TSTP Solution File: GRP437-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 11:47:28 EDT 2022

% Result   : Unsatisfiable 62.90s 63.08s
% Output   : Refutation 63.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   48
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   81 (  81 unt;   0 nHn;  81 RR)
%            Number of literals    :   81 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   15 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),u))))),x),
    file('GRP437-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP437-1.p',unknown),
    [] ).

cnf(3,plain,
    equal(multiply(u,inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,x))),inverse(y))),multiply(y,multiply(w,u))))),x),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(5,plain,
    equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),y)))),multiply(z,multiply(multiply(inverse(z),inverse(x)),u))))),y),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(15,plain,
    equal(multiply(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,u))),x)))),inverse(multiply(multiply(y,multiply(multiply(inverse(y),inverse(multiply(x,z))),inverse(x1))),multiply(x1,w)))),z),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.0,3.0')] ).

cnf(17,plain,
    equal(multiply(u,inverse(multiply(multiply(v,multiply(w,inverse(x))),multiply(x,multiply(y,u))))),multiply(z,multiply(multiply(inverse(z),inverse(multiply(w,y))),inverse(v)))),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.0,3.0')] ).

cnf(27,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,x))),w))),inverse(v))),x),
    inference(spr,[status(thm),theory(equality)],[17,3]),
    [iquote('0:SpR:17.0,3.0')] ).

cnf(83,plain,
    equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),y)))),multiply(z,multiply(multiply(inverse(z),inverse(x)),x1)))),multiply(x2,multiply(multiply(inverse(x2),inverse(y)),u))))),x1),
    inference(spr,[status(thm),theory(equality)],[1,5]),
    [iquote('0:SpR:1.0,5.0')] ).

cnf(104,plain,
    equal(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u))))),multiply(y,multiply(multiply(inverse(y),inverse(multiply(multiply(inverse(z),inverse(multiply(multiply(inverse(w),inverse(multiply(x1,v))),x1))),x))),inverse(z)))),
    inference(spr,[status(thm),theory(equality)],[27,17]),
    [iquote('0:SpR:27.0,17.0')] ).

cnf(105,plain,
    equal(multiply(inverse(u),inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(multiply(multiply(inverse(w),inverse(multiply(multiply(inverse(u),inverse(multiply(x,y))),x))),z))),inverse(w))),y))),z),
    inference(spr,[status(thm),theory(equality)],[27,3]),
    [iquote('0:SpR:27.0,3.0')] ).

cnf(117,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,y))),inverse(z))))),x1))),inverse(v))),inverse(multiply(multiply(z,multiply(x,inverse(x2))),multiply(x2,multiply(y,x1))))),
    inference(spr,[status(thm),theory(equality)],[17,27]),
    [iquote('0:SpR:17.0,27.0')] ).

cnf(119,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,inverse(multiply(w,multiply(x,multiply(multiply(inverse(x),inverse(multiply(y,w))),v))))))),inverse(z))),multiply(x1,multiply(multiply(inverse(x1),inverse(y)),inverse(z)))),
    inference(spr,[status(thm),theory(equality)],[5,27]),
    [iquote('0:SpR:5.0,27.0')] ).

cnf(122,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(v)),inverse(w))),multiply(x,multiply(multiply(inverse(x),inverse(v)),inverse(w)))),
    inference(rew,[status(thm),theory(equality)],[1,119]),
    [iquote('0:Rew:1.0,119.0')] ).

cnf(161,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(multiply(inverse(w),inverse(x)),inverse(y))))),z))),inverse(v))),multiply(multiply(inverse(z),inverse(x)),inverse(y))),
    inference(spr,[status(thm),theory(equality)],[122,27]),
    [iquote('0:SpR:122.0,27.0')] ).

cnf(181,plain,
    equal(inverse(multiply(multiply(u,multiply(v,inverse(w))),multiply(w,multiply(x,y)))),multiply(multiply(inverse(y),inverse(multiply(v,x))),inverse(u))),
    inference(rew,[status(thm),theory(equality)],[161,117]),
    [iquote('0:Rew:161.0,117.0')] ).

