TSTP Solution File: SET186-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET186-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 05:24:52 EDT 2022
% Result : Unsatisfiable 18.07s 18.26s
% Output : Refutation 18.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of clauses : 56 ( 16 unt; 20 nHn; 56 RR)
% Number of literals : 114 ( 0 equ; 40 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(union(x__dfg,y__dfg),y__dfg),
file('SET186-6.p',unknown),
[] ).
cnf(2,axiom,
~ subclass(x__dfg,y__dfg),
file('SET186-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET186-6.p',unknown),
[] ).
cnf(4,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET186-6.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET186-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET186-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET186-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET186-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET186-6.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET186-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET186-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET186-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET186-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET186-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET186-6.p',unknown),
[] ).
cnf(28,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET186-6.p',unknown),
[] ).
cnf(117,plain,
~ member(not_subclass_element(x__dfg,y__dfg),y__dfg),
inference(res,[status(thm),theory(equality)],[5,2]),
[iquote('0:Res:5.1,2.0')] ).
cnf(118,plain,
member(not_subclass_element(x__dfg,y__dfg),x__dfg),
inference(res,[status(thm),theory(equality)],[4,2]),
[iquote('0:Res:4.1,2.0')] ).
cnf(153,plain,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
inference(spr,[status(thm),theory(equality)],[14,12]),
[iquote('0:SpR:14.0,12.1')] ).
cnf(159,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[4,26]),
[iquote('0:Res:4.1,26.1')] ).
cnf(167,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[4,24]),
[iquote('0:Res:4.1,24.0')] ).
cnf(281,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)],[27,5]),
[iquote('0:Res:27.2,5.0')] ).
cnf(361,plain,
( ~ subclass(u,v)
| subclass(u,w)
| member(not_subclass_element(u,w),v) ),
inference(res,[status(thm),theory(equality)],[4,3]),
[iquote('0:Res:4.1,3.0')] ).
cnf(364,plain,
( ~ member(u,universal_class)
| ~ subclass(singleton(u),v)
| member(u,v) ),
inference(res,[status(thm),theory(equality)],[153,3]),
[iquote('0:Res:153.1,3.0')] ).
cnf(540,plain,
( ~ member(u,singleton(v))
| equal(u,v)
| equal(u,v) ),
inference(spl,[status(thm),theory(equality)],[14,10]),
[iquote('0:SpL:14.0,10.0')] ).
cnf(552,plain,
( ~ member(u,singleton(v))
| equal(u,v) ),
inference(obv,[status(thm),theory(equality)],[540]),
[iquote('0:Obv:540.1')] ).
cnf(558,plain,
( subclass(singleton(u),v)
| equal(not_subclass_element(singleton(u),v),u) ),
inference(res,[status(thm),theory(equality)],[4,552]),
[iquote('0:Res:4.1,552.0')] ).
cnf(1276,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[25,3]),
[iquote('0:Res:25.2,3.0')] ).
cnf(2316,plain,
( ~ member(not_subclass_element(complement(complement(u)),v),universal_class)
| member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(res,[status(thm),theory(equality)],[27,159]),
[iquote('0:Res:27.2,159.0')] ).
cnf(3974,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[167,5]),
[iquote('0:Res:167.1,5.0')] ).
cnf(3997,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[3974]),
[iquote('0:Obv:3974.0')] ).
cnf(7611,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)],[361,281]),
[iquote('0:Res:361.2,281.0')] ).
cnf(7615,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[7611]),
[iquote('0:Obv:7611.1')] ).
cnf(7616,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[7615,6]),
[iquote('0:MRR:7615.0,6.0')] ).
cnf(7635,plain,
( subclass(singleton(u),complement(v))
| member(u,v)
| subclass(singleton(u),complement(v)) ),
inference(spr,[status(thm),theory(equality)],[558,7616]),
[iquote('0:SpR:558.1,7616.0')] ).
cnf(7671,plain,
( member(u,v)
| subclass(singleton(u),complement(v)) ),
inference(obv,[status(thm),theory(equality)],[7635]),
[iquote('0:Obv:7635.0')] ).
cnf(9583,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[6,1276]),
[iquote('0:Res:6.0,1276.2')] ).
cnf(9593,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[9583]),
[iquote('0:Con:9583.1')] ).
cnf(9639,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[4,9593]),
[iquote('0:Res:4.1,9593.0')] ).
cnf(9758,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[2316,9639]),
[iquote('0:MRR:2316.0,9639.1')] ).
cnf(23877,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[9758,5]),
[iquote('0:Res:9758.0,5.0')] ).
cnf(23909,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[23877]),
[iquote('0:Obv:23877.0')] ).
