TSTP Solution File: REL008+4 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : REL008+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 : Mon Jul 18 20:01:33 EDT 2022

% Result   : Theorem 85.66s 85.84s
% Output   : Refutation 88.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   15
% Syntax   : Number of clauses     :  115 ( 105 unt;   0 nHn; 115 RR)
%            Number of literals    :  125 (   0 equ;  20 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  13 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(composition(u,one),u),
    file('REL008+4.p',unknown),
    [] ).

cnf(2,axiom,
    equal(converse(converse(u)),u),
    file('REL008+4.p',unknown),
    [] ).

cnf(3,axiom,
    equal(join(u,complement(u)),top),
    file('REL008+4.p',unknown),
    [] ).

cnf(4,axiom,
    equal(meet(u,complement(u)),zero),
    file('REL008+4.p',unknown),
    [] ).

cnf(5,axiom,
    equal(join(u,v),join(v,u)),
    file('REL008+4.p',unknown),
    [] ).

cnf(6,axiom,
    equal(complement(join(complement(u),complement(v))),meet(u,v)),
    file('REL008+4.p',unknown),
    [] ).

cnf(7,axiom,
    equal(join(converse(u),converse(v)),converse(join(u,v))),
    file('REL008+4.p',unknown),
    [] ).

cnf(8,axiom,
    equal(composition(converse(u),converse(v)),converse(composition(v,u))),
    file('REL008+4.p',unknown),
    [] ).

cnf(9,axiom,
    equal(join(join(u,v),w),join(u,join(v,w))),
    file('REL008+4.p',unknown),
    [] ).

cnf(10,axiom,
    equal(composition(composition(u,v),w),composition(u,composition(v,w))),
    file('REL008+4.p',unknown),
    [] ).

cnf(11,axiom,
    equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
    file('REL008+4.p',unknown),
    [] ).

cnf(12,axiom,
    equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
    file('REL008+4.p',unknown),
    [] ).

cnf(13,axiom,
    equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
    file('REL008+4.p',unknown),
    [] ).

cnf(15,axiom,
    equal(join(meet(composition(u,v),w),meet(composition(u,meet(v,composition(converse(u),w))),w)),meet(composition(u,meet(v,composition(converse(u),w))),w)),
    file('REL008+4.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ equal(join(join(composition(skc6,join(skc7,skc8)),composition(skc6,skc7)),composition(skc6,skc8)),join(composition(skc6,skc7),composition(skc6,skc8)))
    | ~ equal(join(join(composition(skc9,skc10),composition(skc9,skc11)),composition(skc9,join(skc10,skc11))),composition(skc9,join(skc10,skc11))) ),
    file('REL008+4.p',unknown),
    [] ).

cnf(18,plain,
    equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
    inference(rew,[status(thm),theory(equality)],[5,12]),
    [iquote('0:Rew:5.0,12.0')] ).

cnf(19,plain,
    equal(join(meet(u,v),complement(join(complement(u),v))),u),
    inference(rew,[status(thm),theory(equality)],[6,13]),
    [iquote('0:Rew:6.0,13.0')] ).

cnf(20,plain,
    ( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
    | ~ equal(join(composition(skc6,join(skc7,skc8)),join(composition(skc6,skc7),composition(skc6,skc8))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
    inference(rew,[status(thm),theory(equality)],[9,17]),
    [iquote('0:Rew:9.0,17.1,9.0,17.0')] ).

cnf(31,plain,
    equal(converse(composition(converse(u),v)),composition(converse(v),u)),
    inference(spr,[status(thm),theory(equality)],[2,8]),
    [iquote('0:SpR:2.0,8.0')] ).

cnf(32,plain,
    equal(converse(composition(u,converse(v))),composition(v,converse(u))),
    inference(spr,[status(thm),theory(equality)],[2,8]),
    [iquote('0:SpR:2.0,8.0')] ).

