%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT091-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 06:49:00 EDT 2022
% Result : Unsatisfiable 0.53s 0.73s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of clauses : 85 ( 85 unt; 0 nHn; 85 RR)
% Number of literals : 85 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(join(meet(u,v),meet(u,join(u,v))),u),
file('LAT091-1.p',unknown),
[] ).
cnf(2,axiom,
equal(join(meet(u,u),meet(v,join(u,u))),u),
file('LAT091-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(meet(u,v),meet(v,join(u,v))),v),
file('LAT091-1.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(meet(join(u,v),join(w,u)),u),u),
file('LAT091-1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(join(meet(u,v),meet(w,u)),u),u),
file('LAT091-1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(join(a,b),join(b,a)),
file('LAT091-1.p',unknown),
[] ).
cnf(17,plain,
equal(join(meet(meet(u,u),meet(v,join(u,u))),meet(meet(u,u),u)),meet(u,u)),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(22,plain,
equal(join(meet(u,u),join(u,u)),u),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(23,plain,
equal(join(u,meet(u,join(meet(join(u,v),join(w,u)),u))),u),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(25,plain,
equal(join(join(u,meet(v,meet(join(u,w),join(x,u)))),meet(join(u,w),join(x,u))),meet(join(u,w),join(x,u))),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
cnf(26,plain,
equal(join(join(meet(u,v),u),u),u),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
cnf(31,plain,
equal(meet(meet(join(u,v),u),u),u),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(33,plain,
equal(meet(meet(u,join(v,meet(w,u))),meet(w,u)),meet(w,u)),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(37,plain,
equal(join(meet(meet(u,u),join(u,u)),meet(meet(u,u),u)),meet(u,u)),
inference(spr,[status(thm),theory(equality)],[22,1]),
[iquote('0:SpR:22.0,1.0')] ).
cnf(42,plain,
equal(join(meet(join(meet(u,v),u),u),meet(join(meet(u,v),u),u)),join(meet(u,v),u)),
inference(spr,[status(thm),theory(equality)],[26,1]),
[iquote('0:SpR:26.0,1.0')] ).
cnf(48,plain,
equal(join(u,meet(u,join(meet(join(u,v),u),u))),u),
inference(spr,[status(thm),theory(equality)],[31,3]),
[iquote('0:SpR:31.0,3.0')] ).
cnf(51,plain,
equal(join(join(u,meet(join(u,v),u)),meet(join(u,v),u)),meet(join(u,v),u)),
inference(spr,[status(thm),theory(equality)],[31,26]),
[iquote('0:SpR:31.0,26.0')] ).
cnf(56,plain,
equal(meet(meet(u,meet(u,v)),meet(u,v)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[1,31]),
[iquote('0:SpR:1.0,31.0')] ).
cnf(59,plain,
equal(meet(meet(u,join(meet(u,v),u)),join(meet(u,v),u)),join(meet(u,v),u)),
inference(spr,[status(thm),theory(equality)],[26,31]),
[iquote('0:SpR:26.0,31.0')] ).
cnf(80,plain,
equal(meet(meet(u,join(v,u)),u),u),
inference(spr,[status(thm),theory(equality)],[48,4]),
[iquote('0:SpR:48.0,4.0')] ).
cnf(81,plain,
equal(meet(meet(u,u),u),u),
inference(spr,[status(thm),theory(equality)],[48,31]),
[iquote('0:SpR:48.0,31.0')] ).
cnf(82,plain,
equal(join(u,meet(u,join(meet(u,u),u))),u),
inference(spr,[status(thm),theory(equality)],[48]),
[iquote('0:SpR:48.0,48.0')] ).
cnf(93,plain,
equal(join(meet(meet(u,u),meet(v,join(u,u))),u),meet(u,u)),
inference(rew,[status(thm),theory(equality)],[81,17]),
[iquote('0:Rew:81.0,17.0')] ).
cnf(94,plain,
equal(join(meet(meet(u,u),join(u,u)),u),meet(u,u)),
inference(rew,[status(thm),theory(equality)],[81,37]),
[iquote('0:Rew:81.0,37.0')] ).
cnf(111,plain,
equal(join(u,meet(meet(u,join(v,u)),join(meet(u,join(v,u)),u))),meet(u,join(v,u))),
inference(spr,[status(thm),theory(equality)],[80,1]),
[iquote('0:SpR:80.0,1.0')] ).
cnf(121,plain,
equal(meet(meet(meet(u,join(v,u)),u),meet(u,join(v,u))),meet(u,join(v,u))),
inference(spr,[status(thm),theory(equality)],[3,80]),
[iquote('0:SpR:3.0,80.0')] ).
