TSTP Solution File: REL001-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL001-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 20:01:21 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of clauses : 53 ( 53 unt; 0 nHn; 53 RR)
% Number of literals : 53 ( 0 equ; 1 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(join(zero,sk1),sk1),
file('REL001-1.p',unknown),
[] ).
cnf(2,axiom,
equal(join(u,v),join(v,u)),
file('REL001-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL001-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL001-1.p',unknown),
[] ).
cnf(5,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL001-1.p',unknown),
[] ).
cnf(7,axiom,
equal(composition(u,one),u),
file('REL001-1.p',unknown),
[] ).
cnf(9,axiom,
equal(converse(converse(u)),u),
file('REL001-1.p',unknown),
[] ).
cnf(11,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL001-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL001-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(u,complement(u)),top),
file('REL001-1.p',unknown),
[] ).
cnf(14,axiom,
equal(meet(u,complement(u)),zero),
file('REL001-1.p',unknown),
[] ).
cnf(15,plain,
equal(join(complement(u),composition(converse(v),complement(composition(v,u)))),complement(u)),
inference(rew,[status(thm),theory(equality)],[2,12]),
[iquote('0:Rew:2.0,12.0')] ).
cnf(16,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[5,4]),
[iquote('0:Rew:5.0,4.0')] ).
cnf(27,plain,
equal(converse(composition(converse(u),v)),composition(converse(v),u)),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(75,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[13,5]),
[iquote('0:SpR:13.0,5.0')] ).
cnf(76,plain,
equal(complement(join(complement(u),complement(v))),meet(v,u)),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(78,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[14,75]),
[iquote('0:Rew:14.0,75.0')] ).
cnf(79,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[5,76]),
[iquote('0:Rew:5.0,76.0')] ).
cnf(85,plain,
equal(meet(top,zero),zero),
inference(spr,[status(thm),theory(equality)],[78,14]),
[iquote('0:SpR:78.0,14.0')] ).
cnf(87,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[78,5]),
[iquote('0:SpR:78.0,5.0')] ).
cnf(90,plain,
equal(meet(zero,top),zero),
inference(rew,[status(thm),theory(equality)],[79,85]),
[iquote('0:Rew:79.0,85.0')] ).
cnf(103,plain,
equal(join(meet(u,complement(complement(u))),complement(top)),u),
inference(spr,[status(thm),theory(equality)],[13,16]),
[iquote('0:SpR:13.0,16.0')] ).
cnf(107,plain,
equal(join(zero,complement(join(complement(u),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[14,16]),
[iquote('0:SpR:14.0,16.0')] ).
cnf(109,plain,
equal(join(zero,complement(join(complement(zero),top))),zero),
inference(spr,[status(thm),theory(equality)],[90,16]),
[iquote('0:SpR:90.0,16.0')] ).
cnf(111,plain,
equal(join(zero,complement(join(top,complement(zero)))),zero),
inference(rew,[status(thm),theory(equality)],[2,109]),
[iquote('0:Rew:2.0,109.0')] ).
cnf(112,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[2,103,78]),
[iquote('0:Rew:2.0,103.0,78.0,103.0')] ).
cnf(114,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[5,107]),
[iquote('0:Rew:5.0,107.0')] ).
cnf(129,plain,
equal(complement(join(zero,zero)),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[78,87]),
[iquote('0:SpR:78.0,87.0')] ).
cnf(138,plain,
equal(meet(join(zero,zero),meet(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[129,14]),
[iquote('0:SpR:129.0,14.0')] ).
cnf(147,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[79,138]),
[iquote('0:Rew:79.0,138.0')] ).
cnf(169,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[147,16]),
[iquote('0:SpR:147.0,16.0')] ).
cnf(175,plain,
equal(join(zero,complement(join(join(zero,zero),complement(meet(top,top))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[2,169]),
[iquote('0:Rew:2.0,169.0')] ).
cnf(176,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[3,175]),
[iquote('0:Rew:3.0,175.0')] ).
cnf(196,plain,
equal(join(zero,join(complement(join(top,complement(zero))),u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[111,3]),
[iquote('0:SpR:111.0,3.0')] ).
cnf(382,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[7,27]),
[iquote('0:SpR:7.0,27.0')] ).
cnf(385,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[9,382]),
[iquote('0:Rew:9.0,382.0')] ).
cnf(394,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[385,7]),
[iquote('0:SpR:385.0,7.0')] ).
cnf(400,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[385,15]),
[iquote('0:SpR:385.0,15.0')] ).
cnf(404,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[394,385]),
[iquote('0:Rew:394.0,385.0')] ).
cnf(411,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[404,400]),
[iquote('0:Rew:404.0,400.0')] ).
cnf(448,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[411,5]),
[iquote('0:SpR:411.0,5.0')] ).
cnf(454,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[78,411]),
[iquote('0:SpR:78.0,411.0')] ).
cnf(459,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[454,129]),
[iquote('0:Rew:454.0,129.0')] ).
cnf(471,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[459,176]),
[iquote('0:Rew:459.0,176.0')] ).
cnf(473,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[448,114]),
[iquote('0:Rew:448.0,114.0')] ).
cnf(494,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[454,471,473]),
[iquote('0:Rew:454.0,471.0,473.0,471.0')] ).
cnf(495,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[13,494]),
[iquote('0:Rew:13.0,494.0')] ).
cnf(502,plain,
equal(join(zero,join(complement(join(top,top)),u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[495,196]),
[iquote('0:Rew:495.0,196.0')] ).
cnf(545,plain,
equal(join(top,top),top),
inference(spr,[status(thm),theory(equality)],[495,411]),
[iquote('0:SpR:495.0,411.0')] ).
cnf(553,plain,
equal(join(zero,join(complement(top),u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[545,502]),
[iquote('0:Rew:545.0,502.0')] ).
cnf(567,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(rew,[status(thm),theory(equality)],[78,553]),
[iquote('0:Rew:78.0,553.0')] ).
cnf(799,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[112,567]),
[iquote('0:SpR:112.0,567.0')] ).
cnf(807,plain,
$false,
inference(unc,[status(thm)],[799,1]),
[iquote('0:UnC:799.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL001-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n023.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 09:18:41 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 524 clauses, backtracked 0 clauses, performed 0 splits and kept 207 clauses.
% 0.20/0.49 SPASS allocated 64025 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.49 0:00:00.03 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.07 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 6, length 53 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : goals_14 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
% 0.20/0.49
%------------------------------------------------------------------------------