TSTP Solution File: GRP413-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP413-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 11:47:15 EDT 2022

% Result   : Unsatisfiable 29.52s 29.69s
% Output   : Refutation 29.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   77 (  77 unt;   0 nHn;  77 RR)
%            Number of literals    :   77 (   0 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   18 (   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(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))),w),
    file('GRP413-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP413-1.p',unknown),
    [] ).

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

cnf(4,plain,
    equal(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)))),x),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(24,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v)))),w),
    inference(spr,[status(thm),theory(equality)],[3,1]),
    [iquote('0:SpR:3.0,1.0')] ).

cnf(29,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(w))),inverse(u))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(w),w),inverse(x))),y))),x)))),u)),multiply(v,inverse(multiply(y,w)))),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.0,3.0')] ).

cnf(39,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,v)))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),w))),x)),
    inference(spr,[status(thm),theory(equality)],[1,24]),
    [iquote('0:SpR:1.0,24.0')] ).

cnf(57,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(multiply(multiply(multiply(inverse(w),w),inverse(multiply(inverse(multiply(v,inverse(w))),x))),w)))),inverse(u))),multiply(inverse(x),y)))),u)),y),
    inference(spr,[status(thm),theory(equality)],[4,3]),
    [iquote('0:SpR:4.0,3.0')] ).

cnf(62,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,v)))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),y))),x)),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),y))),x)),inverse(multiply(inverse(y),w))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),y))),x))),
    inference(spr,[status(thm),theory(equality)],[4,24]),
    [iquote('0:SpR:4.0,24.0')] ).

cnf(88,plain,
    equal(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))),inverse(multiply(inverse(x),y))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))))),y),
    inference(spr,[status(thm),theory(equality)],[1,4]),
    [iquote('0:SpR:1.0,4.0')] ).

cnf(99,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(v),inverse(u))),multiply(inverse(v),w)))),u)),w),
    inference(rew,[status(thm),theory(equality)],[1,57]),
    [iquote('0:Rew:1.0,57.0')] ).

cnf(107,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,inverse(u))),multiply(v,w)))),u)),w),
    inference(spr,[status(thm),theory(equality)],[99]),
    [iquote('0:SpR:99.0,99.0')] ).

cnf(151,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,w)),multiply(inverse(multiply(x,inverse(v))),multiply(x,w))),
    inference(spr,[status(thm),theory(equality)],[107,24]),
    [iquote('0:SpR:107.0,24.0')] ).

cnf(211,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
    inference(spr,[status(thm),theory(equality)],[107,151]),
    [iquote('0:SpR:107.0,151.0')] ).

cnf(223,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(w,inverse(v))),x))),v)))),multiply(u,y)),multiply(inverse(x),multiply(w,y))),
    inference(spr,[status(thm),theory(equality)],[1,151]),
    [iquote('0:SpR:1.0,151.0')] ).

cnf(275,plain,
    equal(multiply(inverse(multiply(inverse(multiply(u,v)),w)),multiply(inverse(multiply(x,v)),multiply(x,y))),multiply(inverse(multiply(z,w)),multiply(z,multiply(u,y)))),
    inference(spr,[status(thm),theory(equality)],[211]),
    [iquote('0:SpR:211.0,211.0')] ).

cnf(297,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(x,multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(y,inverse(v))),multiply(y,x)))),w))),
    inference(spr,[status(thm),theory(equality)],[107,211]),
    [iquote('0:SpR:107.0,211.0')] ).

cnf(749,plain,
    equal(multiply(inverse(u),multiply(inverse(multiply(v,w)),multiply(v,x))),multiply(inverse(multiply(y,inverse(multiply(multiply(multiply(inverse(z),z),inverse(multiply(inverse(multiply(inverse(multiply(x1,w)),inverse(z))),u))),z)))),multiply(y,multiply(x1,x)))),
    inference(spr,[status(thm),theory(equality)],[1,275]),
    [iquote('0:SpR:1.0,275.0')] ).

cnf(784,plain,
    equal(multiply(inverse(u),multiply(inverse(multiply(v,w)),multiply(v,x))),multiply(inverse(u),multiply(inverse(multiply(y,w)),multiply(y,x)))),
    inference(rew,[status(thm),theory(equality)],[223,749]),
    [iquote('0:Rew:223.0,749.0')] ).

