TSTP Solution File: SET136-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET136-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 05:24:25 EDT 2022
% Result : Unsatisfiable 10.37s 10.54s
% Output : Refutation 10.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of clauses : 66 ( 28 unt; 21 nHn; 66 RR)
% Number of literals : 117 ( 0 equ; 36 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('SET136-6.p',unknown),
[] ).
cnf(2,axiom,
member(u__dfg,universal_class),
file('SET136-6.p',unknown),
[] ).
cnf(3,axiom,
equal(set_builder(x__dfg,set_builder(y__dfg,set_builder(u__dfg,null_class))),null_class),
file('SET136-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET136-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET136-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET136-6.p',unknown),
[] ).
cnf(7,axiom,
subclass(u,universal_class),
file('SET136-6.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(u,v)
| subclass(v,u) ),
file('SET136-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET136-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET136-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET136-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET136-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET136-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET136-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET136-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET136-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET136-6.p',unknown),
[] ).
cnf(70,axiom,
( equal(u,null_class)
| equal(intersection(u,regular(u)),null_class) ),
file('SET136-6.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(109,plain,
~ member(u__dfg,complement(universal_class)),
inference(res,[status(thm),theory(equality)],[2,27]),
[iquote('0:Res:2.0,27.1')] ).
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(186,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(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(354,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(407,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(461,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(757,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(1576,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)],[28,186]),
[iquote('0:Res:28.2,186.0')] ).
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(8644,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)],[461,354]),
[iquote('0:Res:461.2,354.0')] ).
cnf(8650,plain,
( ~ subclass(u,universal_class)
| member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(obv,[status(thm),theory(equality)],[8644]),
[iquote('0:Obv:8644.1')] ).
cnf(8651,plain,
( member(not_subclass_element(u,complement(v)),v)
| subclass(u,complement(v)) ),
inference(mrr,[status(thm)],[8650,7]),
[iquote('0:MRR:8650.0,7.0')] ).
cnf(10571,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[7,757]),
[iquote('0:Res:7.0,757.2')] ).
cnf(10581,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[10571]),
[iquote('0:Con:10571.1')] ).
cnf(10634,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[5,10581]),
[iquote('0:Res:5.1,10581.0')] ).
cnf(10758,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[1576,10634]),
[iquote('0:MRR:1576.0,10634.1')] ).
cnf(11367,plain,
( subclass(complement(universal_class),u)
| subclass(complement(universal_class),u) ),
inference(res,[status(thm),theory(equality)],[10634,186]),
[iquote('0:Res:10634.1,186.0')] ).
cnf(11372,plain,
subclass(complement(universal_class),u),
inference(obv,[status(thm),theory(equality)],[11367]),
[iquote('0:Obv:11367.0')] ).
cnf(18746,plain,
( member(u__dfg,union(u,v))
| member(u__dfg,complement(v)) ),
inference(res,[status(thm),theory(equality)],[239,25]),
[iquote('0:Res:239.0,25.0')] ).
cnf(18963,plain,
( member(u__dfg,set_builder(u,v))
| member(u__dfg,complement(v)) ),
inference(spr,[status(thm),theory(equality)],[1,18746]),
[iquote('0:SpR:1.0,18746.0')] ).
cnf(19281,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[10758,6]),
[iquote('0:Res:10758.0,6.0')] ).
cnf(19284,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[19281]),
[iquote('0:Obv:19281.0')] ).
cnf(21028,plain,
( member(u__dfg,null_class)
| member(u__dfg,complement(set_builder(y__dfg,set_builder(u__dfg,null_class)))) ),
inference(spr,[status(thm),theory(equality)],[3,18963]),
[iquote('0:SpR:3.0,18963.0')] ).
cnf(21140,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(21174,plain,
subclass(null_class,u),
inference(mrr,[status(thm)],[21140,9]),
[iquote('0:MRR:21140.0,9.0')] ).
cnf(21183,plain,
( ~ subclass(u,null_class)
| equal(u,null_class) ),
inference(res,[status(thm),theory(equality)],[21174,10]),
[iquote('0:Res:21174.0,10.0')] ).
cnf(21193,plain,
equal(complement(universal_class),null_class),
inference(res,[status(thm),theory(equality)],[11372,21183]),
[iquote('0:Res:11372.0,21183.0')] ).
cnf(21202,plain,
~ member(u__dfg,null_class),
inference(rew,[status(thm),theory(equality)],[21193,109]),
[iquote('0:Rew:21193.0,109.0')] ).
