TSTP Solution File: REL002+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL002+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 20:01:22 EDT 2022
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of clauses : 71 ( 71 unt; 0 nHn; 71 RR)
% Number of literals : 71 ( 0 equ; 2 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 : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(composition(u,one),u),
file('REL002+1.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL002+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(join(skc1,top),top),
file('REL002+1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(u,complement(u)),top),
file('REL002+1.p',unknown),
[] ).
cnf(5,axiom,
equal(meet(u,complement(u)),zero),
file('REL002+1.p',unknown),
[] ).
cnf(6,axiom,
equal(join(u,v),join(v,u)),
file('REL002+1.p',unknown),
[] ).
cnf(7,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL002+1.p',unknown),
[] ).
cnf(9,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL002+1.p',unknown),
[] ).
cnf(10,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL002+1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL002+1.p',unknown),
[] ).
cnf(14,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL002+1.p',unknown),
[] ).
cnf(15,plain,
~ equal(join(top,skc1),top),
inference(rew,[status(thm),theory(equality)],[6,3]),
[iquote('0:Rew:6.0,3.0')] ).
cnf(16,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[6,13]),
[iquote('0:Rew:6.0,13.0')] ).
cnf(17,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[7,14]),
[iquote('0:Rew:7.0,14.0')] ).
cnf(28,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(76,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(77,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(79,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[5,76]),
[iquote('0:Rew:5.0,76.0')] ).
cnf(80,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[7,77]),
[iquote('0:Rew:7.0,77.0')] ).
cnf(87,plain,
equal(join(top,zero),top),
inference(spr,[status(thm),theory(equality)],[79,4]),
[iquote('0:SpR:79.0,4.0')] ).
cnf(88,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[79,7]),
[iquote('0:SpR:79.0,7.0')] ).
cnf(102,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[4,17]),
[iquote('0:SpR:4.0,17.0')] ).
cnf(105,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[7,17]),
[iquote('0:SpR:7.0,17.0')] ).
cnf(106,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[5,17]),
[iquote('0:SpR:5.0,17.0')] ).
cnf(111,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[6,102,79]),
[iquote('0:Rew:6.0,102.0,79.0,102.0')] ).
cnf(112,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[6,105]),
[iquote('0:Rew:6.0,105.0')] ).
cnf(113,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[7,106]),
[iquote('0:Rew:7.0,106.0')] ).
cnf(130,plain,
equal(complement(join(zero,zero)),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[79,88]),
[iquote('0:SpR:79.0,88.0')] ).
cnf(153,plain,
equal(meet(join(zero,zero),meet(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[130,5]),
[iquote('0:SpR:130.0,5.0')] ).
cnf(162,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[80,153]),
[iquote('0:Rew:80.0,153.0')] ).
cnf(169,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[162,17]),
[iquote('0:SpR:162.0,17.0')] ).
cnf(175,plain,
equal(join(zero,complement(join(join(zero,zero),complement(meet(top,top))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[6,169]),
[iquote('0:Rew:6.0,169.0')] ).
cnf(176,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[10,175]),
[iquote('0:Rew:10.0,175.0')] ).
cnf(191,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[10,4]),
[iquote('0:SpR:10.0,4.0')] ).
cnf(198,plain,
equal(join(top,join(zero,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[87,10]),
[iquote('0:SpR:87.0,10.0')] ).
cnf(199,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[4,10]),
[iquote('0:SpR:4.0,10.0')] ).
cnf(228,plain,
equal(join(top,meet(u,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[113,198]),
[iquote('0:SpR:113.0,198.0')] ).
cnf(377,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[1,28]),
[iquote('0:SpR:1.0,28.0')] ).
cnf(380,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,377]),
[iquote('0:Rew:2.0,377.0')] ).
cnf(389,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[380,1]),
[iquote('0:SpR:380.0,1.0')] ).
cnf(395,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[380,16]),
[iquote('0:SpR:380.0,16.0')] ).
cnf(399,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[389,380]),
[iquote('0:Rew:389.0,380.0')] ).
cnf(406,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[399,395]),
[iquote('0:Rew:399.0,395.0')] ).
cnf(442,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[406,7]),
[iquote('0:SpR:406.0,7.0')] ).
cnf(448,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[79,406]),
[iquote('0:SpR:79.0,406.0')] ).
cnf(454,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[448,130]),
[iquote('0:Rew:448.0,130.0')] ).
cnf(465,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[454,176]),
[iquote('0:Rew:454.0,176.0')] ).
