:00:00.01 for inferences.
% 0.39/0.58 0:00:00.00 for the backtracking.
% 0.39/0.58 0:00:00.16 for the reduction.
% 0.39/0.58
% 0.39/0.58
% 0.39/0.58 Here is a proof with depth 6, length 117 :
% 0.39/0.58 % SZS output start Refutation
% See solution above
% 0.41/0.60 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.41/0.60
%------------------------------------------------------------------------------