TSTP Solution File: SET154-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET154-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:24:34 EDT 2022
% Result : Unsatisfiable 15.36s 15.58s
% Output : Refutation 15.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of clauses : 87 ( 32 unt; 32 nHn; 87 RR)
% Number of literals : 163 ( 0 equ; 52 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(union(complement(x__dfg),x__dfg),universal_class),
file('SET154-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET154-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET154-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET154-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET154-6.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET154-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET154-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET154-6.p',unknown),
[] ).
cnf(12,axiom,
member(unordered_pair(u,v),universal_class),
file('SET154-6.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET154-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET154-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET154-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET154-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET154-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET154-6.p',unknown),
[] ).
cnf(27,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET154-6.p',unknown),
[] ).
cnf(44,axiom,
equal(union(u,singleton(u)),successor(u)),
file('SET154-6.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET154-6.p',unknown),
[] ).
cnf(68,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET154-6.p',unknown),
[] ).
cnf(71,axiom,
( ~ member(u,universal_class)
| equal(u,null_class)
| member(apply(choice,u),u) ),
file('SET154-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(union(complement(x__dfg),x__dfg),universal_class)
| ~ subclass(universal_class,union(complement(x__dfg),x__dfg)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.2,1.0')] ).
cnf(122,plain,
~ subclass(universal_class,union(complement(x__dfg),x__dfg)),
inference(mrr,[status(thm)],[117,5]),
[iquote('0:MRR:117.0,5.0')] ).
cnf(129,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.0,12.0')] ).
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(168,plain,
( equal(intersection(u,v),null_class)
| member(regular(intersection(u,v)),v) ),
inference(res,[status(thm),theory(equality)],[67,23]),
[iquote('0:Res:67.1,23.0')] ).
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(556,plain,
( ~ member(singleton(u),universal_class)
| equal(singleton(u),null_class)
| equal(apply(choice,singleton(u)),u) ),
inference(res,[status(thm),theory(equality)],[71,548]),
[iquote('0:Res:71.2,548.0')] ).
cnf(560,plain,
( equal(singleton(u),null_class)
| equal(apply(choice,singleton(u)),u) ),
inference(mrr,[status(thm)],[556,129]),
[iquote('0:MRR:556.0,129.0')] ).
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(626,plain,
( equal(singleton(u),null_class)
| equal(singleton(u),null_class)
| equal(intersection(singleton(u),u),null_class) ),
inference(spr,[status(thm),theory(equality)],[551,68]),
[iquote('0:SpR:551.1,68.1')] ).
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(631,plain,
( equal(singleton(u),null_class)
| equal(intersection(singleton(u),u),null_class) ),
inference(obv,[status(thm),theory(equality)],[626]),
[iquote('0:Obv:626.0')] ).
cnf(864,plain,
( ~ member(u,v)
| ~ member(u,singleton(v))
| equal(singleton(v),null_class)
| member(u,null_class) ),
inference(spr,[status(thm),theory(equality)],[631,24]),
[iquote('0:SpR:631.1,24.2')] ).
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(1272,plain,
( ~ equal(u,singleton(v))
| member(v,u) ),
inference(res,[status(thm),theory(equality)],[7,1227]),
[iquote('1:Res:7.1,1227.0')] ).
cnf(1280,plain,
( equal(u,null_class)
| member(apply(choice,u),u) ),
inference(mrr,[status(thm)],[71,1270]),
[iquote('1:MRR:71.0,1270.0')] ).
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(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(1348,plain,
( ~ member(u,v)
| ~ member(u,singleton(v))
| equal(singleton(v),null_class) ),
inference(mrr,[status(thm)],[864,1345]),
[iquote('1:MRR:864.3,1345.0')] ).
cnf(1858,plain,
~ equal(singleton(u),null_class),
inference(res,[status(thm),theory(equality)],[1272,1345]),
[iquote('1:Res:1272.1,1345.0')] ).
cnf(1883,plain,
equal(apply(choice,singleton(u)),u),
inference(mrr,[status(thm)],[560,1858]),
[iquote('1:MRR:560.0,1858.0')] ).
cnf(1888,plain,
( ~ member(u,v)
| ~ member(u,singleton(v)) ),
inference(mrr,[status(thm)],[1348,1858]),
[iquote('1:MRR:1348.2,1858.0')] ).
cnf(2904,plain,
( ~ member(regular(intersection(complement(u),v)),u)
| equal(intersection(complement(u),v),null_class) ),
inference(res,[status(thm),theory(equality)],[178,25]),
[iquote('0:Res:178.1,25.1')] ).
cnf(3060,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(3074,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[3060]),
[iquote('0:Obv:3060.1')] ).
cnf(4346,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[5,3074]),
[iquote('0:Res:5.0,3074.0')] ).
cnf(4922,plain,
( ~ member(apply(choice,singleton(u)),u)
| equal(singleton(u),null_class) ),
inference(res,[status(thm),theory(equality)],[1280,1888]),
[iquote('1:Res:1280.1,1888.1')] ).
cnf(4939,plain,
( ~ member(u,u)
| equal(singleton(u),null_class) ),
inference(rew,[status(thm),theory(equality)],[1883,4922]),
[iquote('1:Rew:1883.0,4922.0')] ).
