TSTP Solution File: KLE092+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE092+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 : Sun Jul 17 02:28:28 EDT 2022

% Result   : Theorem 4.06s 4.26s
% Output   : Refutation 4.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   17
% Syntax   : Number of clauses     :  102 ( 102 unt;   0 nHn; 102 RR)
%            Number of literals    :  102 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(addition(u,zero),u),
    file('KLE092+1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(addition(u,u),u),
    file('KLE092+1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(multiplication(u,one),u),
    file('KLE092+1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiplication(one,u),u),
    file('KLE092+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(multiplication(antidomain(u),u),zero),
    file('KLE092+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(antidomain(antidomain(u)),domain__dfg(u)),
    file('KLE092+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(multiplication(u,coantidomain(u)),zero),
    file('KLE092+1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ equal(domain__dfg(coantidomain(skc1)),coantidomain(skc1)),
    file('KLE092+1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE092+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
    file('KLE092+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
    file('KLE092+1.p',unknown),
    [] ).

cnf(17,axiom,
    equal(addition(addition(u,v),w),addition(u,addition(v,w))),
    file('KLE092+1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
    file('KLE092+1.p',unknown),
    [] ).

cnf(19,axiom,
    equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
    file('KLE092+1.p',unknown),
    [] ).

cnf(20,axiom,
    equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
    file('KLE092+1.p',unknown),
    [] ).

cnf(21,axiom,
    equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
    file('KLE092+1.p',unknown),
    [] ).

cnf(22,axiom,
    equal(addition(coantidomain(multiplication(u,v)),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),coantidomain(multiplication(coantidomain(coantidomain(u)),v))),
    file('KLE092+1.p',unknown),
    [] ).

cnf(23,plain,
    equal(addition(coantidomain(u),coantidomain(coantidomain(u))),one),
    inference(rew,[status(thm),theory(equality)],[12,14]),
    [iquote('0:Rew:12.0,14.0')] ).

cnf(24,plain,
    equal(addition(domain__dfg(u),antidomain(u)),one),
    inference(rew,[status(thm),theory(equality)],[8,13]),
    [iquote('0:Rew:8.0,13.0')] ).

cnf(25,plain,
    equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,domain__dfg(v)))),antidomain(multiplication(u,domain__dfg(v)))),
    inference(rew,[status(thm),theory(equality)],[8,21]),
    [iquote('0:Rew:8.0,21.0')] ).

cnf(39,plain,
    equal(antidomain(one),zero),
    inference(spr,[status(thm),theory(equality)],[7,3]),
    [iquote('0:SpR:7.0,3.0')] ).

cnf(43,plain,
    equal(coantidomain(one),zero),
    inference(spr,[status(thm),theory(equality)],[9,4]),
    [iquote('0:SpR:9.0,4.0')] ).

cnf(46,plain,
    equal(antidomain(domain__dfg(u)),domain__dfg(antidomain(u))),
    inference(spr,[status(thm),theory(equality)],[8]),
    [iquote('0:SpR:8.0,8.0')] ).

cnf(48,plain,
    equal(antidomain(zero),domain__dfg(one)),
    inference(spr,[status(thm),theory(equality)],[39,8]),
    [iquote('0:SpR:39.0,8.0')] ).

cnf(58,plain,
    equal(addition(domain__dfg(one),zero),one),
    inference(spr,[status(thm),theory(equality)],[39,24]),
    [iquote('0:SpR:39.0,24.0')] ).

cnf(61,plain,
    equal(domain__dfg(one),one),
    inference(rew,[status(thm),theory(equality)],[1,58]),
    [iquote('0:Rew:1.0,58.0')] ).

cnf(62,plain,
    equal(antidomain(zero),one),
    inference(rew,[status(thm),theory(equality)],[61,48]),
    [iquote('0:Rew:61.0,48.0')] ).

cnf(79,plain,
    equal(addition(zero,u),u),
    inference(spr,[status(thm),theory(equality)],[12,1]),
    [iquote('0:SpR:12.0,1.0')] ).