cnf(467,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[442,113]),
[iquote('0:Rew:442.0,113.0')] ).
cnf(468,plain,
equal(join(top,complement(complement(u))),join(top,u)),
inference(rew,[status(thm),theory(equality)],[442,228]),
[iquote('0:Rew:442.0,228.0')] ).
cnf(490,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[448,465,467]),
[iquote('0:Rew:448.0,465.0,467.0,465.0')] ).
cnf(491,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[4,490]),
[iquote('0:Rew:4.0,490.0')] ).
cnf(535,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[491,7]),
[iquote('0:SpR:491.0,7.0')] ).
cnf(556,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[448,10]),
[iquote('0:SpR:448.0,10.0')] ).
cnf(757,plain,
equal(meet(top,join(top,complement(u))),complement(join(zero,meet(zero,u)))),
inference(spr,[status(thm),theory(equality)],[535,88]),
[iquote('0:SpR:535.0,88.0')] ).
cnf(774,plain,
equal(meet(zero,complement(u)),complement(join(top,u))),
inference(spr,[status(thm),theory(equality)],[468,535]),
[iquote('0:SpR:468.0,535.0')] ).
cnf(800,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[111,556]),
[iquote('0:SpR:111.0,556.0')] ).
cnf(806,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[800,467]),
[iquote('0:Rew:800.0,467.0')] ).
cnf(807,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[800,88]),
[iquote('0:Rew:800.0,88.0')] ).
cnf(831,plain,
equal(meet(top,join(top,complement(u))),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[800,757]),
[iquote('0:Rew:800.0,757.0')] ).
cnf(838,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[806,807]),
[iquote('0:Rew:806.0,807.0')] ).
cnf(870,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[838,831]),
[iquote('0:Rew:838.0,831.0')] ).
cnf(928,plain,
equal(meet(u,top),u),
inference(spr,[status(thm),theory(equality)],[838,80]),
[iquote('0:SpR:838.0,80.0')] ).
cnf(1179,plain,
equal(join(u,complement(meet(zero,join(u,top)))),top),
inference(spr,[status(thm),theory(equality)],[870,191]),
[iquote('0:SpR:870.0,191.0')] ).
cnf(1283,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[928,112]),
[iquote('0:SpR:928.0,112.0')] ).
cnf(1290,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[79,1283]),
[iquote('0:Rew:79.0,1283.0')] ).
cnf(1307,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1290,199]),
[iquote('0:SpR:1290.0,199.0')] ).
cnf(1316,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[4,1307,870,774,80]),
[iquote('0:Rew:4.0,1307.0,870.0,1307.0,774.0,1307.0,80.0,1307.0')] ).
cnf(1440,plain,
equal(complement(meet(zero,join(u,top))),top),
inference(spr,[status(thm),theory(equality)],[6,1316]),
[iquote('0:SpR:6.0,1316.0')] ).
cnf(1458,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1440,1179]),
[iquote('0:Rew:1440.0,1179.0')] ).
cnf(1482,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[1458,6]),
[iquote('0:SpR:1458.0,6.0')] ).
cnf(1493,plain,
$false,
inference(unc,[status(thm)],[1482,15]),
[iquote('0:UnC:1482.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.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 : Fri Jul 8 08:34:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.54
% 0.20/0.54 SPASS V 3.9
% 0.20/0.54 SPASS beiseite: Proof found.
% 0.20/0.54 % SZS status Theorem
% 0.20/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.54 SPASS derived 978 clauses, backtracked 0 clauses, performed 0 splits and kept 322 clauses.
% 0.20/0.54 SPASS allocated 86580 KBytes.
% 0.20/0.54 SPASS spent 0:00:00.19 on the problem.
% 0.20/0.54 0:00:00.03 for the input.
% 0.20/0.54 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.54 0:00:00.01 for inferences.
% 0.20/0.54 0:00:00.00 for the backtracking.
% 0.20/0.54 0:00:00.09 for the reduction.
% 0.20/0.54
% 0.20/0.54
% 0.20/0.54 Here is a proof with depth 9, length 71 :
% 0.20/0.54 % SZS output start Refutation
% See solution above
% 0.20/0.54 Formulae used in the proof : composition_identity converse_idempotence goals def_top def_zero maddux1_join_commutativity maddux4_definiton_of_meet converse_multiplicativity maddux2_join_associativity converse_cancellativity maddux3_a_kind_of_de_Morgan
% 0.20/0.54
%------------------------------------------------------------------------------