TSTP Solution File: REL048-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL048-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 20:02:30 EDT 2022
% Result : Unsatisfiable 0.59s 0.85s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of clauses : 102 ( 100 unt; 0 nHn; 102 RR)
% Number of literals : 104 ( 0 equ; 6 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 : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(join(join(sk1,sk2),sk3),sk3),
file('REL048-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ equal(join(sk2,sk3),sk3)
| ~ equal(join(sk1,sk3),sk3) ),
file('REL048-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,v),join(v,u)),
file('REL048-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL048-1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL048-1.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL048-1.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(u,one),u),
file('REL048-1.p',unknown),
[] ).
cnf(10,axiom,
equal(converse(converse(u)),u),
file('REL048-1.p',unknown),
[] ).
cnf(12,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL048-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL048-1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(u,complement(u)),top),
file('REL048-1.p',unknown),
[] ).
cnf(15,axiom,
equal(meet(u,complement(u)),zero),
file('REL048-1.p',unknown),
[] ).
cnf(16,plain,
equal(join(sk3,join(sk1,sk2)),sk3),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(17,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[3,13]),
[iquote('0:Rew:3.0,13.0')] ).
cnf(18,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(30,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[10,12]),
[iquote('0:SpR:10.0,12.0')] ).
cnf(78,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[14,6]),
[iquote('0:SpR:14.0,6.0')] ).
cnf(79,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(81,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[15,78]),
[iquote('0:Rew:15.0,78.0')] ).
cnf(82,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[6,79]),
[iquote('0:Rew:6.0,79.0')] ).
cnf(89,plain,
equal(join(top,zero),top),
inference(spr,[status(thm),theory(equality)],[81,14]),
[iquote('0:SpR:81.0,14.0')] ).
cnf(90,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[81,6]),
[iquote('0:SpR:81.0,6.0')] ).
cnf(103,plain,
equal(join(meet(top,u),complement(join(zero,u))),top),
inference(spr,[status(thm),theory(equality)],[81,18]),
[iquote('0:SpR:81.0,18.0')] ).
cnf(104,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[14,18]),
[iquote('0:SpR:14.0,18.0')] ).
cnf(107,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[6,18]),
[iquote('0:SpR:6.0,18.0')] ).
cnf(108,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[15,18]),
[iquote('0:SpR:15.0,18.0')] ).
cnf(113,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[3,104,81]),
[iquote('0:Rew:3.0,104.0,81.0,104.0')] ).
cnf(114,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[3,107]),
[iquote('0:Rew:3.0,107.0')] ).
cnf(115,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,108]),
[iquote('0:Rew:6.0,108.0')] ).
cnf(132,plain,
equal(complement(join(zero,zero)),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[81,90]),
[iquote('0:SpR:81.0,90.0')] ).
cnf(155,plain,
equal(meet(join(zero,zero),meet(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[132,15]),
[iquote('0:SpR:132.0,15.0')] ).
cnf(164,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[82,155]),
[iquote('0:Rew:82.0,155.0')] ).
cnf(171,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[164,18]),
[iquote('0:SpR:164.0,18.0')] ).
cnf(177,plain,
equal(join(zero,complement(join(join(zero,zero),complement(meet(top,top))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[3,171]),
[iquote('0:Rew:3.0,171.0')] ).
cnf(178,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[4,177]),
[iquote('0:Rew:4.0,177.0')] ).
cnf(193,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[4,14]),
[iquote('0:SpR:4.0,14.0')] ).
cnf(194,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(200,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[14,4]),
[iquote('0:SpR:14.0,4.0')] ).
cnf(205,plain,
equal(join(top,join(zero,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[89,4]),
[iquote('0:SpR:89.0,4.0')] ).
cnf(211,plain,
equal(join(sk2,join(sk3,sk1)),sk3),
inference(rew,[status(thm),theory(equality)],[194,16]),
[iquote('0:Rew:194.0,16.0')] ).
cnf(214,plain,
equal(join(sk2,join(sk1,sk3)),sk3),
inference(rew,[status(thm),theory(equality)],[3,211]),
[iquote('0:Rew:3.0,211.0')] ).
cnf(215,plain,
equal(join(sk1,join(sk3,sk2)),sk3),
inference(rew,[status(thm),theory(equality)],[194,214]),
[iquote('0:Rew:194.0,214.0')] ).
cnf(216,plain,
equal(join(sk1,join(sk2,sk3)),sk3),
inference(rew,[status(thm),theory(equality)],[3,215]),
[iquote('0:Rew:3.0,215.0')] ).
cnf(241,plain,
equal(join(top,meet(u,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[115,205]),
[iquote('0:SpR:115.0,205.0')] ).
cnf(460,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[8,30]),
[iquote('0:SpR:8.0,30.0')] ).
cnf(463,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[10,460]),
[iquote('0:Rew:10.0,460.0')] ).
