TSTP Solution File: REL045+2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : REL045+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 20:02:28 EDT 2022

% Result   : Theorem 3.88s 4.06s
% Output   : Refutation 3.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   40
%            Number of leaves      :   17
% Syntax   : Number of clauses     :  108 ( 108 unt;   0 nHn; 108 RR)
%            Number of literals    :  108 (   0 equ;   3 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    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(composition(u,one),u),
    file('REL045+2.p',unknown),
    [] ).

cnf(2,axiom,
    equal(converse(converse(u)),u),
    file('REL045+2.p',unknown),
    [] ).

cnf(3,axiom,
    equal(join(u,complement(u)),top),
    file('REL045+2.p',unknown),
    [] ).

cnf(4,axiom,
    equal(meet(u,complement(u)),zero),
    file('REL045+2.p',unknown),
    [] ).

cnf(5,axiom,
    equal(join(u,v),join(v,u)),
    file('REL045+2.p',unknown),
    [] ).

cnf(6,axiom,
    equal(complement(join(complement(u),complement(v))),meet(u,v)),
    file('REL045+2.p',unknown),
    [] ).

cnf(7,axiom,
    equal(join(converse(u),converse(v)),converse(join(u,v))),
    file('REL045+2.p',unknown),
    [] ).

cnf(8,axiom,
    equal(composition(converse(u),converse(v)),converse(composition(v,u))),
    file('REL045+2.p',unknown),
    [] ).

cnf(9,axiom,
    equal(join(join(u,v),w),join(u,join(v,w))),
    file('REL045+2.p',unknown),
    [] ).

cnf(10,axiom,
    equal(composition(composition(u,v),w),composition(u,composition(v,w))),
    file('REL045+2.p',unknown),
    [] ).

cnf(11,axiom,
    equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
    file('REL045+2.p',unknown),
    [] ).

cnf(12,axiom,
    equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
    file('REL045+2.p',unknown),
    [] ).

cnf(13,axiom,
    equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
    file('REL045+2.p',unknown),
    [] ).

cnf(14,axiom,
    ~ equal(join(skc1,composition(composition(skc1,converse(skc1)),skc1)),composition(composition(skc1,converse(skc1)),skc1)),
    file('REL045+2.p',unknown),
    [] ).

cnf(15,axiom,
    equal(join(meet(composition(u,v),w),meet(composition(meet(u,composition(w,converse(v))),v),w)),meet(composition(meet(u,composition(w,converse(v))),v),w)),
    file('REL045+2.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('REL045+2.p',unknown),
    [] ).

cnf(17,axiom,
    equal(join(meet(composition(u,v),w),composition(meet(u,composition(w,converse(v))),meet(v,composition(converse(u),w)))),composition(meet(u,composition(w,converse(v))),meet(v,composition(converse(u),w)))),
    file('REL045+2.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(skc1,composition(skc1,composition(converse(skc1),skc1))),composition(skc1,composition(converse(skc1),skc1))),
    inference(rew,[status(thm),theory(equality)],[10,14]),
    [iquote('0:Rew:10.0,14.0')] ).

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(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)],[83,16]),
    [iquote('0:Rew:83.0,16.0')] ).

cnf(85,plain,
    equal(join(meet(composition(u,v),w),meet(w,composition(meet(u,composition(w,converse(v))),v))),meet(w,composition(meet(u,composition(w,converse(v))),v))),
    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(96,plain,
    equal(join(meet(u,complement(v)),meet(u,v)),u),
    inference(spr,[status(thm),theory(equality)],[6,19]),
    [iquote('0:SpR:6.0,19.0')] ).

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(100,plain,
    equal(join(meet(u,v),meet(u,complement(v))),u),
    inference(rew,[status(thm),theory(equality)],[5,96]),
    [iquote('0:Rew:5.0,96.0')] ).