cnf(851,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(inverse(multiply(v,inverse(w))),inverse(u))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(w),w),inverse(x))),multiply(inverse(multiply(y,z)),multiply(y,x1))))),x)))),u)),multiply(v,inverse(multiply(multiply(inverse(multiply(x2,z)),multiply(x2,x1)),w)))),
    inference(spr,[status(thm),theory(equality)],[784,29]),
    [iquote('0:SpR:784.0,29.0')] ).

cnf(975,plain,
    equal(multiply(u,multiply(inverse(multiply(v,w)),multiply(v,x))),multiply(u,multiply(inverse(multiply(y,w)),multiply(y,x)))),
    inference(spr,[status(thm),theory(equality)],[107,784]),
    [iquote('0:SpR:107.0,784.0')] ).

cnf(991,plain,
    equal(multiply(u,inverse(multiply(multiply(inverse(multiply(v,w)),multiply(v,x)),y))),multiply(u,inverse(multiply(multiply(inverse(multiply(z,w)),multiply(z,x)),y)))),
    inference(rew,[status(thm),theory(equality)],[29,851]),
    [iquote('0:Rew:29.0,851.0')] ).

cnf(1750,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,inverse(u))),multiply(v,inverse(multiply(multiply(inverse(multiply(w,x)),multiply(w,y)),z)))))),u)),inverse(multiply(multiply(inverse(multiply(x1,x)),multiply(x1,y)),z))),
    inference(spr,[status(thm),theory(equality)],[991,107]),
    [iquote('0:SpR:991.0,107.0')] ).

cnf(1897,plain,
    equal(inverse(multiply(multiply(inverse(multiply(u,v)),multiply(u,w)),x)),inverse(multiply(multiply(inverse(multiply(y,v)),multiply(y,w)),x))),
    inference(rew,[status(thm),theory(equality)],[107,1750]),
    [iquote('0:Rew:107.0,1750.0')] ).

cnf(2740,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,w)),multiply(v,w)))),u)),multiply(x,inverse(multiply(multiply(multiply(inverse(y),y),inverse(multiply(inverse(multiply(x,inverse(y))),inverse(u)))),y)))),
    inference(spr,[status(thm),theory(equality)],[297,29]),
    [iquote('0:SpR:297.0,29.0')] ).

cnf(2923,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(v,w)),multiply(v,w)))),u)),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[1,2740]),
    [iquote('0:Rew:1.0,2740.0')] ).

cnf(2986,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),u)),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[24,2923]),
    [iquote('0:SpR:24.0,2923.0')] ).

cnf(3117,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(v))),multiply(inverse(w),w)),
    inference(spr,[status(thm),theory(equality)],[2986,24]),
    [iquote('0:SpR:2986.0,24.0')] ).

cnf(3145,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v)))),multiply(multiply(multiply(inverse(w),w),inverse(multiply(inverse(x),x))),w)),
    inference(spr,[status(thm),theory(equality)],[2986,24]),
    [iquote('0:SpR:2986.0,24.0')] ).

cnf(3203,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),u),u),
    inference(rew,[status(thm),theory(equality)],[24,3145]),
    [iquote('0:Rew:24.0,3145.0')] ).

cnf(3482,plain,
    equal(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(u),u),inverse(v)),u))),inverse(multiply(multiply(multiply(inverse(u),u),inverse(v)),u))),inverse(multiply(inverse(w),w))),inverse(u))),inverse(multiply(multiply(multiply(inverse(u),u),inverse(v)),u))),v),
    inference(spr,[status(thm),theory(equality)],[3203,24]),
    [iquote('0:SpR:3203.0,24.0')] ).

cnf(3489,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(w),w))),inverse(u))),v))),u)),v),
    inference(spr,[status(thm),theory(equality)],[3203,107]),
    [iquote('0:SpR:3203.0,107.0')] ).

cnf(3506,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,v)),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[3203,297]),
    [iquote('0:SpR:3203.0,297.0')] ).

cnf(3702,plain,
    equal(multiply(inverse(inverse(u)),inverse(u)),multiply(inverse(v),v)),
    inference(rew,[status(thm),theory(equality)],[3506,3117]),
    [iquote('0:Rew:3506.0,3117.0')] ).

