TSTP Solution File: REL013+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 20:01:39 EDT 2022
% Result : Theorem 0.39s 0.56s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of clauses : 91 ( 89 unt; 0 nHn; 91 RR)
% Number of literals : 93 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(composition(u,one),u),
file('REL013+1.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL013+1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL013+1.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL013+1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL013+1.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL013+1.p',unknown),
[] ).
cnf(7,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL013+1.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL013+1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL013+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(composition(zero,skc3),zero)
| ~ equal(composition(skc2,zero),zero) ),
file('REL013+1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL013+1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL013+1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL013+1.p',unknown),
[] ).
cnf(15,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[5,13]),
[iquote('0:Rew:5.0,13.0')] ).
cnf(16,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[6,14]),
[iquote('0:Rew:6.0,14.0')] ).
cnf(27,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(32,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(33,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(71,plain,
equal(join(join(complement(u),complement(v)),meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(75,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(76,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(78,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,75]),
[iquote('0:Rew:4.0,75.0')] ).
cnf(79,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[6,76]),
[iquote('0:Rew:6.0,76.0')] ).
cnf(82,plain,
equal(join(meet(u,v),join(complement(u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[5,71]),
[iquote('0:Rew:5.0,71.0')] ).
cnf(87,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[3,16]),
[iquote('0:SpR:3.0,16.0')] ).
cnf(91,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,16]),
[iquote('0:SpR:4.0,16.0')] ).
cnf(92,plain,
equal(join(complement(top),meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,87]),
[iquote('0:Rew:5.0,87.0')] ).
cnf(93,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[78,92]),
[iquote('0:Rew:78.0,92.0')] ).
cnf(95,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,91]),
[iquote('0:Rew:6.0,91.0')] ).
cnf(98,plain,
equal(meet(top,zero),zero),
inference(spr,[status(thm),theory(equality)],[78,4]),
[iquote('0:SpR:78.0,4.0')] ).
cnf(100,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[78,6]),
[iquote('0:SpR:78.0,6.0')] ).
cnf(104,plain,
equal(meet(zero,top),zero),
inference(rew,[status(thm),theory(equality)],[79,98]),
[iquote('0:Rew:79.0,98.0')] ).
cnf(108,plain,
equal(join(zero,complement(join(complement(zero),top))),zero),
inference(spr,[status(thm),theory(equality)],[104,16]),
[iquote('0:SpR:104.0,16.0')] ).
cnf(110,plain,
equal(join(zero,complement(join(top,complement(zero)))),zero),
inference(rew,[status(thm),theory(equality)],[5,108]),
[iquote('0:Rew:5.0,108.0')] ).
cnf(139,plain,
equal(meet(top,join(top,complement(zero))),complement(zero)),
inference(spr,[status(thm),theory(equality)],[110,100]),
[iquote('0:SpR:110.0,100.0')] ).
cnf(163,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(169,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[3,9]),
[iquote('0:SpR:3.0,9.0')] ).
cnf(178,plain,
equal(join(complement(u),join(meet(v,u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[163,82]),
[iquote('0:Rew:163.0,82.0')] ).
cnf(184,plain,
equal(join(complement(u),join(complement(v),meet(v,u))),top),
inference(rew,[status(thm),theory(equality)],[5,178]),
[iquote('0:Rew:5.0,178.0')] ).
cnf(248,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[78,15]),
[iquote('0:SpR:78.0,15.0')] ).
cnf(396,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,27]),
[iquote('0:SpR:1.0,27.0')] ).
cnf(399,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,396]),
[iquote('0:Rew:2.0,396.0')] ).
cnf(408,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[399,1]),
[iquote('0:SpR:399.0,1.0')] ).
cnf(414,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[399,15]),
[iquote('0:SpR:399.0,15.0')] ).
cnf(418,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[408,399]),
[iquote('0:Rew:408.0,399.0')] ).
cnf(425,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[418,414]),
[iquote('0:Rew:418.0,414.0')] ).
cnf(462,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[425,6]),
[iquote('0:SpR:425.0,6.0')] ).
cnf(468,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[78,425]),
[iquote('0:SpR:78.0,425.0')] ).