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(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(180,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(226,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(264,plain,
    equal(join(composition(u,v),composition(w,composition(x,v))),composition(join(u,composition(w,x)),v)),
    inference(spr,[status(thm),theory(equality)],[10,11]),
    [iquote('0:SpR:10.0,11.0')] ).

cnf(566,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(569,plain,
    equal(composition(converse(one),u),u),
    inference(rew,[status(thm),theory(equality)],[2,566]),
    [iquote('0:Rew:2.0,566.0')] ).

cnf(590,plain,
    equal(join(meet(composition(u,converse(v)),w),composition(meet(u,composition(w,v)),meet(converse(v),composition(converse(u),w)))),composition(meet(u,composition(w,v)),meet(converse(v),composition(converse(u),w)))),
    inference(spr,[status(thm),theory(equality)],[2,17]),
    [iquote('0:SpR:2.0,17.0')] ).

cnf(611,plain,
    equal(converse(one),one),
    inference(spr,[status(thm),theory(equality)],[569,1]),
    [iquote('0:SpR:569.0,1.0')] ).

cnf(614,plain,
    equal(join(u,composition(v,u)),composition(join(converse(one),v),u)),
    inference(spr,[status(thm),theory(equality)],[569,11]),
    [iquote('0:SpR:569.0,11.0')] ).

cnf(623,plain,
    equal(join(complement(u),complement(composition(one,u))),complement(u)),
    inference(spr,[status(thm),theory(equality)],[569,18]),
    [iquote('0:SpR:569.0,18.0')] ).

cnf(629,plain,
    equal(composition(one,u),u),
    inference(rew,[status(thm),theory(equality)],[611,569]),
    [iquote('0:Rew:611.0,569.0')] ).

cnf(644,plain,
    equal(join(complement(u),complement(u)),complement(u)),
    inference(rew,[status(thm),theory(equality)],[629,623]),
    [iquote('0:Rew:629.0,623.0')] ).

cnf(645,plain,
    equal(join(u,composition(v,u)),composition(join(one,v),u)),
    inference(rew,[status(thm),theory(equality)],[611,614]),
    [iquote('0:Rew:611.0,614.0')] ).

cnf(716,plain,
    equal(meet(u,u),complement(complement(u))),
    inference(spr,[status(thm),theory(equality)],[644,6]),
    [iquote('0:SpR:644.0,6.0')] ).

cnf(722,plain,
    equal(join(zero,zero),zero),
    inference(spr,[status(thm),theory(equality)],[82,644]),
    [iquote('0:SpR:82.0,644.0')] ).

cnf(744,plain,
    equal(join(zero,complement(complement(u))),u),
    inference(rew,[status(thm),theory(equality)],[716,101]),
    [iquote('0:Rew:716.0,101.0')] ).

cnf(785,plain,
    equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
    inference(spr,[status(thm),theory(equality)],[6,744]),
    [iquote('0:SpR:6.0,744.0')] ).

cnf(816,plain,
    equal(join(zero,join(zero,u)),join(zero,u)),
    inference(spr,[status(thm),theory(equality)],[722,9]),
    [iquote('0:SpR:722.0,9.0')] ).

cnf(1067,plain,
    equal(join(zero,u),u),
    inference(spr,[status(thm),theory(equality)],[99,816]),
    [iquote('0:SpR:99.0,816.0')] ).

cnf(1074,plain,
    equal(complement(complement(u)),u),
    inference(rew,[status(thm),theory(equality)],[1067,744]),
    [iquote('0:Rew:1067.0,744.0')] ).

cnf(1075,plain,
    equal(meet(top,u),complement(complement(u))),
    inference(rew,[status(thm),theory(equality)],[1067,106]),
    [iquote('0:Rew:1067.0,106.0')] ).

cnf(1082,plain,
    equal(composition(converse(u),complement(composition(u,top))),zero),
    inference(rew,[status(thm),theory(equality)],[1067,226]),
    [iquote('0:Rew:1067.0,226.0')] ).

