TSTP Solution File: GRP405-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP405-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 11:47:13 EDT 2022

% Result   : Unsatisfiable 230.64s 230.82s
% Output   : Refutation 231.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   94 (  94 unt;   0 nHn;  94 RR)
%            Number of literals    :   94 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   16 (   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(inverse(multiply(inverse(multiply(u,v)),w)),inverse(multiply(v,multiply(inverse(v),v)))))),w),
    file('GRP405-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
    file('GRP405-1.p',unknown),
    [] ).

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

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

cnf(21,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(w),inverse(multiply(v,multiply(inverse(v),v))))))),w),
    inference(spr,[status(thm),theory(equality)],[4,1]),
    [iquote('0:SpR:4.0,1.0')] ).

cnf(28,plain,
    equal(multiply(u,inverse(multiply(inverse(v),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),inverse(multiply(w,multiply(inverse(w),w))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),inverse(multiply(w,multiply(inverse(w),w))))))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(x),y)),v)),inverse(multiply(y,multiply(inverse(y),y)))))),
    inference(spr,[status(thm),theory(equality)],[1,4]),
    [iquote('0:SpR:1.0,4.0')] ).

cnf(30,plain,
    equal(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),x)),y)),inverse(multiply(x,multiply(inverse(x),x)))))),inverse(multiply(v,multiply(inverse(v),v)))))),inverse(multiply(inverse(y),inverse(multiply(w,multiply(inverse(w),w)))))),
    inference(spr,[status(thm),theory(equality)],[1,4]),
    [iquote('0:SpR:1.0,4.0')] ).

cnf(41,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,inverse(multiply(inverse(x),inverse(multiply(y,multiply(inverse(y),y)))))))),multiply(inverse(multiply(inverse(multiply(w,y)),v)),x)),
    inference(spr,[status(thm),theory(equality)],[4,21]),
    [iquote('0:SpR:4.0,21.0')] ).

cnf(56,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),inverse(multiply(v,multiply(inverse(v),v))))))),x)),multiply(inverse(w),y))),inverse(multiply(x,multiply(inverse(x),x))))),y),
    inference(spr,[status(thm),theory(equality)],[3,4]),
    [iquote('0:SpR:3.0,4.0')] ).

cnf(100,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(u),w))),inverse(multiply(v,multiply(inverse(v),v))))),w),
    inference(rew,[status(thm),theory(equality)],[1,56]),
    [iquote('0:Rew:1.0,56.0')] ).

cnf(127,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(inverse(x),v)),multiply(inverse(x),w))),
    inference(spr,[status(thm),theory(equality)],[100,21]),
    [iquote('0:SpR:100.0,21.0')] ).

cnf(136,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),inverse(multiply(v,multiply(inverse(v),v))))),w),
    inference(spr,[status(thm),theory(equality)],[100]),
    [iquote('0:SpR:100.0,100.0')] ).

cnf(185,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
    inference(spr,[status(thm),theory(equality)],[127]),
    [iquote('0:SpR:127.0,127.0')] ).

cnf(210,plain,
    equal(multiply(inverse(multiply(u,multiply(v,inverse(multiply(inverse(w),inverse(multiply(x,multiply(inverse(x),x)))))))),multiply(u,y)),multiply(inverse(w),multiply(inverse(multiply(v,x)),y))),
    inference(spr,[status(thm),theory(equality)],[21,127]),
    [iquote('0:SpR:21.0,127.0')] ).

cnf(244,plain,
    equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,multiply(v,w))),x)),inverse(multiply(multiply(v,w),multiply(inverse(multiply(y,w)),multiply(y,w))))))),x),
    inference(spr,[status(thm),theory(equality)],[185,1]),
    [iquote('0:SpR:185.0,1.0')] ).

cnf(245,plain,
    equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,inverse(multiply(inverse(x),inverse(multiply(multiply(v,w),multiply(inverse(multiply(y,w)),multiply(y,w)))))))),x),
    inference(spr,[status(thm),theory(equality)],[185,21]),
    [iquote('0:SpR:185.0,21.0')] ).

