%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : REL015-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 20:01:40 EDT 2022
% Result : Unsatisfiable 0.20s 0.57s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 62 RR)
% Number of literals : 62 ( 0 equ; 1 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(composition(top,top),top),
file('REL015-1.p',unknown),
[] ).
cnf(2,axiom,
equal(join(u,v),join(v,u)),
file('REL015-1.p',unknown),
[] ).
cnf(3,axiom,
equal(join(join(u,v),w),join(u,join(v,w))),
file('REL015-1.p',unknown),
[] ).
cnf(4,axiom,
equal(join(complement(join(complement(u),complement(v))),complement(join(complement(u),v))),u),
file('REL015-1.p',unknown),
[] ).
cnf(5,axiom,
equal(complement(join(complement(u),complement(v))),meet(u,v)),
file('REL015-1.p',unknown),
[] ).
cnf(7,axiom,
equal(composition(u,one),u),
file('REL015-1.p',unknown),
[] ).
cnf(8,axiom,
equal(join(composition(u,v),composition(w,v)),composition(join(u,w),v)),
file('REL015-1.p',unknown),
[] ).
cnf(9,axiom,
equal(converse(converse(u)),u),
file('REL015-1.p',unknown),
[] ).
cnf(10,axiom,
equal(join(converse(u),converse(v)),converse(join(u,v))),
file('REL015-1.p',unknown),
[] ).
cnf(11,axiom,
equal(composition(converse(u),converse(v)),converse(composition(v,u))),
file('REL015-1.p',unknown),
[] ).
cnf(12,axiom,
equal(join(composition(converse(u),complement(composition(u,v))),complement(v)),complement(v)),
file('REL015-1.p',unknown),
[] ).
cnf(13,axiom,
equal(join(u,complement(u)),top),
file('REL015-1.p',unknown),
[] ).
cnf(14,axiom,
equal(meet(u,complement(u)),zero),
file('REL015-1.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(33,plain,
equal(converse(join(converse(u),v)),join(u,converse(v))),
inference(spr,[status(thm),theory(equality)],[9,10]),
[iquote('0:SpR:9.0,10.0')] ).
cnf(71,plain,
equal(join(join(complement(u),complement(v)),meet(u,v)),top),
inference(spr,[status(thm),theory(equality)],[5,13]),
[iquote('0:SpR:5.0,13.0')] ).
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(78,plain,
equal(complement(top),zero),
inference(rew,[status(thm),theory(equality)],[14,75]),
[iquote('0:Rew:14.0,75.0')] ).
cnf(82,plain,
equal(join(meet(u,v),join(complement(u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[2,71]),
[iquote('0:Rew:2.0,71.0')] ).
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(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(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(185,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(186,plain,
equal(join(u,join(v,w)),join(w,join(u,v))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(192,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(202,plain,
equal(join(complement(u),join(meet(v,u),complement(v))),top),
inference(rew,[status(thm),theory(equality)],[186,82]),
[iquote('0:Rew:186.0,82.0')] ).
cnf(208,plain,
equal(join(complement(u),join(complement(v),meet(v,u))),top),
inference(rew,[status(thm),theory(equality)],[2,202]),
[iquote('0:Rew:2.0,202.0')] ).
cnf(247,plain,
equal(join(zero,composition(converse(u),complement(composition(u,top)))),zero),
inference(spr,[status(thm),theory(equality)],[78,15]),
[iquote('0:SpR:78.0,15.0')] ).
cnf(390,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(393,plain,
equal(composition(converse(one),u),u),
inference(rew,[status(thm),theory(equality)],[9,390]),
[iquote('0:Rew:9.0,390.0')] ).
cnf(402,plain,
equal(converse(one),one),
inference(spr,[status(thm),theory(equality)],[393,7]),
[iquote('0:SpR:393.0,7.0')] ).
cnf(408,plain,
equal(join(complement(u),complement(composition(one,u))),complement(u)),
inference(spr,[status(thm),theory(equality)],[393,15]),
[iquote('0:SpR:393.0,15.0')] ).
cnf(412,plain,
equal(composition(one,u),u),
inference(rew,[status(thm),theory(equality)],[402,393]),
[iquote('0:Rew:402.0,393.0')] ).
cnf(419,plain,
equal(join(complement(u),complement(u)),complement(u)),
inference(rew,[status(thm),theory(equality)],[412,408]),
[iquote('0:Rew:412.0,408.0')] ).
cnf(455,plain,
equal(meet(u,u),complement(complement(u))),
inference(spr,[status(thm),theory(equality)],[419,5]),
[iquote('0:SpR:419.0,5.0')] ).
cnf(461,plain,
equal(join(zero,zero),zero),
inference(spr,[status(thm),theory(equality)],[78,419]),
[iquote('0:SpR:78.0,419.0')] ).
cnf(479,plain,
equal(join(zero,complement(complement(u))),u),
inference(rew,[status(thm),theory(equality)],[455,112]),
[iquote('0:Rew:455.0,112.0')] ).
cnf(535,plain,
equal(join(zero,join(zero,u)),join(zero,u)),
inference(spr,[status(thm),theory(equality)],[461,3]),
[iquote('0:SpR:461.0,3.0')] ).
