%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 05:29:33 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   5 unt;   1 nHn;  12 RR)
%            Number of literals    :   22 (   0 equ;  13 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ equal(skc5,skc4),
    file('SET882+1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(set_difference(unordered_pair(skc4,skc5),singleton(skc5)),singleton(skc4)),
    file('SET882+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ in(u,v)
    | ~ equal(v,singleton(w))
    | equal(u,w) ),
    file('SET882+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,singleton(v))
    | in(u,w) ),
    file('SET882+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ in(u,v)
    | in(w,v)
    | equal(set_difference(unordered_pair(w,u),v),singleton(w)) ),
    file('SET882+1.p',unknown),
    [] ).

cnf(18,plain,
    ( ~ equal(u,singleton(skc5))
    | ~ in(skc4,u) ),
    inference(res,[status(thm),theory(equality)],[8,3]),
    [iquote('0:Res:8.2,3.0')] ).

cnf(20,plain,
    ( ~ in(skc5,singleton(skc5))
    | in(skc4,singleton(skc5)) ),
    inference(res,[status(thm),theory(equality)],[13,6]),
    [iquote('0:Res:13.1,6.0')] ).

cnf(31,plain,
    ( ~ equal(u,v)
    | in(u,singleton(v)) ),
    inference(eqr,[status(thm),theory(equality)],[9]),
    [iquote('0:EqR:9.1')] ).

cnf(36,plain,
    ( ~ equal(skc5,skc5)
    | in(skc4,singleton(skc5)) ),
    inference(res,[status(thm),theory(equality)],[31,20]),
    [iquote('0:Res:31.1,20.0')] ).

cnf(37,plain,
    in(skc4,singleton(skc5)),
    inference(obv,[status(thm),theory(equality)],[36]),
    [iquote('0:Obv:36.0')] ).

cnf(40,plain,
    ~ equal(singleton(skc5),singleton(skc5)),
    inference(res,[status(thm),theory(equality)],[37,18]),
    [iquote('0:Res:37.0,18.1')] ).

cnf(41,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[40]),
    [iquote('0:Obv:40.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET882+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n025.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 : Mon Jul 11 09:00:17 EDT 2022
% 0.13/0.34  % 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 20 clauses, backtracked 0 clauses, performed 0 splits and kept 29 clauses.
% 0.19/0.45  SPASS allocated 85174 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.45  		0:00:00.04 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 3, length 12 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : t23_zfmisc_1 d1_tarski antisymmetry_r2_hidden l39_zfmisc_1
% 0.19/0.45  
%------------------------------------------------------------------------------