cnf(249,plain,
    equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,x)),multiply(inverse(multiply(inverse(multiply(y,z)),multiply(y,w))),multiply(inverse(multiply(v,z)),x))),
    inference(spr,[status(thm),theory(equality)],[185]),
    [iquote('0:SpR:185.0,185.0')] ).

cnf(264,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,x))),multiply(inverse(multiply(inverse(multiply(w,y)),v)),multiply(inverse(multiply(z,y)),multiply(z,x)))),
    inference(spr,[status(thm),theory(equality)],[185]),
    [iquote('0:SpR:185.0,185.0')] ).

cnf(279,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,w)),x)),inverse(multiply(w,multiply(inverse(w),w))))))),multiply(u,y)),multiply(inverse(x),multiply(v,y))),
    inference(spr,[status(thm),theory(equality)],[1,185]),
    [iquote('0:SpR:1.0,185.0')] ).

cnf(313,plain,
    equal(multiply(inverse(multiply(u,inverse(multiply(v,multiply(inverse(v),v))))),multiply(u,w)),multiply(x,multiply(inverse(multiply(inverse(multiply(y,v)),multiply(y,x))),w))),
    inference(spr,[status(thm),theory(equality)],[136,185]),
    [iquote('0:SpR:136.0,185.0')] ).

cnf(320,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,x))),inverse(multiply(multiply(v,w),multiply(inverse(multiply(y,w)),multiply(y,w)))))),x),
    inference(spr,[status(thm),theory(equality)],[185,136]),
    [iquote('0:SpR:185.0,136.0')] ).

cnf(567,plain,
    equal(multiply(inverse(multiply(u,multiply(v,inverse(multiply(inverse(w),inverse(multiply(x,multiply(inverse(x),x)))))))),multiply(u,multiply(v,y))),multiply(inverse(w),multiply(inverse(multiply(z,x)),multiply(z,y)))),
    inference(spr,[status(thm),theory(equality)],[21,264]),
    [iquote('0:SpR:21.0,264.0')] ).

cnf(577,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)],[210,567]),
    [iquote('0:Rew:210.0,567.0')] ).

cnf(751,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)],[136,577]),
    [iquote('0:SpR:136.0,577.0')] ).

cnf(1120,plain,
    equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,multiply(v,inverse(multiply(inverse(x),inverse(multiply(y,multiply(inverse(y),y)))))))),multiply(inverse(multiply(inverse(multiply(z,y)),multiply(z,w))),x)),
    inference(spr,[status(thm),theory(equality)],[21,249]),
    [iquote('0:SpR:21.0,249.0')] ).

cnf(1163,plain,
    equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),x),multiply(inverse(multiply(inverse(multiply(y,v)),multiply(y,w))),x)),
    inference(rew,[status(thm),theory(equality)],[41,1120]),
    [iquote('0:Rew:41.0,1120.0')] ).

cnf(2578,plain,
    equal(multiply(inverse(multiply(u,v)),inverse(multiply(w,inverse(multiply(multiply(u,w),multiply(inverse(multiply(x,w)),multiply(x,w))))))),inverse(multiply(v,multiply(inverse(v),v)))),
    inference(spr,[status(thm),theory(equality)],[136,244]),
    [iquote('0:SpR:136.0,244.0')] ).

cnf(3986,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(v,multiply(inverse(v),v))))),w)),multiply(x,multiply(inverse(multiply(inverse(multiply(y,v)),multiply(y,x))),z)))),inverse(multiply(w,multiply(inverse(w),w))))),multiply(u,z)),
    inference(spr,[status(thm),theory(equality)],[313,136]),
    [iquote('0:SpR:313.0,136.0')] ).

cnf(4165,plain,
    equal(multiply(u,multiply(inverse(multiply(inverse(multiply(v,w)),multiply(v,u))),x)),multiply(y,multiply(inverse(multiply(inverse(multiply(z,w)),multiply(z,y))),x))),
    inference(spr,[status(thm),theory(equality)],[136,313]),
    [iquote('0:SpR:136.0,313.0')] ).

cnf(5022,plain,
    equal(multiply(u,multiply(inverse(multiply(inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(multiply(w,x)),y)),inverse(multiply(x,multiply(inverse(x),x))))))),multiply(v,u))),z)),multiply(x1,multiply(inverse(multiply(inverse(y),multiply(w,x1))),z))),
    inference(spr,[status(thm),theory(equality)],[1,4165]),
    [iquote('0:SpR:1.0,4165.0')] ).