cnf(1087,plain,
    equal(join(complement(u),complement(v)),complement(meet(u,v))),
    inference(rew,[status(thm),theory(equality)],[1067,785]),
    [iquote('0:Rew:1067.0,785.0')] ).

cnf(1098,plain,
    equal(meet(u,u),u),
    inference(rew,[status(thm),theory(equality)],[1074,716]),
    [iquote('0:Rew:1074.0,716.0')] ).

cnf(1111,plain,
    equal(meet(top,u),u),
    inference(rew,[status(thm),theory(equality)],[1074,1075]),
    [iquote('0:Rew:1074.0,1075.0')] ).

cnf(1182,plain,
    equal(complement(zero),top),
    inference(spr,[status(thm),theory(equality)],[1067,3]),
    [iquote('0:SpR:1067.0,3.0')] ).

cnf(1241,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(1504,plain,
    equal(join(top,converse(complement(converse(complement(u))))),join(u,converse(top))),
    inference(spr,[status(thm),theory(equality)],[1241,166]),
    [iquote('0:SpR:1241.0,166.0')] ).

cnf(1951,plain,
    equal(join(complement(u),join(complement(u),u)),top),
    inference(spr,[status(thm),theory(equality)],[1098,180]),
    [iquote('0:SpR:1098.0,180.0')] ).

cnf(1963,plain,
    equal(join(top,complement(u)),top),
    inference(rew,[status(thm),theory(equality)],[5,1951,3]),
    [iquote('0:Rew:5.0,1951.0,3.0,1951.0,5.0,1951.0')] ).

cnf(1974,plain,
    equal(join(u,top),top),
    inference(spr,[status(thm),theory(equality)],[1963,159]),
    [iquote('0:SpR:1963.0,159.0')] ).

cnf(1978,plain,
    equal(join(top,u),top),
    inference(spr,[status(thm),theory(equality)],[1074,1963]),
    [iquote('0:SpR:1074.0,1963.0')] ).

cnf(1983,plain,
    equal(join(u,converse(top)),top),
    inference(rew,[status(thm),theory(equality)],[1978,1504]),
    [iquote('0:Rew:1978.0,1504.0')] ).

cnf(1999,plain,
    equal(join(u,converse(top)),converse(top)),
    inference(spr,[status(thm),theory(equality)],[1974,37]),
    [iquote('0:SpR:1974.0,37.0')] ).

cnf(2004,plain,
    equal(converse(top),top),
    inference(rew,[status(thm),theory(equality)],[1983,1999]),
    [iquote('0:Rew:1983.0,1999.0')] ).

cnf(2030,plain,
    equal(composition(top,complement(composition(top,top))),zero),
    inference(spr,[status(thm),theory(equality)],[2004,1082]),
    [iquote('0:SpR:2004.0,1082.0')] ).

cnf(2037,plain,
    equal(join(complement(u),composition(top,complement(composition(top,u)))),complement(u)),
    inference(spr,[status(thm),theory(equality)],[2004,18]),
    [iquote('0:SpR:2004.0,18.0')] ).

cnf(2121,plain,
    equal(join(zero,composition(u,complement(composition(top,top)))),composition(join(top,u),complement(composition(top,top)))),
    inference(spr,[status(thm),theory(equality)],[2030,11]),
    [iquote('0:SpR:2030.0,11.0')] ).

cnf(2128,plain,
    equal(composition(u,complement(composition(top,top))),zero),
    inference(rew,[status(thm),theory(equality)],[1067,2121,2030,1978]),
    [iquote('0:Rew:1067.0,2121.0,2030.0,2121.0,1978.0,2121.0')] ).

cnf(2223,plain,
    equal(complement(composition(top,top)),zero),
    inference(spr,[status(thm),theory(equality)],[2128,629]),
    [iquote('0:SpR:2128.0,629.0')] ).

