TSTP Solution File: LAT399-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT399-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 06:51:55 EDT 2022
% Result : Unsatisfiable 260.16s 260.35s
% Output : Refutation 261.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 127 ( 127 unt; 0 nHn; 127 RR)
% Number of literals : 127 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(meet(u,v),meet(v,u)),
file('LAT399-1.p',unknown),
[] ).
cnf(2,axiom,
equal(meet(meet(u,v),w),meet(u,meet(v,w))),
file('LAT399-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,v),join(v,u)),
file('LAT399-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('LAT399-1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,meet(u,v)),u),
file('LAT399-1.p',unknown),
[] ).
cnf(6,axiom,
equal(meet(u,join(u,v)),u),
file('LAT399-1.p',unknown),
[] ).
cnf(7,axiom,
equal(meet(u,join(v,w)),upme(u,v,w)),
file('LAT399-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(meet(u,v),meet(u,w)),lome(u,v,w)),
file('LAT399-1.p',unknown),
[] ).
cnf(9,axiom,
equal(meet(join(meet(meet(a,u),v),w),join(meet(meet(a,u),w),v)),join(upme(meet(a,u),v,w),meet(v,w))),
file('LAT399-1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(lome(meet(a,z1),z2,z3),upme(meet(a,z1),z2,z3)),
file('LAT399-1.p',unknown),
[] ).
cnf(11,plain,
equal(upme(u,u,v),u),
inference(rew,[status(thm),theory(equality)],[7,6]),
[iquote('0:Rew:7.0,6.0')] ).
cnf(12,plain,
equal(upme(join(meet(a,meet(u,v)),w),meet(a,meet(u,w)),v),join(meet(v,w),upme(meet(a,u),v,w))),
inference(rew,[status(thm),theory(equality)],[7,9,2,3]),
[iquote('0:Rew:7.0,9.0,2.0,9.0,2.0,9.0,3.0,9.0')] ).
cnf(19,plain,
equal(join(u,meet(v,u)),u),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(25,plain,
equal(join(u,upme(u,v,w)),u),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(26,plain,
equal(meet(join(u,v),w),upme(w,u,v)),
inference(spr,[status(thm),theory(equality)],[7,1]),
[iquote('0:SpR:7.0,1.0')] ).
cnf(30,plain,
equal(meet(u,join(v,w)),upme(u,w,v)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(32,plain,
equal(upme(u,v,w),upme(u,w,v)),
inference(rew,[status(thm),theory(equality)],[7,30]),
[iquote('0:Rew:7.0,30.0')] ).
cnf(43,plain,
equal(join(u,u),u),
inference(spr,[status(thm),theory(equality)],[11,25]),
[iquote('0:SpR:11.0,25.0')] ).
cnf(47,plain,
equal(upme(u,v,v),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[43,7]),
[iquote('0:SpR:43.0,7.0')] ).
cnf(48,plain,
equal(meet(u,u),u),
inference(spr,[status(thm),theory(equality)],[47,11]),
[iquote('0:SpR:47.0,11.0')] ).
cnf(53,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(58,plain,
equal(meet(u,join(v,join(w,x))),upme(u,join(v,w),x)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(60,plain,
equal(join(u,join(meet(u,v),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(62,plain,
equal(join(join(u,v),w),join(v,join(u,w))),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(66,plain,
equal(join(u,join(v,w)),join(v,join(u,w))),
inference(rew,[status(thm),theory(equality)],[4,62]),
[iquote('0:Rew:4.0,62.0')] ).
cnf(70,plain,
equal(upme(u,join(v,w),x),upme(u,v,join(w,x))),
inference(rew,[status(thm),theory(equality)],[7,58]),
[iquote('0:Rew:7.0,58.0')] ).
cnf(117,plain,
equal(upme(u,v,u),u),
inference(spr,[status(thm),theory(equality)],[32,11]),
[iquote('0:SpR:32.0,11.0')] ).
