%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET132-6 : 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 05:24:23 EDT 2022
% Result : Unsatisfiable 14.71s 14.97s
% Output : Refutation 14.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of clauses : 63 ( 26 unt; 20 nHn; 63 RR)
% Number of literals : 113 ( 0 equ; 35 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 : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(union(singleton(u),v),set_builder(u,v)),
file('SET132-6.p',unknown),
[] ).
cnf(2,axiom,
member(u__dfg,universal_class),
file('SET132-6.p',unknown),
[] ).
cnf(3,axiom,
~ member(u__dfg,set_builder(x__dfg,set_builder(y__dfg,set_builder(u__dfg,null_class)))),
file('SET132-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET132-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET132-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET132-6.p',unknown),
[] ).
cnf(7,axiom,
subclass(u,universal_class),
file('SET132-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET132-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET132-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET132-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET132-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET132-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET132-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET132-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET132-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET132-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET132-6.p',unknown),
[] ).
cnf(70,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET132-6.p',unknown),
[] ).
cnf(99,plain,
( member(u__dfg,u)
| member(u__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[2,28]),
[iquote('0:Res:2.0,28.0')] ).
cnf(100,plain,
member(u__dfg,unordered_pair(u__dfg,u)),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(145,plain,
member(u__dfg,singleton(u__dfg)),
inference(spr,[status(thm),theory(equality)],[15,100]),
[iquote('0:SpR:15.0,100.0')] ).
cnf(192,plain,
( ~ member(not_subclass_element(complement(u),v),u)
| subclass(complement(u),v) ),
inference(res,[status(thm),theory(equality)],[5,27]),
[iquote('0:Res:5.1,27.1')] ).
cnf(232,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[5,24]),
[iquote('0:Res:5.1,24.0')] ).
cnf(247,plain,
( member(u__dfg,intersection(complement(u),complement(v)))
| member(u__dfg,union(u,v)) ),
inference(spr,[status(thm),theory(equality)],[29,99]),
[iquote('0:SpR:29.0,99.1')] ).
cnf(366,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)],[28,6]),
[iquote('0:Res:28.2,6.0')] ).
cnf(412,plain,
( ~ subclass(universal_class,u)
| equal(universal_class,u) ),
inference(res,[status(thm),theory(equality)],[7,10]),
[iquote('0:Res:7.0,10.0')] ).
cnf(466,plain,
( ~ subclass(u,v)
| subclass(u,w)
| member(not_subclass_element(u,w),v) ),
inference(res,[status(thm),theory(equality)],[5,4]),
[iquote('0:Res:5.1,4.0')] ).
cnf(994,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[26,4]),
[iquote('0:Res:26.2,4.0')] ).
cnf(1583,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)],[28,192]),
[iquote('0:Res:28.2,192.0')] ).
cnf(5763,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[232,6]),
[iquote('0:Res:232.1,6.0')] ).
cnf(5767,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[5763]),
[iquote('0:Obv:5763.0')] ).
cnf(8458,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)],[466,366]),
[iquote('0:Res:466.2,366.0')] ).
cnf(8464,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[8458]),
[iquote('0:Obv:8458.1')] ).
cnf(8465,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[8464,7]),
[iquote('0:MRR:8464.0,7.0')] ).
cnf(8806,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[7,994]),
[iquote('0:Res:7.0,994.2')] ).
cnf(8813,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[8806]),
[iquote('0:Con:8806.1')] ).
cnf(8858,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[5,8813]),
[iquote('0:Res:5.1,8813.0')] ).
cnf(8941,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[1583,8858]),
[iquote('0:MRR:1583.0,8858.1')] ).
cnf(10636,plain,
( subclass(complement(universal_class),u)
| subclass(complement(universal_class),u) ),
inference(res,[status(thm),theory(equality)],[8858,192]),
[iquote('0:Res:8858.1,192.0')] ).
cnf(10641,plain,
subclass(complement(universal_class),u),
inference(obv,[status(thm),theory(equality)],[10636]),
[iquote('0:Obv:10636.0')] ).
cnf(18714,plain,
( member(u__dfg,union(u,v))
| member(u__dfg,complement(v)) ),
inference(res,[status(thm),theory(equality)],[247,25]),
[iquote('0:Res:247.0,25.0')] ).
cnf(18866,plain,
( member(u__dfg,set_builder(u,v))
| member(u__dfg,complement(v)) ),
inference(spr,[status(thm),theory(equality)],[1,18714]),
[iquote('0:SpR:1.0,18714.0')] ).
cnf(19330,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[8941,6]),
[iquote('0:Res:8941.0,6.0')] ).
cnf(19333,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[19330]),
[iquote('0:Obv:19330.0')] ).
cnf(28005,plain,
( equal(u,null_class)
| subclass(null_class,u) ),
inference(spr,[status(thm),theory(equality)],[70,5767]),
[iquote('0:SpR:70.1,5767.0')] ).
