TSTP Solution File: LAT029-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT029-1 : TPTP v8.1.0. Released v2.2.0.
% 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 : Sun Jul 17 06:48:40 EDT 2022
% Result : Unsatisfiable 0.50s 0.68s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of clauses : 68 ( 62 unt; 0 nHn; 68 RR)
% Number of literals : 80 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 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('LAT029-1.p',unknown),
[] ).
cnf(2,axiom,
equal(join(meet(u,u),meet(v,join(u,u))),u),
file('LAT029-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(meet(u,v),meet(v,join(u,v))),v),
file('LAT029-1.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(meet(join(u,v),join(w,u)),u),u),
file('LAT029-1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(join(meet(u,v),meet(w,u)),u),u),
file('LAT029-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(join(a,a),a)
| ~ equal(meet(a,a),a)
| ~ equal(join(b,a),join(a,b))
| ~ equal(meet(b,a),meet(a,b)) ),
file('LAT029-1.p',unknown),
[] ).
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(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(70,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(71,plain,
equal(meet(meet(u,u),u),u),
inference(spr,[status(thm),theory(equality)],[48,31]),
[iquote('0:SpR:48.0,31.0')] ).
cnf(72,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(83,plain,
equal(join(meet(meet(u,u),join(u,u)),u),meet(u,u)),
inference(rew,[status(thm),theory(equality)],[71,37]),
[iquote('0:Rew:71.0,37.0')] ).
cnf(97,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)],[70,1]),
[iquote('0:SpR:70.0,1.0')] ).
cnf(105,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)],[3,70]),
[iquote('0:SpR:3.0,70.0')] ).
cnf(112,plain,
equal(meet(u,meet(u,join(v,u))),meet(u,join(v,u))),
inference(rew,[status(thm),theory(equality)],[70,105]),
[iquote('0:Rew:70.0,105.0')] ).
cnf(143,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)],[72,3]),
[iquote('0:SpR:72.0,3.0')] ).
cnf(153,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)],[70,143]),
[iquote('0:Rew:70.0,143.0')] ).
cnf(154,plain,
equal(join(meet(u,join(meet(u,u),u)),u),meet(u,join(meet(u,u),u))),
inference(rew,[status(thm),theory(equality)],[112,153]),
[iquote('0:Rew:112.0,153.0')] ).
cnf(213,plain,
equal(meet(meet(meet(u,u),u),u),u),
inference(spr,[status(thm),theory(equality)],[71,56]),
[iquote('0:SpR:71.0,56.0')] ).
cnf(225,plain,
equal(meet(u,u),u),
inference(rew,[status(thm),theory(equality)],[71,213]),
[iquote('0:Rew:71.0,213.0')] ).
cnf(226,plain,
( ~ equal(join(a,a),a)
| ~ equal(a,a)
| ~ equal(join(b,a),join(a,b))
| ~ equal(meet(b,a),meet(a,b)) ),
inference(rew,[status(thm),theory(equality)],[225,6]),
[iquote('0:Rew:225.0,6.1')] ).
cnf(227,plain,
equal(join(u,meet(v,join(u,u))),u),
inference(rew,[status(thm),theory(equality)],[225,2]),
[iquote('0:Rew:225.0,2.0')] ).
cnf(246,plain,
equal(join(meet(u,join(u,u)),u),meet(u,join(u,u))),
inference(rew,[status(thm),theory(equality)],[225,154]),
[iquote('0:Rew:225.0,154.0')] ).
cnf(247,plain,
equal(join(meet(u,join(u,u)),u),u),
inference(rew,[status(thm),theory(equality)],[225,83]),
[iquote('0:Rew:225.0,83.0')] ).
cnf(276,plain,
equal(meet(u,join(u,u)),u),
inference(rew,[status(thm),theory(equality)],[247,246]),
[iquote('0:Rew:247.0,246.0')] ).
cnf(277,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[276,247]),
[iquote('0:Rew:276.0,247.0')] ).
cnf(285,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[277,227]),
[iquote('0:Rew:277.0,227.0')] ).