cnf(2883,plain,
    equal(composition(top,top),complement(zero)),
    inference(spr,[status(thm),theory(equality)],[2223,1074]),
    [iquote('0:SpR:2223.0,1074.0')] ).

cnf(2894,plain,
    equal(composition(top,top),top),
    inference(rew,[status(thm),theory(equality)],[1182,2883]),
    [iquote('0:Rew:1182.0,2883.0')] ).

cnf(2914,plain,
    equal(composition(top,composition(top,u)),composition(top,u)),
    inference(spr,[status(thm),theory(equality)],[2894,10]),
    [iquote('0:SpR:2894.0,10.0')] ).

cnf(2916,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)],[2894,84]),
    [iquote('0:SpR:2894.0,84.0')] ).

cnf(2917,plain,
    equal(join(meet(top,u),meet(u,composition(meet(top,composition(u,converse(top))),top))),meet(u,composition(meet(top,composition(u,converse(top))),top))),
    inference(spr,[status(thm),theory(equality)],[2894,85]),
    [iquote('0:SpR:2894.0,85.0')] ).

cnf(2929,plain,
    equal(join(u,meet(u,composition(u,top))),meet(u,composition(u,top))),
    inference(rew,[status(thm),theory(equality)],[1111,2917,2894,10,2004]),
    [iquote('0:Rew:1111.0,2917.0,2894.0,2917.0,10.0,2917.0,1111.0,2917.0,2004.0,2917.0')] ).

cnf(2930,plain,
    equal(join(u,meet(u,composition(top,composition(top,u)))),meet(u,composition(top,composition(top,u)))),
    inference(rew,[status(thm),theory(equality)],[1111,2916,2004]),
    [iquote('0:Rew:1111.0,2916.0,1111.0,2916.0,2004.0,2916.0')] ).

cnf(2931,plain,
    equal(join(u,meet(u,composition(top,u))),meet(u,composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[2914,2930]),
    [iquote('0:Rew:2914.0,2930.0')] ).

cnf(3318,plain,
    equal(join(complement(composition(top,u)),composition(converse(top),complement(composition(top,u)))),complement(composition(top,u))),
    inference(spr,[status(thm),theory(equality)],[2914,18]),
    [iquote('0:SpR:2914.0,18.0')] ).

cnf(3335,plain,
    equal(join(complement(composition(top,u)),composition(top,complement(composition(top,u)))),complement(composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[2004,3318]),
    [iquote('0:Rew:2004.0,3318.0')] ).

cnf(3336,plain,
    equal(composition(join(one,top),complement(composition(top,u))),complement(composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[645,3335]),
    [iquote('0:Rew:645.0,3335.0')] ).

cnf(3337,plain,
    equal(composition(top,complement(composition(top,u))),complement(composition(top,u))),
    inference(rew,[status(thm),theory(equality)],[1974,3336]),
    [iquote('0:Rew:1974.0,3336.0')] ).

cnf(3338,plain,
    equal(join(complement(u),complement(composition(top,u))),complement(u)),
    inference(rew,[status(thm),theory(equality)],[3337,2037]),
    [iquote('0:Rew:3337.0,2037.0')] ).

cnf(3339,plain,
    equal(complement(meet(u,composition(top,u))),complement(u)),
    inference(rew,[status(thm),theory(equality)],[1087,3338]),
    [iquote('0:Rew:1087.0,3338.0')] ).

cnf(3393,plain,
    equal(meet(u,composition(top,u)),complement(complement(u))),
    inference(spr,[status(thm),theory(equality)],[3339,1074]),
    [iquote('0:SpR:3339.0,1074.0')] ).

cnf(3416,plain,
    equal(meet(u,composition(top,u)),u),
    inference(rew,[status(thm),theory(equality)],[1074,3393]),
    [iquote('0:Rew:1074.0,3393.0')] ).

cnf(3418,plain,
    equal(join(u,u),u),
    inference(rew,[status(thm),theory(equality)],[3416,2931]),
    [iquote('0:Rew:3416.0,2931.0')] ).