cnf(36,plain,
    equal(converse(join(u,converse(v))),join(converse(u),v)),
    inference(spr,[status(thm),theory(equality)],[2,7]),
    [iquote('0:SpR:2.0,7.0')] ).

cnf(37,plain,
    equal(converse(join(converse(u),v)),join(u,converse(v))),
    inference(spr,[status(thm),theory(equality)],[2,7]),
    [iquote('0:SpR:2.0,7.0')] ).

cnf(75,plain,
    equal(join(join(complement(u),complement(v)),meet(u,v)),top),
    inference(spr,[status(thm),theory(equality)],[6,3]),
    [iquote('0:SpR:6.0,3.0')] ).

cnf(79,plain,
    equal(meet(u,complement(u)),complement(top)),
    inference(spr,[status(thm),theory(equality)],[3,6]),
    [iquote('0:SpR:3.0,6.0')] ).

cnf(80,plain,
    equal(complement(join(complement(u),complement(v))),meet(v,u)),
    inference(spr,[status(thm),theory(equality)],[5,6]),
    [iquote('0:SpR:5.0,6.0')] ).

cnf(82,plain,
    equal(complement(top),zero),
    inference(rew,[status(thm),theory(equality)],[4,79]),
    [iquote('0:Rew:4.0,79.0')] ).

cnf(83,plain,
    equal(meet(u,v),meet(v,u)),
    inference(rew,[status(thm),theory(equality)],[6,80]),
    [iquote('0:Rew:6.0,80.0')] ).

cnf(84,plain,
    equal(join(meet(composition(u,v),w),meet(w,composition(u,meet(v,composition(converse(u),w))))),meet(w,composition(u,meet(v,composition(converse(u),w))))),
    inference(rew,[status(thm),theory(equality)],[83,15]),
    [iquote('0:Rew:83.0,15.0')] ).

cnf(88,plain,
    equal(join(meet(u,v),join(complement(u),complement(v))),top),
    inference(rew,[status(thm),theory(equality)],[5,75]),
    [iquote('0:Rew:5.0,75.0')] ).

cnf(93,plain,
    equal(join(meet(u,complement(complement(u))),complement(top)),u),
    inference(spr,[status(thm),theory(equality)],[3,19]),
    [iquote('0:SpR:3.0,19.0')] ).

cnf(97,plain,
    equal(join(zero,complement(join(complement(u),complement(u)))),u),
    inference(spr,[status(thm),theory(equality)],[4,19]),
    [iquote('0:SpR:4.0,19.0')] ).

cnf(98,plain,
    equal(join(complement(top),meet(u,complement(complement(u)))),u),
    inference(rew,[status(thm),theory(equality)],[5,93]),
    [iquote('0:Rew:5.0,93.0')] ).

cnf(99,plain,
    equal(join(zero,meet(u,complement(complement(u)))),u),
    inference(rew,[status(thm),theory(equality)],[82,98]),
    [iquote('0:Rew:82.0,98.0')] ).

cnf(101,plain,
    equal(join(zero,meet(u,u)),u),
    inference(rew,[status(thm),theory(equality)],[6,97]),
    [iquote('0:Rew:6.0,97.0')] ).

cnf(106,plain,
    equal(complement(join(zero,complement(u))),meet(top,u)),
    inference(spr,[status(thm),theory(equality)],[82,6]),
    [iquote('0:SpR:82.0,6.0')] ).

cnf(159,plain,
    equal(join(u,join(v,complement(join(u,v)))),top),
    inference(spr,[status(thm),theory(equality)],[9,3]),
    [iquote('0:SpR:9.0,3.0')] ).

cnf(160,plain,
    equal(join(u,join(v,w)),join(w,join(u,v))),
    inference(spr,[status(thm),theory(equality)],[9,5]),
    [iquote('0:SpR:9.0,5.0')] ).