cnf(288,plain,
equal(meet(join(meet(u,v),u),u),join(meet(u,v),u)),
inference(rew,[status(thm),theory(equality)],[277,42]),
[iquote('0:Rew:277.0,42.0')] ).
cnf(294,plain,
equal(join(u,meet(join(u,v),u)),meet(join(u,v),u)),
inference(rew,[status(thm),theory(equality)],[285,51]),
[iquote('0:Rew:285.0,51.0')] ).
cnf(303,plain,
equal(meet(join(u,v),u),u),
inference(rew,[status(thm),theory(equality)],[285,294]),
[iquote('0:Rew:285.0,294.0')] ).
cnf(337,plain,
( ~ equal(join(a,a),a)
| ~ equal(join(b,a),join(a,b))
| ~ equal(meet(b,a),meet(a,b)) ),
inference(obv,[status(thm),theory(equality)],[226]),
[iquote('0:Obv:226.1')] ).
cnf(338,plain,
( ~ equal(a,a)
| ~ equal(join(b,a),join(a,b))
| ~ equal(meet(b,a),meet(a,b)) ),
inference(rew,[status(thm),theory(equality)],[277,337]),
[iquote('0:Rew:277.0,337.0')] ).
cnf(339,plain,
( ~ equal(join(b,a),join(a,b))
| ~ equal(meet(b,a),meet(a,b)) ),
inference(obv,[status(thm),theory(equality)],[338]),
[iquote('0:Obv:338.0')] ).
cnf(380,plain,
equal(join(join(u,join(u,v)),join(u,v)),join(u,v)),
inference(spr,[status(thm),theory(equality)],[303,26]),
[iquote('0:SpR:303.0,26.0')] ).
cnf(388,plain,
equal(meet(u,join(meet(u,v),u)),join(meet(u,v),u)),
inference(spr,[status(thm),theory(equality)],[26,303]),
[iquote('0:SpR:26.0,303.0')] ).
cnf(803,plain,
equal(meet(join(u,v),join(u,join(u,v))),join(u,join(u,v))),
inference(spr,[status(thm),theory(equality)],[380,303]),
[iquote('0:SpR:380.0,303.0')] ).
cnf(863,plain,
equal(meet(join(meet(u,v),u),u),u),
inference(spr,[status(thm),theory(equality)],[388,70]),
[iquote('0:SpR:388.0,70.0')] ).
cnf(882,plain,
equal(join(meet(u,v),u),u),
inference(rew,[status(thm),theory(equality)],[288,863]),
[iquote('0:Rew:288.0,863.0')] ).
cnf(887,plain,
equal(join(u,meet(meet(u,join(v,u)),u)),meet(u,join(v,u))),
inference(rew,[status(thm),theory(equality)],[882,97]),
[iquote('0:Rew:882.0,97.0')] ).
cnf(911,plain,
equal(meet(u,join(v,u)),u),
inference(rew,[status(thm),theory(equality)],[277,887,70]),
[iquote('0:Rew:277.0,887.0,70.0,887.0')] ).
cnf(914,plain,
equal(join(u,join(u,v)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[911,803]),
[iquote('0:Rew:911.0,803.0')] ).
cnf(996,plain,
equal(join(meet(meet(u,v),u),meet(meet(u,v),u)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[882,1]),
[iquote('0:SpR:882.0,1.0')] ).
cnf(1016,plain,
equal(meet(meet(u,v),u),meet(u,v)),
inference(rew,[status(thm),theory(equality)],[277,996]),
[iquote('0:Rew:277.0,996.0')] ).
cnf(1032,plain,
equal(meet(meet(join(u,v),join(w,v)),v),v),
inference(spr,[status(thm),theory(equality)],[911,33]),
[iquote('0:SpR:911.0,33.0')] ).
cnf(1076,plain,
equal(join(meet(u,join(u,v)),meet(u,join(u,v))),u),
inference(spr,[status(thm),theory(equality)],[914,1]),
[iquote('0:SpR:914.0,1.0')] ).