cnf(111,plain,
    equal(addition(zero,coantidomain(zero)),one),
    inference(spr,[status(thm),theory(equality)],[43,23]),
    [iquote('0:SpR:43.0,23.0')] ).

cnf(113,plain,
    equal(coantidomain(zero),one),
    inference(rew,[status(thm),theory(equality)],[79,111]),
    [iquote('0:Rew:79.0,111.0')] ).

cnf(256,plain,
    equal(addition(u,addition(u,v)),addition(u,v)),
    inference(spr,[status(thm),theory(equality)],[2,17]),
    [iquote('0:SpR:2.0,17.0')] ).

cnf(259,plain,
    equal(addition(domain__dfg(u),addition(antidomain(u),v)),addition(one,v)),
    inference(spr,[status(thm),theory(equality)],[24,17]),
    [iquote('0:SpR:24.0,17.0')] ).

cnf(329,plain,
    equal(addition(domain__dfg(u),one),one),
    inference(spr,[status(thm),theory(equality)],[24,256]),
    [iquote('0:SpR:24.0,256.0')] ).

cnf(335,plain,
    equal(addition(coantidomain(u),one),one),
    inference(spr,[status(thm),theory(equality)],[23,256]),
    [iquote('0:SpR:23.0,256.0')] ).

cnf(339,plain,
    equal(addition(one,domain__dfg(u)),one),
    inference(rew,[status(thm),theory(equality)],[12,329]),
    [iquote('0:Rew:12.0,329.0')] ).

cnf(341,plain,
    equal(addition(one,coantidomain(u)),one),
    inference(rew,[status(thm),theory(equality)],[12,335]),
    [iquote('0:Rew:12.0,335.0')] ).

cnf(350,plain,
    equal(addition(multiplication(u,coantidomain(addition(u,v))),multiplication(v,coantidomain(addition(u,v)))),zero),
    inference(spr,[status(thm),theory(equality)],[20,9]),
    [iquote('0:SpR:20.0,9.0')] ).

cnf(360,plain,
    equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),multiplication(one,v)),
    inference(spr,[status(thm),theory(equality)],[24,20]),
    [iquote('0:SpR:24.0,20.0')] ).

cnf(366,plain,
    equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),multiplication(one,v)),
    inference(spr,[status(thm),theory(equality)],[23,20]),
    [iquote('0:SpR:23.0,20.0')] ).

cnf(373,plain,
    equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),v),
    inference(rew,[status(thm),theory(equality)],[4,360]),
    [iquote('0:Rew:4.0,360.0')] ).

cnf(377,plain,
    equal(addition(multiplication(coantidomain(u),v),multiplication(coantidomain(coantidomain(u)),v)),v),
    inference(rew,[status(thm),theory(equality)],[4,366]),
    [iquote('0:Rew:4.0,366.0')] ).

cnf(427,plain,
    equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),multiplication(u,one)),
    inference(spr,[status(thm),theory(equality)],[24,19]),
    [iquote('0:SpR:24.0,19.0')] ).

cnf(433,plain,
    equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),multiplication(u,one)),
    inference(spr,[status(thm),theory(equality)],[23,19]),
    [iquote('0:SpR:23.0,19.0')] ).

cnf(442,plain,
    equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),u),
    inference(rew,[status(thm),theory(equality)],[3,427]),
    [iquote('0:Rew:3.0,427.0')] ).

cnf(446,plain,
    equal(addition(multiplication(u,coantidomain(v)),multiplication(u,coantidomain(coantidomain(v)))),u),
    inference(rew,[status(thm),theory(equality)],[3,433]),
    [iquote('0:Rew:3.0,433.0')] ).

cnf(464,plain,
    equal(addition(multiplication(u,one),multiplication(u,domain__dfg(v))),multiplication(u,one)),
    inference(spr,[status(thm),theory(equality)],[339,19]),
    [iquote('0:SpR:339.0,19.0')] ).

cnf(472,plain,
    equal(addition(u,multiplication(u,domain__dfg(v))),u),
    inference(rew,[status(thm),theory(equality)],[3,464]),
    [iquote('0:Rew:3.0,464.0')] ).

