TSTP Solution File: REL024-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL024-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 20:01:54 EDT 2022
% Result : Unsatisfiable 37.95s 38.13s
% Output : Refutation 37.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 74 ( 74 unt; 0 nHn; 74 RR)
% Number of literals : 74 ( 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(join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)),composition(meet(sk1,converse(sk2)),sk3)),
file('REL024-1.p',unknown),
[] ).
cnf(2,axiom,
equal(join(u,v),join(v,u)),
file('REL024-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL024-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL024-1.p',unknown),
[] ).
cnf(5,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL024-1.p',unknown),
[] ).
cnf(7,axiom,
equal(composition(u,one),u),
file('REL024-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL024-1.p',unknown),
[] ).
cnf(9,axiom,
equal(converse(converse(u)),u),
file('REL024-1.p',unknown),
[] ).
cnf(10,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL024-1.p',unknown),
[] ).
cnf(11,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL024-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL024-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(u,complement(u)),top),
file('REL024-1.p',unknown),
[] ).
cnf(14,axiom,
equal(meet(u,complement(u)),zero),
file('REL024-1.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(17,plain,
~ equal(join(composition(meet(sk1,converse(sk2)),sk3),composition(meet(sk1,converse(sk2)),meet(sk2,sk3))),composition(meet(sk1,converse(sk2)),sk3)),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(28,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(29,plain,
equal(converse(composition(u,converse(v))),composition(v,converse(u))),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(33,plain,
equal(converse(join(u,converse(v))),join(converse(u),v)),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(76,plain,
equal(meet(u,complement(u)),complement(top)),
inference(spr,[status(thm),theory(equality)],[13,5]),
[iquote('0:SpR:13.0,5.0')] ).
cnf(79,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[14,76]),
[iquote('0:Rew:14.0,76.0')] ).
cnf(88,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(89,plain,
equal(join(meet(u,v),complement(join(v,complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[2,16]),
[iquote('0:SpR:2.0,16.0')] ).
cnf(91,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(92,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(93,plain,
equal(join(complement(top),meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[2,88]),
[iquote('0:Rew:2.0,88.0')] ).
cnf(94,plain,
equal(join(zero,meet(u,complement(complement(u)))),u),
inference(rew,[status(thm),theory(equality)],[79,93]),
[iquote('0:Rew:79.0,93.0')] ).
cnf(95,plain,
equal(join(meet(u,v),meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[2,91]),
[iquote('0:Rew:2.0,91.0')] ).
cnf(96,plain,
equal(join(zero,meet(u,u)),u),
inference(rew,[status(thm),theory(equality)],[5,92]),
[iquote('0:Rew:5.0,92.0')] ).
cnf(101,plain,
equal(complement(join(zero,complement(u))),meet(top,u)),
inference(spr,[status(thm),theory(equality)],[79,5]),
[iquote('0:SpR:79.0,5.0')] ).
cnf(132,plain,
equal(complement(join(meet(top,u),complement(v))),meet(join(zero,complement(u)),v)),
inference(spr,[status(thm),theory(equality)],[101,5]),
[iquote('0:SpR:101.0,5.0')] ).
cnf(135,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,join(zero,complement(v)))),
inference(spr,[status(thm),theory(equality)],[101,5]),
[iquote('0:SpR:101.0,5.0')] ).
cnf(165,plain,
equal(join(meet(u,v),join(complement(join(complement(u),v)),w)),join(u,w)),
inference(spr,[status(thm),theory(equality)],[16,3]),
[iquote('0:SpR:16.0,3.0')] ).
cnf(216,plain,
equal(join(complement(u),composition(v,complement(composition(converse(v),u)))),complement(u)),
inference(spr,[status(thm),theory(equality)],[9,15]),
[iquote('0:SpR:9.0,15.0')] ).
cnf(262,plain,
equal(join(converse(composition(u,v)),composition(w,converse(u))),composition(join(converse(v),w),converse(u))),
inference(spr,[status(thm),theory(equality)],[11,8]),
[iquote('0:SpR:11.0,8.0')] ).
cnf(391,plain,
equal(composition(converse(one),u),converse(converse(u))),
inference(spr,[status(thm),theory(equality)],[7,28]),
[iquote('0:SpR:7.0,28.0')] ).