cnf(28043,plain,
subclass(null_class,u),
inference(mrr,[status(thm)],[28005,9]),
[iquote('0:MRR:28005.0,9.0')] ).
cnf(28052,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[28043,10]),
[iquote('0:Res:28043.0,10.0')] ).
cnf(28062,plain,
member(u__dfg,complement(set_builder(y__dfg,set_builder(u__dfg,null_class)))),
inference(res,[status(thm),theory(equality)],[18866,3]),
[iquote('0:Res:18866.0,3.0')] ).
cnf(28225,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[10641,28052]),
[iquote('0:Res:10641.0,28052.0')] ).
cnf(28290,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[28225,27]),
[iquote('0:SpL:28225.0,27.1')] ).
cnf(28296,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[28290,8813]),
[iquote('0:MRR:28290.0,8813.1')] ).
cnf(28367,plain,
subclass(u,complement(null_class)),
inference(res,[status(thm),theory(equality)],[8465,28296]),
[iquote('0:Res:8465.0,28296.0')] ).
cnf(28382,plain,
equal(complement(null_class),universal_class),
inference(res,[status(thm),theory(equality)],[28367,412]),
[iquote('0:Res:28367.0,412.0')] ).
cnf(28465,plain,
equal(complement(intersection(complement(u),universal_class)),union(u,null_class)),
inference(spr,[status(thm),theory(equality)],[28382,29]),
[iquote('0:SpR:28382.0,29.0')] ).
cnf(31799,plain,
~ member(u__dfg,set_builder(y__dfg,set_builder(u__dfg,null_class))),
inference(res,[status(thm),theory(equality)],[28062,27]),
[iquote('0:Res:28062.0,27.1')] ).
cnf(31998,plain,
member(u__dfg,complement(set_builder(u__dfg,null_class))),
inference(res,[status(thm),theory(equality)],[18866,31799]),
[iquote('0:Res:18866.0,31799.0')] ).
cnf(32003,plain,
( ~ subclass(complement(set_builder(u__dfg,null_class)),u)
| member(u__dfg,u) ),
inference(res,[status(thm),theory(equality)],[31998,4]),
[iquote('0:Res:31998.0,4.0')] ).
cnf(33138,plain,
subclass(complement(union(u,null_class)),intersection(complement(u),universal_class)),
inference(spr,[status(thm),theory(equality)],[28465,19333]),
[iquote('0:SpR:28465.0,19333.0')] ).
cnf(34153,plain,
subclass(complement(set_builder(u,null_class)),intersection(complement(singleton(u)),universal_class)),
inference(spr,[status(thm),theory(equality)],[1,33138]),
[iquote('0:SpR:1.0,33138.0')] ).
cnf(37824,plain,
member(u__dfg,intersection(complement(singleton(u__dfg)),universal_class)),
inference(res,[status(thm),theory(equality)],[34153,32003]),
[iquote('0:Res:34153.0,32003.0')] ).
cnf(37835,plain,
member(u__dfg,complement(singleton(u__dfg))),
inference(res,[status(thm),theory(equality)],[37824,24]),
[iquote('0:Res:37824.0,24.0')] ).
cnf(37848,plain,
~ member(u__dfg,singleton(u__dfg)),
inference(res,[status(thm),theory(equality)],[37835,27]),
[iquote('0:Res:37835.0,27.1')] ).
cnf(37849,plain,
$false,
inference(mrr,[status(thm)],[37848,145]),
[iquote('0:MRR:37848.0,145.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET132-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 02:55:59 EDT 2022
% 0.19/0.34 % CPUTime :
% 14.71/14.97
% 14.71/14.97 SPASS V 3.9
% 14.71/14.97 SPASS beiseite: Proof found.
% 14.71/14.97 % SZS status Theorem
% 14.71/14.97 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.71/14.97 SPASS derived 29949 clauses, backtracked 2049 clauses, performed 17 splits and kept 14180 clauses.
% 14.71/14.97 SPASS allocated 102753 KBytes.
% 14.71/14.97 SPASS spent 0:0:14.36 on the problem.
% 14.71/14.97 0:00:00.04 for the input.
% 14.71/14.97 0:00:00.00 for the FLOTTER CNF translation.
% 14.71/14.97 0:00:00.32 for inferences.
% 14.71/14.97 0:00:01.18 for the backtracking.
% 14.71/14.97 0:0:12.52 for the reduction.
% 14.71/14.97
% 14.71/14.97
% 14.71/14.97 Here is a proof with depth 14, length 63 :
% 14.71/14.97 % SZS output start Refutation
% See solution above
% 14.71/14.97 Formulae used in the proof : definition_of_set_builder prove_member_of_triple3_1 prove_member_of_triple3_2 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets equal_implies_subclass2 subclass_implies_equal unordered_pair2 singleton_set intersection1 intersection2 intersection3 complement1 complement2 union regularity2
% 14.71/14.97
%------------------------------------------------------------------------------