cnf(480,plain,
    equal(addition(multiplication(u,one),multiplication(u,coantidomain(v))),multiplication(u,one)),
    inference(spr,[status(thm),theory(equality)],[341,19]),
    [iquote('0:SpR:341.0,19.0')] ).

cnf(488,plain,
    equal(addition(u,multiplication(u,coantidomain(v))),u),
    inference(rew,[status(thm),theory(equality)],[3,480]),
    [iquote('0:Rew:3.0,480.0')] ).

cnf(538,plain,
    equal(addition(antidomain(zero),antidomain(multiplication(u,domain__dfg(coantidomain(u))))),antidomain(multiplication(u,domain__dfg(coantidomain(u))))),
    inference(spr,[status(thm),theory(equality)],[9,25]),
    [iquote('0:SpR:9.0,25.0')] ).

cnf(560,plain,
    equal(addition(one,antidomain(multiplication(u,domain__dfg(coantidomain(u))))),antidomain(multiplication(u,domain__dfg(coantidomain(u))))),
    inference(rew,[status(thm),theory(equality)],[62,538]),
    [iquote('0:Rew:62.0,538.0')] ).

cnf(633,plain,
    equal(addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u))),coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u))),
    inference(spr,[status(thm),theory(equality)],[7,22]),
    [iquote('0:SpR:7.0,22.0')] ).

cnf(658,plain,
    equal(coantidomain(multiplication(coantidomain(coantidomain(antidomain(u))),u)),one),
    inference(rew,[status(thm),theory(equality)],[341,633,113]),
    [iquote('0:Rew:341.0,633.0,113.0,633.0')] ).

cnf(723,plain,
    equal(multiplication(multiplication(coantidomain(coantidomain(antidomain(u))),u),one),zero),
    inference(spr,[status(thm),theory(equality)],[658,9]),
    [iquote('0:SpR:658.0,9.0')] ).

cnf(745,plain,
    equal(multiplication(coantidomain(coantidomain(antidomain(u))),u),zero),
    inference(rew,[status(thm),theory(equality)],[3,723,18]),
    [iquote('0:Rew:3.0,723.0,18.0,723.0')] ).

cnf(831,plain,
    equal(multiplication(coantidomain(coantidomain(domain__dfg(antidomain(u)))),domain__dfg(u)),zero),
    inference(spr,[status(thm),theory(equality)],[46,745]),
    [iquote('0:SpR:46.0,745.0')] ).

cnf(1482,plain,
    equal(addition(domain__dfg(u),antidomain(u)),addition(one,antidomain(u))),
    inference(spr,[status(thm),theory(equality)],[2,259]),
    [iquote('0:SpR:2.0,259.0')] ).

cnf(1502,plain,
    equal(addition(one,antidomain(u)),one),
    inference(rew,[status(thm),theory(equality)],[24,1482]),
    [iquote('0:Rew:24.0,1482.0')] ).

cnf(1511,plain,
    equal(antidomain(multiplication(u,domain__dfg(coantidomain(u)))),one),
    inference(rew,[status(thm),theory(equality)],[1502,560]),
    [iquote('0:Rew:1502.0,560.0')] ).

cnf(1554,plain,
    equal(multiplication(one,multiplication(u,domain__dfg(coantidomain(u)))),zero),
    inference(spr,[status(thm),theory(equality)],[1511,7]),
    [iquote('0:SpR:1511.0,7.0')] ).

cnf(1595,plain,
    equal(multiplication(u,domain__dfg(coantidomain(u))),zero),
    inference(rew,[status(thm),theory(equality)],[4,1554]),
    [iquote('0:Rew:4.0,1554.0')] ).

cnf(1733,plain,
    equal(addition(multiplication(domain__dfg(u),u),zero),u),
    inference(spr,[status(thm),theory(equality)],[7,373]),
    [iquote('0:SpR:7.0,373.0')] ).

cnf(1758,plain,
    equal(multiplication(domain__dfg(u),u),u),
    inference(rew,[status(thm),theory(equality)],[79,1733,12]),
    [iquote('0:Rew:79.0,1733.0,12.0,1733.0')] ).