cnf(166,plain,
    equal(join(u,join(complement(u),v)),join(top,v)),
    inference(spr,[status(thm),theory(equality)],[3,9]),
    [iquote('0:SpR:3.0,9.0')] ).

cnf(167,plain,
    equal(join(join(u,v),w),join(v,join(u,w))),
    inference(spr,[status(thm),theory(equality)],[5,9]),
    [iquote('0:SpR:5.0,9.0')] ).

cnf(174,plain,
    equal(join(complement(u),join(meet(v,u),complement(v))),top),
    inference(rew,[status(thm),theory(equality)],[160,88]),
    [iquote('0:Rew:160.0,88.0')] ).

cnf(175,plain,
    ( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
    | ~ equal(join(composition(skc6,skc8),join(composition(skc6,join(skc7,skc8)),composition(skc6,skc7))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
    inference(rew,[status(thm),theory(equality)],[160,20]),
    [iquote('0:Rew:160.0,20.1')] ).

cnf(179,plain,
    equal(join(u,join(v,w)),join(v,join(u,w))),
    inference(rew,[status(thm),theory(equality)],[9,167]),
    [iquote('0:Rew:9.0,167.0')] ).

cnf(181,plain,
    equal(join(complement(u),join(complement(v),meet(v,u))),top),
    inference(rew,[status(thm),theory(equality)],[5,174]),
    [iquote('0:Rew:5.0,174.0')] ).

cnf(183,plain,
    ( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
    | ~ equal(join(composition(skc6,skc8),join(composition(skc6,skc7),composition(skc6,join(skc7,skc8)))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
    inference(rew,[status(thm),theory(equality)],[5,175]),
    [iquote('0:Rew:5.0,175.1')] ).

cnf(184,plain,
    ( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
    | ~ equal(join(composition(skc6,skc7),join(composition(skc6,join(skc7,skc8)),composition(skc6,skc8))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
    inference(rew,[status(thm),theory(equality)],[160,183]),
    [iquote('0:Rew:160.0,183.1')] ).

cnf(185,plain,
    ( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
    | ~ equal(join(composition(skc6,skc7),join(composition(skc6,skc8),composition(skc6,join(skc7,skc8)))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
    inference(rew,[status(thm),theory(equality)],[5,184]),
    [iquote('0:Rew:5.0,184.1')] ).

cnf(230,plain,
    equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
    inference(spr,[status(thm),theory(equality)],[82,18]),
    [iquote('0:SpR:82.0,18.0')] ).

cnf(270,plain,
    equal(join(converse(composition(u,v)),composition(w,converse(u))),composition(join(converse(v),w),converse(u))),
    inference(spr,[status(thm),theory(equality)],[8,11]),
    [iquote('0:SpR:8.0,11.0')] ).

cnf(601,plain,
    equal(composition(converse(one),u),converse(converse(u))),
    inference(spr,[status(thm),theory(equality)],[1,31]),
    [iquote('0:SpR:1.0,31.0')] ).

cnf(604,plain,
    equal(composition(converse(one),u),u),
    inference(rew,[status(thm),theory(equality)],[2,601]),
    [iquote('0:Rew:2.0,601.0')] ).

cnf(615,plain,
    equal(converse(one),one),
    inference(spr,[status(thm),theory(equality)],[604,1]),
    [iquote('0:SpR:604.0,1.0')] ).

cnf(618,plain,
    equal(join(u,composition(v,u)),composition(join(converse(one),v),u)),
    inference(spr,[status(thm),theory(equality)],[604,11]),
    [iquote('0:SpR:604.0,11.0')] ).

cnf(627,plain,
    equal(join(complement(u),complement(composition(one,u))),complement(u)),
    inference(spr,[status(thm),theory(equality)],[604,18]),
    [iquote('0:SpR:604.0,18.0')] ).

cnf(633,plain,
    equal(composition(one,u),u),
    inference(rew,[status(thm),theory(equality)],[615,604]),
    [iquote('0:Rew:615.0,604.0')] ).