cnf(127,plain,
equal(join(meet(u,v),meet(u,meet(v,w))),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(128,plain,
equal(meet(u,meet(v,w)),meet(w,meet(u,v))),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(130,plain,
equal(meet(u,meet(v,join(w,x))),upme(meet(u,v),w,x)),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(136,plain,
equal(meet(u,meet(join(v,w),x)),meet(upme(u,v,w),x)),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(137,plain,
equal(meet(u,meet(u,v)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[48,2]),
[iquote('0:SpR:48.0,2.0')] ).
cnf(141,plain,
equal(lome(u,v,meet(v,w)),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[8,127]),
[iquote('0:Rew:8.0,127.0')] ).
cnf(142,plain,
equal(meet(u,upme(v,w,x)),upme(meet(u,v),w,x)),
inference(rew,[status(thm),theory(equality)],[7,130]),
[iquote('0:Rew:7.0,130.0')] ).
cnf(143,plain,
equal(meet(upme(u,v,w),x),upme(meet(u,x),v,w)),
inference(rew,[status(thm),theory(equality)],[142,136,26]),
[iquote('0:Rew:142.0,136.0,26.0,136.0')] ).
cnf(182,plain,
equal(meet(u,meet(v,u)),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[1,137]),
[iquote('0:SpR:1.0,137.0')] ).
cnf(220,plain,
equal(join(meet(u,v),meet(u,w)),lome(u,w,v)),
inference(spr,[status(thm),theory(equality)],[8,3]),
[iquote('0:SpR:8.0,3.0')] ).
cnf(226,plain,
equal(upme(u,meet(v,w),meet(v,x)),meet(u,lome(v,w,x))),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
cnf(228,plain,
equal(join(meet(u,v),meet(w,u)),lome(u,v,w)),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(229,plain,
equal(join(meet(u,v),upme(u,w,x)),lome(u,v,join(w,x))),
inference(spr,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpR:7.0,8.0')] ).
cnf(233,plain,
equal(join(meet(meet(u,v),w),meet(u,meet(v,x))),lome(meet(u,v),w,x)),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(234,plain,
equal(join(meet(u,v),meet(v,w)),lome(v,u,w)),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(243,plain,
equal(lome(u,v,w),lome(u,w,v)),
inference(rew,[status(thm),theory(equality)],[8,220]),
[iquote('0:Rew:8.0,220.0')] ).
cnf(249,plain,
equal(lome(u,meet(v,w),meet(v,x)),lome(meet(u,v),w,x)),
inference(rew,[status(thm),theory(equality)],[8,233,2]),
[iquote('0:Rew:8.0,233.0,2.0,233.0')] ).
cnf(297,plain,
equal(join(upme(u,v,w),meet(join(v,w),x)),lome(join(v,w),u,x)),
inference(spr,[status(thm),theory(equality)],[26,8]),
[iquote('0:SpR:26.0,8.0')] ).
cnf(345,plain,
equal(join(upme(u,v,w),upme(x,v,w)),lome(join(v,w),u,x)),
inference(rew,[status(thm),theory(equality)],[26,297]),
[iquote('0:Rew:26.0,297.0')] ).
cnf(394,plain,
equal(upme(join(meet(a,meet(u,v)),a),meet(u,a),v),join(meet(v,a),upme(meet(a,u),v,a))),
inference(spr,[status(thm),theory(equality)],[182,12]),
[iquote('0:SpR:182.0,12.0')] ).
cnf(401,plain,
equal(upme(join(meet(a,meet(u,v)),w),meet(a,meet(v,w)),u),join(meet(u,w),upme(meet(a,v),u,w))),
inference(spr,[status(thm),theory(equality)],[1,12]),
[iquote('0:SpR:1.0,12.0')] ).
cnf(415,plain,
equal(upme(join(u,meet(a,meet(v,w))),meet(a,meet(v,u)),w),join(meet(w,u),upme(meet(a,v),w,u))),
inference(spr,[status(thm),theory(equality)],[3,12]),
[iquote('0:SpR:3.0,12.0')] ).
cnf(423,plain,
equal(join(meet(u,a),upme(meet(a,v),u,a)),upme(a,meet(v,a),u)),
inference(rew,[status(thm),theory(equality)],[5,394,3]),
[iquote('0:Rew:5.0,394.0,3.0,394.0')] ).
