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 : n015.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 20:01:32 EDT 2022
% Result : Unsatisfiable 85.81s 86.05s
% Output : Refutation 88.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 15
% Syntax : Number of clauses : 115 ( 108 unt; 0 nHn; 115 RR)
% Number of literals : 122 ( 0 equ; 17 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 : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ equal(join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) ),
file('REL008-4.p',unknown),
[] ).
cnf(2,axiom,
equal(join(u,v),join(v,u)),
file('REL008-4.p',unknown),
[] ).
cnf(3,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL008-4.p',unknown),
[] ).
cnf(4,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL008-4.p',unknown),
[] ).
cnf(5,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL008-4.p',unknown),
[] ).
cnf(6,axiom,
equal(composition(composition(u,v),w),composition(u,composition(v,w))),
file('REL008-4.p',unknown),
[] ).
cnf(7,axiom,
equal(composition(u,one),u),
file('REL008-4.p',unknown),
[] ).
cnf(8,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL008-4.p',unknown),
[] ).
cnf(9,axiom,
equal(converse(converse(u)),u),
file('REL008-4.p',unknown),
[] ).
cnf(10,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL008-4.p',unknown),
[] ).
cnf(11,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
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(u,complement(u)),top),
file('REL008-4.p',unknown),
[] ).
cnf(14,axiom,
equal(meet(u,complement(u)),zero),
file('REL008-4.p',unknown),
[] ).
cnf(16,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(18,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[2,12]),
[iquote('0:Rew:2.0,12.0')] ).
cnf(19,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[5,4]),
[iquote('0:Rew:5.0,4.0')] ).
cnf(20,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.1,3.0,1.0')] ).
cnf(31,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(32,plain,
equal(converse(composition(u,converse(v))),composition(v,converse(u))),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(36,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(37,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(75,plain,
equal(join(join(complement(u),complement(v)),meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[5,13]),
[iquote('0:SpR:5.0,13.0')] ).
cnf(79,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[13,5]),
[iquote('0:SpR:13.0,5.0')] ).
cnf(80,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(82,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[14,79]),
[iquote('0:Rew:14.0,79.0')] ).
cnf(83,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[5,80]),
[iquote('0:Rew:5.0,80.0')] ).
cnf(85,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)],[83,16]),
[iquote('0:Rew:83.0,16.0')] ).
cnf(88,plain,
equal(join(meet(u,v),join(complement(u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[2,75]),
[iquote('0:Rew:2.0,75.0')] ).
cnf(93,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[13,19]),
[iquote('0:SpR:13.0,19.0')] ).
cnf(97,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[14,19]),
[iquote('0:SpR:14.0,19.0')] ).
cnf(98,plain,
equal(join(complement(top),meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[2,93]),
[iquote('0:Rew:2.0,93.0')] ).
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)],[5,97]),
[iquote('0:Rew:5.0,97.0')] ).
cnf(106,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[82,5]),
[iquote('0:SpR:82.0,5.0')] ).
cnf(159,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpR:3.0,13.0')] ).
cnf(160,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(166,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[13,3]),
[iquote('0:SpR:13.0,3.0')] ).
cnf(167,plain,
equal(join(join(u,v),w),join(v,join(u,w))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
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(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk3),join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
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)],[3,167]),
[iquote('0:Rew:3.0,167.0')] ).
cnf(181,plain,
equal(join(complement(u),join(complement(v),meet(v,u))),top),
inference(rew,[status(thm),theory(equality)],[2,174]),
[iquote('0:Rew:2.0,174.0')] ).
cnf(183,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk2,sk3)))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
inference(rew,[status(thm),theory(equality)],[2,175]),
[iquote('0:Rew:2.0,175.1')] ).
cnf(184,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk2),join(composition(sk1,join(sk2,sk3)),composition(sk1,sk3))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
inference(rew,[status(thm),theory(equality)],[160,183]),
[iquote('0:Rew:160.0,183.1')] ).
cnf(185,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),join(composition(sk1,sk2),composition(sk1,sk3))) ),
inference(rew,[status(thm),theory(equality)],[2,184]),
[iquote('0:Rew:2.0,184.1')] ).
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)],[11,8]),
[iquote('0:SpR:11.0,8.0')] ).
cnf(601,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[7,31]),
[iquote('0:SpR:7.0,31.0')] ).
cnf(604,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[9,601]),
[iquote('0:Rew:9.0,601.0')] ).
cnf(615,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[604,7]),
[iquote('0:SpR:604.0,7.0')] ).
cnf(618,plain,
equal(join(u,composition(v,u)),composition(join(converse(one),v),u)),
inference(spr,[status(thm),theory(equality)],[604,8]),
[iquote('0:SpR:604.0,8.0')] ).
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)],[648,5]),
[iquote('0:SpR:648.0,5.0')] ).
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)],[5,748]),
[iquote('0:SpR:5.0,748.0')] ).
cnf(820,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[726,3]),
[iquote('0:SpR:726.0,3.0')] ).
cnf(930,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[32,10]),
[iquote('0:SpR:32.0,10.0')] ).
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)],[36,11]),
[iquote('0:SpR:36.0,11.0')] ).
