%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET602+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 05:27:20 EDT 2022

% Result   : Theorem 0.39s 0.56s
% Output   : Refutation 0.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (   6 unt;   3 nHn;  14 RR)
%            Number of literals    :   23 (   0 equ;  11 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(u,empty_set),
    file('SET602+4.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal_set(difference(skc1,skc1),empty_set),
    file('SET602+4.p',unknown),
    [] ).

cnf(7,axiom,
    ( subset(u,v)
    | member(skf3(v,u),u) ),
    file('SET602+4.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ member(u,difference(v,w))
    | member(u,v) ),
    file('SET602+4.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ member(u,v)
    | ~ member(u,difference(w,v)) ),
    file('SET602+4.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ subset(u,v)
    | ~ subset(v,u)
    | equal_set(v,u) ),
    file('SET602+4.p',unknown),
    [] ).

cnf(31,plain,
    ( ~ subset(empty_set,difference(skc1,skc1))
    | ~ subset(difference(skc1,skc1),empty_set) ),
    inference(res,[status(thm),theory(equality)],[24,3]),
    [iquote('0:Res:24.2,3.0')] ).

cnf(34,plain,
    subset(empty_set,u),
    inference(res,[status(thm),theory(equality)],[7,1]),
    [iquote('0:Res:7.1,1.0')] ).

cnf(37,plain,
    ~ subset(difference(skc1,skc1),empty_set),
    inference(mrr,[status(thm)],[31,34]),
    [iquote('0:MRR:31.0,34.0')] ).

cnf(52,plain,
    ( subset(difference(u,v),w)
    | member(skf3(w,difference(u,v)),u) ),
    inference(res,[status(thm),theory(equality)],[7,17]),
    [iquote('0:Res:7.1,17.0')] ).

cnf(67,plain,
    ( ~ member(skf3(u,difference(v,w)),w)
    | subset(difference(v,w),u) ),
    inference(res,[status(thm),theory(equality)],[7,21]),
    [iquote('0:Res:7.1,21.1')] ).

cnf(1044,plain,
    ( subset(difference(u,u),v)
    | subset(difference(u,u),v) ),
    inference(res,[status(thm),theory(equality)],[52,67]),
    [iquote('0:Res:52.1,67.0')] ).

cnf(1046,plain,
    subset(difference(u,u),v),
    inference(obv,[status(thm),theory(equality)],[1044]),
    [iquote('0:Obv:1044.0')] ).

cnf(1047,plain,
    $false,
    inference(unc,[status(thm)],[1046,37]),
    [iquote('0:UnC:1046.0,37.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET602+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n008.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 : Sat Jul  9 20:20:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.39/0.56  
% 0.39/0.56  SPASS V 3.9 
% 0.39/0.56  SPASS beiseite: Proof found.
% 0.39/0.56  % SZS status Theorem
% 0.39/0.56  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.39/0.56  SPASS derived 934 clauses, backtracked 0 clauses, performed 0 splits and kept 700 clauses.
% 0.39/0.56  SPASS allocated 86042 KBytes.
% 0.39/0.56  SPASS spent	0:00:00.21 on the problem.
% 0.39/0.56  		0:00:00.03 for the input.
% 0.39/0.56  		0:00:00.04 for the FLOTTER CNF translation.
% 0.39/0.56  		0:00:00.01 for inferences.
% 0.39/0.56  		0:00:00.00 for the backtracking.
% 0.39/0.56  		0:00:00.10 for the reduction.
% 0.39/0.56  
% 0.39/0.56  
% 0.39/0.56  Here is a proof with depth 2, length 14 :
% 0.39/0.56  % SZS output start Refutation
% See solution above
% 0.39/0.56  Formulae used in the proof : empty_set thI29 subset difference equal_set
% 0.39/0.56  
%------------------------------------------------------------------------------