cnf(3715,plain,
    equal(multiply(u,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(x),y))),multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v)),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),w))),v))))),y),
    inference(rew,[status(thm),theory(equality)],[3506,88]),
    [iquote('0:Rew:3506.0,88.0')] ).

cnf(3729,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(w,v)))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(y),w))),multiply(multiply(multiply(inverse(x),x),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(x))),y))),x))),
    inference(rew,[status(thm),theory(equality)],[3506,62]),
    [iquote('0:Rew:3506.0,62.0')] ).

cnf(3820,plain,
    equal(multiply(u,inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(y),w))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(u,inverse(v))),y))),v))))),x),
    inference(rew,[status(thm),theory(equality)],[3506,3715]),
    [iquote('0:Rew:3506.0,3715.0')] ).

cnf(3838,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),inverse(w)),inverse(w)),
    inference(spr,[status(thm),theory(equality)],[3702,3203]),
    [iquote('0:SpR:3702.0,3203.0')] ).

cnf(3842,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(inverse(v)),inverse(multiply(multiply(multiply(inverse(v),v),inverse(w)),v)))),w),
    inference(spr,[status(thm),theory(equality)],[3702,24]),
    [iquote('0:SpR:3702.0,24.0')] ).

cnf(3849,plain,
    equal(multiply(inverse(u),u),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[3702]),
    [iquote('0:SpR:3702.0,3702.0')] ).

cnf(3911,plain,
    equal(inverse(multiply(multiply(inverse(multiply(u,v)),multiply(u,v)),w)),inverse(multiply(multiply(inverse(inverse(x)),inverse(x)),w))),
    inference(spr,[status(thm),theory(equality)],[3702,1897]),
    [iquote('0:SpR:3702.0,1897.0')] ).

cnf(3917,plain,
    equal(multiply(u,multiply(inverse(multiply(v,w)),multiply(v,w))),multiply(u,multiply(inverse(inverse(x)),inverse(x)))),
    inference(spr,[status(thm),theory(equality)],[3702,975]),
    [iquote('0:SpR:3702.0,975.0')] ).

cnf(3925,plain,
    equal(multiply(inverse(multiply(u,inverse(v))),multiply(u,inverse(multiply(multiply(multiply(inverse(inverse(w)),inverse(w)),inverse(x)),v)))),x),
    inference(spr,[status(thm),theory(equality)],[3702,24]),
    [iquote('0:SpR:3702.0,24.0')] ).

cnf(3975,plain,
    equal(multiply(inverse(multiply(inverse(inverse(u)),inverse(u))),multiply(inverse(v),w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
    inference(spr,[status(thm),theory(equality)],[3702,211]),
    [iquote('0:SpR:3702.0,211.0')] ).

cnf(4034,plain,
    equal(multiply(inverse(inverse(u)),inverse(multiply(multiply(multiply(inverse(u),u),inverse(v)),u))),v),
    inference(rew,[status(thm),theory(equality)],[3838,3482]),
    [iquote('0:Rew:3838.0,3482.0')] ).

cnf(4035,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(u)),v))),u)),v),
    inference(rew,[status(thm),theory(equality)],[3838,3489]),
    [iquote('0:Rew:3838.0,3489.0')] ).

cnf(4045,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),v),v),
    inference(rew,[status(thm),theory(equality)],[4034,3842]),
    [iquote('0:Rew:4034.0,3842.0')] ).

cnf(4047,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
    inference(rew,[status(thm),theory(equality)],[4045,3975]),
    [iquote('0:Rew:4045.0,3975.0')] ).

cnf(4398,plain,
    equal(multiply(u,multiply(inverse(v),v)),multiply(u,multiply(inverse(inverse(w)),inverse(w)))),
    inference(rew,[status(thm),theory(equality)],[4047,3917]),
    [iquote('0:Rew:4047.0,3917.0')] ).

cnf(4704,plain,
    equal(inverse(multiply(multiply(inverse(u),u),v)),inverse(multiply(multiply(inverse(inverse(w)),inverse(w)),v))),
    inference(rew,[status(thm),theory(equality)],[4047,3911]),
    [iquote('0:Rew:4047.0,3911.0')] ).

cnf(4757,plain,
    equal(multiply(inverse(inverse(u)),inverse(multiply(multiply(multiply(inverse(inverse(v)),inverse(v)),inverse(w)),u))),w),
    inference(rew,[status(thm),theory(equality)],[4047,3925]),
    [iquote('0:Rew:4047.0,3925.0')] ).