cnf(503,plain,
equal(lome(u,join(v,w),upme(x,v,w)),meet(u,join(v,w))),
inference(spr,[status(thm),theory(equality)],[26,141]),
[iquote('0:SpR:26.0,141.0')] ).
cnf(505,plain,
equal(lome(u,join(v,w),upme(x,v,w)),upme(u,v,w)),
inference(rew,[status(thm),theory(equality)],[7,503]),
[iquote('0:Rew:7.0,503.0')] ).
cnf(628,plain,
equal(join(u,join(v,w)),join(w,join(v,u))),
inference(spr,[status(thm),theory(equality)],[3,53]),
[iquote('0:SpR:3.0,53.0')] ).
cnf(775,plain,
equal(join(u,lome(u,v,w)),join(u,meet(u,w))),
inference(spr,[status(thm),theory(equality)],[8,60]),
[iquote('0:SpR:8.0,60.0')] ).
cnf(779,plain,
equal(join(u,lome(u,v,w)),u),
inference(rew,[status(thm),theory(equality)],[5,775]),
[iquote('0:Rew:5.0,775.0')] ).
cnf(807,plain,
equal(upme(u,v,lome(v,w,x)),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[779,26]),
[iquote('0:SpR:779.0,26.0')] ).
cnf(879,plain,
equal(join(u,join(v,meet(w,u))),join(v,u)),
inference(spr,[status(thm),theory(equality)],[19,66]),
[iquote('0:SpR:19.0,66.0')] ).
cnf(1126,plain,
equal(join(meet(u,meet(v,w)),meet(v,x)),lome(v,meet(w,u),x)),
inference(spr,[status(thm),theory(equality)],[128,8]),
[iquote('0:SpR:128.0,8.0')] ).
cnf(1137,plain,
equal(join(meet(u,v),meet(w,meet(u,x))),lome(u,v,meet(x,w))),
inference(spr,[status(thm),theory(equality)],[128,8]),
[iquote('0:SpR:128.0,8.0')] ).
cnf(1202,plain,
equal(meet(u,meet(v,w)),meet(w,meet(v,u))),
inference(spr,[status(thm),theory(equality)],[1,128]),
[iquote('0:SpR:1.0,128.0')] ).
cnf(1894,plain,
equal(join(meet(meet(u,v),w),meet(v,meet(x,u))),lome(meet(u,v),w,x)),
inference(spr,[status(thm),theory(equality)],[128,228]),
[iquote('0:SpR:128.0,228.0')] ).
cnf(1902,plain,
equal(join(meet(u,v),meet(w,v)),lome(v,u,w)),
inference(spr,[status(thm),theory(equality)],[1,228]),
[iquote('0:SpR:1.0,228.0')] ).
cnf(1933,plain,
equal(join(meet(u,meet(v,w)),meet(v,meet(x,u))),lome(meet(u,v),w,x)),
inference(rew,[status(thm),theory(equality)],[2,1894]),
[iquote('0:Rew:2.0,1894.0')] ).
cnf(1934,plain,
equal(lome(u,meet(v,w),meet(x,w)),lome(meet(w,u),v,x)),
inference(rew,[status(thm),theory(equality)],[1126,1933]),
[iquote('0:Rew:1126.0,1933.0')] ).
cnf(2877,plain,
equal(upme(u,v,join(w,u)),u),
inference(spr,[status(thm),theory(equality)],[70,117]),
[iquote('0:SpR:70.0,117.0')] ).
cnf(2954,plain,
equal(upme(meet(u,v),w,u),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[5,2877]),
[iquote('0:SpR:5.0,2877.0')] ).
cnf(2955,plain,
equal(upme(meet(u,v),w,v),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[19,2877]),
[iquote('0:SpR:19.0,2877.0')] ).
cnf(2990,plain,
equal(join(meet(u,a),meet(a,v)),upme(a,meet(v,a),u)),
inference(rew,[status(thm),theory(equality)],[2954,423]),
[iquote('0:Rew:2954.0,423.0')] ).
