TSTP Solution File: SET515-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET515-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 : Tue Jul 19 05:26:43 EDT 2022
% Result : Unsatisfiable 0.57s 0.75s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 39 ( 15 unt; 14 nHn; 39 RR)
% Number of literals : 71 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 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,
member(x__dfg,x__dfg),
file('SET515-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET515-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET515-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET515-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET515-6.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET515-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET515-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET515-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET515-6.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET515-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET515-6.p',unknown),
[] ).
cnf(116,plain,
( ~ subclass(x__dfg,u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[1,2]),
[iquote('0:Res:1.0,2.1')] ).
cnf(120,plain,
~ member(x__dfg,complement(x__dfg)),
inference(res,[status(thm),theory(equality)],[1,25]),
[iquote('0:Res:1.0,25.1')] ).
cnf(121,plain,
( ~ member(x__dfg,u)
| member(x__dfg,intersection(u,x__dfg)) ),
inference(res,[status(thm),theory(equality)],[1,24]),
[iquote('0:Res:1.0,24.1')] ).
cnf(131,plain,
member(x__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[5,116]),
[iquote('0:Res:5.0,116.0')] ).
cnf(163,plain,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[13,11]),
[iquote('0:SpR:13.0,11.1')] ).
cnf(209,plain,
( ~ member(u,null_class)
| equal(v,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[68,22]),
[iquote('0:SpL:68.1,22.0')] ).
cnf(643,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[13,9]),
[iquote('0:SpL:13.0,9.0')] ).
cnf(655,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[643]),
[iquote('0:Obv:643.1')] ).
cnf(660,plain,
( equal(singleton(u),null_class)
| equal(regular(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[67,655]),
[iquote('0:Res:67.1,655.0')] ).
cnf(760,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[660,67]),
[iquote('0:SpR:660.1,67.1')] ).
cnf(761,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| equal(intersection(singleton(u),u),null_class) ),
inference(spr,[status(thm),theory(equality)],[660,68]),
[iquote('0:SpR:660.1,68.1')] ).
cnf(763,plain,
( equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[760]),
[iquote('0:Obv:760.0')] ).
cnf(764,plain,
( equal(singleton(u),null_class)
| equal(intersection(singleton(u),u),null_class) ),
inference(obv,[status(thm),theory(equality)],[761]),
[iquote('0:Obv:761.0')] ).
cnf(2390,plain,
( ~ member(x__dfg,singleton(x__dfg))
| equal(singleton(x__dfg),null_class)
| member(x__dfg,null_class) ),
inference(spr,[status(thm),theory(equality)],[764,121]),
[iquote('0:SpR:764.1,121.1')] ).
cnf(2404,plain,
( equal(singleton(x__dfg),null_class)
| member(x__dfg,null_class) ),
inference(mrr,[status(thm)],[2390,763]),
[iquote('0:MRR:2390.0,763.1')] ).
cnf(2406,plain,
equal(singleton(x__dfg),null_class),
inference(spt,[spt(split,[position(s1)])],[2404]),
[iquote('1:Spt:2404.0')] ).
cnf(2412,plain,
( ~ member(x__dfg,universal_class)
| member(x__dfg,null_class) ),
inference(spr,[status(thm),theory(equality)],[2406,163]),
[iquote('1:SpR:2406.0,163.1')] ).
cnf(2438,plain,
member(x__dfg,null_class),
inference(mrr,[status(thm)],[2412,131]),
[iquote('1:MRR:2412.0,131.0')] ).
cnf(2450,plain,
( equal(u,null_class)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[2438,209]),
[iquote('1:Res:2438.0,209.0')] ).
cnf(2473,plain,
equal(complement(x__dfg),null_class),
inference(res,[status(thm),theory(equality)],[2450,120]),
[iquote('1:Res:2450.1,120.0')] ).
cnf(2490,plain,
~ member(x__dfg,null_class),
inference(rew,[status(thm),theory(equality)],[2473,120]),
[iquote('1:Rew:2473.0,120.0')] ).
cnf(2493,plain,
$false,
inference(mrr,[status(thm)],[2490,2438]),
[iquote('1:MRR:2490.0,2438.0')] ).
cnf(2527,plain,
~ equal(singleton(x__dfg),null_class),
inference(spt,[spt(split,[position(sa)])],[2493,2406]),
[iquote('1:Spt:2493.0,2404.0,2406.0')] ).
cnf(2528,plain,
member(x__dfg,null_class),
inference(spt,[spt(split,[position(s2)])],[2404]),
[iquote('1:Spt:2493.0,2404.1')] ).
cnf(2533,plain,
( equal(u,null_class)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[2528,209]),
[iquote('1:Res:2528.0,209.0')] ).
cnf(2540,plain,
equal(complement(x__dfg),null_class),
inference(res,[status(thm),theory(equality)],[2533,120]),
[iquote('1:Res:2533.1,120.0')] ).
cnf(2555,plain,
~ member(x__dfg,null_class),
inference(rew,[status(thm),theory(equality)],[2540,120]),
[iquote('1:Rew:2540.0,120.0')] ).
cnf(2556,plain,
$false,
inference(mrr,[status(thm)],[2555,2528]),
[iquote('1:MRR:2555.0,2528.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET515-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 23:55:00 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.57/0.75
% 0.57/0.75 SPASS V 3.9
% 0.57/0.75 SPASS beiseite: Proof found.
% 0.57/0.75 % SZS status Theorem
% 0.57/0.75 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.75 SPASS derived 2265 clauses, backtracked 50 clauses, performed 2 splits and kept 1059 clauses.
% 0.57/0.75 SPASS allocated 77928 KBytes.
% 0.57/0.75 SPASS spent 0:00:00.37 on the problem.
% 0.57/0.75 0:00:00.04 for the input.
% 0.57/0.75 0:00:00.00 for the FLOTTER CNF translation.
% 0.57/0.75 0:00:00.03 for inferences.
% 0.57/0.75 0:00:00.00 for the backtracking.
% 0.57/0.75 0:00:00.26 for the reduction.
% 0.57/0.75
% 0.57/0.75
% 0.57/0.75 Here is a proof with depth 8, length 39 :
% 0.57/0.75 % SZS output start Refutation
% See solution above
% 0.57/0.75 Formulae used in the proof : prove_no_class_belongs_to_itself_1 subclass_members class_elements_are_sets unordered_pair_member unordered_pair3 singleton_set intersection1 intersection3 complement1 regularity1 regularity2
% 0.57/0.75
%------------------------------------------------------------------------------