TSTP Solution File: SEU323+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 14:36:15 EDT 2022

% Result   : Theorem 0.18s 0.46s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   28 (   9 unt;   0 nHn;  28 RR)
%            Number of literals    :   60 (   0 equ;  36 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    topological_space(skc4),
    file('SEU323+1.p',unknown),
    [] ).

cnf(2,axiom,
    top_str(skc4),
    file('SEU323+1.p',unknown),
    [] ).

cnf(7,axiom,
    element(skc5,powerset(the_carrier(skc4))),
    file('SEU323+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ open_subset(interior(skc4,skc5),skc4),
    file('SEU323+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ element(u,powerset(v))
    | element(subset_complement(v,u),powerset(v)) ),
    file('SEU323+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ element(u,powerset(v))
    | equal(subset_complement(v,subset_complement(v,u)),u) ),
    file('SEU323+1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ top_str(u)
    | ~ element(v,powerset(the_carrier(u)))
    | element(topstr_closure(u,v),powerset(the_carrier(u))) ),
    file('SEU323+1.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ topological_space(u)
    | ~ top_str(u)
    | ~ element(v,powerset(the_carrier(u)))
    | closed_subset(topstr_closure(u,v),u) ),
    file('SEU323+1.p',unknown),
    [] ).

cnf(21,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('SEU323+1.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ topological_space(u)
    | ~ top_str(u)
    | ~ closed_subset(v,u)
    | ~ element(v,powerset(the_carrier(u)))
    | open_subset(subset_complement(the_carrier(u),v),u) ),
    file('SEU323+1.p',unknown),
    [] ).

cnf(24,plain,
    ( ~ topological_space(skc4)
    | ~ closed_subset(u,skc4)
    | ~ element(u,powerset(the_carrier(skc4)))
    | open_subset(subset_complement(the_carrier(skc4),u),skc4) ),
    inference(res,[status(thm),theory(equality)],[2,23]),
    [iquote('0:Res:2.0,23.0')] ).

cnf(27,plain,
    ( ~ topological_space(skc4)
    | ~ element(u,powerset(the_carrier(skc4)))
    | closed_subset(topstr_closure(skc4,u),skc4) ),
    inference(res,[status(thm),theory(equality)],[2,20]),
    [iquote('0:Res:2.0,20.0')] ).

cnf(28,plain,
    ( ~ element(u,powerset(the_carrier(skc4)))
    | element(topstr_closure(skc4,u),powerset(the_carrier(skc4))) ),
    inference(res,[status(thm),theory(equality)],[2,18]),
    [iquote('0:Res:2.0,18.0')] ).

cnf(40,plain,
    ( ~ top_str(skc4)
    | equal(subset_complement(the_carrier(skc4),topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5))),interior(skc4,skc5)) ),
    inference(res,[status(thm),theory(equality)],[7,21]),
    [iquote('0:Res:7.0,21.1')] ).

cnf(45,plain,
    element(subset_complement(the_carrier(skc4),skc5),powerset(the_carrier(skc4))),
    inference(res,[status(thm),theory(equality)],[7,16]),
    [iquote('0:Res:7.0,16.0')] ).

cnf(52,plain,
    ( ~ element(u,powerset(the_carrier(skc4)))
    | closed_subset(topstr_closure(skc4,u),skc4) ),
    inference(mrr,[status(thm)],[27,1]),
    [iquote('0:MRR:27.0,1.0')] ).

cnf(55,plain,
    equal(subset_complement(the_carrier(skc4),topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5))),interior(skc4,skc5)),
    inference(mrr,[status(thm)],[40,2]),
    [iquote('0:MRR:40.0,2.0')] ).

cnf(56,plain,
    ( ~ closed_subset(u,skc4)
    | ~ element(u,powerset(the_carrier(skc4)))
    | open_subset(subset_complement(the_carrier(skc4),u),skc4) ),
    inference(mrr,[status(thm)],[24,1]),
    [iquote('0:MRR:24.0,1.0')] ).

