%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET642+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   25 (   0 equ;  15 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    subset(skc4,skc7),
    file('SET642+3.p',unknown),
    [] ).

cnf(5,axiom,
    ilf_type(u,set_type),
    file('SET642+3.p',unknown),
    [] ).

cnf(10,axiom,
    ilf_type(skc7,relation_type(skc5,skc6)),
    file('SET642+3.p',unknown),
    [] ).

cnf(13,axiom,
    ~ ilf_type(skc4,relation_type(skc5,skc6)),
    file('SET642+3.p',unknown),
    [] ).

cnf(40,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('SET642+3.p',unknown),
    [] ).

cnf(42,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(w,set_type)
    | ~ ilf_type(x,relation_type(v,w))
    | ~ subset(u,x)
    | subset(u,cross_product(v,w)) ),
    file('SET642+3.p',unknown),
    [] ).

cnf(66,plain,
    ( ~ subset(u,cross_product(v,w))
    | ilf_type(u,relation_type(v,w)) ),
    inference(mrr,[status(thm)],[40,5]),
    [iquote('0:MRR:40.0,40.1,40.2,5.0,5.0,5.0')] ).

cnf(68,plain,
    ( ~ subset(u,v)
    | ~ ilf_type(v,relation_type(w,x))
    | subset(u,cross_product(w,x)) ),
    inference(mrr,[status(thm)],[42,5]),
    [iquote('0:MRR:42.0,42.1,42.2,5.0,5.0,5.0')] ).

cnf(71,plain,
    ( ~ subset(u,skc7)
    | subset(u,cross_product(skc5,skc6)) ),
    inference(res,[status(thm),theory(equality)],[10,68]),
    [iquote('0:Res:10.0,68.0')] ).

cnf(73,plain,
    ~ subset(skc4,cross_product(skc5,skc6)),
    inference(res,[status(thm),theory(equality)],[66,13]),
    [iquote('0:Res:66.1,13.0')] ).

cnf(75,plain,
    subset(skc4,cross_product(skc5,skc6)),
    inference(res,[status(thm),theory(equality)],[4,71]),
    [iquote('0:Res:4.0,71.0')] ).

cnf(77,plain,
    $false,
    inference(mrr,[status(thm)],[75,73]),
    [iquote('0:MRR:75.0,73.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET642+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n028.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 09:17:12 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  
% 0.19/0.45  SPASS V 3.9 
% 0.19/0.45  SPASS beiseite: Proof found.
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 37 clauses.
% 0.19/0.45  SPASS allocated 97789 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.45  		0:00:00.03 for the input.
% 0.19/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45  		0:00:00.00 for inferences.
% 0.19/0.45  		0:00:00.00 for the backtracking.
% 0.19/0.45  		0:00:00.00 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 2, length 12 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : prove_relset_1_4 p19 p2 p1
% 0.19/0.45  
%------------------------------------------------------------------------------