%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET151-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 05:24:33 EDT 2022
% Result : Unsatisfiable 2.59s 2.78s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 41 ( 14 unt; 14 nHn; 41 RR)
% Number of literals : 79 ( 0 equ; 30 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 : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(complement(null_class),universal_class),
file('SET151-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET151-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET151-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET151-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET151-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET151-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET151-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET151-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET151-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET151-6.p',unknown),
[] ).
cnf(27,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET151-6.p',unknown),
[] ).
cnf(44,axiom,
equal(union(u,singleton(u)),successor(u)),
file('SET151-6.p',unknown),
[] ).
cnf(67,axiom,
( equal(u,null_class)
| member(regular(u),u) ),
file('SET151-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(complement(null_class),universal_class)
| ~ subclass(universal_class,complement(null_class)) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.2,1.0')] ).
cnf(122,plain,
~ subclass(universal_class,complement(null_class)),
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(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(279,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(351,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(352,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(3899,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class)
| equal(complement(u),null_class) ),
inference(res,[status(thm),theory(equality)],[351,160]),
[iquote('0:Res:351.2,160.0')] ).
cnf(3914,plain,
( ~ subclass(complement(u),u)
| equal(complement(u),null_class) ),
inference(obv,[status(thm),theory(equality)],[3899]),
[iquote('0:Obv:3899.1')] ).
cnf(4089,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[5,3914]),
[iquote('0:Res:5.0,3914.0')] ).
cnf(4102,plain,
equal(complement(intersection(null_class,complement(u))),union(universal_class,u)),
inference(spr,[status(thm),theory(equality)],[4089,27]),
[iquote('0:SpR:4089.0,27.0')] ).
cnf(4116,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[4089,25]),
[iquote('0:SpL:4089.0,25.1')] ).
cnf(4153,plain,
( ~ subclass(u,universal_class)
| ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[351,4116]),
[iquote('0:Res:351.2,4116.0')] ).
cnf(4166,plain,
( ~ member(regular(u),null_class)
| equal(u,null_class) ),
inference(mrr,[status(thm)],[4153,5]),
[iquote('0:MRR:4153.0,5.0')] ).
cnf(4224,plain,
( equal(intersection(null_class,u),null_class)
| equal(intersection(null_class,u),null_class) ),
inference(res,[status(thm),theory(equality)],[178,4166]),
[iquote('0:Res:178.1,4166.0')] ).
cnf(4227,plain,
equal(intersection(null_class,u),null_class),
inference(obv,[status(thm),theory(equality)],[4224]),
[iquote('0:Obv:4224.0')] ).
cnf(4228,plain,
equal(union(universal_class,u),complement(null_class)),
inference(rew,[status(thm),theory(equality)],[4227,4102]),
[iquote('0:Rew:4227.0,4102.0')] ).
cnf(4327,plain,
( ~ member(u,null_class)
| member(u,v) ),
inference(spl,[status(thm),theory(equality)],[4227,23]),
[iquote('0:SpL:4227.0,23.0')] ).
cnf(4342,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[4116,4327]),
[iquote('0:MRR:4116.0,4327.1')] ).
cnf(4414,plain,
equal(complement(null_class),successor(universal_class)),
inference(spr,[status(thm),theory(equality)],[4228,44]),
[iquote('0:SpR:4228.0,44.0')] ).
cnf(4421,plain,
~ subclass(universal_class,successor(universal_class)),
inference(rew,[status(thm),theory(equality)],[4414,122]),
[iquote('0:Rew:4414.0,122.0')] ).
cnf(9605,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)],[352,279]),
[iquote('0:Res:352.2,279.0')] ).
cnf(9609,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[9605]),
[iquote('0:Obv:9605.1')] ).
cnf(9610,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[9609,5]),
[iquote('0:MRR:9609.0,5.0')] ).
cnf(10040,plain,
( member(not_subclass_element(u,successor(universal_class)),null_class)
| subclass(u,complement(null_class)) ),
inference(spr,[status(thm),theory(equality)],[4414,9610]),
[iquote('0:SpR:4414.0,9610.0')] ).
cnf(10076,plain,
( member(not_subclass_element(u,successor(universal_class)),null_class)
| subclass(u,successor(universal_class)) ),
inference(rew,[status(thm),theory(equality)],[4414,10040]),
[iquote('0:Rew:4414.0,10040.1')] ).
cnf(10077,plain,
subclass(u,successor(universal_class)),
inference(mrr,[status(thm)],[10076,4342]),
[iquote('0:MRR:10076.0,4342.0')] ).
cnf(10078,plain,
$false,
inference(unc,[status(thm)],[10077,4421]),
[iquote('0:UnC:10077.0,4421.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET151-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n003.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 : Sun Jul 10 11:36:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.59/2.78
% 2.59/2.78 SPASS V 3.9
% 2.59/2.78 SPASS beiseite: Proof found.
% 2.59/2.78 % SZS status Theorem
% 2.59/2.78 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.59/2.78 SPASS derived 8606 clauses, backtracked 817 clauses, performed 5 splits and kept 5168 clauses.
% 2.59/2.78 SPASS allocated 84364 KBytes.
% 2.59/2.78 SPASS spent 0:00:02.37 on the problem.
% 2.59/2.78 0:00:00.04 for the input.
% 2.59/2.78 0:00:00.00 for the FLOTTER CNF translation.
% 2.59/2.78 0:00:00.10 for inferences.
% 2.59/2.78 0:00:00.08 for the backtracking.
% 2.59/2.78 0:00:02.07 for the reduction.
% 2.59/2.78
% 2.59/2.78
% 2.59/2.78 Here is a proof with depth 7, length 41 :
% 2.59/2.78 % SZS output start Refutation
% See solution above
% 2.59/2.78 Formulae used in the proof : prove_complement_of_null_class_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal intersection1 intersection2 complement1 complement2 union successor regularity1
% 2.59/2.78
%------------------------------------------------------------------------------