cnf(80,plain,
    ( ~ element(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),powerset(the_carrier(skc4)))
    | equal(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),subset_complement(the_carrier(skc4),interior(skc4,skc5))) ),
    inference(spr,[status(thm),theory(equality)],[55,17]),
    [iquote('0:SpR:55.0,17.1')] ).

cnf(84,plain,
    ( ~ closed_subset(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),skc4)
    | ~ element(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),powerset(the_carrier(skc4)))
    | open_subset(interior(skc4,skc5),skc4) ),
    inference(spr,[status(thm),theory(equality)],[55,56]),
    [iquote('0:SpR:55.0,56.2')] ).

cnf(87,plain,
    ( ~ closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4)
    | ~ element(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),powerset(the_carrier(skc4)))
    | open_subset(interior(skc4,skc5),skc4) ),
    inference(rew,[status(thm),theory(equality)],[80,84]),
    [iquote('0:Rew:80.1,84.0')] ).

cnf(88,plain,
    ( ~ closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4)
    | ~ element(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),powerset(the_carrier(skc4))) ),
    inference(mrr,[status(thm)],[87,9]),
    [iquote('0:MRR:87.2,9.0')] ).

cnf(183,plain,
    ( ~ element(subset_complement(the_carrier(skc4),skc5),powerset(the_carrier(skc4)))
    | ~ closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4) ),
    inference(res,[status(thm),theory(equality)],[28,88]),
    [iquote('0:Res:28.1,88.1')] ).

cnf(186,plain,
    ~ closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4),
    inference(mrr,[status(thm)],[183,45]),
    [iquote('0:MRR:183.0,45.0')] ).

cnf(247,plain,
    ( ~ element(subset_complement(the_carrier(skc4),skc5),powerset(the_carrier(skc4)))
    | equal(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),subset_complement(the_carrier(skc4),interior(skc4,skc5))) ),
    inference(res,[status(thm),theory(equality)],[28,80]),
    [iquote('0:Res:28.1,80.0')] ).

cnf(250,plain,
    equal(topstr_closure(skc4,subset_complement(the_carrier(skc4),skc5)),subset_complement(the_carrier(skc4),interior(skc4,skc5))),
    inference(mrr,[status(thm)],[247,45]),
    [iquote('0:MRR:247.0,45.0')] ).

cnf(273,plain,
    ( ~ element(subset_complement(the_carrier(skc4),skc5),powerset(the_carrier(skc4)))
    | closed_subset(subset_complement(the_carrier(skc4),interior(skc4,skc5)),skc4) ),
    inference(spr,[status(thm),theory(equality)],[250,52]),
    [iquote('0:SpR:250.0,52.1')] ).

cnf(286,plain,
    $false,
    inference(mrr,[status(thm)],[273,45,186]),
    [iquote('0:MRR:273.0,273.1,45.0,186.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n006.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 : Mon Jun 20 12:20:40 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.46  
% 0.18/0.46  SPASS V 3.9 
% 0.18/0.46  SPASS beiseite: Proof found.
% 0.18/0.46  % SZS status Theorem
% 0.18/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.46  SPASS derived 192 clauses, backtracked 0 clauses, performed 0 splits and kept 96 clauses.
% 0.18/0.46  SPASS allocated 97849 KBytes.
% 0.18/0.46  SPASS spent	0:00:00.12 on the problem.
% 0.18/0.46  		0:00:00.04 for the input.
% 0.18/0.46  		0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.46  		0:00:00.00 for inferences.
% 0.18/0.46  		0:00:00.00 for the backtracking.
% 0.18/0.46  		0:00:00.02 for the reduction.
% 0.18/0.46  
% 0.18/0.46  
% 0.18/0.46  Here is a proof with depth 4, length 28 :
% 0.18/0.46  % SZS output start Refutation
% See solution above
% 0.18/0.46  Formulae used in the proof : t51_tops_1 dt_k3_subset_1 involutiveness_k3_subset_1 dt_k6_pre_topc fc2_tops_1 d1_tops_1 fc3_tops_1
% 0.18/0.46  
%------------------------------------------------------------------------------