cnf(394,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[9,391]),
[iquote('0:Rew:9.0,391.0')] ).
cnf(403,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[394,7]),
[iquote('0:SpR:394.0,7.0')] ).
cnf(409,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[394,15]),
[iquote('0:SpR:394.0,15.0')] ).
cnf(413,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[403,394]),
[iquote('0:Rew:403.0,394.0')] ).
cnf(420,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[413,409]),
[iquote('0:Rew:413.0,409.0')] ).
cnf(456,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[420,5]),
[iquote('0:SpR:420.0,5.0')] ).
cnf(462,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[79,420]),
[iquote('0:SpR:79.0,420.0')] ).
cnf(480,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[456,96]),
[iquote('0:Rew:456.0,96.0')] ).
cnf(569,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[462,3]),
[iquote('0:SpR:462.0,3.0')] ).
cnf(617,plain,
equal(join(converse(u),composition(v,converse(w))),converse(join(u,composition(w,converse(v))))),
inference(spr,[status(thm),theory(equality)],[29,10]),
[iquote('0:SpR:29.0,10.0')] ).
cnf(638,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),composition(join(converse(v),w),converse(u))),
inference(rew,[status(thm),theory(equality)],[617,262]),
[iquote('0:Rew:617.0,262.0')] ).
cnf(708,plain,
equal(composition(join(converse(u),v),converse(w)),converse(composition(w,join(u,converse(v))))),
inference(spr,[status(thm),theory(equality)],[33,11]),
[iquote('0:SpR:33.0,11.0')] ).
cnf(741,plain,
equal(converse(join(composition(u,v),composition(u,converse(w)))),converse(composition(u,join(v,converse(w))))),
inference(rew,[status(thm),theory(equality)],[708,638]),
[iquote('0:Rew:708.0,638.0')] ).
cnf(822,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[94,569]),
[iquote('0:SpR:94.0,569.0')] ).
cnf(828,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[822,480]),
[iquote('0:Rew:822.0,480.0')] ).
cnf(829,plain,
equal(meet(top,u),complement(complement(u))),
inference(rew,[status(thm),theory(equality)],[822,101]),
[iquote('0:Rew:822.0,101.0')] ).
cnf(841,plain,
equal(complement(join(complement(u),meet(top,v))),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[822,135]),
[iquote('0:Rew:822.0,135.0')] ).
cnf(843,plain,
equal(complement(join(meet(top,u),complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[822,132]),
[iquote('0:Rew:822.0,132.0')] ).
cnf(860,plain,
equal(meet(top,u),u),
inference(rew,[status(thm),theory(equality)],[828,829]),
[iquote('0:Rew:828.0,829.0')] ).
cnf(906,plain,
equal(complement(join(complement(u),v)),meet(u,complement(v))),
inference(rew,[status(thm),theory(equality)],[860,841]),
[iquote('0:Rew:860.0,841.0')] ).
cnf(909,plain,
equal(join(meet(u,v),join(meet(u,complement(v)),w)),join(u,w)),
inference(rew,[status(thm),theory(equality)],[906,165]),
[iquote('0:Rew:906.0,165.0')] ).
cnf(910,plain,
equal(complement(join(u,complement(v))),meet(complement(u),v)),
inference(rew,[status(thm),theory(equality)],[860,843]),
[iquote('0:Rew:860.0,843.0')] ).
cnf(911,plain,
equal(join(meet(u,v),meet(complement(v),u)),u),
inference(rew,[status(thm),theory(equality)],[910,89]),
[iquote('0:Rew:910.0,89.0')] ).
cnf(2790,plain,
equal(join(u,composition(v,complement(composition(converse(v),complement(u))))),u),
inference(spr,[status(thm),theory(equality)],[828,216]),
[iquote('0:SpR:828.0,216.0')] ).
cnf(4184,plain,
equal(join(u,meet(complement(complement(v)),u)),join(meet(u,v),u)),
inference(spr,[status(thm),theory(equality)],[911,909]),
[iquote('0:SpR:911.0,909.0')] ).
cnf(4227,plain,
equal(join(u,meet(v,u)),join(u,meet(u,v))),
inference(rew,[status(thm),theory(equality)],[828,4184,2]),
[iquote('0:Rew:828.0,4184.0,2.0,4184.0')] ).