cnf(4940,plain,
~ member(u,u),
inference(mrr,[status(thm)],[4939,1858]),
[iquote('1:MRR:4939.1,1858.0')] ).
cnf(4941,plain,
$false,
inference(unc,[status(thm)],[4940,1270]),
[iquote('1:UnC:4940.0,1270.0')] ).
cnf(4946,plain,
subclass(null_class,u),
inference(spt,[spt(split,[position(s2)])],[1218]),
[iquote('1:Spt:4941.0,1218.0')] ).
cnf(4951,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[4946,8]),
[iquote('1:Res:4946.0,8.0')] ).
cnf(4964,plain,
equal(complement(intersection(null_class,complement(u))),union(universal_class,u)),
inference(spr,[status(thm),theory(equality)],[4346,27]),
[iquote('0:SpR:4346.0,27.0')] ).
cnf(4973,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[4346,25]),
[iquote('0:SpL:4346.0,25.1')] ).
cnf(6596,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(6598,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[6596]),
[iquote('0:Obv:6596.0')] ).
cnf(6630,plain,
equal(intersection(u,null_class),null_class),
inference(res,[status(thm),theory(equality)],[6598,4951]),
[iquote('1:Res:6598.0,4951.0')] ).
cnf(6855,plain,
( ~ member(u,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[6630,22]),
[iquote('1:SpL:6630.0,22.0')] ).
cnf(6874,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[4973,6855]),
[iquote('1:MRR:4973.0,6855.1')] ).
cnf(6904,plain,
equal(intersection(null_class,u),null_class),
inference(res,[status(thm),theory(equality)],[178,6874]),
[iquote('1:Res:178.1,6874.0')] ).
cnf(6918,plain,
equal(union(universal_class,u),complement(null_class)),
inference(rew,[status(thm),theory(equality)],[6904,4964]),
[iquote('1:Rew:6904.0,4964.0')] ).
cnf(7024,plain,
equal(complement(null_class),successor(universal_class)),
inference(spr,[status(thm),theory(equality)],[6918,44]),
[iquote('1:SpR:6918.0,44.0')] ).
cnf(11933,plain,
( ~ subclass(u,universal_class)
| subclass(u,complement(v))
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(res,[status(thm),theory(equality)],[344,272]),
[iquote('0:Res:344.2,272.0')] ).
cnf(11939,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[11933]),
[iquote('0:Obv:11933.1')] ).
cnf(11940,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[11939,5]),
[iquote('0:MRR:11939.0,5.0')] ).
cnf(12485,plain,
subclass(u,complement(null_class)),
inference(res,[status(thm),theory(equality)],[11940,6874]),
[iquote('1:Res:11940.0,6874.0')] ).
cnf(31944,plain,
( equal(intersection(complement(u),u),null_class)
| equal(intersection(complement(u),u),null_class) ),
inference(res,[status(thm),theory(equality)],[168,2904]),
[iquote('0:Res:168.1,2904.0')] ).
cnf(31951,plain,
equal(intersection(complement(u),u),null_class),
inference(obv,[status(thm),theory(equality)],[31944]),
[iquote('0:Obv:31944.0')] ).
cnf(32009,plain,
equal(union(complement(u),u),complement(null_class)),
inference(spr,[status(thm),theory(equality)],[31951,27]),
[iquote('0:SpR:31951.0,27.0')] ).
cnf(32083,plain,
subclass(u,successor(universal_class)),
inference(rew,[status(thm),theory(equality)],[7024,12485]),
[iquote('1:Rew:7024.0,12485.0')] ).
cnf(32112,plain,
equal(union(complement(u),u),successor(universal_class)),
inference(rew,[status(thm),theory(equality)],[7024,32009]),
[iquote('1:Rew:7024.0,32009.0')] ).
cnf(32114,plain,
~ subclass(universal_class,successor(universal_class)),
inference(rew,[status(thm),theory(equality)],[32112,122]),
[iquote('1:Rew:32112.0,122.0')] ).
cnf(32121,plain,
$false,
inference(mrr,[status(thm)],[32114,32083]),
[iquote('1:MRR:32114.0,32083.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET154-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 23:48:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 15.36/15.58
% 15.36/15.58 SPASS V 3.9
% 15.36/15.58 SPASS beiseite: Proof found.
% 15.36/15.58 % SZS status Theorem
% 15.36/15.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.36/15.58 SPASS derived 24861 clauses, backtracked 2393 clauses, performed 9 splits and kept 12609 clauses.
% 15.36/15.58 SPASS allocated 102499 KBytes.
% 15.36/15.58 SPASS spent 0:0:15.20 on the problem.
% 15.36/15.58 0:00:00.04 for the input.
% 15.36/15.58 0:00:00.00 for the FLOTTER CNF translation.
% 15.36/15.58 0:00:00.29 for inferences.
% 15.36/15.58 0:00:01.07 for the backtracking.
% 15.36/15.58 0:0:13.58 for the reduction.
% 15.36/15.58
% 15.36/15.58
% 15.36/15.58 Here is a proof with depth 9, length 87 :
% 15.36/15.58 % SZS output start Refutation
% See solution above
% 15.36/15.58 Formulae used in the proof : prove_union_with_complement_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair_member unordered_pairs_in_universal singleton_set intersection1 intersection2 intersection3 complement1 complement2 union successor regularity1 regularity2 choice2
% 15.58/15.83
%------------------------------------------------------------------------------