cnf(648,plain,
    equal(join(complement(u),complement(u)),complement(u)),
    inference(rew,[status(thm),theory(equality)],[633,627]),
    [iquote('0:Rew:633.0,627.0')] ).

cnf(649,plain,
    equal(join(u,composition(v,u)),composition(join(one,v),u)),
    inference(rew,[status(thm),theory(equality)],[615,618]),
    [iquote('0:Rew:615.0,618.0')] ).

cnf(720,plain,
    equal(meet(u,u),complement(complement(u))),
    inference(spr,[status(thm),theory(equality)],[648,6]),
    [iquote('0:SpR:648.0,6.0')] ).

cnf(726,plain,
    equal(join(zero,zero),zero),
    inference(spr,[status(thm),theory(equality)],[82,648]),
    [iquote('0:SpR:82.0,648.0')] ).

cnf(748,plain,
    equal(join(zero,complement(complement(u))),u),
    inference(rew,[status(thm),theory(equality)],[720,101]),
    [iquote('0:Rew:720.0,101.0')] ).

cnf(789,plain,
    equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
    inference(spr,[status(thm),theory(equality)],[6,748]),
    [iquote('0:SpR:6.0,748.0')] ).

cnf(820,plain,
    equal(join(zero,join(zero,u)),join(zero,u)),
    inference(spr,[status(thm),theory(equality)],[726,9]),
    [iquote('0:SpR:726.0,9.0')] ).

cnf(930,plain,
    equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
    inference(spr,[status(thm),theory(equality)],[32,7]),
    [iquote('0:SpR:32.0,7.0')] ).

cnf(953,plain,
    equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
    inference(rew,[status(thm),theory(equality)],[930,270]),
    [iquote('0:Rew:930.0,270.0')] ).

cnf(1018,plain,
    equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
    inference(spr,[status(thm),theory(equality)],[36,8]),
    [iquote('0:SpR:36.0,8.0')] ).

cnf(1058,plain,
    equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
    inference(rew,[status(thm),theory(equality)],[1018,953]),
    [iquote('0:Rew:1018.0,953.0')] ).

cnf(1071,plain,
    equal(join(zero,u),u),
    inference(spr,[status(thm),theory(equality)],[99,820]),
    [iquote('0:SpR:99.0,820.0')] ).

cnf(1078,plain,
    equal(complement(complement(u)),u),
    inference(rew,[status(thm),theory(equality)],[1071,748]),
    [iquote('0:Rew:1071.0,748.0')] ).

cnf(1079,plain,
    equal(meet(top,u),complement(complement(u))),
    inference(rew,[status(thm),theory(equality)],[1071,106]),
    [iquote('0:Rew:1071.0,106.0')] ).

cnf(1090,plain,
    equal(composition(converse(u),complement(composition(u,top))),zero),
    inference(rew,[status(thm),theory(equality)],[1071,230]),
    [iquote('0:Rew:1071.0,230.0')] ).

cnf(1091,plain,
    equal(join(complement(u),complement(v)),complement(meet(u,v))),
    inference(rew,[status(thm),theory(equality)],[1071,789]),
    [iquote('0:Rew:1071.0,789.0')] ).

cnf(1102,plain,
    equal(meet(u,u),u),
    inference(rew,[status(thm),theory(equality)],[1078,720]),
    [iquote('0:Rew:1078.0,720.0')] ).

cnf(1115,plain,
    equal(meet(top,u),u),
    inference(rew,[status(thm),theory(equality)],[1078,1079]),
    [iquote('0:Rew:1078.0,1079.0')] ).

cnf(1186,plain,
    equal(complement(zero),top),
    inference(spr,[status(thm),theory(equality)],[1071,3]),
    [iquote('0:SpR:1071.0,3.0')] ).