cnf(5078,plain,
    equal(multiply(u,multiply(inverse(multiply(inverse(v),multiply(w,u))),x)),multiply(y,multiply(inverse(multiply(inverse(v),multiply(w,y))),x))),
    inference(rew,[status(thm),theory(equality)],[279,5022]),
    [iquote('0:Rew:279.0,5022.0')] ).

cnf(5234,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(w,multiply(inverse(multiply(inverse(x),multiply(y,w))),z)))),inverse(multiply(v,multiply(inverse(v),v))))),multiply(inverse(multiply(inverse(x),multiply(y,u))),z)),
    inference(spr,[status(thm),theory(equality)],[5078,136]),
    [iquote('0:SpR:5078.0,136.0')] ).

cnf(5404,plain,
    equal(multiply(u,multiply(inverse(multiply(v,multiply(w,u))),x)),multiply(y,multiply(inverse(multiply(v,multiply(w,y))),x))),
    inference(spr,[status(thm),theory(equality)],[320,5078]),
    [iquote('0:SpR:320.0,5078.0')] ).

cnf(5454,plain,
    equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(w,inverse(multiply(v,multiply(inverse(v),v)))))))),x),multiply(w,x)),
    inference(rew,[status(thm),theory(equality)],[5234,3986]),
    [iquote('0:Rew:5234.0,3986.0')] ).

cnf(5946,plain,
    equal(multiply(u,inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(x,y))),inverse(multiply(w,multiply(inverse(w),w))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(x,y))),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(x,y))),inverse(multiply(w,multiply(inverse(w),w))))))))))),multiply(x,inverse(multiply(v,inverse(multiply(y,multiply(inverse(y),y))))))),
    inference(spr,[status(thm),theory(equality)],[5454,3]),
    [iquote('0:SpR:5454.0,3.0')] ).

cnf(8183,plain,
    equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(v,multiply(inverse(v),v)))),w),
    inference(spr,[status(thm),theory(equality)],[2578,245]),
    [iquote('0:SpR:2578.0,245.0')] ).

cnf(9307,plain,
    equal(multiply(inverse(u),u),multiply(v,multiply(inverse(multiply(inverse(multiply(w,x)),multiply(w,v))),inverse(multiply(x,multiply(inverse(x),x)))))),
    inference(spr,[status(thm),theory(equality)],[8183,5404]),
    [iquote('0:SpR:8183.0,5404.0')] ).

cnf(9754,plain,
    equal(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),w)),x)),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(y,multiply(inverse(y),y)))))),inverse(multiply(inverse(x),inverse(multiply(multiply(inverse(multiply(inverse(multiply(z,x1)),multiply(z,inverse(multiply(u,y))))),inverse(multiply(x1,multiply(inverse(x1),x1)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(z,x1)),multiply(z,inverse(multiply(u,y))))),inverse(multiply(x1,multiply(inverse(x1),x1))))),multiply(inverse(multiply(inverse(multiply(z,x1)),multiply(z,inverse(multiply(u,y))))),inverse(multiply(x1,multiply(inverse(x1),x1)))))))))),
    inference(spr,[status(thm),theory(equality)],[9307,30]),
    [iquote('0:SpR:9307.0,30.0')] ).

cnf(9762,plain,
    equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(v,w)),multiply(v,inverse(multiply(inverse(multiply(u,x)),y))))),inverse(multiply(w,multiply(inverse(w),w))))),inverse(multiply(x,multiply(inverse(x),x)))))),inverse(multiply(inverse(multiply(inverse(z),z)),inverse(multiply(y,multiply(inverse(y),y)))))),
    inference(spr,[status(thm),theory(equality)],[9307,4]),
    [iquote('0:SpR:9307.0,4.0')] ).

cnf(9775,plain,
    equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(multiply(x,multiply(y,w))),multiply(inverse(multiply(inverse(multiply(z,x1)),multiply(z,inverse(multiply(x,multiply(y,u)))))),inverse(multiply(x1,multiply(inverse(x1),x1))))))),
    inference(spr,[status(thm),theory(equality)],[9307,5404]),
    [iquote('0:SpR:9307.0,5404.0')] ).

