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 : n029.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 : Theorem 0.63s 0.86s
% Output : Refutation 0.70s
% 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(composition(u,one),u),
file('REL048+1.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL048+1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL048+1.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL048+1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(join(skc3,skc4),skc5),skc5),
file('REL048+1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,v),join(v,u)),
file('REL048+1.p',unknown),
[] ).
cnf(7,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL048+1.p',unknown),
[] ).
cnf(9,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL048+1.p',unknown),
[] ).
cnf(10,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL048+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(join(skc4,skc5),skc5)
| ~ equal(join(skc3,skc5),skc5) ),
file('REL048+1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL048+1.p',unknown),
[] ).
cnf(15,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL048+1.p',unknown),
[] ).
cnf(16,plain,
equal(join(skc5,join(skc3,skc4)),skc5),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(17,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[6,14]),
[iquote('0:Rew:6.0,14.0')] ).
cnf(18,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[7,15]),
[iquote('0:Rew:7.0,15.0')] ).
cnf(30,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,9]),
[iquote('0:SpR:2.0,9.0')] ).
cnf(78,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(79,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(81,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,78]),
[iquote('0:Rew:4.0,78.0')] ).
cnf(82,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[7,79]),
[iquote('0:Rew:7.0,79.0')] ).
cnf(89,plain,
equal(join(top,zero),top),
inference(spr,[status(thm),theory(equality)],[81,3]),
[iquote('0:SpR:81.0,3.0')] ).
cnf(90,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[81,7]),
[iquote('0:SpR:81.0,7.0')] ).
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)],[3,18]),
[iquote('0:SpR:3.0,18.0')] ).
cnf(107,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[7,18]),
[iquote('0:SpR:7.0,18.0')] ).
cnf(108,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,18]),
[iquote('0:SpR:4.0,18.0')] ).
cnf(113,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[6,104,81]),
[iquote('0:Rew:6.0,104.0,81.0,104.0')] ).
cnf(114,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[6,107]),
[iquote('0:Rew:6.0,107.0')] ).
cnf(115,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[7,108]),
[iquote('0:Rew:7.0,108.0')] ).
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)],[132,4]),
[iquote('0:SpR:132.0,4.0')] ).
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)],[6,171]),
[iquote('0:Rew:6.0,171.0')] ).
cnf(178,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[10,177]),
[iquote('0:Rew:10.0,177.0')] ).
cnf(193,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[10,3]),
[iquote('0:SpR:10.0,3.0')] ).
cnf(194,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.0')] ).
cnf(200,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[3,10]),
[iquote('0:SpR:3.0,10.0')] ).
cnf(205,plain,
equal(join(top,join(zero,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[89,10]),
[iquote('0:SpR:89.0,10.0')] ).
cnf(211,plain,
equal(join(skc4,join(skc5,skc3)),skc5),
inference(rew,[status(thm),theory(equality)],[194,16]),
[iquote('0:Rew:194.0,16.0')] ).
cnf(214,plain,
equal(join(skc4,join(skc3,skc5)),skc5),
inference(rew,[status(thm),theory(equality)],[6,211]),
[iquote('0:Rew:6.0,211.0')] ).
cnf(215,plain,
equal(join(skc3,join(skc5,skc4)),skc5),
inference(rew,[status(thm),theory(equality)],[194,214]),
[iquote('0:Rew:194.0,214.0')] ).
cnf(216,plain,
equal(join(skc3,join(skc4,skc5)),skc5),
inference(rew,[status(thm),theory(equality)],[6,215]),
[iquote('0:Rew:6.0,215.0')] ).
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)],[1,30]),
[iquote('0:SpR:1.0,30.0')] ).
cnf(463,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,460]),
[iquote('0:Rew:2.0,460.0')] ).
cnf(472,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[463,1]),
[iquote('0:SpR:463.0,1.0')] ).
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)],[489,7]),
[iquote('0:SpR:489.0,7.0')] ).
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)],[3,573]),
[iquote('0:Rew:3.0,573.0')] ).
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)],[7,550]),
[iquote('0:SpR:7.0,550.0')] ).
cnf(621,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[574,7]),
[iquote('0:SpR:574.0,7.0')] ).
cnf(645,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[531,10]),
[iquote('0:SpR:531.0,10.0')] ).
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)],[682,10]),
[iquote('0:SpR:682.0,10.0')] ).
