TSTP Solution File: SET125-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET125-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 05:24:21 EDT 2022
% Result : Unsatisfiable 27.06s 27.25s
% Output : Refutation 27.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 50 ( 19 unt; 13 nHn; 50 RR)
% Number of literals : 91 ( 0 equ; 33 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 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('SET125-6.p',unknown),
[] ).
cnf(2,axiom,
member(x__dfg,z__dfg),
file('SET125-6.p',unknown),
[] ).
cnf(3,axiom,
~ member(x__dfg,set_builder(y__dfg,z__dfg)),
file('SET125-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET125-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET125-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET125-6.p',unknown),
[] ).
cnf(7,axiom,
subclass(u,universal_class),
file('SET125-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET125-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET125-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET125-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET125-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET125-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET125-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET125-6.p',unknown),
[] ).
cnf(97,plain,
( ~ subclass(z__dfg,u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[2,4]),
[iquote('0:Res:2.0,4.1')] ).
cnf(101,plain,
~ member(x__dfg,complement(z__dfg)),
inference(res,[status(thm),theory(equality)],[2,27]),
[iquote('0:Res:2.0,27.1')] ).
cnf(109,plain,
( ~ subclass(u,set_builder(y__dfg,z__dfg))
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[4,3]),
[iquote('0:Res:4.2,3.0')] ).
cnf(121,plain,
member(x__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[7,97]),
[iquote('0:Res:7.0,97.0')] ).
cnf(164,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(190,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[5,25]),
[iquote('0:Res:5.1,25.0')] ).
cnf(203,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(681,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(684,plain,
( ~ member(not_subclass_element(u,intersection(v,w)),w)
| ~ member(not_subclass_element(u,intersection(v,w)),v)
| subclass(u,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[26,6]),
[iquote('0:Res:26.2,6.0')] ).
cnf(5277,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)],[28,164]),
[iquote('0:Res:28.2,164.0')] ).
cnf(6424,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[190,6]),
[iquote('0:Res:190.1,6.0')] ).
cnf(6426,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[6424]),
[iquote('0:Obv:6424.0')] ).
cnf(7575,plain,
( subclass(intersection(intersection(u,v),w),x)
| member(not_subclass_element(intersection(intersection(u,v),w),x),v) ),
inference(res,[status(thm),theory(equality)],[203,25]),
[iquote('0:Res:203.1,25.0')] ).
cnf(11509,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[7,681]),
[iquote('0:Res:7.0,681.2')] ).
cnf(11518,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[11509]),
[iquote('0:Con:11509.1')] ).
cnf(11563,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[5,11518]),
[iquote('0:Res:5.1,11518.0')] ).
cnf(11687,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[5277,11563]),
[iquote('0:MRR:5277.0,11563.1')] ).
cnf(13403,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u))
| subclass(u,intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[5,684]),
[iquote('0:Res:5.1,684.0')] ).
cnf(13420,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u)) ),
inference(obv,[status(thm),theory(equality)],[13403]),
[iquote('0:Obv:13403.1')] ).
cnf(20938,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[11687,6]),
[iquote('0:Res:11687.0,6.0')] ).
cnf(20941,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[20938]),
[iquote('0:Obv:20938.0')] ).
cnf(20986,plain,
~ member(x__dfg,complement(complement(set_builder(y__dfg,z__dfg)))),
inference(res,[status(thm),theory(equality)],[20941,109]),
[iquote('0:Res:20941.0,109.0')] ).
cnf(21009,plain,
( ~ member(x__dfg,universal_class)
| member(x__dfg,complement(set_builder(y__dfg,z__dfg))) ),
inference(res,[status(thm),theory(equality)],[28,20986]),
[iquote('0:Res:28.2,20986.0')] ).
cnf(21010,plain,
member(x__dfg,complement(set_builder(y__dfg,z__dfg))),
inference(mrr,[status(thm)],[21009,121]),
[iquote('0:MRR:21009.0,121.0')] ).
