TSTP Solution File: SET163-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET163-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 05:24:40 EDT 2022
% Result : Unsatisfiable 1.98s 2.16s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of clauses : 70 ( 27 unt; 25 nHn; 70 RR)
% Number of literals : 126 ( 0 equ; 39 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(union(universal_class,x__dfg),universal_class),
file('SET163-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET163-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET163-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET163-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET163-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET163-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET163-6.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET163-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET163-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET163-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET163-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET163-6.p',unknown),
[] ).
cnf(27,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET163-6.p',unknown),
[] ).
cnf(44,axiom,
equal(union(u,singleton(u)),successor(u)),
file('SET163-6.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET163-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(union(universal_class,x__dfg),universal_class)
| ~ subclass(universal_class,union(universal_class,x__dfg)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.2,1.0')] ).
cnf(122,plain,
~ subclass(universal_class,union(universal_class,x__dfg)),
inference(mrr,[status(thm)],[117,5]),
[iquote('0:MRR:117.0,5.0')] ).
cnf(160,plain,
( ~ member(regular(complement(u)),u)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[67,25]),
[iquote('0:Res:67.1,25.1')] ).
cnf(169,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[3,23]),
[iquote('0:Res:3.1,23.0')] ).
cnf(178,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),u) ),
inference(res,[status(thm),theory(equality)],[67,22]),
[iquote('0:Res:67.1,22.0')] ).
cnf(272,plain,
( ~ member(not_subclass_element(u,complement(v)),universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[26,4]),
[iquote('0:Res:26.2,4.0')] ).
cnf(343,plain,
( ~ subclass(u,v)
| equal(u,null_class)
| member(regular(u),v) ),
inference(res,[status(thm),theory(equality)],[67,2]),
[iquote('0:Res:67.1,2.0')] ).
cnf(344,plain,
( ~ subclass(u,v)
| subclass(u,w)
| member(not_subclass_element(u,w),v) ),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.1,2.0')] ).
cnf(536,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(548,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[536]),
[iquote('0:Obv:536.1')] ).
cnf(551,plain,
( equal(singleton(u),null_class)
| equal(regular(singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[67,548]),
[iquote('0:Res:67.1,548.0')] ).
cnf(552,plain,
( subclass(singleton(u),v)
| equal(not_subclass_element(singleton(u),v),u) ),
inference(res,[status(thm),theory(equality)],[3,548]),
[iquote('0:Res:3.1,548.0')] ).
cnf(625,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[551,67]),
[iquote('0:SpR:551.1,67.1')] ).
cnf(630,plain,
( equal(singleton(u),null_class)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[625]),
[iquote('0:Obv:625.0')] ).
cnf(1212,plain,
( subclass(singleton(u),v)
| subclass(singleton(u),v)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[552,3]),
[iquote('0:SpR:552.1,3.1')] ).
cnf(1217,plain,
( subclass(singleton(u),v)
| member(u,singleton(u)) ),
inference(obv,[status(thm),theory(equality)],[1212]),
[iquote('0:Obv:1212.0')] ).
cnf(1218,plain,
( subclass(null_class,u)
| member(v,singleton(v)) ),
inference(rew,[status(thm),theory(equality)],[630,1217]),
[iquote('0:Rew:630.0,1217.0')] ).
cnf(1222,plain,
member(u,singleton(u)),
inference(spt,[spt(split,[position(s1)])],[1218]),
[iquote('1:Spt:1218.1')] ).
cnf(1227,plain,
( ~ subclass(singleton(u),v)
| member(u,v) ),
inference(res,[status(thm),theory(equality)],[1222,2]),
[iquote('1:Res:1222.0,2.0')] ).
cnf(1270,plain,
member(u,universal_class),
inference(res,[status(thm),theory(equality)],[5,1227]),
[iquote('1:Res:5.0,1227.0')] ).
cnf(1309,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[272,1270]),
[iquote('1:MRR:272.0,1270.0')] ).
cnf(1320,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[1270,160]),
[iquote('1:Res:1270.0,160.0')] ).
cnf(1331,plain,
equal(complement(intersection(null_class,complement(u))),union(universal_class,u)),
inference(spr,[status(thm),theory(equality)],[1320,27]),
[iquote('1:SpR:1320.0,27.0')] ).
cnf(1343,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[1320,25]),
[iquote('1:SpL:1320.0,25.1')] ).
cnf(1345,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[1343,1270]),
[iquote('1:MRR:1343.0,1270.0')] ).
cnf(2134,plain,
( member(not_subclass_element(u,union(universal_class,v)),intersection(null_class,complement(v)))
| subclass(u,complement(intersection(null_class,complement(v)))) ),
inference(spr,[status(thm),theory(equality)],[1331,1309]),
[iquote('1:SpR:1331.0,1309.0')] ).
cnf(2156,plain,
( member(not_subclass_element(u,union(universal_class,v)),intersection(null_class,complement(v)))
| subclass(u,union(universal_class,v)) ),
inference(rew,[status(thm),theory(equality)],[1331,2134]),
[iquote('1:Rew:1331.0,2134.1')] ).
cnf(2903,plain,
equal(intersection(null_class,u),null_class),
inference(res,[status(thm),theory(equality)],[178,1345]),
[iquote('1:Res:178.1,1345.0')] ).
cnf(2944,plain,
( member(not_subclass_element(u,union(universal_class,v)),null_class)
| subclass(u,union(universal_class,v)) ),
inference(rew,[status(thm),theory(equality)],[2903,2156]),
[iquote('1:Rew:2903.0,2156.0')] ).
