%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET762+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 05:28:30 EDT 2022

% Result   : Theorem 1.95s 2.14s
% Output   : Refutation 1.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   11 (   6 unt;   2 nHn;  11 RR)
%            Number of literals    :   17 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ~ member(u,empty_set),
    file('SET762+4.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal_set(image2(skc3,empty_set),empty_set),
    file('SET762+4.p',unknown),
    [] ).

cnf(8,axiom,
    ( subset(u,v)
    | member(skf39(v,u),u) ),
    file('SET762+4.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ subset(u,v)
    | ~ subset(v,u)
    | equal_set(v,u) ),
    file('SET762+4.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ member(u,image2(v,w))
    | member(skf64(w,x,y),w) ),
    file('SET762+4.p',unknown),
    [] ).

cnf(144,plain,
    ( ~ subset(empty_set,image2(skc3,empty_set))
    | ~ subset(image2(skc3,empty_set),empty_set) ),
    inference(res,[status(thm),theory(equality)],[36,4]),
    [iquote('0:Res:36.2,4.0')] ).

cnf(151,plain,
    subset(empty_set,u),
    inference(res,[status(thm),theory(equality)],[8,2]),
    [iquote('0:Res:8.1,2.0')] ).

cnf(154,plain,
    ~ subset(image2(skc3,empty_set),empty_set),
    inference(mrr,[status(thm)],[144,151]),
    [iquote('0:MRR:144.0,151.0')] ).

cnf(502,plain,
    ( subset(image2(u,v),w)
    | member(skf64(v,x,y),v) ),
    inference(res,[status(thm),theory(equality)],[8,51]),
    [iquote('0:Res:8.1,51.0')] ).

cnf(3038,plain,
    subset(image2(u,empty_set),v),
    inference(res,[status(thm),theory(equality)],[502,2]),
    [iquote('0:Res:502.1,2.0')] ).

cnf(3066,plain,
    $false,
    inference(unc,[status(thm)],[3038,154]),
    [iquote('0:UnC:3038.0,154.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET762+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 05:56:37 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.95/2.14  
% 1.95/2.14  SPASS V 3.9 
% 1.95/2.14  SPASS beiseite: Proof found.
% 1.95/2.14  % SZS status Theorem
% 1.95/2.14  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.95/2.14  SPASS derived 2915 clauses, backtracked 0 clauses, performed 2 splits and kept 2035 clauses.
% 1.95/2.14  SPASS allocated 91851 KBytes.
% 1.95/2.14  SPASS spent	0:00:01.75 on the problem.
% 1.95/2.14  		0:00:00.03 for the input.
% 1.95/2.14  		0:00:00.73 for the FLOTTER CNF translation.
% 1.95/2.14  		0:00:00.07 for inferences.
% 1.95/2.14  		0:00:00.00 for the backtracking.
% 1.95/2.14  		0:00:00.85 for the reduction.
% 1.95/2.14  
% 1.95/2.14  
% 1.95/2.14  Here is a proof with depth 2, length 11 :
% 1.95/2.14  % SZS output start Refutation
% See solution above
% 1.95/2.14  Formulae used in the proof : empty_set thIIa12 subset equal_set image2
% 1.95/2.14  
%------------------------------------------------------------------------------