cnf(304,plain,
    equal(multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(multiply(inverse(w),inverse(multiply(x,y))),x))),z))),inverse(v)),inverse(multiply(y,multiply(w,multiply(z,u))))),
    inference(spr,[status(thm),theory(equality)],[27,181]),
    [iquote('0:SpR:27.0,181.0')] ).

cnf(307,plain,
    equal(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u))))),multiply(y,inverse(multiply(v,multiply(w,multiply(x,y)))))),
    inference(rew,[status(thm),theory(equality)],[304,104]),
    [iquote('0:Rew:304.0,104.0')] ).

cnf(308,plain,
    equal(multiply(inverse(u),inverse(multiply(multiply(v,inverse(multiply(w,multiply(u,multiply(x,v))))),w))),x),
    inference(rew,[status(thm),theory(equality)],[304,105]),
    [iquote('0:Rew:304.0,105.0')] ).

cnf(322,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,inverse(multiply(x,multiply(y,multiply(v,w)))))))),inverse(y))),x),
    inference(spr,[status(thm),theory(equality)],[308,27]),
    [iquote('0:SpR:308.0,27.0')] ).

cnf(340,plain,
    equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,x))),w))),multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(y,x))),y)))),
    inference(spr,[status(thm),theory(equality)],[27,308]),
    [iquote('0:SpR:27.0,308.0')] ).

cnf(613,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(inverse(w),inverse(multiply(multiply(inverse(x),inverse(multiply(y,z))),y))))),inverse(w)))),inverse(v))),inverse(multiply(multiply(inverse(x),inverse(multiply(x1,z))),x1))),
    inference(spr,[status(thm),theory(equality)],[340,27]),
    [iquote('0:SpR:340.0,27.0')] ).

cnf(663,plain,
    equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,w))),v)),inverse(multiply(multiply(inverse(u),inverse(multiply(x,w))),x))),
    inference(rew,[status(thm),theory(equality)],[27,613]),
    [iquote('0:Rew:27.0,613.0')] ).

cnf(718,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,inverse(multiply(multiply(inverse(x),inverse(multiply(y,z))),y)))))),inverse(x1))),multiply(inverse(x),inverse(multiply(multiply(x1,multiply(v,w)),z)))),
    inference(spr,[status(thm),theory(equality)],[663,322]),
    [iquote('0:SpR:663.0,322.0')] ).

cnf(792,plain,
    equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),inverse(u)))))),v)),inverse(multiply(y,inverse(multiply(z,multiply(x1,multiply(multiply(inverse(x1),inverse(multiply(x,z))),y))))))),
    inference(spr,[status(thm),theory(equality)],[5,663]),
    [iquote('0:SpR:5.0,663.0')] ).

cnf(803,plain,
    equal(inverse(multiply(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),inverse(u)))))),v)),inverse(x)),
    inference(rew,[status(thm),theory(equality)],[1,792]),
    [iquote('0:Rew:1.0,792.0')] ).

cnf(1045,plain,
    equal(inverse(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),u))))),v)),inverse(x)),
    inference(spr,[status(thm),theory(equality)],[307,803]),
    [iquote('0:SpR:307.0,803.0')] ).

cnf(1130,plain,
    equal(inverse(multiply(multiply(u,multiply(multiply(inverse(u),inverse(multiply(v,multiply(inverse(w),inverse(x))))),inverse(y))),multiply(y,multiply(v,inverse(w))))),inverse(x)),
    inference(spr,[status(thm),theory(equality)],[181,1045]),
    [iquote('0:SpR:181.0,1045.0')] ).

cnf(1142,plain,
    equal(multiply(multiply(inverse(inverse(u)),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(inverse(u),inverse(x))))),w))),inverse(v)),inverse(x)),
    inference(rew,[status(thm),theory(equality)],[181,1130]),
    [iquote('0:Rew:181.0,1130.0')] ).

cnf(1281,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(inverse(w))),multiply(inverse(inverse(x)),inverse(multiply(multiply(inverse(y),inverse(multiply(z,multiply(inverse(x),inverse(w))))),z)))))),inverse(v))),inverse(y)),
    inference(spr,[status(thm),theory(equality)],[1142,27]),
    [iquote('0:SpR:1142.0,27.0')] ).

