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  
%------------------------------------------------------------------------------