cnf(731,plain,
equal(join(zero,u),u),
inference(spr,[status(thm),theory(equality)],[110,535]),
[iquote('0:SpR:110.0,535.0')] ).
cnf(737,plain,
equal(complement(complement(u)),u),
inference(rew,[status(thm),theory(equality)],[731,479]),
[iquote('0:Rew:731.0,479.0')] ).
cnf(743,plain,
equal(composition(converse(u),complement(composition(u,top))),zero),
inference(rew,[status(thm),theory(equality)],[731,247]),
[iquote('0:Rew:731.0,247.0')] ).
cnf(760,plain,
equal(meet(u,u),u),
inference(rew,[status(thm),theory(equality)],[737,455]),
[iquote('0:Rew:737.0,455.0')] ).
cnf(816,plain,
equal(complement(zero),top),
inference(spr,[status(thm),theory(equality)],[731,13]),
[iquote('0:SpR:731.0,13.0')] ).
cnf(876,plain,
equal(join(u,converse(complement(converse(u)))),converse(top)),
inference(spr,[status(thm),theory(equality)],[13,33]),
[iquote('0:SpR:13.0,33.0')] ).
cnf(1092,plain,
equal(join(top,converse(complement(converse(complement(u))))),join(u,converse(top))),
inference(spr,[status(thm),theory(equality)],[876,192]),
[iquote('0:SpR:876.0,192.0')] ).
cnf(1482,plain,
equal(join(complement(u),join(complement(u),u)),top),
inference(spr,[status(thm),theory(equality)],[760,208]),
[iquote('0:SpR:760.0,208.0')] ).
cnf(1494,plain,
equal(join(top,complement(u)),top),
inference(rew,[status(thm),theory(equality)],[2,1482,13]),
[iquote('0:Rew:2.0,1482.0,13.0,1482.0,2.0,1482.0')] ).
cnf(1505,plain,
equal(join(u,top),top),
inference(spr,[status(thm),theory(equality)],[1494,185]),
[iquote('0:SpR:1494.0,185.0')] ).
cnf(1509,plain,
equal(join(top,u),top),
inference(spr,[status(thm),theory(equality)],[737,1494]),
[iquote('0:SpR:737.0,1494.0')] ).
cnf(1514,plain,
equal(join(u,converse(top)),top),
inference(rew,[status(thm),theory(equality)],[1509,1092]),
[iquote('0:Rew:1509.0,1092.0')] ).
cnf(1530,plain,
equal(join(u,converse(top)),converse(top)),
inference(spr,[status(thm),theory(equality)],[1505,33]),
[iquote('0:SpR:1505.0,33.0')] ).
cnf(1535,plain,
equal(converse(top),top),
inference(rew,[status(thm),theory(equality)],[1514,1530]),
[iquote('0:Rew:1514.0,1530.0')] ).
cnf(1555,plain,
equal(composition(top,complement(composition(top,top))),zero),
inference(spr,[status(thm),theory(equality)],[1535,743]),
[iquote('0:SpR:1535.0,743.0')] ).
cnf(1634,plain,
equal(join(zero,composition(u,complement(composition(top,top)))),composition(join(top,u),complement(composition(top,top)))),
inference(spr,[status(thm),theory(equality)],[1555,8]),
[iquote('0:SpR:1555.0,8.0')] ).
cnf(1638,plain,
equal(composition(u,complement(composition(top,top))),zero),
inference(rew,[status(thm),theory(equality)],[731,1634,1555,1509]),
[iquote('0:Rew:731.0,1634.0,1555.0,1634.0,1509.0,1634.0')] ).
cnf(1711,plain,
equal(complement(composition(top,top)),zero),
inference(spr,[status(thm),theory(equality)],[1638,412]),
[iquote('0:SpR:1638.0,412.0')] ).
cnf(2006,plain,
equal(composition(top,top),complement(zero)),
inference(spr,[status(thm),theory(equality)],[1711,737]),
[iquote('0:SpR:1711.0,737.0')] ).
cnf(2017,plain,
equal(composition(top,top),top),
inference(rew,[status(thm),theory(equality)],[816,2006]),
[iquote('0:Rew:816.0,2006.0')] ).
cnf(2018,plain,
$false,
inference(mrr,[status(thm)],[2017,1]),
[iquote('0:MRR:2017.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : REL015-1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 10:40:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.57
% 0.20/0.57 SPASS V 3.9
% 0.20/0.57 SPASS beiseite: Proof found.
% 0.20/0.57 % SZS status Theorem
% 0.20/0.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.57 SPASS derived 1284 clauses, backtracked 0 clauses, performed 0 splits and kept 419 clauses.
% 0.20/0.57 SPASS allocated 65081 KBytes.
% 0.20/0.57 SPASS spent 0:00:00.21 on the problem.
% 0.20/0.57 0:00:00.04 for the input.
% 0.20/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.57 0:00:00.01 for inferences.
% 0.20/0.57 0:00:00.00 for the backtracking.
% 0.20/0.57 0:00:00.14 for the reduction.
% 0.20/0.57
% 0.20/0.57
% 0.20/0.57 Here is a proof with depth 11, length 62 :
% 0.20/0.57 % SZS output start Refutation
% See solution above
% 0.20/0.57 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
% 0.20/0.57
%------------------------------------------------------------------------------