cnf(1091,plain,
equal(meet(u,join(u,v)),u),
inference(rew,[status(thm),theory(equality)],[277,1076]),
[iquote('0:Rew:277.0,1076.0')] ).
cnf(1178,plain,
equal(join(join(u,v),u),join(u,v)),
inference(spr,[status(thm),theory(equality)],[1091,285]),
[iquote('0:SpR:1091.0,285.0')] ).
cnf(1202,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[1016,285]),
[iquote('0:SpR:1016.0,285.0')] ).
cnf(1228,plain,
equal(meet(meet(u,v),meet(v,u)),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[1202,33]),
[iquote('0:SpR:1202.0,33.0')] ).
cnf(1407,plain,
equal(meet(meet(join(u,v),join(v,w)),v),v),
inference(spr,[status(thm),theory(equality)],[1178,1032]),
[iquote('0:SpR:1178.0,1032.0')] ).
cnf(1894,plain,
equal(meet(meet(u,v),meet(v,u)),meet(u,v)),
inference(spr,[status(thm),theory(equality)],[1228,1016]),
[iquote('0:SpR:1228.0,1016.0')] ).
cnf(1954,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[1228,1894]),
[iquote('0:Rew:1228.0,1894.0')] ).
cnf(1962,plain,
( ~ equal(join(b,a),join(a,b))
| ~ equal(meet(a,b),meet(a,b)) ),
inference(rew,[status(thm),theory(equality)],[1954,339]),
[iquote('0:Rew:1954.0,339.1')] ).
cnf(1971,plain,
equal(meet(u,meet(join(v,u),join(u,w))),u),
inference(rew,[status(thm),theory(equality)],[1954,1407]),
[iquote('0:Rew:1954.0,1407.0')] ).
cnf(2047,plain,
~ equal(join(b,a),join(a,b)),
inference(obv,[status(thm),theory(equality)],[1962]),
[iquote('0:Obv:1962.1')] ).
cnf(2834,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)],[1971,25]),
[iquote('0:SpR:1971.0,25.0')] ).
cnf(2909,plain,
equal(meet(join(u,v),join(v,u)),join(u,v)),
inference(rew,[status(thm),theory(equality)],[1202,2834]),
[iquote('0:Rew:1202.0,2834.0')] ).
cnf(2934,plain,
equal(meet(join(u,v),join(v,u)),join(v,u)),
inference(spr,[status(thm),theory(equality)],[2909,1954]),
[iquote('0:SpR:2909.0,1954.0')] ).
cnf(2992,plain,
equal(join(u,v),join(v,u)),
inference(rew,[status(thm),theory(equality)],[2909,2934]),
[iquote('0:Rew:2909.0,2934.0')] ).
cnf(2993,plain,
$false,
inference(unc,[status(thm)],[2992,2047]),
[iquote('0:UnC:2992.0,2047.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT029-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % 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 : Wed Jun 29 22:08:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.50/0.68
% 0.50/0.68 SPASS V 3.9
% 0.50/0.68 SPASS beiseite: Proof found.
% 0.50/0.68 % SZS status Theorem
% 0.50/0.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.50/0.68 SPASS derived 2208 clauses, backtracked 0 clauses, performed 0 splits and kept 471 clauses.
% 0.50/0.68 SPASS allocated 65789 KBytes.
% 0.50/0.68 SPASS spent 0:00:00.32 on the problem.
% 0.50/0.68 0:00:00.04 for the input.
% 0.50/0.68 0:00:00.00 for the FLOTTER CNF translation.
% 0.50/0.68 0:00:00.02 for inferences.
% 0.50/0.68 0:00:00.00 for the backtracking.
% 0.50/0.68 0:00:00.24 for the reduction.
% 0.50/0.68
% 0.50/0.68
% 0.50/0.68 Here is a proof with depth 9, length 68 :
% 0.50/0.68 % SZS output start Refutation
% See solution above
% 0.50/0.68 Formulae used in the proof : wal_absorbtion_1 wal_absorbtion_2 wal_absorbtion_3 wal_absorbtion_4 wal_absorbtion_5 prove_normal_axioms
% 0.50/0.68
%------------------------------------------------------------------------------