cnf(2992,plain,
equal(upme(a,meet(u,a),v),lome(a,v,u)),
inference(rew,[status(thm),theory(equality)],[234,2990]),
[iquote('0:Rew:234.0,2990.0')] ).
cnf(3160,plain,
equal(join(meet(u,v),upme(meet(u,w),x,y)),lome(u,v,upme(w,x,y))),
inference(spr,[status(thm),theory(equality)],[142,8]),
[iquote('0:SpR:142.0,8.0')] ).
cnf(3612,plain,
equal(upme(a,u,meet(v,a)),lome(a,u,v)),
inference(spr,[status(thm),theory(equality)],[2992,32]),
[iquote('0:SpR:2992.0,32.0')] ).
cnf(3626,plain,
equal(upme(a,meet(a,u),v),lome(a,v,u)),
inference(spr,[status(thm),theory(equality)],[1,2992]),
[iquote('0:SpR:1.0,2992.0')] ).
cnf(3706,plain,
equal(meet(meet(u,v),lome(u,v,w)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[226,11]),
[iquote('0:SpR:226.0,11.0')] ).
cnf(3707,plain,
equal(upme(u,meet(v,w),meet(v,x)),meet(u,lome(v,x,w))),
inference(spr,[status(thm),theory(equality)],[226,32]),
[iquote('0:SpR:226.0,32.0')] ).
cnf(3762,plain,
equal(meet(u,meet(v,lome(u,v,w))),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[2,3706]),
[iquote('0:Rew:2.0,3706.0')] ).
cnf(3771,plain,
equal(meet(u,lome(v,w,x)),meet(u,lome(v,x,w))),
inference(rew,[status(thm),theory(equality)],[226,3707]),
[iquote('0:Rew:226.0,3707.0')] ).
cnf(4055,plain,
equal(join(meet(u,meet(v,w)),upme(meet(u,v),x,y)),lome(meet(u,v),w,join(x,y))),
inference(spr,[status(thm),theory(equality)],[2,229]),
[iquote('0:SpR:2.0,229.0')] ).
cnf(4095,plain,
equal(lome(u,meet(v,w),upme(v,x,y)),lome(meet(u,v),w,join(x,y))),
inference(rew,[status(thm),theory(equality)],[3160,4055]),
[iquote('0:Rew:3160.0,4055.0')] ).
cnf(5025,plain,
equal(upme(a,u,meet(a,v)),lome(a,u,v)),
inference(spr,[status(thm),theory(equality)],[1,3612]),
[iquote('0:SpR:1.0,3612.0')] ).
cnf(5042,plain,
equal(upme(meet(a,u),meet(a,v),w),meet(lome(a,w,v),u)),
inference(spr,[status(thm),theory(equality)],[3626,143]),
[iquote('0:SpR:3626.0,143.0')] ).
cnf(5346,plain,
equal(upme(meet(a,u),v,meet(a,w)),meet(lome(a,v,w),u)),
inference(spr,[status(thm),theory(equality)],[5025,143]),
[iquote('0:SpR:5025.0,143.0')] ).
cnf(6102,plain,
equal(join(join(u,meet(a,meet(v,w))),join(meet(w,u),upme(meet(a,v),w,u))),join(u,meet(a,meet(v,w)))),
inference(spr,[status(thm),theory(equality)],[415,25]),
[iquote('0:SpR:415.0,25.0')] ).
cnf(6207,plain,
equal(join(u,join(meet(a,meet(v,w)),upme(meet(a,v),w,u))),join(u,meet(a,meet(v,w)))),
inference(rew,[status(thm),theory(equality)],[628,6102,879,53]),
[iquote('0:Rew:628.0,6102.0,879.0,6102.0,53.0,6102.0,628.0,6102.0')] ).
cnf(6208,plain,
equal(join(u,lome(meet(a,v),w,join(w,u))),join(u,meet(a,meet(v,w)))),
inference(rew,[status(thm),theory(equality)],[4095,6207,3160]),
[iquote('0:Rew:4095.0,6207.0,3160.0,6207.0')] ).
cnf(6675,plain,
equal(join(join(meet(a,meet(u,v)),w),join(meet(u,w),upme(meet(a,v),u,w))),join(meet(a,meet(u,v)),w)),
inference(spr,[status(thm),theory(equality)],[401,25]),
[iquote('0:SpR:401.0,25.0')] ).