cnf(1884,plain,
    equal(addition(zero,multiplication(antidomain(domain__dfg(u)),antidomain(u))),antidomain(domain__dfg(u))),
    inference(spr,[status(thm),theory(equality)],[7,442]),
    [iquote('0:SpR:7.0,442.0')] ).

cnf(1886,plain,
    equal(addition(zero,multiplication(u,antidomain(coantidomain(u)))),u),
    inference(spr,[status(thm),theory(equality)],[1595,442]),
    [iquote('0:SpR:1595.0,442.0')] ).

cnf(1899,plain,
    equal(multiplication(u,antidomain(coantidomain(u))),u),
    inference(rew,[status(thm),theory(equality)],[79,1886]),
    [iquote('0:Rew:79.0,1886.0')] ).

cnf(1908,plain,
    equal(domain__dfg(antidomain(u)),antidomain(u)),
    inference(rew,[status(thm),theory(equality)],[79,1884,1758,46]),
    [iquote('0:Rew:79.0,1884.0,1758.0,1884.0,46.0,1884.0')] ).

cnf(1909,plain,
    equal(antidomain(domain__dfg(u)),antidomain(u)),
    inference(rew,[status(thm),theory(equality)],[1908,46]),
    [iquote('0:Rew:1908.0,46.0')] ).

cnf(1943,plain,
    equal(multiplication(coantidomain(coantidomain(antidomain(u))),domain__dfg(u)),zero),
    inference(rew,[status(thm),theory(equality)],[1908,831]),
    [iquote('0:Rew:1908.0,831.0')] ).

cnf(3220,plain,
    equal(addition(multiplication(coantidomain(antidomain(u)),u),zero),u),
    inference(spr,[status(thm),theory(equality)],[745,377]),
    [iquote('0:SpR:745.0,377.0')] ).

cnf(3223,plain,
    equal(addition(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),zero),coantidomain(coantidomain(coantidomain(u)))),
    inference(spr,[status(thm),theory(equality)],[9,377]),
    [iquote('0:SpR:9.0,377.0')] ).

cnf(3246,plain,
    equal(multiplication(coantidomain(antidomain(u)),u),u),
    inference(rew,[status(thm),theory(equality)],[79,3220,12]),
    [iquote('0:Rew:79.0,3220.0,12.0,3220.0')] ).

cnf(3257,plain,
    equal(multiplication(coantidomain(u),coantidomain(coantidomain(coantidomain(u)))),coantidomain(coantidomain(coantidomain(u)))),
    inference(rew,[status(thm),theory(equality)],[79,3223,12]),
    [iquote('0:Rew:79.0,3223.0,12.0,3223.0')] ).

cnf(3286,plain,
    equal(addition(domain__dfg(u),multiplication(coantidomain(antidomain(domain__dfg(u))),antidomain(u))),coantidomain(antidomain(domain__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[3246,442]),
    [iquote('0:SpR:3246.0,442.0')] ).

cnf(3287,plain,
    equal(addition(multiplication(coantidomain(antidomain(antidomain(u))),domain__dfg(u)),antidomain(u)),coantidomain(antidomain(antidomain(u)))),
    inference(spr,[status(thm),theory(equality)],[3246,442]),
    [iquote('0:SpR:3246.0,442.0')] ).

cnf(3306,plain,
    equal(addition(domain__dfg(u),multiplication(coantidomain(antidomain(u)),antidomain(u))),coantidomain(antidomain(u))),
    inference(rew,[status(thm),theory(equality)],[1909,3286]),
    [iquote('0:Rew:1909.0,3286.0')] ).

cnf(3307,plain,
    equal(addition(antidomain(u),multiplication(coantidomain(domain__dfg(u)),domain__dfg(u))),coantidomain(domain__dfg(u))),
    inference(rew,[status(thm),theory(equality)],[12,3287,8]),
    [iquote('0:Rew:12.0,3287.0,8.0,3287.0')] ).

