%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 05:25:52 EDT 2022

% Result   : Theorem 1.51s 1.69s
% Output   : Refutation 1.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   4 unt;   3 nHn;  10 RR)
%            Number of literals    :   19 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(skc3,skc2),
    file('SET355+4.p',unknown),
    [] ).

cnf(3,axiom,
    ~ subset(skc3,sum__dfg(skc2)),
    file('SET355+4.p',unknown),
    [] ).

cnf(8,axiom,
    ( subset(u,v)
    | member(skf3(v,u),u) ),
    file('SET355+4.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ member(skf3(u,v),u)
    | subset(w,u) ),
    file('SET355+4.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ member(u,v)
    | ~ member(v,w)
    | member(u,sum__dfg(w)) ),
    file('SET355+4.p',unknown),
    [] ).

cnf(172,plain,
    ( ~ member(u,v)
    | subset(u,w)
    | member(skf3(w,u),sum__dfg(v)) ),
    inference(res,[status(thm),theory(equality)],[8,29]),
    [iquote('0:Res:8.1,29.0')] ).

cnf(2379,plain,
    ( ~ member(u,v)
    | subset(u,sum__dfg(v))
    | subset(w,sum__dfg(v)) ),
    inference(res,[status(thm),theory(equality)],[172,13]),
    [iquote('0:Res:172.2,13.0')] ).

cnf(2383,plain,
    ( ~ member(u,v)
    | subset(u,sum__dfg(v)) ),
    inference(con,[status(thm)],[2379]),
    [iquote('0:Con:2379.2')] ).

cnf(6765,plain,
    ~ member(skc3,skc2),
    inference(res,[status(thm),theory(equality)],[2383,3]),
    [iquote('0:Res:2383.1,3.0')] ).

cnf(6784,plain,
    $false,
    inference(mrr,[status(thm)],[6765,1]),
    [iquote('0:MRR:6765.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 03:29:25 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 1.51/1.69  
% 1.51/1.69  SPASS V 3.9 
% 1.51/1.69  SPASS beiseite: Proof found.
% 1.51/1.69  % SZS status Theorem
% 1.51/1.69  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.51/1.69  SPASS derived 5499 clauses, backtracked 0 clauses, performed 0 splits and kept 2518 clauses.
% 1.51/1.69  SPASS allocated 90092 KBytes.
% 1.51/1.69  SPASS spent	0:00:01.28 on the problem.
% 1.51/1.69  		0:00:00.03 for the input.
% 1.51/1.69  		0:00:00.04 for the FLOTTER CNF translation.
% 1.51/1.69  		0:00:00.05 for inferences.
% 1.51/1.69  		0:00:00.00 for the backtracking.
% 1.51/1.69  		0:00:01.11 for the reduction.
% 1.51/1.69  
% 1.51/1.69  
% 1.51/1.69  Here is a proof with depth 3, length 10 :
% 1.51/1.69  % SZS output start Refutation
% See solution above
% 1.51/1.69  Formulae used in the proof : thI43 subset sum__dfg product empty_set
% 1.51/1.69  
%------------------------------------------------------------------------------