cnf(1343,plain,
    equal(multiply(inverse(u),inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(inverse(w))),inverse(inverse(x)))),multiply(inverse(x),inverse(w))))),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[718,1281]),
    [iquote('0:Rew:718.0,1281.0')] ).

cnf(1767,plain,
    equal(multiply(u,multiply(inverse(u),inverse(v))),multiply(w,multiply(multiply(inverse(w),inverse(multiply(multiply(x,multiply(multiply(inverse(x),inverse(inverse(y))),inverse(inverse(z)))),multiply(inverse(z),inverse(y))))),inverse(v)))),
    inference(spr,[status(thm),theory(equality)],[1343,122]),
    [iquote('0:SpR:1343.0,122.0')] ).

cnf(1785,plain,
    equal(inverse(multiply(multiply(inverse(u),inverse(inverse(v))),inverse(v))),inverse(multiply(multiply(inverse(u),inverse(multiply(w,inverse(multiply(multiply(x,multiply(multiply(inverse(x),inverse(inverse(y))),inverse(inverse(z)))),multiply(inverse(z),inverse(y))))))),w))),
    inference(spr,[status(thm),theory(equality)],[1343,663]),
    [iquote('0:SpR:1343.0,663.0')] ).

cnf(1848,plain,
    equal(multiply(u,multiply(inverse(u),inverse(v))),multiply(w,multiply(inverse(w),inverse(v)))),
    inference(rew,[status(thm),theory(equality)],[1343,1767]),
    [iquote('0:Rew:1343.0,1767.0')] ).

cnf(1936,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(inverse(v),multiply(inverse(w),inverse(multiply(x,multiply(y,multiply(inverse(y),inverse(w))))))))),inverse(v))),x),
    inference(spr,[status(thm),theory(equality)],[1848,322]),
    [iquote('0:SpR:1848.0,322.0')] ).

cnf(1987,plain,
    equal(multiply(u,multiply(inverse(u),inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(inverse(w))),inverse(inverse(x)))),multiply(inverse(x),inverse(w)))))),multiply(y,inverse(y))),
    inference(spr,[status(thm),theory(equality)],[1343,1848]),
    [iquote('0:SpR:1343.0,1848.0')] ).

cnf(1995,plain,
    equal(multiply(u,inverse(u)),multiply(v,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[1343,1987]),
    [iquote('0:Rew:1343.0,1987.0')] ).

cnf(2007,plain,
    equal(multiply(u,multiply(v,inverse(v))),multiply(w,multiply(inverse(w),inverse(inverse(u))))),
    inference(spr,[status(thm),theory(equality)],[1995,1848]),
    [iquote('0:SpR:1995.0,1848.0')] ).

cnf(2070,plain,
    equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(u,multiply(x,inverse(x)))))),w))),v),
    inference(spr,[status(thm),theory(equality)],[1995,308]),
    [iquote('0:SpR:1995.0,308.0')] ).

cnf(2079,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(w)))),x))),inverse(v))),inverse(x)),
    inference(spr,[status(thm),theory(equality)],[1995,27]),
    [iquote('0:SpR:1995.0,27.0')] ).

cnf(2778,plain,
    equal(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,multiply(u,multiply(x,inverse(x)))))),w))),multiply(multiply(y,inverse(multiply(z,multiply(x1,multiply(multiply(inverse(x1),inverse(v)),y))))),z)),
    inference(spr,[status(thm),theory(equality)],[1045,2070]),
    [iquote('0:SpR:1045.0,2070.0')] ).

cnf(2783,plain,
    equal(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(x,v))),inverse(u)))))),multiply(y,multiply(z,multiply(multiply(inverse(z),inverse(multiply(multiply(x1,inverse(x1)),y))),x)))),
    inference(spr,[status(thm),theory(equality)],[15,2070]),
    [iquote('0:SpR:15.0,2070.0')] ).

cnf(2820,plain,
    equal(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(multiply(w,inverse(w)),u))),x))),x),
    inference(rew,[status(thm),theory(equality)],[1,2783]),
    [iquote('0:Rew:1.0,2783.0')] ).

cnf(2823,plain,
    equal(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(x)),u))))),v),x),
    inference(rew,[status(thm),theory(equality)],[2070,2778]),
    [iquote('0:Rew:2070.0,2778.0')] ).