cnf(4811,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(multiply(inverse(v),v),inverse(u))),w))),u),multiply(inverse(inverse(v)),inverse(multiply(w,v)))),
    inference(rew,[status(thm),theory(equality)],[4047,39]),
    [iquote('0:Rew:4047.0,39.0')] ).

cnf(4812,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),w))),multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(multiply(multiply(inverse(x),x),inverse(u))),v))),u)),multiply(inverse(inverse(x)),inverse(multiply(w,x)))),
    inference(rew,[status(thm),theory(equality)],[4047,3729]),
    [iquote('0:Rew:4047.0,3729.0')] ).

cnf(5357,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),w))),multiply(inverse(inverse(x)),inverse(multiply(v,x)))),multiply(inverse(inverse(x)),inverse(multiply(w,x)))),
    inference(rew,[status(thm),theory(equality)],[4811,4812]),
    [iquote('0:Rew:4811.0,4812.0')] ).

cnf(6148,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),w),w),
    inference(spr,[status(thm),theory(equality)],[3849,3203]),
    [iquote('0:SpR:3849.0,3203.0')] ).

cnf(6167,plain,
    ~ equal(multiply(multiply(inverse(u),u),a2),a2),
    inference(spl,[status(thm),theory(equality)],[3849,2]),
    [iquote('0:SpL:3849.0,2.0')] ).

cnf(6374,plain,
    equal(multiply(u,multiply(inverse(v),v)),multiply(u,multiply(inverse(w),w))),
    inference(spr,[status(thm),theory(equality)],[4398]),
    [iquote('0:SpR:4398.0,4398.0')] ).

cnf(6629,plain,
    equal(inverse(multiply(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(v)),w))),v)),w),
    inference(spr,[status(thm),theory(equality)],[3849,4035]),
    [iquote('0:SpR:3849.0,4035.0')] ).

cnf(6743,plain,
    equal(inverse(multiply(multiply(inverse(u),u),v)),inverse(multiply(multiply(inverse(w),w),v))),
    inference(spr,[status(thm),theory(equality)],[4704]),
    [iquote('0:SpR:4704.0,4704.0')] ).

cnf(6926,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(w),x))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(y),w))),multiply(multiply(multiply(inverse(v),v),inverse(multiply(inverse(multiply(multiply(inverse(z),z),inverse(v))),y))),v))))),x),
    inference(spr,[status(thm),theory(equality)],[6743,3820]),
    [iquote('0:SpR:6743.0,3820.0')] ).

cnf(7014,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(v)),inverse(multiply(w,v))))),w),
    inference(rew,[status(thm),theory(equality)],[5357,6926,4811]),
    [iquote('0:Rew:5357.0,6926.0,5357.0,6926.0,4811.0,6926.0')] ).

cnf(7057,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(v)),inverse(multiply(inverse(w),w))))),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[3849,7014]),
    [iquote('0:SpR:3849.0,7014.0')] ).

cnf(7098,plain,
    equal(multiply(inverse(u),inverse(multiply(multiply(multiply(inverse(inverse(v)),inverse(v)),inverse(w)),x))),multiply(inverse(multiply(inverse(inverse(x)),u)),w)),
    inference(spr,[status(thm),theory(equality)],[4757,4047]),
    [iquote('0:SpR:4757.0,4047.0')] ).

cnf(7117,plain,
    equal(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(multiply(multiply(inverse(inverse(v)),inverse(v)),inverse(w)),multiply(inverse(x),x)))),w),
    inference(spr,[status(thm),theory(equality)],[6374,4757]),
    [iquote('0:SpR:6374.0,4757.0')] ).

cnf(7122,plain,
    equal(multiply(inverse(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(v),v)))),w),w),
    inference(rew,[status(thm),theory(equality)],[7098,7117]),
    [iquote('0:Rew:7098.0,7117.0')] ).

cnf(7447,plain,
    equal(multiply(inverse(u),u),multiply(inverse(inverse(multiply(inverse(v),v))),inverse(multiply(inverse(w),w)))),
    inference(spr,[status(thm),theory(equality)],[7122,3849]),
    [iquote('0:SpR:7122.0,3849.0')] ).