cnf(3370,plain,
    equal(addition(multiplication(domain__dfg(coantidomain(coantidomain(u))),coantidomain(u)),coantidomain(coantidomain(u))),domain__dfg(coantidomain(coantidomain(u)))),
    inference(spr,[status(thm),theory(equality)],[1758,446]),
    [iquote('0:SpR:1758.0,446.0')] ).

cnf(3381,plain,
    equal(addition(zero,multiplication(u,coantidomain(coantidomain(u)))),u),
    inference(spr,[status(thm),theory(equality)],[9,446]),
    [iquote('0:SpR:9.0,446.0')] ).

cnf(3390,plain,
    equal(multiplication(u,coantidomain(coantidomain(u))),u),
    inference(rew,[status(thm),theory(equality)],[79,3381]),
    [iquote('0:Rew:79.0,3381.0')] ).

cnf(3391,plain,
    equal(coantidomain(coantidomain(coantidomain(u))),coantidomain(u)),
    inference(rew,[status(thm),theory(equality)],[3390,3257]),
    [iquote('0:Rew:3390.0,3257.0')] ).

cnf(3427,plain,
    equal(addition(coantidomain(coantidomain(u)),multiplication(domain__dfg(coantidomain(coantidomain(u))),coantidomain(u))),domain__dfg(coantidomain(coantidomain(u)))),
    inference(rew,[status(thm),theory(equality)],[12,3370]),
    [iquote('0:Rew:12.0,3370.0')] ).

cnf(4152,plain,
    equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,domain__dfg(v)),coantidomain(u))),zero),
    inference(spr,[status(thm),theory(equality)],[472,350]),
    [iquote('0:SpR:472.0,350.0')] ).

cnf(4153,plain,
    equal(addition(multiplication(u,coantidomain(u)),multiplication(multiplication(u,coantidomain(v)),coantidomain(u))),zero),
    inference(spr,[status(thm),theory(equality)],[488,350]),
    [iquote('0:SpR:488.0,350.0')] ).

cnf(4163,plain,
    equal(addition(multiplication(multiplication(u,domain__dfg(v)),coantidomain(u)),multiplication(multiplication(u,antidomain(v)),coantidomain(u))),zero),
    inference(spr,[status(thm),theory(equality)],[442,350]),
    [iquote('0:SpR:442.0,350.0')] ).

cnf(4252,plain,
    equal(multiplication(u,multiplication(domain__dfg(v),coantidomain(u))),zero),
    inference(rew,[status(thm),theory(equality)],[79,4152,9,18]),
    [iquote('0:Rew:79.0,4152.0,9.0,4152.0,18.0,4152.0')] ).

cnf(4253,plain,
    equal(multiplication(u,multiplication(coantidomain(v),coantidomain(u))),zero),
    inference(rew,[status(thm),theory(equality)],[79,4153,9,18]),
    [iquote('0:Rew:79.0,4153.0,9.0,4153.0,18.0,4153.0')] ).

cnf(4272,plain,
    equal(addition(multiplication(u,multiplication(domain__dfg(v),coantidomain(u))),multiplication(u,multiplication(antidomain(v),coantidomain(u)))),zero),
    inference(rew,[status(thm),theory(equality)],[18,4163]),
    [iquote('0:Rew:18.0,4163.0,18.0,4163.0')] ).

cnf(4273,plain,
    equal(addition(zero,multiplication(u,multiplication(antidomain(v),coantidomain(u)))),zero),
    inference(rew,[status(thm),theory(equality)],[4252,4272]),
    [iquote('0:Rew:4252.0,4272.0')] ).

cnf(4274,plain,
    equal(multiplication(u,multiplication(antidomain(v),coantidomain(u))),zero),
    inference(rew,[status(thm),theory(equality)],[79,4273]),
    [iquote('0:Rew:79.0,4273.0')] ).

cnf(15206,plain,
    equal(multiplication(coantidomain(antidomain(u)),antidomain(u)),zero),
    inference(spr,[status(thm),theory(equality)],[3390,4274]),
    [iquote('0:SpR:3390.0,4274.0')] ).