cnf(3022,plain,
    equal(multiply(multiply(u,inverse(multiply(v,multiply(w,multiply(multiply(x,inverse(x)),u))))),v),inverse(w)),
    inference(spr,[status(thm),theory(equality)],[322,2820]),
    [iquote('0:SpR:322.0,2820.0')] ).

cnf(3457,plain,
    equal(multiply(u,inverse(multiply(multiply(v,multiply(multiply(inverse(v),inverse(w)),inverse(x))),multiply(x,w)))),u),
    inference(spr,[status(thm),theory(equality)],[2823,1]),
    [iquote('0:SpR:2823.0,1.0')] ).

cnf(3592,plain,
    equal(multiply(multiply(u,inverse(u)),v),multiply(multiply(w,inverse(w)),v)),
    inference(spr,[status(thm),theory(equality)],[2820,2823]),
    [iquote('0:SpR:2820.0,2823.0')] ).

cnf(3610,plain,
    equal(inverse(multiply(multiply(inverse(u),inverse(inverse(v))),inverse(v))),inverse(multiply(multiply(inverse(u),inverse(w)),w))),
    inference(rew,[status(thm),theory(equality)],[3457,1785]),
    [iquote('0:Rew:3457.0,1785.0')] ).

cnf(3717,plain,
    equal(multiply(multiply(u,inverse(u)),inverse(multiply(v,inverse(v)))),multiply(w,inverse(w))),
    inference(spr,[status(thm),theory(equality)],[3592,1995]),
    [iquote('0:SpR:3592.0,1995.0')] ).

cnf(3844,plain,
    equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(w,inverse(w)),multiply(inverse(multiply(x,inverse(x))),inverse(inverse(u))))),
    inference(spr,[status(thm),theory(equality)],[3592,2007]),
    [iquote('0:SpR:3592.0,2007.0')] ).

cnf(3957,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(w)))),multiply(x,inverse(x))))),inverse(v))),inverse(multiply(y,inverse(y)))),
    inference(spr,[status(thm),theory(equality)],[3717,27]),
    [iquote('0:SpR:3717.0,27.0')] ).

cnf(4081,plain,
    equal(inverse(multiply(u,inverse(u))),inverse(multiply(v,inverse(v)))),
    inference(rew,[status(thm),theory(equality)],[2079,3957]),
    [iquote('0:Rew:2079.0,3957.0')] ).

cnf(4145,plain,
    equal(inverse(multiply(u,inverse(u))),inverse(multiply(multiply(v,inverse(v)),inverse(multiply(w,inverse(w)))))),
    inference(spr,[status(thm),theory(equality)],[4081]),
    [iquote('0:SpR:4081.0,4081.0')] ).

cnf(4973,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(inverse(v),multiply(w,multiply(multiply(x,inverse(x)),inverse(y)))))),inverse(v))),multiply(y,inverse(w))),
    inference(spr,[status(thm),theory(equality)],[3022,122]),
    [iquote('0:SpR:3022.0,122.0')] ).

cnf(5129,plain,
    equal(multiply(u,inverse(multiply(inverse(v),multiply(w,multiply(multiply(inverse(w),inverse(multiply(multiply(inverse(x),inverse(y)),y))),u))))),multiply(inverse(x),inverse(inverse(v)))),
    inference(spr,[status(thm),theory(equality)],[3610,1]),
    [iquote('0:SpR:3610.0,1.0')] ).

cnf(5149,plain,
    equal(inverse(multiply(u,inverse(u))),inverse(multiply(multiply(inverse(multiply(v,inverse(v))),inverse(w)),w))),
    inference(spr,[status(thm),theory(equality)],[3610,4145]),
    [iquote('0:SpR:3610.0,4145.0')] ).

cnf(5419,plain,
    equal(multiply(u,inverse(multiply(inverse(v),multiply(w,multiply(multiply(inverse(w),inverse(multiply(multiply(inverse(multiply(x,inverse(x))),inverse(y)),y))),u))))),v),
    inference(spr,[status(thm),theory(equality)],[5149,1]),
    [iquote('0:SpR:5149.0,1.0')] ).