cnf(486,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[462,95]),
[iquote('0:Rew:462.0,95.0')] ).
cnf(536,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[468,9]),
[iquote('0:SpR:468.0,9.0')] ).
cnf(682,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[93,536]),
[iquote('0:SpR:93.0,536.0')] ).
cnf(689,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[682,486]),
[iquote('0:Rew:682.0,486.0')] ).
cnf(690,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[682,100]),
[iquote('0:Rew:682.0,100.0')] ).
cnf(694,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[682,248]),
[iquote('0:Rew:682.0,248.0')] ).
cnf(714,plain,
equal(meet(u,u),u),
inference(rew,[status(thm),theory(equality)],[689,462]),
[iquote('0:Rew:689.0,462.0')] ).
cnf(717,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[689,690]),
[iquote('0:Rew:689.0,690.0')] ).
cnf(718,plain,
equal(join(top,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[717,139]),
[iquote('0:Rew:717.0,139.0')] ).
cnf(779,plain,
equal(complement(zero),top),
inference(spr,[status(thm),theory(equality)],[78,689]),
[iquote('0:SpR:78.0,689.0')] ).
cnf(780,plain,
equal(join(top,top),top),
inference(rew,[status(thm),theory(equality)],[779,718]),
[iquote('0:Rew:779.0,718.0')] ).
cnf(795,plain,
equal(join(top,join(top,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[780,9]),
[iquote('0:SpR:780.0,9.0')] ).
cnf(802,plain,
equal(join(u,zero),u),
inference(spr,[status(thm),theory(equality)],[682,5]),
[iquote('0:SpR:682.0,5.0')] ).
cnf(849,plain,
equal(join(converse(zero),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[682,32]),
[iquote('0:SpR:682.0,32.0')] ).
cnf(850,plain,
equal(join(converse(zero),u),u),
inference(rew,[status(thm),theory(equality)],[2,849]),
[iquote('0:Rew:2.0,849.0')] ).
cnf(892,plain,
equal(converse(zero),zero),
inference(spr,[status(thm),theory(equality)],[850,802]),
[iquote('0:SpR:850.0,802.0')] ).
cnf(930,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[3,33]),
[iquote('0:SpR:3.0,33.0')] ).
cnf(1070,plain,
equal(join(top,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[930,795]),
[iquote('0:SpR:930.0,795.0')] ).
cnf(1104,plain,
equal(join(converse(top),top),converse(converse(top))),
inference(spr,[status(thm),theory(equality)],[1070,32]),
[iquote('0:SpR:1070.0,32.0')] ).
cnf(1107,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1070,1104,5,2]),
[iquote('0:Rew:1070.0,1104.0,5.0,1104.0,2.0,1104.0')] ).
cnf(1108,plain,
equal(join(u,converse(complement(converse(u)))),top),
inference(rew,[status(thm),theory(equality)],[1107,930]),
[iquote('0:Rew:1107.0,930.0')] ).
cnf(1120,plain,
equal(join(top,converse(u)),converse(join(top,u))),
inference(spr,[status(thm),theory(equality)],[1107,7]),
[iquote('0:SpR:1107.0,7.0')] ).
cnf(1124,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1107,694]),
[iquote('0:SpR:1107.0,694.0')] ).
cnf(1190,plain,
equal(join(composition(u,complement(composition(top,top))),zero),composition(join(u,top),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[1124,12]),
[iquote('0:SpR:1124.0,12.0')] ).
cnf(1194,plain,
equal(composition(join(u,top),complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[682,1190,5]),
[iquote('0:Rew:682.0,1190.0,5.0,1190.0')] ).
cnf(1205,plain,
equal(join(top,converse(complement(converse(complement(u))))),join(u,top)),
inference(spr,[status(thm),theory(equality)],[1108,169]),
[iquote('0:SpR:1108.0,169.0')] ).
cnf(1228,plain,
equal(converse(join(top,complement(converse(complement(u))))),join(u,top)),
inference(rew,[status(thm),theory(equality)],[1120,1205]),
[iquote('0:Rew:1120.0,1205.0')] ).