cnf(21052,plain,
( ~ subclass(complement(set_builder(y__dfg,z__dfg)),u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[21010,4]),
[iquote('0:Res:21010.0,4.0')] ).
cnf(23701,plain,
( subclass(complement(complement(u)),intersection(u,complement(complement(u))))
| subclass(complement(complement(u)),intersection(u,complement(complement(u)))) ),
inference(res,[status(thm),theory(equality)],[11687,13420]),
[iquote('0:Res:11687.0,13420.0')] ).
cnf(23751,plain,
subclass(complement(complement(u)),intersection(u,complement(complement(u)))),
inference(obv,[status(thm),theory(equality)],[23701]),
[iquote('0:Obv:23701.0')] ).
cnf(31927,plain,
( ~ subclass(intersection(u,complement(complement(u))),complement(complement(u)))
| equal(intersection(u,complement(complement(u))),complement(complement(u))) ),
inference(res,[status(thm),theory(equality)],[23751,10]),
[iquote('0:Res:23751.0,10.0')] ).
cnf(31937,plain,
equal(intersection(u,complement(complement(u))),complement(complement(u))),
inference(mrr,[status(thm)],[31927,6426]),
[iquote('0:MRR:31927.0,6426.0')] ).
cnf(48682,plain,
( subclass(intersection(intersection(u,v),w),v)
| subclass(intersection(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[7575,6]),
[iquote('0:Res:7575.1,6.0')] ).
cnf(48700,plain,
subclass(intersection(intersection(u,v),w),v),
inference(obv,[status(thm),theory(equality)],[48682]),
[iquote('0:Obv:48682.0')] ).
cnf(49310,plain,
subclass(complement(complement(intersection(u,v))),v),
inference(spr,[status(thm),theory(equality)],[31937,48700]),
[iquote('0:SpR:31937.0,48700.0')] ).
cnf(49510,plain,
subclass(complement(union(u,v)),complement(v)),
inference(spr,[status(thm),theory(equality)],[29,49310]),
[iquote('0:SpR:29.0,49310.0')] ).
cnf(49598,plain,
subclass(complement(set_builder(u,v)),complement(v)),
inference(spr,[status(thm),theory(equality)],[1,49510]),
[iquote('0:SpR:1.0,49510.0')] ).
cnf(49693,plain,
member(x__dfg,complement(z__dfg)),
inference(res,[status(thm),theory(equality)],[49598,21052]),
[iquote('0:Res:49598.0,21052.0')] ).
cnf(49694,plain,
$false,
inference(mrr,[status(thm)],[49693,101]),
[iquote('0:MRR:49693.0,101.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET125-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n026.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 23:39:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 27.06/27.25
% 27.06/27.25 SPASS V 3.9
% 27.06/27.25 SPASS beiseite: Proof found.
% 27.06/27.25 % SZS status Theorem
% 27.06/27.25 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.06/27.25 SPASS derived 37931 clauses, backtracked 641 clauses, performed 10 splits and kept 15707 clauses.
% 27.06/27.25 SPASS allocated 117384 KBytes.
% 27.06/27.25 SPASS spent 0:0:26.44 on the problem.
% 27.06/27.25 0:00:00.04 for the input.
% 27.06/27.25 0:00:00.00 for the FLOTTER CNF translation.
% 27.06/27.25 0:00:00.40 for inferences.
% 27.06/27.25 0:00:02.11 for the backtracking.
% 27.06/27.25 0:0:23.57 for the reduction.
% 27.06/27.25
% 27.06/27.25
% 27.06/27.25 Here is a proof with depth 8, length 50 :
% 27.06/27.25 % SZS output start Refutation
% See solution above
% 27.06/27.25 Formulae used in the proof : definition_of_set_builder prove_set_builder_alternate_defn3_1 prove_set_builder_alternate_defn3_2 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal intersection1 intersection2 intersection3 complement1 complement2 union
% 27.06/27.25
%------------------------------------------------------------------------------