cnf(9858,plain,
    equal(multiply(inverse(u),u),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[9307]),
    [iquote('0:SpR:9307.0,9307.0')] ).

cnf(10023,plain,
    equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(multiply(x,multiply(y,w))),multiply(x,multiply(y,u))))),
    inference(rew,[status(thm),theory(equality)],[8183,9775]),
    [iquote('0:Rew:8183.0,9775.0')] ).

cnf(10047,plain,
    equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(v,multiply(inverse(v),v))))),v),
    inference(rew,[status(thm),theory(equality)],[1,9762,8183]),
    [iquote('0:Rew:1.0,9762.0,8183.0,9762.0')] ).

cnf(10090,plain,
    equal(multiply(u,inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),w)),x)),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(y,multiply(inverse(y),y)))))),inverse(multiply(inverse(x),inverse(multiply(multiply(u,y),multiply(inverse(multiply(u,y)),multiply(u,y))))))),
    inference(rew,[status(thm),theory(equality)],[8183,9754]),
    [iquote('0:Rew:8183.0,9754.0')] ).

cnf(10119,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),multiply(inverse(v),w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
    inference(spr,[status(thm),theory(equality)],[9858,185]),
    [iquote('0:SpR:9858.0,185.0')] ).

cnf(10137,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),v),multiply(inverse(multiply(inverse(multiply(w,x)),multiply(w,x))),v)),
    inference(spr,[status(thm),theory(equality)],[9858,1163]),
    [iquote('0:SpR:9858.0,1163.0')] ).

cnf(10159,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),multiply(inverse(inverse(v)),inverse(v))))),v),
    inference(spr,[status(thm),theory(equality)],[9858,8183]),
    [iquote('0:SpR:9858.0,8183.0')] ).

cnf(10161,plain,
    equal(multiply(u,multiply(inverse(multiply(v,w)),multiply(v,w))),multiply(u,multiply(inverse(x),x))),
    inference(spr,[status(thm),theory(equality)],[9858,751]),
    [iquote('0:SpR:9858.0,751.0')] ).

cnf(10238,plain,
    equal(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w)),multiply(inverse(multiply(x,v)),multiply(x,u))),
    inference(spr,[status(thm),theory(equality)],[9858,185]),
    [iquote('0:SpR:9858.0,185.0')] ).

cnf(10315,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),inverse(multiply(v,multiply(inverse(x),x))))),w),
    inference(spr,[status(thm),theory(equality)],[9858,136]),
    [iquote('0:SpR:9858.0,136.0')] ).

cnf(10324,plain,
    equal(multiply(inverse(u),inverse(multiply(inverse(multiply(inverse(multiply(inverse(v),v)),w)),inverse(multiply(u,multiply(inverse(u),u)))))),w),
    inference(spr,[status(thm),theory(equality)],[9858,1]),
    [iquote('0:SpR:9858.0,1.0')] ).

cnf(10427,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(w),w)))),inverse(multiply(v,multiply(inverse(v),v)))),
    inference(spr,[status(thm),theory(equality)],[9858,21]),
    [iquote('0:SpR:9858.0,21.0')] ).

cnf(10448,plain,
    equal(multiply(inverse(u),inverse(multiply(inverse(v),inverse(multiply(u,multiply(inverse(u),u)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(w),w)),x)),v)),inverse(multiply(x,multiply(inverse(x),x)))))),
    inference(spr,[status(thm),theory(equality)],[9858,4]),
    [iquote('0:SpR:9858.0,4.0')] ).

cnf(10614,plain,
    equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(v,multiply(inverse(w),w))))),v),
    inference(spr,[status(thm),theory(equality)],[9858,10047]),
    [iquote('0:SpR:9858.0,10047.0')] ).

cnf(11072,plain,
    equal(inverse(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),v)))),inverse(multiply(inverse(w),w))),
    inference(spr,[status(thm),theory(equality)],[9858,10614]),
    [iquote('0:SpR:9858.0,10614.0')] ).