cnf(130,plain,
equal(meet(u,meet(u,join(v,u))),meet(u,join(v,u))),
inference(rew,[status(thm),theory(equality)],[80,121]),
[iquote('0:Rew:80.0,121.0')] ).
cnf(134,plain,
equal(join(meet(u,meet(u,join(meet(join(u,v),join(w,u)),u))),meet(meet(u,join(meet(join(u,v),join(w,u)),u)),u)),meet(u,join(meet(join(u,v),join(w,u)),u))),
inference(spr,[status(thm),theory(equality)],[23,3]),
[iquote('0:SpR:23.0,3.0')] ).
cnf(135,plain,
equal(join(meet(u,meet(u,join(meet(join(u,v),join(w,u)),u))),meet(u,u)),u),
inference(spr,[status(thm),theory(equality)],[23,1]),
[iquote('0:SpR:23.0,1.0')] ).
cnf(162,plain,
equal(join(meet(u,join(meet(join(u,v),join(w,u)),u)),meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[130,135]),
[iquote('0:Rew:130.0,135.0')] ).
cnf(164,plain,
equal(join(meet(u,meet(u,join(meet(join(u,v),join(w,u)),u))),u),meet(u,join(meet(join(u,v),join(w,u)),u))),
inference(rew,[status(thm),theory(equality)],[80,134]),
[iquote('0:Rew:80.0,134.0')] ).
cnf(165,plain,
equal(join(meet(u,join(meet(join(u,v),join(w,u)),u)),u),meet(u,join(meet(join(u,v),join(w,u)),u))),
inference(rew,[status(thm),theory(equality)],[130,164]),
[iquote('0:Rew:130.0,164.0')] ).
cnf(175,plain,
equal(join(meet(u,meet(u,join(meet(u,u),u))),meet(meet(u,join(meet(u,u),u)),u)),meet(u,join(meet(u,u),u))),
inference(spr,[status(thm),theory(equality)],[82,3]),
[iquote('0:SpR:82.0,3.0')] ).
cnf(187,plain,
equal(join(meet(u,meet(u,join(meet(u,u),u))),u),meet(u,join(meet(u,u),u))),
inference(rew,[status(thm),theory(equality)],[80,175]),
[iquote('0:Rew:80.0,175.0')] ).
cnf(188,plain,
equal(join(meet(u,join(meet(u,u),u)),u),meet(u,join(meet(u,u),u))),
inference(rew,[status(thm),theory(equality)],[130,187]),
[iquote('0:Rew:130.0,187.0')] ).
cnf(260,plain,
equal(meet(meet(join(u,u),u),meet(v,join(u,u))),meet(v,join(u,u))),
inference(spr,[status(thm),theory(equality)],[2,33]),
[iquote('0:SpR:2.0,33.0')] ).
cnf(261,plain,
equal(meet(meet(join(u,v),v),meet(v,join(u,v))),meet(v,join(u,v))),
inference(spr,[status(thm),theory(equality)],[3,33]),
[iquote('0:SpR:3.0,33.0')] ).
cnf(283,plain,
equal(meet(meet(meet(u,u),u),u),u),
inference(spr,[status(thm),theory(equality)],[81,56]),
[iquote('0:SpR:81.0,56.0')] ).
cnf(297,plain,
equal(meet(u,u),u),
inference(rew,[status(thm),theory(equality)],[81,283]),
[iquote('0:Rew:81.0,283.0')] ).
cnf(298,plain,
equal(join(u,meet(v,join(u,u))),u),
inference(rew,[status(thm),theory(equality)],[297,2]),
[iquote('0:Rew:297.0,2.0')] ).
cnf(320,plain,
equal(join(meet(u,join(u,u)),u),meet(u,join(u,u))),
inference(rew,[status(thm),theory(equality)],[297,188]),
[iquote('0:Rew:297.0,188.0')] ).
cnf(321,plain,
equal(join(meet(u,join(u,u)),u),u),
inference(rew,[status(thm),theory(equality)],[297,94]),
[iquote('0:Rew:297.0,94.0')] ).
cnf(322,plain,
equal(join(meet(u,meet(v,join(u,u))),u),u),
inference(rew,[status(thm),theory(equality)],[297,93]),
[iquote('0:Rew:297.0,93.0')] ).
cnf(329,plain,
equal(join(meet(u,join(meet(join(u,v),join(w,u)),u)),u),u),
inference(rew,[status(thm),theory(equality)],[297,162]),
[iquote('0:Rew:297.0,162.0')] ).
