%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET095+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 05:23:56 EDT 2022

% Result   : Theorem 0.19s 0.48s
% Output   : Refutation 0.19s
% 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    :   17 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 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('SET095+4.p',unknown),
    [] ).

cnf(3,axiom,
    ~ subset(singleton(skc3),skc2),
    file('SET095+4.p',unknown),
    [] ).

cnf(8,axiom,
    ( subset(u,v)
    | member(skf3(v,u),u) ),
    file('SET095+4.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ member(u,singleton(v))
    | equal(u,v) ),
    file('SET095+4.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ member(skf3(u,v),u)
    | subset(w,u) ),
    file('SET095+4.p',unknown),
    [] ).

cnf(54,plain,
    ( subset(singleton(u),v)
    | equal(skf3(v,singleton(u)),u) ),
    inference(res,[status(thm),theory(equality)],[8,11]),
    [iquote('0:Res:8.1,11.0')] ).

cnf(360,plain,
    ( ~ member(u,v)
    | subset(singleton(u),v)
    | subset(w,v) ),
    inference(spl,[status(thm),theory(equality)],[54,13]),
    [iquote('0:SpL:54.1,13.0')] ).

cnf(361,plain,
    ( ~ member(u,v)
    | subset(singleton(u),v) ),
    inference(con,[status(thm)],[360]),
    [iquote('0:Con:360.2')] ).

cnf(447,plain,
    ~ member(skc3,skc2),
    inference(res,[status(thm),theory(equality)],[361,3]),
    [iquote('0:Res:361.1,3.0')] ).

cnf(448,plain,
    $false,
    inference(mrr,[status(thm)],[447,1]),
    [iquote('0:MRR:447.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET095+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul 11 00:06:00 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.48  
% 0.19/0.48  SPASS V 3.9 
% 0.19/0.48  SPASS beiseite: Proof found.
% 0.19/0.48  % SZS status Theorem
% 0.19/0.48  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.48  SPASS derived 408 clauses, backtracked 0 clauses, performed 0 splits and kept 244 clauses.
% 0.19/0.48  SPASS allocated 85453 KBytes.
% 0.19/0.48  SPASS spent	0:00:00.13 on the problem.
% 0.19/0.48  		0:00:00.03 for the input.
% 0.19/0.48  		0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.48  		0:00:00.01 for inferences.
% 0.19/0.48  		0:00:00.00 for the backtracking.
% 0.19/0.48  		0:00:00.03 for the reduction.
% 0.19/0.48  
% 0.19/0.48  
% 0.19/0.48  Here is a proof with depth 3, length 10 :
% 0.19/0.48  % SZS output start Refutation
% See solution above
% 0.19/0.48  Formulae used in the proof : thI44 subset singleton
% 0.19/0.48  
%------------------------------------------------------------------------------