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 : n007.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 : Unsatisfiable 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of clauses : 69 ( 69 unt; 0 nHn; 69 RR)
% Number of literals : 69 ( 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(sk1,top),top),
file('REL002-1.p',unknown),
[] ).
cnf(2,axiom,
equal(join(u,v),join(v,u)),
file('REL002-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL002-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL002-1.p',unknown),
[] ).
cnf(5,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL002-1.p',unknown),
[] ).
cnf(7,axiom,
equal(composition(u,one),u),
file('REL002-1.p',unknown),
[] ).
cnf(9,axiom,
equal(converse(converse(u)),u),
file('REL002-1.p',unknown),
[] ).
cnf(11,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL002-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL002-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(u,complement(u)),top),
file('REL002-1.p',unknown),
[] ).
cnf(14,axiom,
equal(meet(u,complement(u)),zero),
file('REL002-1.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(86,plain,
equal(join(top,zero),top),
inference(spr,[status(thm),theory(equality)],[78,13]),
[iquote('0:SpR:78.0,13.0')] ).
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(101,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(104,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[5,16]),
[iquote('0:SpR:5.0,16.0')] ).
cnf(105,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(110,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[2,101,78]),
[iquote('0:Rew:2.0,101.0,78.0,101.0')] ).
cnf(111,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[2,104]),
[iquote('0:Rew:2.0,104.0')] ).
cnf(112,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[5,105]),
[iquote('0:Rew:5.0,105.0')] ).
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(152,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(161,plain,
equal(meet(meet(top,top),join(zero,zero)),zero),
inference(rew,[status(thm),theory(equality)],[79,152]),
[iquote('0:Rew:79.0,152.0')] ).
cnf(168,plain,
equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),meet(top,top)),
inference(spr,[status(thm),theory(equality)],[161,16]),
[iquote('0:SpR:161.0,16.0')] ).
cnf(174,plain,
equal(join(zero,complement(join(join(zero,zero),complement(meet(top,top))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[2,168]),
[iquote('0:Rew:2.0,168.0')] ).
cnf(175,plain,
equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),meet(top,top)),
inference(rew,[status(thm),theory(equality)],[3,174]),
[iquote('0:Rew:3.0,174.0')] ).
cnf(190,plain,
equal(join(u,join(v,complement(join(u,v)))),top),
inference(spr,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpR:3.0,13.0')] ).
cnf(197,plain,
equal(join(u,join(complement(u),v)),join(top,v)),
inference(spr,[status(thm),theory(equality)],[13,3]),
[iquote('0:SpR:13.0,3.0')] ).
cnf(201,plain,
equal(join(top,join(zero,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[86,3]),
[iquote('0:SpR:86.0,3.0')] ).
cnf(227,plain,
equal(join(top,meet(u,u)),join(top,u)),
inference(spr,[status(thm),theory(equality)],[112,201]),
[iquote('0:SpR:112.0,201.0')] ).
cnf(376,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(379,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[9,376]),
[iquote('0:Rew:9.0,376.0')] ).
cnf(388,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[379,7]),
[iquote('0:SpR:379.0,7.0')] ).
cnf(394,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[379,15]),
[iquote('0:SpR:379.0,15.0')] ).
cnf(398,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[388,379]),
[iquote('0:Rew:388.0,379.0')] ).
cnf(405,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[398,394]),
[iquote('0:Rew:398.0,394.0')] ).
cnf(441,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[405,5]),
[iquote('0:SpR:405.0,5.0')] ).
cnf(447,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[78,405]),
[iquote('0:SpR:78.0,405.0')] ).
cnf(453,plain,
equal(meet(top,top),complement(zero)),
inference(rew,[status(thm),theory(equality)],[447,129]),
[iquote('0:Rew:447.0,129.0')] ).
cnf(464,plain,
equal(join(zero,complement(join(zero,join(zero,complement(complement(zero)))))),complement(zero)),
inference(rew,[status(thm),theory(equality)],[453,175]),
[iquote('0:Rew:453.0,175.0')] ).
cnf(466,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[441,112]),
[iquote('0:Rew:441.0,112.0')] ).
cnf(467,plain,
equal(join(top,complement(complement(u))),join(top,u)),
inference(rew,[status(thm),theory(equality)],[441,227]),
[iquote('0:Rew:441.0,227.0')] ).