cnf(5606,plain,
equal(converse(join(composition(u,v),composition(u,w))),converse(composition(u,join(v,w)))),
inference(spr,[status(thm),theory(equality)],[9,741]),
[iquote('0:SpR:9.0,741.0')] ).
cnf(18375,plain,
equal(join(u,complement(composition(converse(one),complement(u)))),u),
inference(spr,[status(thm),theory(equality)],[413,2790]),
[iquote('0:SpR:413.0,2790.0')] ).
cnf(18387,plain,
equal(join(u,u),u),
inference(rew,[status(thm),theory(equality)],[828,18375,413,403]),
[iquote('0:Rew:828.0,18375.0,413.0,18375.0,403.0,18375.0')] ).
cnf(18610,plain,
equal(join(meet(u,v),meet(u,complement(v))),join(u,meet(u,complement(v)))),
inference(spr,[status(thm),theory(equality)],[18387,909]),
[iquote('0:SpR:18387.0,909.0')] ).
cnf(18678,plain,
equal(join(u,meet(u,complement(v))),u),
inference(rew,[status(thm),theory(equality)],[95,18610]),
[iquote('0:Rew:95.0,18610.0')] ).
cnf(18738,plain,
equal(join(u,meet(u,v)),u),
inference(spr,[status(thm),theory(equality)],[828,18678]),
[iquote('0:SpR:828.0,18678.0')] ).
cnf(18766,plain,
equal(join(u,meet(v,u)),u),
inference(rew,[status(thm),theory(equality)],[18738,4227]),
[iquote('0:Rew:18738.0,4227.0')] ).
cnf(81929,plain,
equal(join(composition(u,v),composition(u,w)),converse(converse(composition(u,join(v,w))))),
inference(spr,[status(thm),theory(equality)],[5606,9]),
[iquote('0:SpR:5606.0,9.0')] ).
cnf(82151,plain,
equal(join(composition(u,v),composition(u,w)),composition(u,join(v,w))),
inference(rew,[status(thm),theory(equality)],[9,81929]),
[iquote('0:Rew:9.0,81929.0')] ).
cnf(82154,plain,
~ equal(composition(meet(sk1,converse(sk2)),join(sk3,meet(sk2,sk3))),composition(meet(sk1,converse(sk2)),sk3)),
inference(rew,[status(thm),theory(equality)],[82151,17]),
[iquote('0:Rew:82151.0,17.0')] ).
cnf(82226,plain,
~ equal(composition(meet(sk1,converse(sk2)),sk3),composition(meet(sk1,converse(sk2)),sk3)),
inference(rew,[status(thm),theory(equality)],[18766,82154]),
[iquote('0:Rew:18766.0,82154.0')] ).
cnf(82227,plain,
$false,
inference(obv,[status(thm),theory(equality)],[82226]),
[iquote('0:Obv:82226.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL024-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n011.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 12:48:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 37.95/38.13
% 37.95/38.13 SPASS V 3.9
% 37.95/38.13 SPASS beiseite: Proof found.
% 37.95/38.13 % SZS status Theorem
% 37.95/38.13 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.95/38.13 SPASS derived 49715 clauses, backtracked 0 clauses, performed 0 splits and kept 5951 clauses.
% 37.95/38.13 SPASS allocated 130207 KBytes.
% 37.95/38.13 SPASS spent 0:0:36.29 on the problem.
% 37.95/38.13 0:00:00.03 for the input.
% 37.95/38.13 0:00:00.00 for the FLOTTER CNF translation.
% 37.95/38.13 0:00:00.34 for inferences.
% 37.95/38.13 0:00:00.00 for the backtracking.
% 37.95/38.13 0:0:35.84 for the reduction.
% 37.95/38.13
% 37.95/38.13
% 37.95/38.13 Here is a proof with depth 6, length 74 :
% 37.95/38.13 % SZS output start Refutation
% See solution above
% 37.95/38.13 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 composition_distributivity_7 converse_idempotence_8 converse_additivity_9 converse_multiplicativity_10 converse_cancellativity_11 def_top_12 def_zero_13
% 37.95/38.13
%------------------------------------------------------------------------------