cnf(6801,plain,
equal(join(u,join(meet(a,meet(v,w)),upme(meet(a,w),v,u))),join(meet(a,meet(v,w)),u)),
inference(rew,[status(thm),theory(equality)],[628,6675,879]),
[iquote('0:Rew:628.0,6675.0,879.0,6675.0,628.0,6675.0,628.0,6675.0')] ).
cnf(6802,plain,
equal(join(u,lome(a,meet(v,w),upme(w,v,u))),join(meet(a,meet(v,w)),u)),
inference(rew,[status(thm),theory(equality)],[3160,6801]),
[iquote('0:Rew:3160.0,6801.0')] ).
cnf(12046,plain,
equal(meet(u,meet(v,lome(u,w,x))),meet(v,lome(u,w,x))),
inference(spr,[status(thm),theory(equality)],[807,2955]),
[iquote('0:SpR:807.0,2955.0')] ).
cnf(12123,plain,
equal(meet(u,lome(v,u,w)),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[12046,3762]),
[iquote('0:Rew:12046.0,3762.0')] ).
cnf(15608,plain,
equal(upme(u,meet(v,w),meet(x,w)),meet(lome(w,v,x),u)),
inference(spr,[status(thm),theory(equality)],[1902,26]),
[iquote('0:SpR:1902.0,26.0')] ).
cnf(25953,plain,
equal(meet(u,lome(v,w,x)),meet(lome(v,x,w),u)),
inference(spr,[status(thm),theory(equality)],[3771,1]),
[iquote('0:SpR:3771.0,1.0')] ).
cnf(33161,plain,
equal(lome(u,join(v,w),v),upme(u,v,w)),
inference(spr,[status(thm),theory(equality)],[11,505]),
[iquote('0:SpR:11.0,505.0')] ).
cnf(33313,plain,
equal(lome(u,v,join(v,w)),upme(u,v,w)),
inference(rew,[status(thm),theory(equality)],[243,33161]),
[iquote('0:Rew:243.0,33161.0')] ).
cnf(33315,plain,
equal(join(u,upme(meet(a,v),w,u)),join(u,meet(a,meet(v,w)))),
inference(rew,[status(thm),theory(equality)],[33313,6208]),
[iquote('0:Rew:33313.0,6208.0')] ).
cnf(69706,plain,
equal(lome(u,meet(v,w),upme(w,x,y)),lome(meet(w,u),v,join(x,y))),
inference(spr,[status(thm),theory(equality)],[26,1934]),
[iquote('0:SpR:26.0,1934.0')] ).
cnf(69810,plain,
equal(join(u,lome(meet(v,a),w,join(w,u))),join(meet(a,meet(w,v)),u)),
inference(rew,[status(thm),theory(equality)],[69706,6802]),
[iquote('0:Rew:69706.0,6802.0')] ).
cnf(69817,plain,
equal(join(u,upme(meet(v,a),w,u)),join(meet(a,meet(w,v)),u)),
inference(rew,[status(thm),theory(equality)],[33313,69810]),
[iquote('0:Rew:33313.0,69810.0')] ).
cnf(78462,plain,
equal(join(u,upme(a,v,u)),join(u,meet(a,meet(a,v)))),
inference(spr,[status(thm),theory(equality)],[48,33315]),
[iquote('0:SpR:48.0,33315.0')] ).
cnf(78570,plain,
equal(join(u,upme(a,v,u)),join(u,meet(a,v))),
inference(rew,[status(thm),theory(equality)],[137,78462]),
[iquote('0:Rew:137.0,78462.0')] ).
cnf(79003,plain,
equal(join(u,upme(a,u,v)),join(u,meet(a,v))),
inference(spr,[status(thm),theory(equality)],[32,78570]),
[iquote('0:SpR:32.0,78570.0')] ).
cnf(112616,plain,
equal(join(upme(u,v,w),v),lome(join(v,w),u,v)),
inference(spr,[status(thm),theory(equality)],[11,345]),
[iquote('0:SpR:11.0,345.0')] ).