cnf(3484,plain,
    equal(join(u,join(u,v)),join(u,v)),
    inference(spr,[status(thm),theory(equality)],[3418,9]),
    [iquote('0:SpR:3418.0,9.0')] ).

cnf(3653,plain,
    equal(join(meet(u,v),u),u),
    inference(spr,[status(thm),theory(equality)],[100,3484]),
    [iquote('0:SpR:100.0,3484.0')] ).

cnf(3666,plain,
    equal(join(u,meet(u,v)),u),
    inference(rew,[status(thm),theory(equality)],[5,3653]),
    [iquote('0:Rew:5.0,3653.0')] ).

cnf(3672,plain,
    equal(meet(u,composition(u,top)),u),
    inference(rew,[status(thm),theory(equality)],[3666,2929]),
    [iquote('0:Rew:3666.0,2929.0')] ).

cnf(6948,plain,
    equal(join(u,composition(v,composition(w,u))),composition(join(one,composition(v,w)),u)),
    inference(spr,[status(thm),theory(equality)],[629,264]),
    [iquote('0:SpR:629.0,264.0')] ).

cnf(6964,plain,
    ~ equal(composition(join(one,composition(skc1,converse(skc1))),skc1),composition(skc1,composition(converse(skc1),skc1))),
    inference(rew,[status(thm),theory(equality)],[6948,20]),
    [iquote('0:Rew:6948.0,20.0')] ).

cnf(17039,plain,
    equal(join(meet(composition(u,converse(top)),u),composition(u,meet(converse(top),composition(converse(u),u)))),composition(u,meet(converse(top),composition(converse(u),u)))),
    inference(spr,[status(thm),theory(equality)],[3672,590]),
    [iquote('0:SpR:3672.0,590.0')] ).

cnf(17098,plain,
    equal(join(u,composition(u,composition(converse(u),u))),composition(u,composition(converse(u),u))),
    inference(rew,[status(thm),theory(equality)],[3672,17039,83,1111,2004]),
    [iquote('0:Rew:3672.0,17039.0,83.0,17039.0,1111.0,17039.0,2004.0,17039.0')] ).

cnf(17099,plain,
    equal(composition(join(one,composition(u,converse(u))),u),composition(u,composition(converse(u),u))),
    inference(rew,[status(thm),theory(equality)],[6948,17098]),
    [iquote('0:Rew:6948.0,17098.0')] ).

cnf(17100,plain,
    $false,
    inference(unc,[status(thm)],[17099,6964]),
    [iquote('0:UnC:17099.0,6964.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : REL045+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jul  8 09:05:45 EDT 2022
% 0.12/0.35  % CPUTime  : 
% 3.88/4.06  
% 3.88/4.06  SPASS V 3.9 
% 3.88/4.06  SPASS beiseite: Proof found.
% 3.88/4.06  % SZS status Theorem
% 3.88/4.06  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 3.88/4.06  SPASS derived 10833 clauses, backtracked 0 clauses, performed 0 splits and kept 2377 clauses.
% 3.88/4.06  SPASS allocated 106802 KBytes.
% 3.88/4.06  SPASS spent	0:00:03.69 on the problem.
% 3.88/4.06  		0:00:00.04 for the input.
% 3.88/4.06  		0:00:00.03 for the FLOTTER CNF translation.
% 3.88/4.06  		0:00:00.08 for inferences.
% 3.88/4.06  		0:00:00.00 for the backtracking.
% 3.88/4.06  		0:00:03.51 for the reduction.
% 3.88/4.06  
% 3.88/4.06  
% 3.88/4.06  Here is a proof with depth 14, length 108 :
% 3.88/4.06  % SZS output start Refutation
% See solution above
% 3.97/4.20  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 goals modular_law_2 modular_law_1 dedekind_law
% 3.97/4.20  
%------------------------------------------------------------------------------