cnf(1586,plain,
equal(join(complement(u),join(complement(u),u)),top),
inference(spr,[status(thm),theory(equality)],[714,184]),
[iquote('0:SpR:714.0,184.0')] ).
cnf(1598,plain,
equal(join(top,complement(u)),top),
inference(rew,[status(thm),theory(equality)],[5,1586,3]),
[iquote('0:Rew:5.0,1586.0,3.0,1586.0,5.0,1586.0')] ).
cnf(1599,plain,
equal(join(u,top),converse(top)),
inference(rew,[status(thm),theory(equality)],[1598,1228]),
[iquote('0:Rew:1598.0,1228.0')] ).
cnf(1600,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1107,1599]),
[iquote('0:Rew:1107.0,1599.0')] ).
cnf(1612,plain,
equal(composition(top,complement(composition(top,top))),composition(u,complement(composition(top,top)))),
inference(rew,[status(thm),theory(equality)],[1600,1194]),
[iquote('0:Rew:1600.0,1194.0')] ).
cnf(1620,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[1124,1612]),
[iquote('0:Rew:1124.0,1612.0')] ).
cnf(1687,plain,
equal(composition(converse(complement(composition(top,top))),u),converse(zero)),
inference(spr,[status(thm),theory(equality)],[1620,27]),
[iquote('0:SpR:1620.0,27.0')] ).
cnf(1688,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[1620,418]),
[iquote('0:SpR:1620.0,418.0')] ).
cnf(1689,plain,
equal(composition(u,zero),zero),
inference(rew,[status(thm),theory(equality)],[1688,1620]),
[iquote('0:Rew:1688.0,1620.0')] ).
cnf(1697,plain,
( ~ equal(composition(zero,skc3),zero)
| ~ equal(zero,zero) ),
inference(rew,[status(thm),theory(equality)],[1689,11]),
[iquote('0:Rew:1689.0,11.1')] ).
cnf(1750,plain,
equal(composition(converse(complement(composition(top,top))),u),zero),
inference(rew,[status(thm),theory(equality)],[892,1687]),
[iquote('0:Rew:892.0,1687.0')] ).
cnf(1751,plain,
equal(composition(converse(zero),u),zero),
inference(rew,[status(thm),theory(equality)],[1688,1750]),
[iquote('0:Rew:1688.0,1750.0')] ).
cnf(1752,plain,
equal(composition(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[892,1751]),
[iquote('0:Rew:892.0,1751.0')] ).
cnf(1760,plain,
~ equal(composition(zero,skc3),zero),
inference(obv,[status(thm),theory(equality)],[1697]),
[iquote('0:Obv:1697.1')] ).
cnf(1761,plain,
~ equal(zero,zero),
inference(rew,[status(thm),theory(equality)],[1752,1760]),
[iquote('0:Rew:1752.0,1760.0')] ).
cnf(1762,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1761]),
[iquote('0:Obv:1761.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n008.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 12:22:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.39/0.56
% 0.39/0.56 SPASS V 3.9
% 0.39/0.56 SPASS beiseite: Proof found.
% 0.39/0.56 % SZS status Theorem
% 0.39/0.56 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.56 SPASS derived 1141 clauses, backtracked 0 clauses, performed 0 splits and kept 372 clauses.
% 0.39/0.56 SPASS allocated 86841 KBytes.
% 0.39/0.56 SPASS spent 0:00:00.21 on the problem.
% 0.39/0.56 0:00:00.03 for the input.
% 0.39/0.56 0:00:00.03 for the FLOTTER CNF translation.
% 0.39/0.56 0:00:00.01 for inferences.
% 0.39/0.56 0:00:00.00 for the backtracking.
% 0.39/0.56 0:00:00.12 for the reduction.
% 0.39/0.56
% 0.39/0.56
% 0.39/0.56 Here is a proof with depth 10, length 91 :
% 0.39/0.56 % SZS output start Refutation
% See solution above
% 0.39/0.56 Formulae used in the proof : composition_identity converse_idempotence def_top def_zero maddux1_join_commutativity maddux4_definiton_of_meet converse_additivity converse_multiplicativity maddux2_join_associativity goals composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan
% 0.39/0.57
%------------------------------------------------------------------------------