TSTP Solution File: REL023+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL023+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 20:01:52 EDT 2022
% Result : Theorem 2.92s 3.17s
% Output : Refutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 57 RR)
% Number of literals : 57 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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('REL023+1.p',unknown),
[] ).
cnf(2,axiom,
equal(converse(converse(u)),u),
file('REL023+1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(u,complement(u)),top),
file('REL023+1.p',unknown),
[] ).
cnf(4,axiom,
equal(meet(u,complement(u)),zero),
file('REL023+1.p',unknown),
[] ).
cnf(5,axiom,
equal(join(u,v),join(v,u)),
file('REL023+1.p',unknown),
[] ).
cnf(6,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL023+1.p',unknown),
[] ).
cnf(8,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL023+1.p',unknown),
[] ).
cnf(9,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL023+1.p',unknown),
[] ).
cnf(11,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL023+1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL023+1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL023+1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(join(composition(meet(skc5,converse(skc4)),meet(skc4,skc3)),composition(skc5,meet(skc4,skc3))),composition(skc5,meet(skc4,skc3))),
file('REL023+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)],[5,12]),
[iquote('0:Rew:5.0,12.0')] ).
cnf(16,plain,
equal(join(meet(u,v),complement(join(complement(u),v))),u),
inference(rew,[status(thm),theory(equality)],[6,13]),
[iquote('0:Rew:6.0,13.0')] ).
cnf(17,plain,
~ equal(composition(join(skc5,meet(skc5,converse(skc4))),meet(skc4,skc3)),composition(skc5,meet(skc4,skc3))),
inference(rew,[status(thm),theory(equality)],[5,14,11]),
[iquote('0:Rew:5.0,14.0,11.0,14.0')] ).
cnf(28,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(76,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(77,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(79,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[4,76]),
[iquote('0:Rew:4.0,76.0')] ).
cnf(80,plain,
equal(meet(u,v),meet(v,u)),
inference(rew,[status(thm),theory(equality)],[6,77]),
[iquote('0:Rew:6.0,77.0')] ).
cnf(81,plain,
~ equal(composition(join(skc5,meet(skc5,converse(skc4))),meet(skc3,skc4)),composition(skc5,meet(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[80,17]),
[iquote('0:Rew:80.0,17.0')] ).
cnf(89,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(92,plain,
equal(join(meet(u,complement(v)),meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[6,16]),
[iquote('0:SpR:6.0,16.0')] ).
cnf(93,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(94,plain,
equal(join(complement(top),meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[5,89]),
[iquote('0:Rew:5.0,89.0')] ).
cnf(95,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[79,94]),
[iquote('0:Rew:79.0,94.0')] ).
cnf(96,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[5,92]),
[iquote('0:Rew:5.0,92.0')] ).
cnf(97,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[6,93]),
[iquote('0:Rew:6.0,93.0')] ).
cnf(102,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[79,6]),
[iquote('0:SpR:79.0,6.0')] ).
cnf(136,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[102,6]),
[iquote('0:SpR:102.0,6.0')] ).
cnf(166,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[16,9]),
[iquote('0:SpR:16.0,9.0')] ).
cnf(217,plain,
equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[2,15]),
[iquote('0:SpR:2.0,15.0')] ).
cnf(392,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(395,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[2,392]),
[iquote('0:Rew:2.0,392.0')] ).
cnf(404,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[395,1]),
[iquote('0:SpR:395.0,1.0')] ).
cnf(410,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[395,15]),
[iquote('0:SpR:395.0,15.0')] ).
cnf(414,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[404,395]),
[iquote('0:Rew:404.0,395.0')] ).
cnf(421,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[414,410]),
[iquote('0:Rew:414.0,410.0')] ).
cnf(457,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[421,6]),
[iquote('0:SpR:421.0,6.0')] ).
cnf(463,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[79,421]),
[iquote('0:SpR:79.0,421.0')] ).
cnf(481,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[457,97]),
[iquote('0:Rew:457.0,97.0')] ).
cnf(570,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[463,9]),
[iquote('0:SpR:463.0,9.0')] ).
cnf(823,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[95,570]),
[iquote('0:SpR:95.0,570.0')] ).
cnf(829,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[823,481]),
[iquote('0:Rew:823.0,481.0')] ).
cnf(830,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[823,102]),
[iquote('0:Rew:823.0,102.0')] ).
cnf(849,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[823,136]),
[iquote('0:Rew:823.0,136.0')] ).
cnf(861,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[829,830]),
[iquote('0:Rew:829.0,830.0')] ).
cnf(907,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[861,849]),
[iquote('0:Rew:861.0,849.0')] ).
cnf(910,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[907,166]),
[iquote('0:Rew:907.0,166.0')] ).
cnf(2790,plain,
equal(join(u,composition(v,complement(composition(converse(v),complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[829,217]),
[iquote('0:SpR:829.0,217.0')] ).
cnf(18375,plain,
equal(join(u,complement(composition(converse(one),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[414,2790]),
[iquote('0:SpR:414.0,2790.0')] ).
cnf(18387,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[829,18375,414,404]),
[iquote('0:Rew:829.0,18375.0,414.0,18375.0,404.0,18375.0')] ).
cnf(18613,plain,
equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[18387,910]),
[iquote('0:SpR:18387.0,910.0')] ).
cnf(18678,plain,
equal(join(u,meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[96,18613]),
[iquote('0:Rew:96.0,18613.0')] ).
cnf(18738,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[829,18678]),
[iquote('0:SpR:829.0,18678.0')] ).
cnf(18767,plain,
~ equal(composition(skc5,meet(skc3,skc4)),composition(skc5,meet(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[18738,81]),
[iquote('0:Rew:18738.0,81.0')] ).
cnf(18812,plain,
$false,
inference(obv,[status(thm),theory(equality)],[18767]),
[iquote('0:Obv:18767.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL023+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 09:35:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.92/3.17
% 2.92/3.17 SPASS V 3.9
% 2.92/3.17 SPASS beiseite: Proof found.
% 2.92/3.17 % SZS status Theorem
% 2.92/3.17 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.92/3.17 SPASS derived 11442 clauses, backtracked 0 clauses, performed 0 splits and kept 1767 clauses.
% 2.92/3.17 SPASS allocated 101671 KBytes.
% 2.92/3.17 SPASS spent 0:00:02.70 on the problem.
% 2.92/3.17 0:00:00.03 for the input.
% 2.92/3.17 0:00:00.02 for the FLOTTER CNF translation.
% 2.92/3.17 0:00:00.08 for inferences.
% 2.92/3.17 0:00:00.00 for the backtracking.
% 2.92/3.17 0:00:02.53 for the reduction.
% 2.92/3.17
% 2.92/3.17
% 2.92/3.17 Here is a proof with depth 6, length 57 :
% 2.92/3.17 % SZS output start Refutation
% See solution above
% 2.92/3.17 Formulae used in the proof : composition_identity converse_idempotence def_top def_zero maddux1_join_commutativity maddux4_definiton_of_meet converse_multiplicativity maddux2_join_associativity composition_distributivity converse_cancellativity maddux3_a_kind_of_de_Morgan goals
% 2.92/3.17
%------------------------------------------------------------------------------