cnf(7499,plain,
    ~ equal(multiply(multiply(inverse(inverse(multiply(inverse(u),u))),inverse(multiply(inverse(v),v))),a2),a2),
    inference(spl,[status(thm),theory(equality)],[7122,6167]),
    [iquote('0:SpL:7122.0,6167.0')] ).

cnf(7696,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),inverse(multiply(inverse(w),w))),
    inference(spr,[status(thm),theory(equality)],[7447,7014]),
    [iquote('0:SpR:7447.0,7014.0')] ).

cnf(9642,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),inverse(multiply(inverse(w),w))))),v),
    inference(spr,[status(thm),theory(equality)],[6629,7057]),
    [iquote('0:SpR:6629.0,7057.0')] ).

cnf(9765,plain,
    equal(multiply(multiply(inverse(u),u),inverse(inverse(multiply(inverse(v),v)))),multiply(inverse(w),w)),
    inference(spr,[status(thm),theory(equality)],[4045,9642]),
    [iquote('0:SpR:4045.0,9642.0')] ).

cnf(10338,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(inverse(inverse(inverse(inverse(multiply(inverse(v),v))))),inverse(multiply(inverse(w),w))))),multiply(inverse(x),x)),
    inference(spr,[status(thm),theory(equality)],[9765,7014]),
    [iquote('0:SpR:9765.0,7014.0')] ).

cnf(10474,plain,
    equal(inverse(inverse(inverse(multiply(inverse(u),u)))),multiply(inverse(v),v)),
    inference(rew,[status(thm),theory(equality)],[9642,10338]),
    [iquote('0:Rew:9642.0,10338.0')] ).

cnf(10533,plain,
    equal(multiply(multiply(inverse(u),u),inverse(multiply(multiply(inverse(v),v),inverse(multiply(w,inverse(multiply(inverse(x),x))))))),w),
    inference(spr,[status(thm),theory(equality)],[10474,7014]),
    [iquote('0:SpR:10474.0,7014.0')] ).

cnf(10620,plain,
    equal(inverse(inverse(multiply(multiply(inverse(u),u),inverse(multiply(inverse(v),v))))),multiply(inverse(w),w)),
    inference(spr,[status(thm),theory(equality)],[7696,10474]),
    [iquote('0:SpR:7696.0,10474.0')] ).

cnf(16932,plain,
    equal(multiply(multiply(multiply(inverse(u),u),inverse(multiply(multiply(inverse(v),v),inverse(multiply(multiply(inverse(w),w),inverse(multiply(inverse(x),x))))))),y),y),
    inference(spr,[status(thm),theory(equality)],[10620,6148]),
    [iquote('0:SpR:10620.0,6148.0')] ).

cnf(17276,plain,
    equal(multiply(multiply(inverse(u),u),v),v),
    inference(rew,[status(thm),theory(equality)],[10533,16932]),
    [iquote('0:Rew:10533.0,16932.0')] ).

cnf(17277,plain,
    $false,
    inference(unc,[status(thm)],[17276,7499]),
    [iquote('0:UnC:17276.0,7499.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GRP413-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n016.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 21:01:30 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 29.52/29.69  
% 29.52/29.69  SPASS V 3.9 
% 29.52/29.69  SPASS beiseite: Proof found.
% 29.52/29.69  % SZS status Theorem
% 29.52/29.69  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 29.52/29.69  SPASS derived 12337 clauses, backtracked 0 clauses, performed 0 splits and kept 3140 clauses.
% 29.52/29.69  SPASS allocated 121949 KBytes.
% 29.52/29.69  SPASS spent	0:0:29.33 on the problem.
% 29.52/29.69  		0:00:00.04 for the input.
% 29.52/29.69  		0:00:00.00 for the FLOTTER CNF translation.
% 29.52/29.69  		0:00:00.19 for inferences.
% 29.52/29.69  		0:00:00.00 for the backtracking.
% 29.52/29.69  		0:0:29.08 for the reduction.
% 29.52/29.69  
% 29.52/29.69  
% 29.52/29.69  Here is a proof with depth 18, length 77 :
% 29.52/29.69  % SZS output start Refutation
% See solution above
% 29.90/30.09  Formulae used in the proof : single_axiom prove_these_axioms_2
% 29.90/30.09  
%------------------------------------------------------------------------------