cnf(1245,plain,
    equal(join(u,converse(complement(converse(u)))),converse(top)),
    inference(spr,[status(thm),theory(equality)],[3,37]),
    [iquote('0:SpR:3.0,37.0')] ).

cnf(1508,plain,
    equal(join(top,converse(complement(converse(complement(u))))),join(u,converse(top))),
    inference(spr,[status(thm),theory(equality)],[1245,166]),
    [iquote('0:SpR:1245.0,166.0')] ).

cnf(1955,plain,
    equal(join(complement(u),join(complement(u),u)),top),
    inference(spr,[status(thm),theory(equality)],[1102,181]),
    [iquote('0:SpR:1102.0,181.0')] ).

cnf(1967,plain,
    equal(join(top,complement(u)),top),
    inference(rew,[status(thm),theory(equality)],[5,1955,3]),
    [iquote('0:Rew:5.0,1955.0,3.0,1955.0,5.0,1955.0')] ).

cnf(1978,plain,
    equal(join(u,top),top),
    inference(spr,[status(thm),theory(equality)],[1967,159]),
    [iquote('0:SpR:1967.0,159.0')] ).

cnf(1982,plain,
    equal(join(top,u),top),
    inference(spr,[status(thm),theory(equality)],[1078,1967]),
    [iquote('0:SpR:1078.0,1967.0')] ).

cnf(1990,plain,
    equal(join(u,converse(top)),top),
    inference(rew,[status(thm),theory(equality)],[1982,1508]),
    [iquote('0:Rew:1982.0,1508.0')] ).

cnf(2003,plain,
    equal(join(u,converse(top)),converse(top)),
    inference(spr,[status(thm),theory(equality)],[1978,37]),
    [iquote('0:SpR:1978.0,37.0')] ).

cnf(2008,plain,
    equal(converse(top),top),
    inference(rew,[status(thm),theory(equality)],[1990,2003]),
    [iquote('0:Rew:1990.0,2003.0')] ).

cnf(2034,plain,
    equal(composition(top,complement(composition(top,top))),zero),
    inference(spr,[status(thm),theory(equality)],[2008,1090]),
    [iquote('0:SpR:2008.0,1090.0')] ).

cnf(2041,plain,
    equal(join(complement(u),composition(top,complement(composition(top,u)))),complement(u)),
    inference(spr,[status(thm),theory(equality)],[2008,18]),
    [iquote('0:SpR:2008.0,18.0')] ).

cnf(2125,plain,
    equal(join(zero,composition(u,complement(composition(top,top)))),composition(join(top,u),complement(composition(top,top)))),
    inference(spr,[status(thm),theory(equality)],[2034,11]),
    [iquote('0:SpR:2034.0,11.0')] ).

cnf(2132,plain,
    equal(composition(u,complement(composition(top,top))),zero),
    inference(rew,[status(thm),theory(equality)],[1071,2125,2034,1982]),
    [iquote('0:Rew:1071.0,2125.0,2034.0,2125.0,1982.0,2125.0')] ).

cnf(2227,plain,
    equal(complement(composition(top,top)),zero),
    inference(spr,[status(thm),theory(equality)],[2132,633]),
    [iquote('0:SpR:2132.0,633.0')] ).

cnf(2752,plain,
    equal(join(join(u,v),w),join(u,join(w,v))),
    inference(spr,[status(thm),theory(equality)],[179,5]),
    [iquote('0:SpR:179.0,5.0')] ).

cnf(2852,plain,
    equal(join(u,join(v,w)),join(u,join(w,v))),
    inference(rew,[status(thm),theory(equality)],[9,2752]),
    [iquote('0:Rew:9.0,2752.0')] ).

cnf(2887,plain,
    equal(composition(top,top),complement(zero)),
    inference(spr,[status(thm),theory(equality)],[2227,1078]),
    [iquote('0:SpR:2227.0,1078.0')] ).

