TSTP Solution File: SET124-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET124-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 33.54s 33.69s
% Output : Refutation 33.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 52 ( 21 unt; 14 nHn; 52 RR)
% Number of literals : 93 ( 0 equ; 32 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; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(union(singleton(u),v),set_builder(u,v)),
file('SET124-6.p',unknown),
[] ).
cnf(2,axiom,
member(x__dfg,universal_class),
file('SET124-6.p',unknown),
[] ).
cnf(3,axiom,
~ member(x__dfg,set_builder(x__dfg,z__dfg)),
file('SET124-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET124-6.p',unknown),
[] ).
cnf(5,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET124-6.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET124-6.p',unknown),
[] ).
cnf(7,axiom,
subclass(u,universal_class),
file('SET124-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET124-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET124-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET124-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET124-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET124-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET124-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET124-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET124-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET124-6.p',unknown),
[] ).
cnf(99,plain,
( member(x__dfg,u)
| member(x__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[2,28]),
[iquote('0:Res:2.0,28.0')] ).
cnf(100,plain,
member(x__dfg,unordered_pair(x__dfg,u)),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(117,plain,
( ~ subclass(u,set_builder(x__dfg,z__dfg))
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[4,3]),
[iquote('0:Res:4.2,3.0')] ).
cnf(143,plain,
member(x__dfg,singleton(x__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(218,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(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(734,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(737,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(1607,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(6487,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[218,6]),
[iquote('0:Res:218.1,6.0')] ).
cnf(6491,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[6487]),
[iquote('0:Obv:6487.0')] ).
cnf(6562,plain,
( subclass(intersection(intersection(u,v),w),x)
| member(not_subclass_element(intersection(intersection(u,v),w),x),u) ),
inference(res,[status(thm),theory(equality)],[232,24]),
[iquote('0:Res:232.1,24.0')] ).
cnf(9376,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[7,734]),
[iquote('0:Res:7.0,734.2')] ).
cnf(9383,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[9376]),
[iquote('0:Con:9376.1')] ).
cnf(9425,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[5,9383]),
[iquote('0:Res:5.1,9383.0')] ).
cnf(9505,plain,
( member(not_subclass_element(complement(complement(u)),v),u)
| subclass(complement(complement(u)),v) ),
inference(mrr,[status(thm)],[1607,9425]),
[iquote('0:MRR:1607.0,9425.1')] ).
cnf(12583,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)],[5,737]),
[iquote('0:Res:5.1,737.0')] ).
cnf(12598,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u)) ),
inference(obv,[status(thm),theory(equality)],[12583]),
[iquote('0:Obv:12583.1')] ).
cnf(19854,plain,
( subclass(complement(complement(u)),u)
| subclass(complement(complement(u)),u) ),
inference(res,[status(thm),theory(equality)],[9505,6]),
[iquote('0:Res:9505.0,6.0')] ).
cnf(19857,plain,
subclass(complement(complement(u)),u),
inference(obv,[status(thm),theory(equality)],[19854]),
[iquote('0:Obv:19854.0')] ).
cnf(19900,plain,
~ member(x__dfg,complement(complement(set_builder(x__dfg,z__dfg)))),
inference(res,[status(thm),theory(equality)],[19857,117]),
[iquote('0:Res:19857.0,117.0')] ).
cnf(19928,plain,
member(x__dfg,complement(set_builder(x__dfg,z__dfg))),
inference(res,[status(thm),theory(equality)],[99,19900]),
[iquote('0:Res:99.1,19900.0')] ).
cnf(19967,plain,
( ~ subclass(complement(set_builder(x__dfg,z__dfg)),u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[19928,4]),
[iquote('0:Res:19928.0,4.0')] ).
cnf(21971,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)],[9505,12598]),
[iquote('0:Res:9505.0,12598.0')] ).
cnf(22003,plain,
subclass(complement(complement(u)),intersection(u,complement(complement(u)))),
inference(obv,[status(thm),theory(equality)],[21971]),
[iquote('0:Obv:21971.0')] ).
cnf(25166,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)],[22003,10]),
[iquote('0:Res:22003.0,10.0')] ).
cnf(25175,plain,
equal(intersection(u,complement(complement(u))),complement(complement(u))),
inference(mrr,[status(thm)],[25166,6491]),
[iquote('0:MRR:25166.0,6491.0')] ).
cnf(47439,plain,
( subclass(intersection(intersection(u,v),w),u)
| subclass(intersection(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[6562,6]),
[iquote('0:Res:6562.1,6.0')] ).
cnf(47457,plain,
subclass(intersection(intersection(u,v),w),u),
inference(obv,[status(thm),theory(equality)],[47439]),
[iquote('0:Obv:47439.0')] ).
cnf(47588,plain,
subclass(complement(complement(intersection(u,v))),u),
inference(spr,[status(thm),theory(equality)],[25175,47457]),
[iquote('0:SpR:25175.0,47457.0')] ).
cnf(48206,plain,
subclass(complement(union(u,v)),complement(u)),
inference(spr,[status(thm),theory(equality)],[29,47588]),
[iquote('0:SpR:29.0,47588.0')] ).
cnf(48410,plain,
subclass(complement(set_builder(u,v)),complement(singleton(u))),
inference(spr,[status(thm),theory(equality)],[1,48206]),
[iquote('0:SpR:1.0,48206.0')] ).
cnf(49341,plain,
member(x__dfg,complement(singleton(x__dfg))),
inference(res,[status(thm),theory(equality)],[48410,19967]),
[iquote('0:Res:48410.0,19967.0')] ).
cnf(50367,plain,
~ member(x__dfg,singleton(x__dfg)),
inference(res,[status(thm),theory(equality)],[49341,27]),
[iquote('0:Res:49341.0,27.1')] ).
cnf(50369,plain,
$false,
inference(mrr,[status(thm)],[50367,143]),
[iquote('0:MRR:50367.0,143.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET124-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jul 9 20:00:16 EDT 2022
% 0.14/0.36 % CPUTime :
% 33.54/33.69
% 33.54/33.69 SPASS V 3.9
% 33.54/33.69 SPASS beiseite: Proof found.
% 33.54/33.69 % SZS status Theorem
% 33.54/33.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.54/33.69 SPASS derived 38185 clauses, backtracked 2603 clauses, performed 15 splits and kept 16811 clauses.
% 33.54/33.69 SPASS allocated 117150 KBytes.
% 33.54/33.69 SPASS spent 0:0:32.81 on the problem.
% 33.54/33.69 0:00:00.04 for the input.
% 33.54/33.69 0:00:00.00 for the FLOTTER CNF translation.
% 33.54/33.69 0:00:00.46 for inferences.
% 33.54/33.69 0:00:02.72 for the backtracking.
% 33.54/33.69 0:0:29.21 for the reduction.
% 33.54/33.69
% 33.54/33.69
% 33.54/33.69 Here is a proof with depth 9, length 52 :
% 33.54/33.69 % SZS output start Refutation
% See solution above
% 33.54/33.69 Formulae used in the proof : definition_of_set_builder prove_set_builder_alternate_defn2_1 prove_set_builder_alternate_defn2_2 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal unordered_pair2 singleton_set intersection1 intersection2 intersection3 complement1 complement2 union
% 33.54/33.69
%------------------------------------------------------------------------------