%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET917+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 05:29:47 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   7 unt;   1 nHn;   9 RR)
%            Number of literals    :   11 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ disjoint(singleton(skc4),skc5),
    file('SET917+1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SET917+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( in(u,v)
    | disjoint(singleton(u),v) ),
    file('SET917+1.p',unknown),
    [] ).

cnf(8,axiom,
    ~ equal(set_intersection2(singleton(skc4),skc5),singleton(skc4)),
    file('SET917+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ in(u,v)
    | equal(set_intersection2(v,singleton(u)),singleton(u)) ),
    file('SET917+1.p',unknown),
    [] ).

cnf(11,plain,
    ~ equal(set_intersection2(skc5,singleton(skc4)),singleton(skc4)),
    inference(rew,[status(thm),theory(equality)],[5,8]),
    [iquote('0:Rew:5.0,8.0')] ).

cnf(12,plain,
    in(skc4,skc5),
    inference(res,[status(thm),theory(equality)],[6,3]),
    [iquote('0:Res:6.1,3.0')] ).

cnf(14,plain,
    ~ in(skc4,skc5),
    inference(res,[status(thm),theory(equality)],[10,11]),
    [iquote('0:Res:10.1,11.0')] ).

cnf(15,plain,
    $false,
    inference(mrr,[status(thm)],[14,12]),
    [iquote('0:MRR:14.0,12.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET917+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 12:15:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.43  
% 0.19/0.43  SPASS V 3.9 
% 0.19/0.43  SPASS beiseite: Proof found.
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.43  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.19/0.43  SPASS allocated 85097 KBytes.
% 0.19/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.43  		0:00:00.03 for the input.
% 0.19/0.43  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.43  		0:00:00.00 for inferences.
% 0.19/0.43  		0:00:00.00 for the backtracking.
% 0.19/0.43  		0:00:00.00 for the reduction.
% 0.19/0.43  
% 0.19/0.43  
% 0.19/0.43  Here is a proof with depth 1, length 9 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : t58_zfmisc_1 commutativity_k3_xboole_0 l28_zfmisc_1 l32_zfmisc_1
% 0.19/0.43  
%------------------------------------------------------------------------------