cnf(5536,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),inverse(multiply(w,inverse(w)))),multiply(inverse(multiply(x,inverse(x))),inverse(y))))),inverse(v))),y),
    inference(spr,[status(thm),theory(equality)],[5149,27]),
    [iquote('0:SpR:5149.0,27.0')] ).

cnf(5558,plain,
    equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(multiply(inverse(multiply(w,inverse(w))),inverse(x)),x),multiply(inverse(multiply(y,inverse(y))),inverse(inverse(u))))),
    inference(spr,[status(thm),theory(equality)],[5149,2007]),
    [iquote('0:SpR:5149.0,2007.0')] ).

cnf(5690,plain,
    equal(multiply(inverse(multiply(u,inverse(u))),inverse(inverse(v))),v),
    inference(rew,[status(thm),theory(equality)],[5129,5419]),
    [iquote('0:Rew:5129.0,5419.0')] ).

cnf(5692,plain,
    equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(w,inverse(w)),u)),
    inference(rew,[status(thm),theory(equality)],[5690,3844]),
    [iquote('0:Rew:5690.0,3844.0')] ).

cnf(5695,plain,
    equal(multiply(u,multiply(v,inverse(v))),multiply(multiply(multiply(inverse(multiply(w,inverse(w))),inverse(x)),x),u)),
    inference(rew,[status(thm),theory(equality)],[5690,5558]),
    [iquote('0:Rew:5690.0,5558.0')] ).

cnf(5696,plain,
    equal(inverse(multiply(inverse(multiply(u,inverse(u))),inverse(v))),v),
    inference(rew,[status(thm),theory(equality)],[2079,5536]),
    [iquote('0:Rew:2079.0,5536.0')] ).

cnf(6145,plain,
    equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,multiply(w,multiply(multiply(inverse(w),inverse(multiply(inverse(x),v))),y)))),multiply(multiply(z,inverse(z)),multiply(x,x1)))),multiply(x2,multiply(multiply(inverse(x2),inverse(y)),u))))),x1),
    inference(spr,[status(thm),theory(equality)],[5690,83]),
    [iquote('0:SpR:5690.0,83.0')] ).

cnf(6273,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(multiply(inverse(v),w),inverse(multiply(x,inverse(x)))))),inverse(v))),inverse(w)),
    inference(spr,[status(thm),theory(equality)],[5696,27]),
    [iquote('0:SpR:5696.0,27.0')] ).

cnf(6428,plain,
    equal(inverse(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u)))))),multiply(v,multiply(w,multiply(x,inverse(multiply(y,inverse(y))))))),
    inference(spr,[status(thm),theory(equality)],[307,5696]),
    [iquote('0:SpR:307.0,5696.0')] ).

cnf(6509,plain,
    equal(multiply(u,inverse(multiply(inverse(multiply(v,multiply(multiply(w,inverse(w)),x))),multiply(y,multiply(multiply(inverse(y),inverse(z)),u))))),inverse(multiply(inverse(x),inverse(multiply(z,v))))),
    inference(spr,[status(thm),theory(equality)],[5692,5]),
    [iquote('0:SpR:5692.0,5.0')] ).

cnf(6737,plain,
    equal(inverse(multiply(inverse(multiply(u,v)),inverse(multiply(w,inverse(multiply(x,multiply(y,multiply(multiply(inverse(y),inverse(multiply(inverse(u),x))),w)))))))),v),
    inference(rew,[status(thm),theory(equality)],[6509,6145]),
    [iquote('0:Rew:6509.0,6145.0')] ).

cnf(6743,plain,
    equal(inverse(multiply(inverse(multiply(u,v)),inverse(inverse(u)))),v),
    inference(rew,[status(thm),theory(equality)],[1,6737]),
    [iquote('0:Rew:1.0,6737.0')] ).

cnf(6930,plain,
    equal(inverse(multiply(u,multiply(v,multiply(multiply(inverse(v),inverse(multiply(w,u))),x)))),inverse(multiply(inverse(w),inverse(inverse(x))))),
    inference(spr,[status(thm),theory(equality)],[1,6743]),
    [iquote('0:SpR:1.0,6743.0')] ).