cnf(2981,plain,
subclass(u,union(universal_class,v)),
inference(mrr,[status(thm)],[2944,1345]),
[iquote('1:MRR:2944.0,1345.0')] ).
cnf(2982,plain,
$false,
inference(unc,[status(thm)],[2981,122]),
[iquote('1:UnC:2981.0,122.0')] ).
cnf(2988,plain,
subclass(null_class,u),
inference(spt,[spt(split,[position(s2)])],[1218]),
[iquote('1:Spt:2982.0,1218.0')] ).
cnf(2991,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[2988,8]),
[iquote('1:Res:2988.0,8.0')] ).
cnf(3753,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[343,160]),
[iquote('0:Res:343.2,160.0')] ).
cnf(3768,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[3753]),
[iquote('0:Obv:3753.1')] ).
cnf(3777,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[5,3768]),
[iquote('0:Res:5.0,3768.0')] ).
cnf(3789,plain,
equal(complement(intersection(null_class,complement(u))),union(universal_class,u)),
inference(spr,[status(thm),theory(equality)],[3777,27]),
[iquote('0:SpR:3777.0,27.0')] ).
cnf(3804,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[3777,25]),
[iquote('0:SpL:3777.0,25.1')] ).
cnf(4716,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[169,4]),
[iquote('0:Res:169.1,4.0')] ).
cnf(4718,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[4716]),
[iquote('0:Obv:4716.0')] ).
cnf(4749,plain,
equal(intersection(u,null_class),null_class),
inference(res,[status(thm),theory(equality)],[4718,2991]),
[iquote('1:Res:4718.0,2991.0')] ).
cnf(4977,plain,
( ~ member(u,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[4749,22]),
[iquote('1:SpL:4749.0,22.0')] ).
cnf(4996,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[3804,4977]),
[iquote('1:MRR:3804.0,4977.1')] ).
cnf(5026,plain,
equal(intersection(null_class,u),null_class),
inference(res,[status(thm),theory(equality)],[178,4996]),
[iquote('1:Res:178.1,4996.0')] ).
cnf(5042,plain,
equal(union(universal_class,u),complement(null_class)),
inference(rew,[status(thm),theory(equality)],[5026,3789]),
[iquote('1:Rew:5026.0,3789.0')] ).
cnf(5080,plain,
~ subclass(universal_class,complement(null_class)),
inference(rew,[status(thm),theory(equality)],[5042,122]),
[iquote('1:Rew:5042.0,122.0')] ).
cnf(5146,plain,
equal(complement(null_class),successor(universal_class)),
inference(spr,[status(thm),theory(equality)],[5042,44]),
[iquote('1:SpR:5042.0,44.0')] ).
cnf(5155,plain,
~ subclass(universal_class,successor(universal_class)),
inference(rew,[status(thm),theory(equality)],[5146,5080]),
[iquote('1:Rew:5146.0,5080.0')] ).
cnf(5189,plain,
( ~ member(u,universal_class)
| member(u,null_class)
| member(u,successor(universal_class)) ),
inference(spr,[status(thm),theory(equality)],[5146,26]),
[iquote('1:SpR:5146.0,26.2')] ).
cnf(5209,plain,
( ~ member(u,universal_class)
| member(u,successor(universal_class)) ),
inference(mrr,[status(thm)],[5189,4996]),
[iquote('1:MRR:5189.1,4996.0')] ).
cnf(5690,plain,
( ~ member(not_subclass_element(u,successor(universal_class)),universal_class)
| subclass(u,successor(universal_class)) ),
inference(res,[status(thm),theory(equality)],[5209,4]),
[iquote('1:Res:5209.1,4.0')] ).
cnf(8326,plain,
( ~ subclass(u,universal_class)
| subclass(u,successor(universal_class))
| subclass(u,successor(universal_class)) ),
inference(res,[status(thm),theory(equality)],[344,5690]),
[iquote('1:Res:344.2,5690.0')] ).
cnf(8331,plain,
( ~ subclass(u,universal_class)
| subclass(u,successor(universal_class)) ),
inference(obv,[status(thm),theory(equality)],[8326]),
[iquote('1:Obv:8326.1')] ).
cnf(8332,plain,
subclass(u,successor(universal_class)),
inference(mrr,[status(thm)],[8331,5]),
[iquote('1:MRR:8331.0,5.0')] ).
cnf(8333,plain,
$false,
inference(unc,[status(thm)],[8332,5155]),
[iquote('1:UnC:8332.0,5155.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET163-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.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 : Mon Jul 11 02:43:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.16
% 1.98/2.16 SPASS V 3.9
% 1.98/2.16 SPASS beiseite: Proof found.
% 1.98/2.16 % SZS status Theorem
% 1.98/2.16 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.98/2.16 SPASS derived 6940 clauses, backtracked 481 clauses, performed 4 splits and kept 4139 clauses.
% 1.98/2.16 SPASS allocated 83052 KBytes.
% 1.98/2.16 SPASS spent 0:00:01.77 on the problem.
% 1.98/2.16 0:00:00.04 for the input.
% 1.98/2.16 0:00:00.00 for the FLOTTER CNF translation.
% 1.98/2.16 0:00:00.08 for inferences.
% 1.98/2.16 0:00:00.08 for the backtracking.
% 1.98/2.16 0:00:01.51 for the reduction.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Here is a proof with depth 9, length 70 :
% 1.98/2.16 % SZS output start Refutation
% See solution above
% 1.98/2.16 Formulae used in the proof : prove_union_with_universal_class_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal unordered_pair_member singleton_set intersection1 intersection2 complement1 complement2 union successor regularity1
% 1.98/2.16
%------------------------------------------------------------------------------