cnf(11172,plain,
    equal(multiply(u,multiply(inverse(v),v)),multiply(u,multiply(inverse(w),w))),
    inference(spr,[status(thm),theory(equality)],[10161]),
    [iquote('0:SpR:10161.0,10161.0')] ).

cnf(11400,plain,
    equal(multiply(inverse(u),u),multiply(inverse(multiply(inverse(v),v)),multiply(inverse(w),w))),
    inference(spr,[status(thm),theory(equality)],[11172,9858]),
    [iquote('0:SpR:11172.0,9858.0')] ).

cnf(11530,plain,
    equal(multiply(inverse(multiply(u,multiply(inverse(v),v))),multiply(u,multiply(w,x))),multiply(inverse(multiply(inverse(multiply(w,y)),multiply(inverse(z),z))),multiply(inverse(multiply(x1,y)),multiply(x1,x)))),
    inference(spr,[status(thm),theory(equality)],[11172,264]),
    [iquote('0:SpR:11172.0,264.0')] ).

cnf(12619,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),multiply(inverse(w),w)))),v),
    inference(spr,[status(thm),theory(equality)],[9858,10159]),
    [iquote('0:SpR:9858.0,10159.0')] ).

cnf(12629,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),v))),multiply(inverse(w),w)),
    inference(spr,[status(thm),theory(equality)],[11400,10159]),
    [iquote('0:SpR:11400.0,10159.0')] ).

cnf(12764,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(multiply(v,w)),multiply(v,x)))),multiply(inverse(x),w)),
    inference(spr,[status(thm),theory(equality)],[185,12619]),
    [iquote('0:SpR:185.0,12619.0')] ).

cnf(14295,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),v),multiply(inverse(multiply(inverse(w),w)),v)),
    inference(spr,[status(thm),theory(equality)],[10137]),
    [iquote('0:SpR:10137.0,10137.0')] ).

cnf(15646,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(inverse(w),w)),multiply(inverse(multiply(x,v)),multiply(x,multiply(inverse(multiply(inverse(y),y)),inverse(multiply(u,multiply(inverse(z),z))))))),
    inference(spr,[status(thm),theory(equality)],[10614,10238]),
    [iquote('0:SpR:10614.0,10238.0')] ).

cnf(15755,plain,
    equal(multiply(inverse(multiply(inverse(u),multiply(inverse(v),v))),multiply(inverse(w),w)),multiply(inverse(multiply(x,multiply(inverse(y),y))),multiply(x,u))),
    inference(spr,[status(thm),theory(equality)],[11172,10238]),
    [iquote('0:SpR:11172.0,10238.0')] ).

cnf(17405,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),inverse(multiply(inverse(v),inverse(multiply(inverse(multiply(inverse(w),w)),multiply(inverse(inverse(multiply(inverse(w),w))),inverse(multiply(inverse(w),w)))))))),v),
    inference(spr,[status(thm),theory(equality)],[10427,12619]),
    [iquote('0:SpR:10427.0,12619.0')] ).

cnf(18116,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),v)),multiply(inverse(w),w))),inverse(multiply(v,multiply(inverse(x),x))))),inverse(multiply(inverse(y),y))),
    inference(spr,[status(thm),theory(equality)],[12629,10315]),
    [iquote('0:SpR:12629.0,10315.0')] ).

cnf(18223,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(w),w))),inverse(multiply(v,multiply(inverse(x),x))))),u),
    inference(spr,[status(thm),theory(equality)],[11172,10315]),
    [iquote('0:SpR:11172.0,10315.0')] ).

cnf(18245,plain,
    equal(multiply(inverse(u),u),inverse(multiply(inverse(v),v))),
    inference(rew,[status(thm),theory(equality)],[18223,18116]),
    [iquote('0:Rew:18223.0,18116.0')] ).

cnf(18457,plain,
    equal(multiply(multiply(inverse(u),u),v),multiply(inverse(multiply(inverse(w),w)),v)),
    inference(spr,[status(thm),theory(equality)],[18245,14295]),
    [iquote('0:SpR:18245.0,14295.0')] ).