cnf(2898,plain,
    equal(composition(top,top),top),
    inference(rew,[status(thm),theory(equality)],[1186,2887]),
    [iquote('0:Rew:1186.0,2887.0')] ).

cnf(2918,plain,
    equal(composition(top,composition(top,u)),composition(top,u)),
    inference(spr,[status(thm),theory(equality)],[2898,10]),
    [iquote('0:SpR:2898.0,10.0')] ).

cnf(2920,plain,
    equal(join(meet(top,u),meet(u,composition(top,meet(top,composition(converse(top),u))))),meet(u,composition(top,meet(top,composition(converse(top),u))))),
    inference(spr,[status(thm),theory(equality)],[2898,84]),
    [iquote('0:SpR:2898.0,84.0')] ).

cnf(2934,plain,
    equal(join(u,meet(u,composition(top,composition(top,u)))),meet(u,composition(top,composition(top,u)))),
    inference(rew,[status(thm),theory(equality)],[1115,2920,2008]),
    [iquote('0:Rew:1115.0,2920.0,1115.0,2920.0,2008.0,2920.0')] ).

cnf(2935,plain,
    equal(join(u,meet(u,composition(top,u))),meet(u,composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[2918,2934]),
    [iquote('0:Rew:2918.0,2934.0')] ).

cnf(3322,plain,
    equal(join(complement(composition(top,u)),composition(converse(top),complement(composition(top,u)))),complement(composition(top,u))),
    inference(spr,[status(thm),theory(equality)],[2918,18]),
    [iquote('0:SpR:2918.0,18.0')] ).

cnf(3339,plain,
    equal(join(complement(composition(top,u)),composition(top,complement(composition(top,u)))),complement(composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[2008,3322]),
    [iquote('0:Rew:2008.0,3322.0')] ).

cnf(3340,plain,
    equal(composition(join(one,top),complement(composition(top,u))),complement(composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[649,3339]),
    [iquote('0:Rew:649.0,3339.0')] ).

cnf(3341,plain,
    equal(composition(top,complement(composition(top,u))),complement(composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[1978,3340]),
    [iquote('0:Rew:1978.0,3340.0')] ).

cnf(3342,plain,
    equal(join(complement(u),complement(composition(top,u))),complement(u)),
    inference(rew,[status(thm),theory(equality)],[3341,2041]),
    [iquote('0:Rew:3341.0,2041.0')] ).

cnf(3343,plain,
    equal(complement(meet(u,composition(top,u))),complement(u)),
    inference(rew,[status(thm),theory(equality)],[1091,3342]),
    [iquote('0:Rew:1091.0,3342.0')] ).

cnf(3397,plain,
    equal(meet(u,composition(top,u)),complement(complement(u))),
    inference(spr,[status(thm),theory(equality)],[3343,1078]),
    [iquote('0:SpR:3343.0,1078.0')] ).

cnf(3420,plain,
    equal(meet(u,composition(top,u)),u),
    inference(rew,[status(thm),theory(equality)],[1078,3397]),
    [iquote('0:Rew:1078.0,3397.0')] ).

cnf(3422,plain,
    equal(join(u,u),u),
    inference(rew,[status(thm),theory(equality)],[3420,2935]),
    [iquote('0:Rew:3420.0,2935.0')] ).

cnf(3488,plain,
    equal(join(u,join(u,v)),join(u,v)),
    inference(spr,[status(thm),theory(equality)],[3422,9]),
    [iquote('0:SpR:3422.0,9.0')] ).

cnf(5919,plain,
    equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
    inference(spr,[status(thm),theory(equality)],[2,1058]),
    [iquote('0:SpR:2.0,1058.0')] ).

cnf(32194,plain,
    equal(join(join(u,join(v,w)),x),join(u,join(join(w,v),x))),
    inference(spr,[status(thm),theory(equality)],[2852,9]),
    [iquote('0:SpR:2852.0,9.0')] ).