cnf(6968,plain,
    equal(multiply(u,inverse(multiply(inverse(v),inverse(inverse(u))))),v),
    inference(rew,[status(thm),theory(equality)],[6930,1]),
    [iquote('0:Rew:6930.0,1.0')] ).

cnf(10703,plain,
    equal(multiply(u,inverse(multiply(v,inverse(v)))),u),
    inference(spr,[status(thm),theory(equality)],[1995,6968]),
    [iquote('0:SpR:1995.0,6968.0')] ).

cnf(10768,plain,
    equal(inverse(multiply(u,inverse(multiply(v,multiply(w,multiply(x,u)))))),multiply(v,multiply(w,x))),
    inference(rew,[status(thm),theory(equality)],[10703,6428]),
    [iquote('0:Rew:10703.0,6428.0')] ).

cnf(10780,plain,
    equal(multiply(u,multiply(multiply(inverse(u),inverse(multiply(inverse(v),w))),inverse(v))),inverse(w)),
    inference(rew,[status(thm),theory(equality)],[10703,6273]),
    [iquote('0:Rew:10703.0,6273.0')] ).

cnf(11012,plain,
    equal(inverse(multiply(u,multiply(multiply(v,inverse(v)),inverse(w)))),multiply(w,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[10780,4973]),
    [iquote('0:Rew:10780.0,4973.0')] ).

cnf(11015,plain,
    equal(inverse(multiply(inverse(u),inverse(multiply(v,multiply(w,multiply(inverse(w),inverse(u))))))),v),
    inference(rew,[status(thm),theory(equality)],[10780,1936]),
    [iquote('0:Rew:10780.0,1936.0')] ).

cnf(11108,plain,
    equal(multiply(u,multiply(v,inverse(v))),u),
    inference(rew,[status(thm),theory(equality)],[10768,11015]),
    [iquote('0:Rew:10768.0,11015.0')] ).

cnf(11153,plain,
    equal(multiply(multiply(u,inverse(u)),v),v),
    inference(rew,[status(thm),theory(equality)],[11108,5692]),
    [iquote('0:Rew:11108.0,5692.0')] ).

cnf(11201,plain,
    equal(multiply(multiply(multiply(inverse(multiply(u,inverse(u))),inverse(v)),v),w),w),
    inference(rew,[status(thm),theory(equality)],[11108,5695]),
    [iquote('0:Rew:11108.0,5695.0')] ).

cnf(11556,plain,
    equal(inverse(multiply(u,inverse(v))),multiply(v,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[11153,11012]),
    [iquote('0:Rew:11153.0,11012.0')] ).

cnf(12376,plain,
    equal(multiply(multiply(inverse(u),u),v),v),
    inference(rew,[status(thm),theory(equality)],[11153,11201,11556]),
    [iquote('0:Rew:11153.0,11201.0,11556.0,11201.0')] ).

cnf(12377,plain,
    $false,
    inference(unc,[status(thm)],[12376,2]),
    [iquote('0:UnC:12376.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 20:55:09 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 62.90/63.08  
% 62.90/63.08  SPASS V 3.9 
% 62.90/63.08  SPASS beiseite: Proof found.
% 62.90/63.08  % SZS status Theorem
% 62.90/63.08  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 62.90/63.08  SPASS derived 10371 clauses, backtracked 0 clauses, performed 0 splits and kept 4559 clauses.
% 62.90/63.08  SPASS allocated 118964 KBytes.
% 62.90/63.08  SPASS spent	0:01:02.72 on the problem.
% 62.90/63.08  		0:00:00.02 for the input.
% 62.90/63.08  		0:00:00.00 for the FLOTTER CNF translation.
% 62.90/63.08  		0:00:00.09 for inferences.
% 62.90/63.08  		0:00:00.00 for the backtracking.
% 62.90/63.08  		0:01:02.58 for the reduction.
% 62.90/63.08  
% 62.90/63.08  
% 62.90/63.08  Here is a proof with depth 22, length 81 :
% 62.90/63.08  % SZS output start Refutation
% See solution above
% 63.33/63.52  Formulae used in the proof : single_axiom prove_these_axioms_2
% 63.33/63.52  
%------------------------------------------------------------------------------