cnf(351,plain,
equal(meet(u,join(u,u)),u),
inference(rew,[status(thm),theory(equality)],[321,320]),
[iquote('0:Rew:321.0,320.0')] ).
cnf(352,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[351,321]),
[iquote('0:Rew:351.0,321.0')] ).
cnf(356,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[352,298]),
[iquote('0:Rew:352.0,298.0')] ).
cnf(357,plain,
equal(join(meet(u,meet(v,u)),u),u),
inference(rew,[status(thm),theory(equality)],[352,322]),
[iquote('0:Rew:352.0,322.0')] ).
cnf(359,plain,
equal(meet(meet(u,u),meet(v,u)),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[352,260]),
[iquote('0:Rew:352.0,260.0')] ).
cnf(366,plain,
equal(meet(join(meet(u,v),u),u),join(meet(u,v),u)),
inference(rew,[status(thm),theory(equality)],[352,42]),
[iquote('0:Rew:352.0,42.0')] ).
cnf(370,plain,
equal(join(u,meet(join(u,v),u)),meet(join(u,v),u)),
inference(rew,[status(thm),theory(equality)],[356,51]),
[iquote('0:Rew:356.0,51.0')] ).
cnf(375,plain,
equal(meet(u,meet(v,u)),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[297,359]),
[iquote('0:Rew:297.0,359.0')] ).
cnf(377,plain,
equal(join(meet(u,v),v),v),
inference(rew,[status(thm),theory(equality)],[375,357]),
[iquote('0:Rew:375.0,357.0')] ).
cnf(391,plain,
equal(meet(join(u,v),u),u),
inference(rew,[status(thm),theory(equality)],[356,370]),
[iquote('0:Rew:356.0,370.0')] ).
cnf(400,plain,
equal(meet(u,join(meet(join(u,v),join(w,u)),u)),u),
inference(rew,[status(thm),theory(equality)],[165,329]),
[iquote('0:Rew:165.0,329.0')] ).
cnf(465,plain,
equal(join(meet(meet(u,v),v),meet(meet(u,v),v)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[377,1]),
[iquote('0:SpR:377.0,1.0')] ).
cnf(481,plain,
equal(meet(meet(u,v),v),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[352,465]),
[iquote('0:Rew:352.0,465.0')] ).
cnf(482,plain,
equal(meet(u,join(meet(u,v),u)),join(meet(u,v),u)),
inference(rew,[status(thm),theory(equality)],[481,59]),
[iquote('0:Rew:481.0,59.0')] ).
cnf(878,plain,
equal(join(u,join(meet(u,v),u)),u),
inference(spr,[status(thm),theory(equality)],[366,356]),
[iquote('0:SpR:366.0,356.0')] ).
cnf(889,plain,
equal(meet(join(u,join(u,v)),join(u,v)),join(u,join(u,v))),
inference(spr,[status(thm),theory(equality)],[391,366]),
[iquote('0:SpR:391.0,366.0')] ).
cnf(984,plain,
equal(meet(u,join(meet(u,join(v,u)),u)),u),
inference(spr,[status(thm),theory(equality)],[878,400]),
[iquote('0:SpR:878.0,400.0')] ).
cnf(1003,plain,
equal(join(meet(u,join(v,u)),u),u),
inference(rew,[status(thm),theory(equality)],[482,984]),
[iquote('0:Rew:482.0,984.0')] ).
cnf(1004,plain,
equal(join(u,meet(meet(u,join(v,u)),u)),meet(u,join(v,u))),
inference(rew,[status(thm),theory(equality)],[1003,111]),
[iquote('0:Rew:1003.0,111.0')] ).
cnf(1007,plain,
equal(meet(u,join(v,u)),u),
inference(rew,[status(thm),theory(equality)],[352,1004,80]),
[iquote('0:Rew:352.0,1004.0,80.0,1004.0')] ).
cnf(1011,plain,
equal(join(meet(u,v),u),u),
inference(rew,[status(thm),theory(equality)],[1007,482]),
[iquote('0:Rew:1007.0,482.0')] ).
cnf(1018,plain,
equal(meet(meet(join(u,v),v),v),v),
inference(rew,[status(thm),theory(equality)],[1007,261]),
[iquote('0:Rew:1007.0,261.0')] ).
cnf(1030,plain,
equal(meet(join(u,v),v),v),
inference(rew,[status(thm),theory(equality)],[481,1018]),
[iquote('0:Rew:481.0,1018.0')] ).