cnf(32489,plain,
    equal(join(u,join(v,join(w,x))),join(u,join(w,join(v,x)))),
    inference(rew,[status(thm),theory(equality)],[9,32194]),
    [iquote('0:Rew:9.0,32194.0,9.0,32194.0,9.0,32194.0')] ).

cnf(116007,plain,
    equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
    inference(spr,[status(thm),theory(equality)],[5919,2]),
    [iquote('0:SpR:5919.0,2.0')] ).

cnf(116285,plain,
    equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
    inference(rew,[status(thm),theory(equality)],[2,116007]),
    [iquote('0:Rew:2.0,116007.0')] ).

cnf(116288,plain,
    ( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
    | ~ equal(join(composition(skc6,skc7),composition(skc6,join(skc8,join(skc7,skc8)))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
    inference(rew,[status(thm),theory(equality)],[116285,185]),
    [iquote('0:Rew:116285.0,185.1')] ).

cnf(116638,plain,
    ( ~ equal(join(composition(skc9,skc10),join(composition(skc9,skc11),composition(skc9,join(skc10,skc11)))),composition(skc9,join(skc10,skc11)))
    | ~ equal(join(composition(skc6,skc7),composition(skc6,join(skc7,skc8))),join(composition(skc6,skc7),composition(skc6,skc8))) ),
    inference(rew,[status(thm),theory(equality)],[3422,116288,160]),
    [iquote('0:Rew:3422.0,116288.1,160.0,116288.1')] ).

cnf(116639,plain,
    ( ~ equal(composition(skc9,join(skc10,join(skc10,join(skc11,skc11)))),composition(skc9,join(skc10,skc11)))
    | ~ equal(composition(skc6,join(skc7,join(skc7,skc8))),composition(skc6,join(skc7,skc8))) ),
    inference(rew,[status(thm),theory(equality)],[116285,116638,32489]),
    [iquote('0:Rew:116285.0,116638.1,116285.0,116638.1,32489.0,116638.0,116285.0,116638.0,116285.0,116638.0')] ).

cnf(116640,plain,
    ( ~ equal(composition(skc9,join(skc10,skc11)),composition(skc9,join(skc10,skc11)))
    | ~ equal(composition(skc6,join(skc7,skc8)),composition(skc6,join(skc7,skc8))) ),
    inference(rew,[status(thm),theory(equality)],[3488,116639,3422]),
    [iquote('0:Rew:3488.0,116639.1,3422.0,116639.0,3488.0,116639.0')] ).

cnf(116641,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[116640]),
    [iquote('0:Obv:116640.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : REL008+4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Fri Jul  8 11:16:52 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 85.66/85.84  
% 85.66/85.84  SPASS V 3.9 
% 85.66/85.84  SPASS beiseite: Proof found.
% 85.66/85.84  % SZS status Theorem
% 85.66/85.84  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 85.66/85.84  SPASS derived 70239 clauses, backtracked 0 clauses, performed 0 splits and kept 9017 clauses.
% 85.66/85.84  SPASS allocated 204000 KBytes.
% 85.66/85.84  SPASS spent	0:1:25.35 on the problem.
% 85.66/85.84  		0:00:00.04 for the input.
% 85.66/85.84  		0:00:00.03 for the FLOTTER CNF translation.
% 85.66/85.84  		0:00:00.53 for inferences.
% 85.66/85.84  		0:00:00.00 for the backtracking.
% 85.66/85.84  		0:1:24.61 for the reduction.
% 85.66/85.84  
% 85.66/85.84  
% 85.66/85.84  Here is a proof with depth 13, length 115 :
% 85.66/85.84  % SZS output start Refutation
% See solution above
% 88.76/88.95  Formulae used in the proof : composition_identity converse_idempotence def_top def_zero maddux1_join_commutativity maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity composition_associativity composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan modular_law_1 goals
% 88.76/88.95  
%------------------------------------------------------------------------------