cnf(489,plain,
equal(join(zero,complement(zero)),complement(zero)),
inference(rew,[status(thm),theory(equality)],[447,464,466]),
[iquote('0:Rew:447.0,464.0,466.0,464.0')] ).
cnf(490,plain,
equal(complement(zero),top),
inference(rew,[status(thm),theory(equality)],[13,489]),
[iquote('0:Rew:13.0,489.0')] ).
cnf(534,plain,
equal(complement(join(top,complement(u))),meet(zero,u)),
inference(spr,[status(thm),theory(equality)],[490,5]),
[iquote('0:SpR:490.0,5.0')] ).
cnf(555,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[447,3]),
[iquote('0:SpR:447.0,3.0')] ).
cnf(756,plain,
equal(meet(top,join(top,complement(u))),complement(join(zero,meet(zero,u)))),
inference(spr,[status(thm),theory(equality)],[534,87]),
[iquote('0:SpR:534.0,87.0')] ).
cnf(774,plain,
equal(meet(zero,complement(u)),complement(join(top,u))),
inference(spr,[status(thm),theory(equality)],[467,534]),
[iquote('0:SpR:467.0,534.0')] ).
cnf(799,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[110,555]),
[iquote('0:SpR:110.0,555.0')] ).
cnf(805,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[799,466]),
[iquote('0:Rew:799.0,466.0')] ).
cnf(806,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[799,87]),
[iquote('0:Rew:799.0,87.0')] ).
cnf(830,plain,
equal(meet(top,join(top,complement(u))),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[799,756]),
[iquote('0:Rew:799.0,756.0')] ).
cnf(837,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[805,806]),
[iquote('0:Rew:805.0,806.0')] ).
cnf(869,plain,
equal(join(top,complement(u)),complement(meet(zero,u))),
inference(rew,[status(thm),theory(equality)],[837,830]),
[iquote('0:Rew:837.0,830.0')] ).
cnf(927,plain,
equal(meet(u,top),u),
inference(spr,[status(thm),theory(equality)],[837,79]),
[iquote('0:SpR:837.0,79.0')] ).
cnf(1176,plain,
equal(join(u,complement(meet(zero,join(u,top)))),top),
inference(spr,[status(thm),theory(equality)],[869,190]),
[iquote('0:SpR:869.0,190.0')] ).
cnf(1282,plain,
equal(join(u,meet(u,complement(top))),u),
inference(spr,[status(thm),theory(equality)],[927,111]),
[iquote('0:SpR:927.0,111.0')] ).
cnf(1289,plain,
equal(join(u,meet(u,zero)),u),
inference(rew,[status(thm),theory(equality)],[78,1282]),
[iquote('0:Rew:78.0,1282.0')] ).
cnf(1305,plain,
equal(join(u,complement(u)),join(top,meet(complement(u),zero))),
inference(spr,[status(thm),theory(equality)],[1289,197]),
[iquote('0:SpR:1289.0,197.0')] ).
cnf(1315,plain,
equal(complement(meet(zero,join(top,u))),top),
inference(rew,[status(thm),theory(equality)],[13,1305,869,774,79]),
[iquote('0:Rew:13.0,1305.0,869.0,1305.0,774.0,1305.0,79.0,1305.0')] ).
cnf(1434,plain,
equal(complement(meet(zero,join(u,top))),top),
inference(spr,[status(thm),theory(equality)],[2,1315]),
[iquote('0:SpR:2.0,1315.0')] ).
cnf(1456,plain,
equal(join(u,top),top),
inference(rew,[status(thm),theory(equality)],[1434,1176]),
[iquote('0:Rew:1434.0,1176.0')] ).
cnf(1457,plain,
$false,
inference(unc,[status(thm)],[1456,1]),
[iquote('0:UnC:1456.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL002-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.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 11:11:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.53
% 0.19/0.53 SPASS V 3.9
% 0.19/0.53 SPASS beiseite: Proof found.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.53 SPASS derived 951 clauses, backtracked 0 clauses, performed 0 splits and kept 310 clauses.
% 0.19/0.53 SPASS allocated 64594 KBytes.
% 0.19/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.53 0:00:00.03 for the input.
% 0.19/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.53 0:00:00.01 for inferences.
% 0.19/0.53 0:00:00.00 for the backtracking.
% 0.19/0.53 0:00:00.10 for the reduction.
% 0.19/0.53
% 0.19/0.53
% 0.19/0.53 Here is a proof with depth 8, length 69 :
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.53 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
% 0.19/0.53
%------------------------------------------------------------------------------