TSTP Solution File: SET134-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET134-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 05:24:24 EDT 2022
% Result : Unsatisfiable 8.41s 8.63s
% Output : Refutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of clauses : 39 ( 16 unt; 11 nHn; 39 RR)
% Number of literals : 65 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(union(singleton(u),v),set_builder(u,v)),
file('SET134-6.p',unknown),
[] ).
cnf(2,axiom,
member(u__dfg,universal_class),
file('SET134-6.p',unknown),
[] ).
cnf(3,axiom,
equal(set_builder(u__dfg,set_builder(y__dfg,set_builder(z__dfg,null_class))),null_class),
file('SET134-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET134-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET134-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET134-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET134-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET134-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET134-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET134-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET134-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET134-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET134-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET134-6.p',unknown),
[] ).
cnf(30,axiom,
equal(intersection(complement(intersection(u,v)),complement(intersection(complement(u),complement(v)))),symmetric_difference(u,v)),
file('SET134-6.p',unknown),
[] ).
cnf(70,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET134-6.p',unknown),
[] ).
cnf(95,plain,
equal(intersection(complement(intersection(u,v)),union(u,v)),symmetric_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[29,30]),
[iquote('0:Rew:29.0,30.0')] ).
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(110,plain,
( ~ member(u__dfg,u)
| member(u__dfg,intersection(u,universal_class)) ),
inference(res,[status(thm),theory(equality)],[2,26]),
[iquote('0:Res:2.0,26.1')] ).
cnf(118,plain,
member(u__dfg,intersection(universal_class,universal_class)),
inference(res,[status(thm),theory(equality)],[2,110]),
[iquote('0:Res:2.0,110.0')] ).
cnf(138,plain,
member(u__dfg,singleton(u__dfg)),
inference(spr,[status(thm),theory(equality)],[15,100]),
[iquote('0:SpR:15.0,100.0')] ).
cnf(228,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(239,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(581,plain,
( ~ member(u,symmetric_difference(v,w))
| member(u,complement(intersection(v,w))) ),
inference(spl,[status(thm),theory(equality)],[95,24]),
[iquote('0:SpL:95.0,24.0')] ).
cnf(5776,plain,
( ~ member(u,symmetric_difference(v,w))
| ~ member(u,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[581,27]),
[iquote('0:Res:581.1,27.1')] ).
cnf(5913,plain,
( subclass(intersection(u,v),u)
| subclass(intersection(u,v),u) ),
inference(res,[status(thm),theory(equality)],[228,6]),
[iquote('0:Res:228.1,6.0')] ).
cnf(5917,plain,
subclass(intersection(u,v),u),
inference(obv,[status(thm),theory(equality)],[5913]),
[iquote('0:Obv:5913.0')] ).
cnf(18745,plain,
( member(u__dfg,union(u,v))
| member(u__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[239,24]),
[iquote('0:Res:239.0,24.0')] ).
cnf(18825,plain,
( member(u__dfg,set_builder(u,v))
| member(u__dfg,complement(singleton(u))) ),
inference(spr,[status(thm),theory(equality)],[1,18745]),
[iquote('0:SpR:1.0,18745.0')] ).
cnf(21553,plain,
~ member(u__dfg,symmetric_difference(universal_class,universal_class)),
inference(res,[status(thm),theory(equality)],[118,5776]),
[iquote('0:Res:118.0,5776.1')] ).
cnf(21760,plain,
( member(u__dfg,null_class)
| member(u__dfg,complement(singleton(u__dfg))) ),
inference(spr,[status(thm),theory(equality)],[3,18825]),
[iquote('0:SpR:3.0,18825.0')] ).
cnf(21814,plain,
( ~ member(u__dfg,singleton(u__dfg))
| member(u__dfg,null_class) ),
inference(res,[status(thm),theory(equality)],[21760,27]),
[iquote('0:Res:21760.1,27.1')] ).
cnf(21815,plain,
member(u__dfg,null_class),
inference(mrr,[status(thm)],[21814,138]),
[iquote('0:MRR:21814.0,138.0')] ).
cnf(21820,plain,
( ~ subclass(null_class,u)
| member(u__dfg,u) ),
inference(res,[status(thm),theory(equality)],[21815,4]),
[iquote('0:Res:21815.0,4.0')] ).
cnf(21868,plain,
( equal(u,null_class)
| subclass(null_class,u) ),
inference(spr,[status(thm),theory(equality)],[70,5917]),
[iquote('0:SpR:70.1,5917.0')] ).
cnf(21902,plain,
subclass(null_class,u),
inference(mrr,[status(thm)],[21868,9]),
[iquote('0:MRR:21868.0,9.0')] ).
cnf(21903,plain,
member(u__dfg,u),
inference(mrr,[status(thm)],[21820,21902]),
[iquote('0:MRR:21820.0,21902.0')] ).
cnf(21904,plain,
$false,
inference(unc,[status(thm)],[21903,21553]),
[iquote('0:UnC:21903.0,21553.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET134-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 21:24:13 EDT 2022
% 0.20/0.35 % CPUTime :
% 8.41/8.63
% 8.41/8.63 SPASS V 3.9
% 8.41/8.63 SPASS beiseite: Proof found.
% 8.41/8.63 % SZS status Theorem
% 8.41/8.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.41/8.63 SPASS derived 17807 clauses, backtracked 975 clauses, performed 9 splits and kept 8727 clauses.
% 8.41/8.63 SPASS allocated 93891 KBytes.
% 8.41/8.63 SPASS spent 0:00:08.11 on the problem.
% 8.41/8.63 0:00:00.04 for the input.
% 8.41/8.63 0:00:00.00 for the FLOTTER CNF translation.
% 8.41/8.63 0:00:00.23 for inferences.
% 8.41/8.63 0:00:00.65 for the backtracking.
% 8.41/8.63 0:00:06.99 for the reduction.
% 8.41/8.63
% 8.41/8.63
% 8.41/8.63 Here is a proof with depth 7, length 39 :
% 8.41/8.63 % SZS output start Refutation
% See solution above
% 8.41/8.63 Formulae used in the proof : definition_of_set_builder prove_corollary_2_to_member_of_triple_1 prove_corollary_2_to_member_of_triple_2 subclass_members not_subclass_members1 not_subclass_members2 equal_implies_subclass2 unordered_pair2 singleton_set intersection1 intersection3 complement1 complement2 union symmetric_difference regularity2
% 8.41/8.63
%------------------------------------------------------------------------------