cnf(21378,plain,
    equal(multiply(u,inverse(multiply(inverse(v),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(inverse(multiply(inverse(x),x)),inverse(multiply(inverse(y),y))))),inverse(multiply(w,multiply(inverse(w),w))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(inverse(multiply(inverse(x),x)),inverse(multiply(inverse(y),y))))),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(inverse(multiply(inverse(multiply(u,w)),multiply(inverse(multiply(inverse(x),x)),inverse(multiply(inverse(y),y))))),inverse(multiply(w,multiply(inverse(w),w))))))))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(z),z)),x1)),v)),inverse(multiply(x1,multiply(inverse(x1),x1)))))),
    inference(spr,[status(thm),theory(equality)],[11072,28]),
    [iquote('0:SpR:11072.0,28.0')] ).

cnf(21755,plain,
    equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),u)),v)),w)),inverse(multiply(v,multiply(inverse(v),v))))),w),
    inference(rew,[status(thm),theory(equality)],[17405,21378,5946]),
    [iquote('0:Rew:17405.0,21378.0,5946.0,21378.0')] ).

cnf(21762,plain,
    equal(multiply(inverse(u),inverse(multiply(inverse(v),inverse(multiply(u,multiply(inverse(u),u)))))),v),
    inference(rew,[status(thm),theory(equality)],[21755,10448]),
    [iquote('0:Rew:21755.0,10448.0')] ).

cnf(21768,plain,
    equal(inverse(multiply(inverse(u),inverse(multiply(multiply(v,w),multiply(inverse(multiply(v,w)),multiply(v,w)))))),multiply(v,inverse(multiply(inverse(u),inverse(multiply(w,multiply(inverse(w),w))))))),
    inference(rew,[status(thm),theory(equality)],[21755,10090]),
    [iquote('0:Rew:21755.0,10090.0')] ).

cnf(21784,plain,
    equal(multiply(inverse(multiply(inverse(u),u)),v),v),
    inference(rew,[status(thm),theory(equality)],[21762,10324]),
    [iquote('0:Rew:21762.0,10324.0')] ).

cnf(21816,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(v),w)),
    inference(rew,[status(thm),theory(equality)],[21784,10119]),
    [iquote('0:Rew:21784.0,10119.0')] ).

cnf(21823,plain,
    equal(inverse(multiply(inverse(u),multiply(inverse(v),v))),u),
    inference(rew,[status(thm),theory(equality)],[21784,12619]),
    [iquote('0:Rew:21784.0,12619.0')] ).

cnf(21824,plain,
    equal(inverse(inverse(multiply(u,multiply(inverse(v),v)))),u),
    inference(rew,[status(thm),theory(equality)],[21784,10614]),
    [iquote('0:Rew:21784.0,10614.0')] ).

cnf(22575,plain,
    equal(multiply(multiply(inverse(u),u),v),v),
    inference(rew,[status(thm),theory(equality)],[21784,18457]),
    [iquote('0:Rew:21784.0,18457.0')] ).

cnf(22922,plain,
    equal(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),multiply(inverse(w),v)),
    inference(rew,[status(thm),theory(equality)],[21784,12764]),
    [iquote('0:Rew:21784.0,12764.0')] ).

cnf(22955,plain,
    equal(multiply(inverse(multiply(u,v)),multiply(inverse(w),w)),multiply(inverse(multiply(x,v)),multiply(x,inverse(multiply(u,multiply(inverse(y),y)))))),
    inference(rew,[status(thm),theory(equality)],[21784,15646]),
    [iquote('0:Rew:21784.0,15646.0')] ).

cnf(23409,plain,
    equal(multiply(inverse(multiply(u,multiply(inverse(v),v))),multiply(u,multiply(w,x))),multiply(multiply(w,y),multiply(inverse(multiply(z,y)),multiply(z,x)))),
    inference(rew,[status(thm),theory(equality)],[21823,11530]),
    [iquote('0:Rew:21823.0,11530.0')] ).

cnf(24062,plain,
    equal(multiply(u,multiply(inverse(v),v)),multiply(inverse(multiply(w,multiply(inverse(x),x))),multiply(w,u))),
    inference(rew,[status(thm),theory(equality)],[21823,15755]),
    [iquote('0:Rew:21823.0,15755.0')] ).

