%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 05:30:13 EDT 2022

% Result   : Theorem 0.18s 0.46s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   8 unt;   0 nHn;  11 RR)
%            Number of literals    :   17 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    in(skc7,cartesian_product2(skc11,skc10)),
    file('SET983+1.p',unknown),
    [] ).

cnf(4,axiom,
    in(skc7,cartesian_product2(skc8,skc9)),
    file('SET983+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SET983+1.p',unknown),
    [] ).

cnf(8,axiom,
    ~ in(skc7,cartesian_product2(set_intersection2(skc11,skc8),set_intersection2(skc10,skc9))),
    file('SET983+1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(cartesian_product2(set_intersection2(u,v),set_intersection2(w,x)),set_intersection2(cartesian_product2(u,w),cartesian_product2(v,x))),
    file('SET983+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ in(u,v)
    | ~ in(u,w)
    | ~ equal(x,set_intersection2(w,v))
    | in(u,x) ),
    file('SET983+1.p',unknown),
    [] ).

cnf(16,plain,
    ~ in(skc7,cartesian_product2(set_intersection2(skc8,skc11),set_intersection2(skc9,skc10))),
    inference(rew,[status(thm),theory(equality)],[6,8]),
    [iquote('0:Rew:6.0,8.0,6.0,8.0')] ).

cnf(17,plain,
    ~ in(skc7,set_intersection2(cartesian_product2(skc8,skc9),cartesian_product2(skc11,skc10))),
    inference(rew,[status(thm),theory(equality)],[11,16]),
    [iquote('0:Rew:11.0,16.0')] ).

cnf(136,plain,
    ( ~ in(u,v)
    | ~ in(u,w)
    | in(u,set_intersection2(w,v)) ),
    inference(eqr,[status(thm),theory(equality)],[12]),
    [iquote('0:EqR:12.2')] ).

cnf(278,plain,
    ( ~ in(skc7,cartesian_product2(skc11,skc10))
    | ~ in(skc7,cartesian_product2(skc8,skc9)) ),
    inference(res,[status(thm),theory(equality)],[136,17]),
    [iquote('0:Res:136.2,17.0')] ).

cnf(283,plain,
    $false,
    inference(mrr,[status(thm)],[278,3,4]),
    [iquote('0:MRR:278.0,278.1,3.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n014.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 : Sun Jul 10 15:13:05 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.46  
% 0.18/0.46  SPASS V 3.9 
% 0.18/0.46  SPASS beiseite: Proof found.
% 0.18/0.46  % SZS status Theorem
% 0.18/0.46  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.46  SPASS derived 200 clauses, backtracked 0 clauses, performed 0 splits and kept 106 clauses.
% 0.18/0.46  SPASS allocated 85391 KBytes.
% 0.18/0.46  SPASS spent	0:00:00.12 on the problem.
% 0.18/0.46  		0:00:00.03 for the input.
% 0.18/0.46  		0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.46  		0:00:00.00 for inferences.
% 0.18/0.46  		0:00:00.00 for the backtracking.
% 0.18/0.46  		0:00:00.02 for the reduction.
% 0.18/0.46  
% 0.18/0.46  
% 0.18/0.46  Here is a proof with depth 2, length 11 :
% 0.18/0.46  % SZS output start Refutation
% See solution above
% 0.18/0.46  Formulae used in the proof : t137_zfmisc_1 commutativity_k3_xboole_0 t123_zfmisc_1 d3_xboole_0
% 0.18/0.46  
%------------------------------------------------------------------------------