TSTP Solution File: GRP584-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   95 (  95 unt;   0 nHn;  95 RR)
%            Number of literals    :   95 (   0 equ;   1 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    :    9 (   9 usr;   6 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('GRP584-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
    file('GRP584-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(double_divide(u,identity),inverse(u)),
    file('GRP584-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(double_divide(u,inverse(u)),identity),
    file('GRP584-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(b,a),multiply(a,b)),
    file('GRP584-1.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(17,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(18,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(19,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(21,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)],[3,17]),
    [iquote('0:Rew:3.0,17.0')] ).

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)],[4,21]),
    [iquote('0:SpR:4.0,21.0')] ).

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)],[3,21]),
    [iquote('0:SpR:3.0,21.0')] ).

cnf(66,plain,
    equal(double_divide(double_divide(inverse(u),identity),inverse(identity)),double_divide(identity,u)),
    inference(spr,[status(thm),theory(equality)],[4,21]),
    [iquote('0:SpR:4.0,21.0')] ).

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)],[7,21]),
    [iquote('0:SpR:7.0,21.0')] ).

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(100,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)],[4,18]),
    [iquote('0:SpR:4.0,18.0')] ).

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)],[21,18]),
    [iquote('0:SpR:21.0,18.0')] ).

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)],[64,18]),
    [iquote('0:SpR:64.0,18.0')] ).

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)],[65,18]),
    [iquote('0:SpR:65.0,18.0')] ).

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)],[69,18]),
    [iquote('0:SpR:69.0,18.0')] ).

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(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)],[161,19]),
    [iquote('0:Rew:161.0,19.0')] ).

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)],[161,100]),
    [iquote('0:Rew:161.0,100.0')] ).

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(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(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(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(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(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(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(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(810,plain,
    $false,
    inference(unc,[status(thm)],[809,5]),
    [iquote('0:UnC:809.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n027.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 17:22:32 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.19/0.47  
% 0.19/0.47  SPASS V 3.9 
% 0.19/0.47  SPASS beiseite: Proof found.
% 0.19/0.47  % SZS status Theorem
% 0.19/0.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.47  SPASS derived 479 clauses, backtracked 0 clauses, performed 0 splits and kept 140 clauses.
% 0.19/0.47  SPASS allocated 63867 KBytes.
% 0.19/0.47  SPASS spent	0:00:00.11 on the problem.
% 0.19/0.47  		0:00:00.04 for the input.
% 0.19/0.47  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47  		0:00:00.00 for inferences.
% 0.19/0.47  		0:00:00.00 for the backtracking.
% 0.19/0.47  		0:00:00.05 for the reduction.
% 0.19/0.47  
% 0.19/0.47  
% 0.19/0.47  Here is a proof with depth 6, length 95 :
% 0.19/0.47  % SZS output start Refutation
% See solution above
% 0.19/0.48  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.19/0.48  
%------------------------------------------------------------------------------