cnf(24925,plain,
    equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(multiply(x,w)),multiply(x,u)))),
    inference(rew,[status(thm),theory(equality)],[21816,10023]),
    [iquote('0:Rew:21816.0,10023.0')] ).

cnf(26899,plain,
    equal(inverse(multiply(inverse(u),v)),multiply(inverse(v),u)),
    inference(rew,[status(thm),theory(equality)],[21816,22922]),
    [iquote('0:Rew:21816.0,22922.0')] ).

cnf(27437,plain,
    equal(multiply(inverse(u),multiply(inverse(inverse(multiply(u,multiply(inverse(u),u)))),v)),v),
    inference(rew,[status(thm),theory(equality)],[26899,21762]),
    [iquote('0:Rew:26899.0,21762.0')] ).

cnf(27532,plain,
    equal(multiply(inverse(u),multiply(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[21824,27437]),
    [iquote('0:Rew:21824.0,27437.0')] ).

cnf(27655,plain,
    equal(multiply(u,multiply(inverse(v),v)),multiply(w,multiply(inverse(w),u))),
    inference(rew,[status(thm),theory(equality)],[21816,24925]),
    [iquote('0:Rew:21816.0,24925.0')] ).

cnf(27707,plain,
    equal(multiply(u,multiply(inverse(v),v)),u),
    inference(rew,[status(thm),theory(equality)],[22575,24062,26899,21816]),
    [iquote('0:Rew:22575.0,24062.0,26899.0,24062.0,21816.0,24062.0')] ).

cnf(27718,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[27707,21824]),
    [iquote('0:Rew:27707.0,21824.0')] ).

cnf(27720,plain,
    equal(multiply(u,multiply(inverse(u),v)),v),
    inference(rew,[status(thm),theory(equality)],[27707,27655]),
    [iquote('0:Rew:27707.0,27655.0')] ).

cnf(28214,plain,
    equal(multiply(inverse(u),inverse(v)),inverse(multiply(v,u))),
    inference(rew,[status(thm),theory(equality)],[27707,22955,21816]),
    [iquote('0:Rew:27707.0,22955.0,21816.0,22955.0,27707.0,22955.0')] ).

cnf(28431,plain,
    equal(multiply(multiply(u,v),multiply(inverse(v),w)),multiply(u,w)),
    inference(rew,[status(thm),theory(equality)],[27532,23409,27707,21816]),
    [iquote('0:Rew:27532.0,23409.0,27707.0,23409.0,21816.0,23409.0')] ).

cnf(28833,plain,
    equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
    inference(rew,[status(thm),theory(equality)],[27718,21768,28214,28431,21816,27720]),
    [iquote('0:Rew:27718.0,21768.0,28214.0,21768.0,28431.0,21768.0,21816.0,21768.0,27718.0,21768.0,28214.0,21768.0,27720.0,21768.0')] ).

cnf(28834,plain,
    $false,
    inference(unc,[status(thm)],[28833,2]),
    [iquote('0:UnC:28833.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP405-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n028.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 : Tue Jun 14 07:07:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 230.64/230.82  
% 230.64/230.82  SPASS V 3.9 
% 230.64/230.82  SPASS beiseite: Proof found.
% 230.64/230.82  % SZS status Theorem
% 230.64/230.82  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 230.64/230.82  SPASS derived 25361 clauses, backtracked 0 clauses, performed 0 splits and kept 6886 clauses.
% 230.64/230.82  SPASS allocated 209327 KBytes.
% 230.64/230.82  SPASS spent	0:3:50.41 on the problem.
% 230.64/230.82  		0:00:00.03 for the input.
% 230.64/230.82  		0:00:00.00 for the FLOTTER CNF translation.
% 230.64/230.82  		0:00:00.44 for inferences.
% 230.64/230.82  		0:00:00.00 for the backtracking.
% 230.64/230.82  		0:3:49.91 for the reduction.
% 230.64/230.82  
% 230.64/230.82  
% 230.64/230.82  Here is a proof with depth 16, length 94 :
% 230.64/230.82  % SZS output start Refutation
% See solution above
% 231.54/231.80  Formulae used in the proof : single_axiom prove_these_axioms_3
% 231.54/231.80  
%------------------------------------------------------------------------------