%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% 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 05:27:47 EDT 2022

% Result   : Theorem 0.18s 0.45s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   14 (   0 equ;   8 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ilf_type(u,set_type),
    file('SET643+3.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ ilf_type(u,set_type)
    | subset(u,u) ),
    file('SET643+3.p',unknown),
    [] ).

cnf(13,axiom,
    ~ ilf_type(cross_product(skc2,skc3),relation_type(skc2,skc3)),
    file('SET643+3.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,set_type)
    | ~ subset(u,cross_product(v,w))
    | ilf_type(u,relation_type(v,w)) ),
    file('SET643+3.p',unknown),
    [] ).

cnf(45,plain,
    subset(u,u),
    inference(mrr,[status(thm)],[12,3]),
    [iquote('0:MRR:12.0,3.0')] ).

cnf(68,plain,
    ( ~ subset(u,cross_product(v,w))
    | ilf_type(u,relation_type(v,w)) ),
    inference(mrr,[status(thm)],[39,3]),
    [iquote('0:MRR:39.0,39.1,39.2,3.0,3.0,3.0')] ).

cnf(74,plain,
    ~ subset(cross_product(skc2,skc3),cross_product(skc2,skc3)),
    inference(res,[status(thm),theory(equality)],[68,13]),
    [iquote('0:Res:68.1,13.0')] ).

cnf(76,plain,
    $false,
    inference(mrr,[status(thm)],[74,45]),
    [iquote('0:MRR:74.0,45.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n026.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 Jul 10 04:24:41 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.45  
% 0.18/0.45  SPASS V 3.9 
% 0.18/0.45  SPASS beiseite: Proof found.
% 0.18/0.45  % SZS status Theorem
% 0.18/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.45  SPASS derived 2 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.18/0.45  SPASS allocated 97799 KBytes.
% 0.18/0.45  SPASS spent	0:00:00.10 on the problem.
% 0.18/0.45  		0:00:00.04 for the input.
% 0.18/0.45  		0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.45  		0:00:00.00 for inferences.
% 0.18/0.45  		0:00:00.00 for the backtracking.
% 0.18/0.45  		0:00:00.00 for the reduction.
% 0.18/0.45  
% 0.18/0.45  
% 0.18/0.45  Here is a proof with depth 1, length 8 :
% 0.18/0.45  % SZS output start Refutation
% See solution above
% 0.18/0.45  Formulae used in the proof : p19 p10 prove_relset_1_5 p1
% 0.18/0.45  
%------------------------------------------------------------------------------