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)],[1071,13]),
[iquote('0:SpR:1071.0,13.0')] ).
cnf(1245,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[13,37]),
[iquote('0:SpR:13.0,37.0')] ).
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)],[2,1955,13]),
[iquote('0:Rew:2.0,1955.0,13.0,1955.0,2.0,1955.0')] ).
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)],[2034,8]),
[iquote('0:SpR:2034.0,8.0')] ).
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)],[179,2]),
[iquote('0:SpR:179.0,2.0')] ).
cnf(2852,plain,
equal(join(u,join(v,w)),join(u,join(w,v))),
inference(rew,[status(thm),theory(equality)],[3,2752]),
[iquote('0:Rew:3.0,2752.0')] ).
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)],[2898,6]),
[iquote('0:SpR:2898.0,6.0')] ).
cnf(2921,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)],[2898,85]),
[iquote('0:SpR:2898.0,85.0')] ).
cnf(2933,plain,
equal(join(u,meet(u,composition(top,composition(top,u)))),meet(u,composition(top,composition(top,u)))),
inference(rew,[status(thm),theory(equality)],[1115,2921,2008]),
[iquote('0:Rew:1115.0,2921.0,1115.0,2921.0,2008.0,2921.0')] ).
cnf(2934,plain,
equal(join(u,meet(u,composition(top,u))),meet(u,composition(top,u))),
inference(rew,[status(thm),theory(equality)],[2918,2933]),
[iquote('0:Rew:2918.0,2933.0')] ).
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)],[3420,2934]),
[iquote('0:Rew:3420.0,2934.0')] ).
cnf(3488,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[3422,3]),
[iquote('0:SpR:3422.0,3.0')] ).
cnf(5919,plain,
equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[9,1058]),
[iquote('0:SpR:9.0,1058.0')] ).
cnf(32194,plain,
equal(join(join(u,join(v,w)),x),join(u,join(join(w,v),x))),
inference(spr,[status(thm),theory(equality)],[2852,3]),
[iquote('0:SpR:2852.0,3.0')] ).
cnf(32489,plain,
equal(join(u,join(v,join(w,x))),join(u,join(w,join(v,x)))),
inference(rew,[status(thm),theory(equality)],[3,32194]),
[iquote('0:Rew:3.0,32194.0,3.0,32194.0,3.0,32194.0')] ).
cnf(116006,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[5919,9]),
[iquote('0:SpR:5919.0,9.0')] ).
cnf(116284,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[9,116006]),
[iquote('0:Rew:9.0,116006.0')] ).
cnf(116287,plain,
( ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3)))
| ~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3))) ),
inference(rew,[status(thm),theory(equality)],[116284,185]),
[iquote('0:Rew:116284.0,185.1')] ).
cnf(116637,plain,
~ equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3))),
inference(obv,[status(thm),theory(equality)],[116287]),
[iquote('0:Obv:116287.0')] ).
cnf(116638,plain,
~ equal(composition(sk1,join(sk2,join(sk2,join(sk3,sk3)))),composition(sk1,join(sk2,sk3))),
inference(rew,[status(thm),theory(equality)],[32489,116637,116284]),
[iquote('0:Rew:32489.0,116637.0,116284.0,116637.0,116284.0,116637.0')] ).
cnf(116639,plain,
~ equal(composition(sk1,join(sk2,sk3)),composition(sk1,join(sk2,sk3))),
inference(rew,[status(thm),theory(equality)],[3488,116638,3422]),
[iquote('0:Rew:3488.0,116638.0,3422.0,116638.0')] ).
cnf(116640,plain,
$false,
inference(obv,[status(thm),theory(equality)],[116639]),
[iquote('0:Obv:116639.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL008-4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n015.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 : Fri Jul 8 08:41:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 85.81/86.05
% 85.81/86.05 SPASS V 3.9
% 85.81/86.05 SPASS beiseite: Proof found.
% 85.81/86.05 % SZS status Theorem
% 85.81/86.05 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 85.81/86.05 SPASS derived 70238 clauses, backtracked 0 clauses, performed 0 splits and kept 9016 clauses.
% 85.81/86.05 SPASS allocated 181967 KBytes.
% 85.81/86.05 SPASS spent 0:1:25.57 on the problem.
% 85.81/86.05 0:00:00.03 for the input.
% 85.81/86.05 0:00:00.00 for the FLOTTER CNF translation.
% 85.81/86.05 0:00:00.54 for inferences.
% 85.81/86.05 0:00:00.00 for the backtracking.
% 85.81/86.05 0:1:24.85 for the reduction.
% 85.81/86.05
% 85.81/86.05
% 85.81/86.05 Here is a proof with depth 13, length 115 :
% 85.81/86.05 % SZS output start Refutation
% See solution above
% 88.90/89.15 Formulae used in the proof : goals_17 maddux1_join_commutativity_1 maddux2_join_associativity_2 maddux3_a_kind_of_de_Morgan_3 maddux4_definiton_of_meet_4 composition_associativity_5 composition_identity_6 composition_distributivity_7 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10 converse_cancellativity_11 def_top_12 def_zero_13 modular_law_1_15
% 88.90/89.15
%------------------------------------------------------------------------------