cnf(472,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[463,8]),
[iquote('0:SpR:463.0,8.0')] ).
cnf(478,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[463,17]),
[iquote('0:SpR:463.0,17.0')] ).
cnf(482,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[472,463]),
[iquote('0:Rew:472.0,463.0')] ).
cnf(489,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[482,478]),
[iquote('0:Rew:482.0,478.0')] ).
cnf(525,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[489,6]),
[iquote('0:SpR:489.0,6.0')] ).
cnf(531,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[81,489]),
[iquote('0:SpR:81.0,489.0')] ).
cnf(537,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[531,132]),
[iquote('0:Rew:531.0,132.0')] ).
cnf(548,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[537,178]),
[iquote('0:Rew:537.0,178.0')] ).
cnf(550,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[525,115]),
[iquote('0:Rew:525.0,115.0')] ).
cnf(551,plain,
equal(join(top,complement(complement(u))),join(top,u)),
inference(rew,[status(thm),theory(equality)],[525,241]),
[iquote('0:Rew:525.0,241.0')] ).
cnf(573,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[531,548,550]),
[iquote('0:Rew:531.0,548.0,550.0,548.0')] ).
cnf(574,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[14,573]),
[iquote('0:Rew:14.0,573.0')] ).
cnf(601,plain,
equal(meet(top,complement(u)),complement(u)),
inference(spr,[status(thm),theory(equality)],[550,90]),
[iquote('0:SpR:550.0,90.0')] ).
cnf(607,plain,
equal(join(zero,complement(meet(u,v))),join(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[6,550]),
[iquote('0:SpR:6.0,550.0')] ).
cnf(621,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[574,6]),
[iquote('0:SpR:574.0,6.0')] ).
cnf(645,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[531,4]),
[iquote('0:SpR:531.0,4.0')] ).
cnf(671,plain,
equal(join(complement(u),complement(join(zero,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[601,103]),
[iquote('0:SpR:601.0,103.0')] ).
cnf(682,plain,
equal(join(complement(u),meet(top,u)),top),
inference(rew,[status(thm),theory(equality)],[90,671]),
[iquote('0:Rew:90.0,671.0')] ).
cnf(737,plain,
equal(join(complement(u),join(meet(top,u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[682,4]),
[iquote('0:SpR:682.0,4.0')] ).
cnf(865,plain,
equal(meet(top,join(top,complement(u))),complement(join(zero,meet(zero,u)))),
inference(spr,[status(thm),theory(equality)],[621,90]),
[iquote('0:SpR:621.0,90.0')] ).
cnf(883,plain,
equal(meet(zero,complement(u)),complement(join(top,u))),
inference(spr,[status(thm),theory(equality)],[551,621]),
[iquote('0:SpR:551.0,621.0')] ).
cnf(909,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[113,645]),
[iquote('0:SpR:113.0,645.0')] ).
cnf(916,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[909,550]),
[iquote('0:Rew:909.0,550.0')] ).
cnf(917,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[909,90]),
[iquote('0:Rew:909.0,90.0')] ).
cnf(927,plain,
equal(join(complement(u),complement(v)),complement(meet(u,v))),
inference(rew,[status(thm),theory(equality)],[909,607]),
[iquote('0:Rew:909.0,607.0')] ).
cnf(941,plain,
equal(meet(top,join(top,complement(u))),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[909,865]),
[iquote('0:Rew:909.0,865.0')] ).
cnf(948,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[916,917]),
[iquote('0:Rew:916.0,917.0')] ).
cnf(952,plain,
equal(join(complement(u),join(u,v)),join(top,v)),
inference(rew,[status(thm),theory(equality)],[948,737]),
[iquote('0:Rew:948.0,737.0')] ).
cnf(978,plain,
equal(join(u,join(v,complement(u))),join(top,v)),
inference(rew,[status(thm),theory(equality)],[194,952]),
[iquote('0:Rew:194.0,952.0')] ).
cnf(982,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[948,941]),
[iquote('0:Rew:948.0,941.0')] ).
cnf(1049,plain,
equal(meet(u,top),u),
inference(spr,[status(thm),theory(equality)],[948,82]),
[iquote('0:SpR:948.0,82.0')] ).
cnf(1307,plain,
equal(join(u,complement(meet(zero,join(u,top)))),top),
inference(spr,[status(thm),theory(equality)],[982,193]),
[iquote('0:SpR:982.0,193.0')] ).
cnf(1391,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[1049,114]),
[iquote('0:SpR:1049.0,114.0')] ).
cnf(1398,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[81,1391]),
[iquote('0:Rew:81.0,1391.0')] ).
cnf(1435,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1398,200]),
[iquote('0:SpR:1398.0,200.0')] ).
cnf(1445,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[14,1435,982,883,82]),
[iquote('0:Rew:14.0,1435.0,982.0,1435.0,883.0,1435.0,82.0,1435.0')] ).