cnf(21209,plain,
member(u__dfg,complement(set_builder(y__dfg,set_builder(u__dfg,null_class)))),
inference(mrr,[status(thm)],[21028,21202]),
[iquote('0:MRR:21028.0,21202.0')] ).
cnf(21308,plain,
( ~ member(u,universal_class)
| ~ member(u,null_class) ),
inference(spl,[status(thm),theory(equality)],[21193,27]),
[iquote('0:SpL:21193.0,27.1')] ).
cnf(21315,plain,
~ member(u,null_class),
inference(mrr,[status(thm)],[21308,10581]),
[iquote('0:MRR:21308.0,10581.1')] ).
cnf(21355,plain,
subclass(u,complement(null_class)),
inference(res,[status(thm),theory(equality)],[8651,21315]),
[iquote('0:Res:8651.0,21315.0')] ).
cnf(21375,plain,
equal(complement(null_class),universal_class),
inference(res,[status(thm),theory(equality)],[21355,407]),
[iquote('0:Res:21355.0,407.0')] ).
cnf(21451,plain,
equal(complement(intersection(complement(u),universal_class)),union(u,null_class)),
inference(spr,[status(thm),theory(equality)],[21375,29]),
[iquote('0:SpR:21375.0,29.0')] ).
cnf(22542,plain,
~ member(u__dfg,set_builder(y__dfg,set_builder(u__dfg,null_class))),
inference(res,[status(thm),theory(equality)],[21209,27]),
[iquote('0:Res:21209.0,27.1')] ).
cnf(22549,plain,
member(u__dfg,complement(set_builder(u__dfg,null_class))),
inference(res,[status(thm),theory(equality)],[18963,22542]),
[iquote('0:Res:18963.0,22542.0')] ).
cnf(22554,plain,
( ~ subclass(complement(set_builder(u__dfg,null_class)),u)
| member(u__dfg,u) ),
inference(res,[status(thm),theory(equality)],[22549,4]),
[iquote('0:Res:22549.0,4.0')] ).
cnf(24531,plain,
subclass(complement(union(u,null_class)),intersection(complement(u),universal_class)),
inference(spr,[status(thm),theory(equality)],[21451,19284]),
[iquote('0:SpR:21451.0,19284.0')] ).
cnf(25343,plain,
subclass(complement(set_builder(u,null_class)),intersection(complement(singleton(u)),universal_class)),
inference(spr,[status(thm),theory(equality)],[1,24531]),
[iquote('0:SpR:1.0,24531.0')] ).
cnf(27567,plain,
member(u__dfg,intersection(complement(singleton(u__dfg)),universal_class)),
inference(res,[status(thm),theory(equality)],[25343,22554]),
[iquote('0:Res:25343.0,22554.0')] ).
cnf(27574,plain,
member(u__dfg,complement(singleton(u__dfg))),
inference(res,[status(thm),theory(equality)],[27567,24]),
[iquote('0:Res:27567.0,24.0')] ).
cnf(27599,plain,
~ member(u__dfg,singleton(u__dfg)),
inference(res,[status(thm),theory(equality)],[27574,27]),
[iquote('0:Res:27574.0,27.1')] ).
cnf(27600,plain,
$false,
inference(mrr,[status(thm)],[27599,138]),
[iquote('0:MRR:27599.0,138.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET136-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n028.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 : Sat Jul 9 16:23:56 EDT 2022
% 0.15/0.36 % CPUTime :
% 10.37/10.54
% 10.37/10.54 SPASS V 3.9
% 10.37/10.54 SPASS beiseite: Proof found.
% 10.37/10.54 % SZS status Theorem
% 10.37/10.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.37/10.54 SPASS derived 21897 clauses, backtracked 975 clauses, performed 12 splits and kept 10245 clauses.
% 10.37/10.54 SPASS allocated 96529 KBytes.
% 10.37/10.54 SPASS spent 0:00:09.96 on the problem.
% 10.37/10.54 0:00:00.04 for the input.
% 10.37/10.54 0:00:00.00 for the FLOTTER CNF translation.
% 10.37/10.54 0:00:00.27 for inferences.
% 10.37/10.54 0:00:00.69 for the backtracking.
% 10.37/10.54 0:00:08.73 for the reduction.
% 10.37/10.54
% 10.37/10.54
% 10.37/10.54 Here is a proof with depth 14, length 66 :
% 10.37/10.54 % SZS output start Refutation
% See solution above
% 10.37/10.54 Formulae used in the proof : definition_of_set_builder prove_corollary_4_to_member_of_triple_1 prove_corollary_4_to_member_of_triple_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
% 10.37/10.54
%------------------------------------------------------------------------------