%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET877+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:29:31 EDT 2022

% Result   : Theorem 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   11 (   6 unt;   0 nHn;  11 RR)
%            Number of literals    :   17 (   0 equ;   7 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    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ equal(skc5,skc4),
    file('SET877+1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SET877+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(set_intersection2(singleton(skc4),singleton(skc5)),singleton(skc4)),
    file('SET877+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ equal(set_intersection2(u,singleton(v)),singleton(v))
    | in(v,u) ),
    file('SET877+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ in(u,v)
    | ~ equal(v,singleton(w))
    | equal(u,w) ),
    file('SET877+1.p',unknown),
    [] ).

cnf(50,plain,
    ( ~ equal(set_intersection2(singleton(u),v),singleton(u))
    | in(u,v) ),
    inference(spl,[status(thm),theory(equality)],[5,9]),
    [iquote('0:SpL:5.0,9.0')] ).

cnf(80,plain,
    ( ~ in(u,singleton(v))
    | equal(u,v) ),
    inference(eqr,[status(thm),theory(equality)],[10]),
    [iquote('0:EqR:10.1')] ).

cnf(93,plain,
    ( ~ equal(singleton(skc4),singleton(skc4))
    | in(skc4,singleton(skc5)) ),
    inference(spl,[status(thm),theory(equality)],[6,50]),
    [iquote('0:SpL:6.0,50.0')] ).

cnf(95,plain,
    in(skc4,singleton(skc5)),
    inference(obv,[status(thm),theory(equality)],[93]),
    [iquote('0:Obv:93.0')] ).

cnf(96,plain,
    equal(skc5,skc4),
    inference(res,[status(thm),theory(equality)],[95,80]),
    [iquote('0:Res:95.0,80.0')] ).

cnf(99,plain,
    $false,
    inference(mrr,[status(thm)],[96,3]),
    [iquote('0:MRR:96.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET877+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n010.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 19:41:30 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 72 clauses, backtracked 0 clauses, performed 0 splits and kept 45 clauses.
% 0.20/0.44  SPASS allocated 85145 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.20/0.44  		0:00:00.03 for the input.
% 0.20/0.44  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.00 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 3, length 11 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : t18_zfmisc_1 commutativity_k3_xboole_0 l30_zfmisc_1 d1_tarski idempotence_k3_xboole_0
% 0.20/0.44  
%------------------------------------------------------------------------------