cnf(112620,plain,
equal(join(upme(u,v,w),w),lome(join(v,w),u,w)),
inference(spr,[status(thm),theory(equality)],[117,345]),
[iquote('0:SpR:117.0,345.0')] ).
cnf(112905,plain,
equal(join(u,upme(v,u,w)),lome(join(u,w),v,u)),
inference(rew,[status(thm),theory(equality)],[3,112616]),
[iquote('0:Rew:3.0,112616.0')] ).
cnf(112908,plain,
equal(lome(join(u,v),a,u),join(u,meet(a,v))),
inference(rew,[status(thm),theory(equality)],[112905,79003]),
[iquote('0:Rew:112905.0,79003.0')] ).
cnf(112958,plain,
equal(join(u,upme(v,w,u)),lome(join(w,u),v,u)),
inference(rew,[status(thm),theory(equality)],[3,112620]),
[iquote('0:Rew:3.0,112620.0')] ).
cnf(112964,plain,
equal(lome(join(u,v),meet(w,a),v),join(meet(a,meet(u,w)),v)),
inference(rew,[status(thm),theory(equality)],[112958,69817]),
[iquote('0:Rew:112958.0,69817.0')] ).
cnf(112965,plain,
equal(lome(join(u,v),meet(a,w),v),join(v,meet(a,meet(w,u)))),
inference(rew,[status(thm),theory(equality)],[112958,33315]),
[iquote('0:Rew:112958.0,33315.0')] ).
cnf(117074,plain,
equal(meet(a,join(u,meet(a,v))),meet(join(u,v),a)),
inference(spr,[status(thm),theory(equality)],[112908,12123]),
[iquote('0:SpR:112908.0,12123.0')] ).
cnf(117244,plain,
equal(lome(a,u,v),upme(a,u,v)),
inference(rew,[status(thm),theory(equality)],[5025,117074,7,26]),
[iquote('0:Rew:5025.0,117074.0,7.0,117074.0,26.0,117074.0')] ).
cnf(118049,plain,
equal(upme(meet(a,u),meet(a,v),w),meet(upme(a,w,v),u)),
inference(rew,[status(thm),theory(equality)],[117244,5042]),
[iquote('0:Rew:117244.0,5042.0')] ).
cnf(118167,plain,
equal(upme(meet(a,u),v,meet(a,w)),meet(upme(a,v,w),u)),
inference(rew,[status(thm),theory(equality)],[117244,5346]),
[iquote('0:Rew:117244.0,5346.0')] ).
cnf(118561,plain,
equal(upme(meet(a,u),meet(a,v),w),upme(meet(a,u),w,v)),
inference(rew,[status(thm),theory(equality)],[143,118049]),
[iquote('0:Rew:143.0,118049.0')] ).
cnf(118609,plain,
equal(upme(meet(a,u),v,meet(a,w)),upme(meet(a,u),v,w)),
inference(rew,[status(thm),theory(equality)],[143,118167]),
[iquote('0:Rew:143.0,118167.0')] ).
cnf(120349,plain,
equal(upme(a,meet(u,v),meet(u,w)),lome(meet(a,u),v,w)),
inference(spr,[status(thm),theory(equality)],[117244,249]),
[iquote('0:SpR:117244.0,249.0')] ).
cnf(120480,plain,
equal(lome(meet(a,u),v,w),meet(a,lome(u,v,w))),
inference(rew,[status(thm),theory(equality)],[226,120349]),
[iquote('0:Rew:226.0,120349.0')] ).
cnf(120481,plain,
~ equal(meet(a,lome(z1,z2,z3)),upme(meet(a,z1),z2,z3)),
inference(rew,[status(thm),theory(equality)],[120480,10]),
[iquote('0:Rew:120480.0,10.0')] ).
cnf(130083,plain,
equal(join(meet(a,meet(u,v)),meet(meet(v,a),w)),meet(join(u,meet(meet(v,a),w)),meet(v,a))),
inference(spr,[status(thm),theory(equality)],[112964,141]),
[iquote('0:SpR:112964.0,141.0')] ).
