TSTP Solution File: SEU324+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 14:36:16 EDT 2022
% Result : Theorem 0.42s 0.60s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 43 ( 15 unt; 6 nHn; 43 RR)
% Number of literals : 101 ( 0 equ; 55 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
top_str(skc7),
file('SEU324+1.p',unknown),
[] ).
cnf(2,axiom,
topological_space(skc6),
file('SEU324+1.p',unknown),
[] ).
cnf(3,axiom,
top_str(skc6),
file('SEU324+1.p',unknown),
[] ).
cnf(8,axiom,
element(skc9,powerset(the_carrier(skc7))),
file('SEU324+1.p',unknown),
[] ).
cnf(9,axiom,
element(skc8,powerset(the_carrier(skc6))),
file('SEU324+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ top_str(u)
| one_sorted_str(u) ),
file('SEU324+1.p',unknown),
[] ).
cnf(11,axiom,
( skP0(u,v)
| open_subset(v,u) ),
file('SEU324+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ skP0(skc7,skc9)
| ~ open_subset(skc8,skc6) ),
file('SEU324+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ skP0(skc7,skc9)
| equal(interior(skc6,skc8),skc8) ),
file('SEU324+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ equal(interior(u,v),v)
| skP0(u,v) ),
file('SEU324+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ element(u,powerset(v))
| element(subset_complement(v,u),powerset(v)) ),
file('SEU324+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ element(u,powerset(v))
| equal(subset_complement(v,subset_complement(v,u)),u) ),
file('SEU324+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ topological_space(u)
| ~ top_str(u)
| ~ element(v,powerset(the_carrier(u)))
| open_subset(interior(u,v),u) ),
file('SEU324+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ top_str(u)
| ~ closed_subset(v,u)
| ~ element(v,powerset(the_carrier(u)))
| equal(topstr_closure(u,v),v) ),
file('SEU324+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ top_str(u)
| ~ open_subset(v,u)
| ~ element(v,powerset(the_carrier(u)))
| closed_subset(subset_complement(the_carrier(u),v),u) ),
file('SEU324+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ top_str(u)
| ~ element(v,powerset(the_carrier(u)))
| equal(subset_complement(the_carrier(u),topstr_closure(u,subset_complement(the_carrier(u),v))),interior(u,v)) ),
file('SEU324+1.p',unknown),
[] ).
cnf(51,plain,
one_sorted_str(skc6),
inference(res,[status(thm),theory(equality)],[3,10]),
[iquote('0:Res:3.0,10.0')] ).
cnf(60,plain,
( ~ element(u,powerset(the_carrier(skc7)))
| equal(subset_complement(the_carrier(skc7),topstr_closure(skc7,subset_complement(the_carrier(skc7),u))),interior(skc7,u)) ),
inference(res,[status(thm),theory(equality)],[1,36]),
[iquote('0:Res:1.0,36.0')] ).
cnf(63,plain,
( ~ open_subset(u,skc7)
| ~ element(u,powerset(the_carrier(skc7)))
| closed_subset(subset_complement(the_carrier(skc7),u),skc7) ),
inference(res,[status(thm),theory(equality)],[1,31]),
[iquote('0:Res:1.0,31.0')] ).
cnf(74,plain,
one_sorted_str(skc7),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(91,plain,
~ skP0(skc7,skc9),
inference(spt,[spt(split,[position(s1)])],[18]),
[iquote('1:Spt:18.0')] ).
cnf(187,plain,
( ~ top_str(u)
| ~ element(v,powerset(the_carrier(u)))
| ~ closed_subset(subset_complement(the_carrier(u),v),u)
| equal(topstr_closure(u,subset_complement(the_carrier(u),v)),subset_complement(the_carrier(u),v)) ),
inference(res,[status(thm),theory(equality)],[24,30]),
[iquote('0:Res:24.1,30.2')] ).
cnf(349,plain,
( ~ element(u,powerset(the_carrier(skc7)))
| ~ open_subset(subset_complement(the_carrier(skc7),u),skc7)
| ~ element(subset_complement(the_carrier(skc7),u),powerset(the_carrier(skc7)))
| closed_subset(u,skc7) ),
inference(spr,[status(thm),theory(equality)],[25,63]),
[iquote('0:SpR:25.1,63.2')] ).
cnf(352,plain,
( ~ element(u,powerset(the_carrier(skc7)))
| ~ open_subset(subset_complement(the_carrier(skc7),u),skc7)
| closed_subset(u,skc7) ),
inference(mrr,[status(thm)],[349,24]),
[iquote('0:MRR:349.2,24.1')] ).
cnf(372,plain,
( ~ element(u,powerset(the_carrier(skc7)))
| skP0(skc7,subset_complement(the_carrier(skc7),u))
| closed_subset(u,skc7) ),
inference(res,[status(thm),theory(equality)],[11,352]),
[iquote('0:Res:11.1,352.1')] ).
cnf(375,plain,
( ~ element(u,powerset(the_carrier(skc7)))
| ~ element(subset_complement(the_carrier(skc7),u),powerset(the_carrier(skc7)))
| skP0(skc7,u)
| closed_subset(subset_complement(the_carrier(skc7),u),skc7) ),
inference(spr,[status(thm),theory(equality)],[25,372]),
[iquote('0:SpR:25.1,372.1')] ).
cnf(377,plain,
( ~ element(u,powerset(the_carrier(skc7)))
| skP0(skc7,u)
| closed_subset(subset_complement(the_carrier(skc7),u),skc7) ),
inference(mrr,[status(thm)],[375,24]),
[iquote('0:MRR:375.1,24.1')] ).