cnf(15217,plain,
    equal(addition(domain__dfg(u),zero),coantidomain(antidomain(u))),
    inference(rew,[status(thm),theory(equality)],[15206,3306]),
    [iquote('0:Rew:15206.0,3306.0')] ).

cnf(15218,plain,
    equal(coantidomain(antidomain(u)),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[79,15217,12]),
    [iquote('0:Rew:79.0,15217.0,12.0,15217.0')] ).

cnf(15223,plain,
    equal(multiplication(coantidomain(domain__dfg(u)),domain__dfg(u)),zero),
    inference(rew,[status(thm),theory(equality)],[15218,1943]),
    [iquote('0:Rew:15218.0,1943.0')] ).

cnf(15389,plain,
    equal(addition(antidomain(u),zero),coantidomain(domain__dfg(u))),
    inference(rew,[status(thm),theory(equality)],[15223,3307]),
    [iquote('0:Rew:15223.0,3307.0')] ).

cnf(15394,plain,
    equal(antidomain(u),coantidomain(domain__dfg(u))),
    inference(rew,[status(thm),theory(equality)],[79,15389,12]),
    [iquote('0:Rew:79.0,15389.0,12.0,15389.0')] ).

cnf(15406,plain,
    equal(multiplication(u,coantidomain(domain__dfg(coantidomain(u)))),u),
    inference(rew,[status(thm),theory(equality)],[15394,1899]),
    [iquote('0:Rew:15394.0,1899.0')] ).

cnf(18423,plain,
    equal(multiplication(domain__dfg(coantidomain(coantidomain(u))),coantidomain(u)),zero),
    inference(spr,[status(thm),theory(equality)],[15406,4253]),
    [iquote('0:SpR:15406.0,4253.0')] ).

cnf(18434,plain,
    equal(addition(coantidomain(coantidomain(u)),zero),domain__dfg(coantidomain(coantidomain(u)))),
    inference(rew,[status(thm),theory(equality)],[18423,3427]),
    [iquote('0:Rew:18423.0,3427.0')] ).

cnf(18437,plain,
    equal(domain__dfg(coantidomain(coantidomain(u))),coantidomain(coantidomain(u))),
    inference(rew,[status(thm),theory(equality)],[79,18434,12]),
    [iquote('0:Rew:79.0,18434.0,12.0,18434.0')] ).

cnf(18583,plain,
    equal(domain__dfg(coantidomain(u)),coantidomain(u)),
    inference(spr,[status(thm),theory(equality)],[3391,18437]),
    [iquote('0:SpR:3391.0,18437.0')] ).

cnf(18597,plain,
    $false,
    inference(unc,[status(thm)],[18583,11]),
    [iquote('0:UnC:18583.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE092+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n009.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 : Thu Jun 16 15:05:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 4.06/4.26  
% 4.06/4.26  SPASS V 3.9 
% 4.06/4.26  SPASS beiseite: Proof found.
% 4.06/4.26  % SZS status Theorem
% 4.06/4.26  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 4.06/4.26  SPASS derived 12241 clauses, backtracked 0 clauses, performed 0 splits and kept 2790 clauses.
% 4.06/4.26  SPASS allocated 104730 KBytes.
% 4.06/4.26  SPASS spent	0:00:03.91 on the problem.
% 4.06/4.26  		0:00:00.04 for the input.
% 4.06/4.26  		0:00:00.03 for the FLOTTER CNF translation.
% 4.06/4.26  		0:00:00.08 for inferences.
% 4.06/4.26  		0:00:00.00 for the backtracking.
% 4.06/4.26  		0:00:03.73 for the reduction.
% 4.06/4.26  
% 4.06/4.26  
% 4.06/4.26  Here is a proof with depth 5, length 102 :
% 4.06/4.26  % SZS output start Refutation
% See solution above
% 4.12/4.35  Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity domain1 domain4 codomain1 goals additive_commutativity domain3 codomain3 additive_associativity multiplicative_associativity right_distributivity left_distributivity domain2 codomain2
% 4.12/4.35  
%------------------------------------------------------------------------------