cnf(1035,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[1030,889]),
[iquote('0:Rew:1030.0,889.0')] ).
cnf(1121,plain,
equal(meet(meet(join(u,v),join(w,v)),v),v),
inference(spr,[status(thm),theory(equality)],[1007,33]),
[iquote('0:SpR:1007.0,33.0')] ).
cnf(1138,plain,
equal(join(meet(meet(u,v),u),meet(meet(u,v),u)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[1011,1]),
[iquote('0:SpR:1011.0,1.0')] ).
cnf(1163,plain,
equal(meet(meet(u,v),u),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[352,1138]),
[iquote('0:Rew:352.0,1138.0')] ).
cnf(1200,plain,
equal(join(meet(u,join(u,v)),meet(u,join(u,v))),u),
inference(spr,[status(thm),theory(equality)],[1035,1]),
[iquote('0:SpR:1035.0,1.0')] ).
cnf(1216,plain,
equal(meet(u,join(u,v)),u),
inference(rew,[status(thm),theory(equality)],[352,1200]),
[iquote('0:Rew:352.0,1200.0')] ).
cnf(1359,plain,
equal(join(join(u,v),u),join(u,v)),
inference(spr,[status(thm),theory(equality)],[1216,356]),
[iquote('0:SpR:1216.0,356.0')] ).
cnf(1431,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[1163,356]),
[iquote('0:SpR:1163.0,356.0')] ).
cnf(1570,plain,
equal(meet(meet(u,v),meet(v,u)),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[1431,33]),
[iquote('0:SpR:1431.0,33.0')] ).
cnf(1723,plain,
equal(meet(meet(join(u,v),join(v,w)),v),v),
inference(spr,[status(thm),theory(equality)],[1359,1121]),
[iquote('0:SpR:1359.0,1121.0')] ).
cnf(2343,plain,
equal(meet(meet(u,v),meet(v,u)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[1570,1163]),
[iquote('0:SpR:1570.0,1163.0')] ).
cnf(2410,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[1570,2343]),
[iquote('0:Rew:1570.0,2343.0')] ).
cnf(2447,plain,
equal(meet(u,meet(join(v,u),join(u,w))),u),
inference(rew,[status(thm),theory(equality)],[2410,1723]),
[iquote('0:Rew:2410.0,1723.0')] ).
cnf(3269,plain,
equal(join(join(u,v),meet(join(u,v),join(v,u))),meet(join(u,v),join(v,u))),
inference(spr,[status(thm),theory(equality)],[2447,25]),
[iquote('0:SpR:2447.0,25.0')] ).
cnf(3351,plain,
equal(meet(join(u,v),join(v,u)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[1431,3269]),
[iquote('0:Rew:1431.0,3269.0')] ).
cnf(3379,plain,
equal(meet(join(u,v),join(v,u)),join(v,u)),
inference(spr,[status(thm),theory(equality)],[3351,2410]),
[iquote('0:SpR:3351.0,2410.0')] ).
cnf(3442,plain,
equal(join(u,v),join(v,u)),
inference(rew,[status(thm),theory(equality)],[3351,3379]),
[iquote('0:Rew:3351.0,3379.0')] ).
cnf(3443,plain,
$false,
inference(unc,[status(thm)],[3442,6]),
[iquote('0:UnC:3442.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LAT091-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Wed Jun 29 19:08:28 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.53/0.73
% 0.53/0.73 SPASS V 3.9
% 0.53/0.73 SPASS beiseite: Proof found.
% 0.53/0.73 % SZS status Theorem
% 0.53/0.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.73 SPASS derived 2573 clauses, backtracked 0 clauses, performed 0 splits and kept 588 clauses.
% 0.53/0.73 SPASS allocated 66479 KBytes.
% 0.53/0.73 SPASS spent 0:00:00.39 on the problem.
% 0.53/0.73 0:00:00.03 for the input.
% 0.53/0.73 0:00:00.00 for the FLOTTER CNF translation.
% 0.53/0.73 0:00:00.02 for inferences.
% 0.53/0.73 0:00:00.00 for the backtracking.
% 0.53/0.73 0:00:00.32 for the reduction.
% 0.53/0.73
% 0.53/0.73
% 0.53/0.73 Here is a proof with depth 8, length 85 :
% 0.53/0.73 % SZS output start Refutation
% See solution above
% 0.53/0.73 Formulae used in the proof : wal_absorbtion_1 wal_absorbtion_2 wal_absorbtion_3 wal_absorbtion_4 wal_absorbtion_5 prove_normal_axioms_4
% 0.53/0.73
%------------------------------------------------------------------------------