cnf(1102,plain,
( ~ top_str(skc7)
| ~ element(u,powerset(the_carrier(skc7)))
| ~ closed_subset(subset_complement(the_carrier(skc7),u),skc7)
| ~ element(u,powerset(the_carrier(skc7)))
| equal(subset_complement(the_carrier(skc7),subset_complement(the_carrier(skc7),u)),interior(skc7,u)) ),
inference(spr,[status(thm),theory(equality)],[187,60]),
[iquote('0:SpR:187.3,60.1')] ).
cnf(1115,plain,
( ~ top_str(skc7)
| ~ closed_subset(subset_complement(the_carrier(skc7),u),skc7)
| ~ element(u,powerset(the_carrier(skc7)))
| equal(subset_complement(the_carrier(skc7),subset_complement(the_carrier(skc7),u)),interior(skc7,u)) ),
inference(obv,[status(thm),theory(equality)],[1102]),
[iquote('0:Obv:1102.1')] ).
cnf(1116,plain,
( ~ top_str(skc7)
| ~ closed_subset(subset_complement(the_carrier(skc7),u),skc7)
| ~ element(u,powerset(the_carrier(skc7)))
| equal(interior(skc7,u),u) ),
inference(rew,[status(thm),theory(equality)],[25,1115]),
[iquote('0:Rew:25.1,1115.3')] ).
cnf(1117,plain,
( ~ closed_subset(subset_complement(the_carrier(skc7),u),skc7)
| ~ element(u,powerset(the_carrier(skc7)))
| equal(interior(skc7,u),u) ),
inference(ssi,[status(thm)],[1116,1,74]),
[iquote('0:SSi:1116.0,1.0,74.0')] ).
cnf(1854,plain,
( ~ element(u,powerset(the_carrier(skc7)))
| ~ element(u,powerset(the_carrier(skc7)))
| skP0(skc7,u)
| equal(interior(skc7,u),u) ),
inference(res,[status(thm),theory(equality)],[377,1117]),
[iquote('0:Res:377.2,1117.0')] ).
cnf(1858,plain,
( ~ element(u,powerset(the_carrier(skc7)))
| skP0(skc7,u)
| equal(interior(skc7,u),u) ),
inference(obv,[status(thm),theory(equality)],[1854]),
[iquote('0:Obv:1854.0')] ).
cnf(1859,plain,
( ~ element(u,powerset(the_carrier(skc7)))
| skP0(skc7,u) ),
inference(mrr,[status(thm)],[1858,19]),
[iquote('0:MRR:1858.2,19.0')] ).
cnf(1866,plain,
skP0(skc7,skc9),
inference(res,[status(thm),theory(equality)],[8,1859]),
[iquote('0:Res:8.0,1859.0')] ).
cnf(1879,plain,
$false,
inference(mrr,[status(thm)],[1866,91]),
[iquote('1:MRR:1866.0,91.0')] ).
cnf(1880,plain,
skP0(skc7,skc9),
inference(spt,[spt(split,[position(sa)])],[1879,91]),
[iquote('1:Spt:1879.0,18.0,91.0')] ).
cnf(1881,plain,
equal(interior(skc6,skc8),skc8),
inference(spt,[spt(split,[position(s2)])],[18]),
[iquote('1:Spt:1879.0,18.1')] ).
cnf(1883,plain,
~ open_subset(skc8,skc6),
inference(mrr,[status(thm)],[15,1866]),
[iquote('0:MRR:15.0,1866.0')] ).
cnf(1885,plain,
( ~ topological_space(skc6)
| ~ top_str(skc6)
| ~ element(skc8,powerset(the_carrier(skc6)))
| open_subset(skc8,skc6) ),
inference(spr,[status(thm),theory(equality)],[1881,29]),
[iquote('1:SpR:1881.0,29.3')] ).
cnf(1909,plain,
( ~ element(skc8,powerset(the_carrier(skc6)))
| open_subset(skc8,skc6) ),
inference(ssi,[status(thm)],[1885,2,3,51]),
[iquote('1:SSi:1885.1,1885.0,2.0,3.0,51.0,2.0,3.0,51.0')] ).
cnf(1910,plain,
open_subset(skc8,skc6),
inference(mrr,[status(thm)],[1909,9]),
[iquote('1:MRR:1909.0,9.0')] ).
cnf(1911,plain,
$false,
inference(mrr,[status(thm)],[1910,1883]),
[iquote('1:MRR:1910.0,1883.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 06:24:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.60
% 0.42/0.60 SPASS V 3.9
% 0.42/0.60 SPASS beiseite: Proof found.
% 0.42/0.60 % SZS status Theorem
% 0.42/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.60 SPASS derived 1426 clauses, backtracked 5 clauses, performed 1 splits and kept 380 clauses.
% 0.42/0.60 SPASS allocated 99203 KBytes.
% 0.42/0.60 SPASS spent 0:00:00.24 on the problem.
% 0.42/0.60 0:00:00.03 for the input.
% 0.42/0.60 0:00:00.02 for the FLOTTER CNF translation.
% 0.42/0.60 0:00:00.03 for inferences.
% 0.42/0.60 0:00:00.00 for the backtracking.
% 0.42/0.60 0:00:00.14 for the reduction.
% 0.42/0.60
% 0.42/0.60
% 0.42/0.60 Here is a proof with depth 6, length 43 :
% 0.42/0.60 % SZS output start Refutation
% See solution above
% 0.42/0.60 Formulae used in the proof : t55_tops_1 dt_l1_pre_topc dt_k3_subset_1 involutiveness_k3_subset_1 fc6_tops_1 t52_pre_topc t30_tops_1 d1_tops_1
% 0.42/0.60
%------------------------------------------------------------------------------