cnf(1563,plain,
equal(complement(meet(zero,join(u,top))),top),
inference(spr,[status(thm),theory(equality)],[3,1445]),
[iquote('0:SpR:3.0,1445.0')] ).
cnf(1585,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1563,1307]),
[iquote('0:Rew:1563.0,1307.0')] ).
cnf(1631,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[1585,3]),
[iquote('0:SpR:1585.0,3.0')] ).
cnf(1652,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1631,978]),
[iquote('0:Rew:1631.0,978.0')] ).
cnf(3861,plain,
equal(join(u,complement(meet(v,u))),top),
inference(spr,[status(thm),theory(equality)],[927,1652]),
[iquote('0:SpR:927.0,1652.0')] ).
cnf(3875,plain,
equal(complement(meet(u,complement(v))),join(complement(u),v)),
inference(spr,[status(thm),theory(equality)],[916,927]),
[iquote('0:SpR:916.0,927.0')] ).
cnf(4007,plain,
equal(complement(meet(u,meet(v,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[3861,927]),
[iquote('0:SpR:3861.0,927.0')] ).
cnf(4332,plain,
equal(meet(u,meet(v,complement(u))),complement(top)),
inference(spr,[status(thm),theory(equality)],[4007,916]),
[iquote('0:SpR:4007.0,916.0')] ).
cnf(4367,plain,
equal(meet(u,meet(v,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[81,4332]),
[iquote('0:Rew:81.0,4332.0')] ).
cnf(4392,plain,
equal(join(zero,meet(u,complement(meet(v,complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[4367,114]),
[iquote('0:SpR:4367.0,114.0')] ).
cnf(4418,plain,
equal(meet(u,complement(meet(v,complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[909,4392]),
[iquote('0:Rew:909.0,4392.0')] ).
cnf(4419,plain,
equal(meet(u,join(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[3875,4418]),
[iquote('0:Rew:3875.0,4418.0')] ).
cnf(4795,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[916,4419]),
[iquote('0:SpR:916.0,4419.0')] ).
cnf(4886,plain,
equal(meet(join(sk2,sk3),sk3),join(sk2,sk3)),
inference(spr,[status(thm),theory(equality)],[216,4795]),
[iquote('0:SpR:216.0,4795.0')] ).
cnf(4924,plain,
equal(join(sk2,sk3),sk3),
inference(rew,[status(thm),theory(equality)],[4795,4886,82]),
[iquote('0:Rew:4795.0,4886.0,82.0,4886.0')] ).
cnf(4925,plain,
equal(join(sk1,sk3),sk3),
inference(rew,[status(thm),theory(equality)],[4924,216]),
[iquote('0:Rew:4924.0,216.0')] ).
cnf(4926,plain,
( ~ equal(sk3,sk3)
| ~ equal(join(sk1,sk3),sk3) ),
inference(rew,[status(thm),theory(equality)],[4924,2]),
[iquote('0:Rew:4924.0,2.0')] ).
cnf(4939,plain,
~ equal(join(sk1,sk3),sk3),
inference(obv,[status(thm),theory(equality)],[4926]),
[iquote('0:Obv:4926.0')] ).
cnf(4940,plain,
~ equal(sk3,sk3),
inference(rew,[status(thm),theory(equality)],[4925,4939]),
[iquote('0:Rew:4925.0,4939.0')] ).
cnf(4941,plain,
$false,
inference(obv,[status(thm),theory(equality)],[4940]),
[iquote('0:Obv:4940.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : REL048-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jul 8 08:38:25 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.59/0.85
% 0.59/0.85 SPASS V 3.9
% 0.59/0.85 SPASS beiseite: Proof found.
% 0.59/0.85 % SZS status Theorem
% 0.59/0.85 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.59/0.85 SPASS derived 3152 clauses, backtracked 0 clauses, performed 0 splits and kept 693 clauses.
% 0.59/0.85 SPASS allocated 67626 KBytes.
% 0.59/0.85 SPASS spent 0:00:00.47 on the problem.
% 0.59/0.85 0:00:00.03 for the input.
% 0.59/0.85 0:00:00.00 for the FLOTTER CNF translation.
% 0.59/0.85 0:00:00.03 for inferences.
% 0.59/0.85 0:00:00.00 for the backtracking.
% 0.59/0.85 0:00:00.39 for the reduction.
% 0.59/0.85
% 0.59/0.85
% 0.59/0.85 Here is a proof with depth 11, length 102 :
% 0.59/0.85 % SZS output start Refutation
% See solution above
% 0.69/0.87 Formulae used in the proof : goals_14 goals_15 maddux1_join_commutativity_1 maddux2_join_associativity_2 maddux3_a_kind_of_de_Morgan_3 maddux4_definiton_of_meet_4 composition_identity_6 converse_idempotence_8 converse_multiplicativity_10 converse_cancellativity_11 def_top_12 def_zero_13
% 0.69/0.87
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