cnf(130380,plain,
equal(upme(meet(a,u),v,meet(u,meet(a,w))),upme(a,meet(v,u),meet(w,u))),
inference(rew,[status(thm),theory(equality)],[117244,130083,1137,142,7,1202,2]),
[iquote('0:Rew:117244.0,130083.0,1137.0,130083.0,142.0,130083.0,7.0,130083.0,1202.0,130083.0,2.0,130083.0')] ).
cnf(130381,plain,
equal(upme(meet(a,u),v,meet(u,meet(a,w))),meet(a,lome(u,w,v))),
inference(rew,[status(thm),theory(equality)],[25953,130380,15608]),
[iquote('0:Rew:25953.0,130380.0,15608.0,130380.0')] ).
cnf(132367,plain,
equal(meet(meet(a,u),join(v,meet(a,meet(u,w)))),meet(join(w,v),meet(a,u))),
inference(spr,[status(thm),theory(equality)],[112965,12123]),
[iquote('0:SpR:112965.0,12123.0')] ).
cnf(132613,plain,
equal(upme(meet(a,u),v,meet(a,meet(u,w))),upme(meet(a,u),w,v)),
inference(rew,[status(thm),theory(equality)],[142,132367,7,2,128]),
[iquote('0:Rew:142.0,132367.0,7.0,132367.0,2.0,132367.0,142.0,132367.0,7.0,132367.0,128.0,132367.0')] ).
cnf(132614,plain,
equal(upme(meet(a,u),v,meet(u,w)),upme(meet(a,u),w,v)),
inference(rew,[status(thm),theory(equality)],[118609,132613]),
[iquote('0:Rew:118609.0,132613.0')] ).
cnf(132618,plain,
equal(upme(meet(a,u),meet(a,v),w),meet(a,lome(u,v,w))),
inference(rew,[status(thm),theory(equality)],[132614,130381]),
[iquote('0:Rew:132614.0,130381.0')] ).
cnf(132619,plain,
equal(meet(a,lome(u,v,w)),upme(meet(a,u),w,v)),
inference(rew,[status(thm),theory(equality)],[118561,132618]),
[iquote('0:Rew:118561.0,132618.0')] ).
cnf(132620,plain,
~ equal(upme(meet(a,z1),z3,z2),upme(meet(a,z1),z2,z3)),
inference(rew,[status(thm),theory(equality)],[132619,120481]),
[iquote('0:Rew:132619.0,120481.0')] ).
cnf(132809,plain,
~ equal(upme(meet(a,z1),z2,z3),upme(meet(a,z1),z2,z3)),
inference(rew,[status(thm),theory(equality)],[32,132620]),
[iquote('0:Rew:32.0,132620.0')] ).
cnf(132810,plain,
$false,
inference(obv,[status(thm),theory(equality)],[132809]),
[iquote('0:Obv:132809.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT399-1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 30 02:37:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 260.16/260.35
% 260.16/260.35 SPASS V 3.9
% 260.16/260.35 SPASS beiseite: Proof found.
% 260.16/260.35 % SZS status Theorem
% 260.16/260.35 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 260.16/260.35 SPASS derived 86430 clauses, backtracked 0 clauses, performed 0 splits and kept 14480 clauses.
% 260.16/260.35 SPASS allocated 181109 KBytes.
% 260.16/260.35 SPASS spent 0:4:19.88 on the problem.
% 260.16/260.35 0:00:00.04 for the input.
% 260.16/260.35 0:00:00.00 for the FLOTTER CNF translation.
% 260.16/260.35 0:00:00.63 for inferences.
% 260.16/260.35 0:00:00.00 for the backtracking.
% 260.16/260.35 0:4:19.09 for the reduction.
% 260.16/260.35
% 260.16/260.35
% 260.16/260.35 Here is a proof with depth 10, length 127 :
% 260.16/260.35 % SZS output start Refutation
% See solution above
% 261.71/261.89 Formulae used in the proof : commutativity associativity commutativity_001 associativity_002 absorption absorption_003 definition_of_upme definition_of_lome conjecture conjecture_1
% 261.71/261.89
%------------------------------------------------------------------------------