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(1310,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(1394,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(1401,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[81,1394]),
[iquote('0:Rew:81.0,1394.0')] ).
cnf(1438,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1401,200]),
[iquote('0:SpR:1401.0,200.0')] ).
cnf(1448,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[3,1438,982,883,82]),
[iquote('0:Rew:3.0,1438.0,982.0,1438.0,883.0,1438.0,82.0,1438.0')] ).
cnf(1566,plain,
equal(complement(meet(zero,join(u,top))),top),
inference(spr,[status(thm),theory(equality)],[6,1448]),
[iquote('0:SpR:6.0,1448.0')] ).
cnf(1590,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1566,1310]),
[iquote('0:Rew:1566.0,1310.0')] ).
cnf(1635,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[1590,6]),
[iquote('0:SpR:1590.0,6.0')] ).
cnf(1658,plain,
equal(join(u,join(v,complement(u))),top),
inference(rew,[status(thm),theory(equality)],[1635,978]),
[iquote('0:Rew:1635.0,978.0')] ).
cnf(3865,plain,
equal(join(u,complement(meet(v,u))),top),
inference(spr,[status(thm),theory(equality)],[927,1658]),
[iquote('0:SpR:927.0,1658.0')] ).
cnf(3879,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(4011,plain,
equal(complement(meet(u,meet(v,complement(u)))),top),
inference(spr,[status(thm),theory(equality)],[3865,927]),
[iquote('0:SpR:3865.0,927.0')] ).
cnf(4336,plain,
equal(meet(u,meet(v,complement(u))),complement(top)),
inference(spr,[status(thm),theory(equality)],[4011,916]),
[iquote('0:SpR:4011.0,916.0')] ).
cnf(4371,plain,
equal(meet(u,meet(v,complement(u))),zero),
inference(rew,[status(thm),theory(equality)],[81,4336]),
[iquote('0:Rew:81.0,4336.0')] ).
cnf(4396,plain,
equal(join(zero,meet(u,complement(meet(v,complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[4371,114]),
[iquote('0:SpR:4371.0,114.0')] ).
cnf(4422,plain,
equal(meet(u,complement(meet(v,complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[909,4396]),
[iquote('0:Rew:909.0,4396.0')] ).
cnf(4423,plain,
equal(meet(u,join(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[3879,4422]),
[iquote('0:Rew:3879.0,4422.0')] ).
cnf(4799,plain,
equal(meet(u,join(v,u)),u),
inference(spr,[status(thm),theory(equality)],[916,4423]),
[iquote('0:SpR:916.0,4423.0')] ).
cnf(4890,plain,
equal(meet(join(skc4,skc5),skc5),join(skc4,skc5)),
inference(spr,[status(thm),theory(equality)],[216,4799]),
[iquote('0:SpR:216.0,4799.0')] ).
cnf(4928,plain,
equal(join(skc4,skc5),skc5),
inference(rew,[status(thm),theory(equality)],[4799,4890,82]),
[iquote('0:Rew:4799.0,4890.0,82.0,4890.0')] ).
cnf(4929,plain,
equal(join(skc3,skc5),skc5),
inference(rew,[status(thm),theory(equality)],[4928,216]),
[iquote('0:Rew:4928.0,216.0')] ).
cnf(4930,plain,
( ~ equal(skc5,skc5)
| ~ equal(join(skc3,skc5),skc5) ),
inference(rew,[status(thm),theory(equality)],[4928,12]),
[iquote('0:Rew:4928.0,12.0')] ).
cnf(4943,plain,
~ equal(join(skc3,skc5),skc5),
inference(obv,[status(thm),theory(equality)],[4930]),
[iquote('0:Obv:4930.0')] ).
cnf(4944,plain,
~ equal(skc5,skc5),
inference(rew,[status(thm),theory(equality)],[4929,4943]),
[iquote('0:Rew:4929.0,4943.0')] ).
cnf(4945,plain,
$false,
inference(obv,[status(thm),theory(equality)],[4944]),
[iquote('0:Obv:4944.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : REL048+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n029.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 15:21:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.63/0.86
% 0.63/0.86 SPASS V 3.9
% 0.63/0.86 SPASS beiseite: Proof found.
% 0.63/0.86 % SZS status Theorem
% 0.63/0.86 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/0.86 SPASS derived 3154 clauses, backtracked 0 clauses, performed 0 splits and kept 694 clauses.
% 0.63/0.86 SPASS allocated 89607 KBytes.
% 0.63/0.86 SPASS spent 0:00:00.51 on the problem.
% 0.63/0.86 0:00:00.03 for the input.
% 0.63/0.86 0:00:00.02 for the FLOTTER CNF translation.
% 0.63/0.86 0:00:00.03 for inferences.
% 0.63/0.86 0:00:00.00 for the backtracking.
% 0.63/0.86 0:00:00.39 for the reduction.
% 0.63/0.86
% 0.63/0.86
% 0.63/0.86 Here is a proof with depth 11, length 102 :
% 0.63/0.86 % SZS output start Refutation
% See solution above
% 0.70/0.88 Formulae used in the proof : composition_identity converse_idempotence def_top def_zero goals maddux1_join_commutativity maddux4_definiton_of_meet converse_multiplicativity maddux2_join_associativity converse_cancellativity maddux3_a_kind_of_de_Morgan
% 0.70/0.88
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