cnf(23936,plain,
subclass(complement(union(u,v)),intersection(complement(u),complement(v))),
inference(spr,[status(thm),theory(equality)],[28,23909]),
[iquote('0:SpR:28.0,23909.0')] ).
cnf(30719,plain,
subclass(complement(y__dfg),intersection(complement(x__dfg),complement(y__dfg))),
inference(spr,[status(thm),theory(equality)],[1,23936]),
[iquote('0:SpR:1.0,23936.0')] ).
cnf(30741,plain,
( ~ subclass(intersection(complement(x__dfg),complement(y__dfg)),complement(y__dfg))
| equal(intersection(complement(x__dfg),complement(y__dfg)),complement(y__dfg)) ),
inference(res,[status(thm),theory(equality)],[30719,9]),
[iquote('0:Res:30719.0,9.0')] ).
cnf(30743,plain,
equal(intersection(complement(x__dfg),complement(y__dfg)),complement(y__dfg)),
inference(mrr,[status(thm)],[30741,3997]),
[iquote('0:MRR:30741.0,3997.0')] ).
cnf(30871,plain,
equal(complement(complement(y__dfg)),union(x__dfg,y__dfg)),
inference(spr,[status(thm),theory(equality)],[30743,28]),
[iquote('0:SpR:30743.0,28.0')] ).
cnf(30906,plain,
( ~ member(u,complement(y__dfg))
| member(u,complement(x__dfg)) ),
inference(spl,[status(thm),theory(equality)],[30743,23]),
[iquote('0:SpL:30743.0,23.0')] ).
cnf(31028,plain,
equal(complement(complement(y__dfg)),y__dfg),
inference(rew,[status(thm),theory(equality)],[1,30871]),
[iquote('0:Rew:1.0,30871.0')] ).
cnf(32706,plain,
( member(u,complement(y__dfg))
| subclass(singleton(u),y__dfg) ),
inference(spr,[status(thm),theory(equality)],[31028,7671]),
[iquote('0:SpR:31028.0,7671.1')] ).
cnf(37214,plain,
( subclass(singleton(u),y__dfg)
| member(u,complement(x__dfg)) ),
inference(res,[status(thm),theory(equality)],[32706,30906]),
[iquote('0:Res:32706.0,30906.0')] ).
cnf(37243,plain,
( ~ member(u,x__dfg)
| subclass(singleton(u),y__dfg) ),
inference(res,[status(thm),theory(equality)],[37214,26]),
[iquote('0:Res:37214.1,26.1')] ).
cnf(37248,plain,
( ~ member(u,x__dfg)
| ~ member(u,universal_class)
| member(u,y__dfg) ),
inference(res,[status(thm),theory(equality)],[37243,364]),
[iquote('0:Res:37243.1,364.1')] ).
cnf(37249,plain,
( ~ member(u,x__dfg)
| member(u,y__dfg) ),
inference(mrr,[status(thm)],[37248,9593]),
[iquote('0:MRR:37248.1,9593.1')] ).
cnf(37311,plain,
~ member(not_subclass_element(x__dfg,y__dfg),x__dfg),
inference(res,[status(thm),theory(equality)],[37249,117]),
[iquote('0:Res:37249.1,117.0')] ).
cnf(37325,plain,
$false,
inference(mrr,[status(thm)],[37311,118]),
[iquote('0:MRR:37311.0,118.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET186-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 07:48:17 EDT 2022
% 0.15/0.36 % CPUTime :
% 18.07/18.26
% 18.07/18.26 SPASS V 3.9
% 18.07/18.26 SPASS beiseite: Proof found.
% 18.07/18.26 % SZS status Theorem
% 18.07/18.26 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.07/18.26 SPASS derived 29508 clauses, backtracked 3319 clauses, performed 10 splits and kept 15076 clauses.
% 18.07/18.26 SPASS allocated 103891 KBytes.
% 18.07/18.26 SPASS spent 0:0:17.58 on the problem.
% 18.07/18.26 0:00:00.04 for the input.
% 18.07/18.26 0:00:00.00 for the FLOTTER CNF translation.
% 18.07/18.26 0:00:00.34 for inferences.
% 18.07/18.26 0:00:01.39 for the backtracking.
% 18.07/18.26 0:0:15.51 for the reduction.
% 18.07/18.26
% 18.07/18.26
% 18.07/18.26 Here is a proof with depth 12, length 56 :
% 18.07/18.26 % SZS output start Refutation
% See solution above
% 18.07/18.26 Formulae used in the proof : prove_subclass_property4_1 prove_subclass_property4_2 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal unordered_pair_member unordered_pair3 singleton_set intersection1 intersection2 intersection3 complement1 complement2 union
% 18.07/18.26
%------------------------------------------------------------------------------