%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 05:30:08 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (  13 unt;   0 nHn;  14 RR)
%            Number of literals    :   15 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    subset(skc9,skc8),
    file('SET971+1.p',unknown),
    [] ).

cnf(3,axiom,
    subset(skc6,skc7),
    file('SET971+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SET971+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ subset(u,v)
    | equal(set_intersection2(u,v),u) ),
    file('SET971+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(set_intersection2(cartesian_product2(skc9,skc7),cartesian_product2(skc8,skc6)),cartesian_product2(skc9,skc6)),
    file('SET971+1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(cartesian_product2(set_intersection2(u,v),set_intersection2(w,x)),set_intersection2(cartesian_product2(u,w),cartesian_product2(v,x))),
    file('SET971+1.p',unknown),
    [] ).

cnf(11,plain,
    ~ equal(set_intersection2(cartesian_product2(skc8,skc6),cartesian_product2(skc9,skc7)),cartesian_product2(skc9,skc6)),
    inference(rew,[status(thm),theory(equality)],[7,9]),
    [iquote('0:Rew:7.0,9.0')] ).

cnf(12,plain,
    equal(set_intersection2(skc6,skc7),skc6),
    inference(res,[status(thm),theory(equality)],[3,8]),
    [iquote('0:Res:3.0,8.0')] ).

cnf(13,plain,
    equal(set_intersection2(skc9,skc8),skc9),
    inference(res,[status(thm),theory(equality)],[2,8]),
    [iquote('0:Res:2.0,8.0')] ).

cnf(14,plain,
    equal(set_intersection2(skc8,skc9),skc9),
    inference(rew,[status(thm),theory(equality)],[7,13]),
    [iquote('0:Rew:7.0,13.0')] ).

cnf(44,plain,
    equal(set_intersection2(cartesian_product2(u,skc6),cartesian_product2(v,skc7)),cartesian_product2(set_intersection2(u,v),skc6)),
    inference(spr,[status(thm),theory(equality)],[12,10]),
    [iquote('0:SpR:12.0,10.0')] ).

cnf(57,plain,
    ~ equal(cartesian_product2(set_intersection2(skc8,skc9),skc6),cartesian_product2(skc9,skc6)),
    inference(rew,[status(thm),theory(equality)],[44,11]),
    [iquote('0:Rew:44.0,11.0')] ).

cnf(58,plain,
    ~ equal(cartesian_product2(skc9,skc6),cartesian_product2(skc9,skc6)),
    inference(rew,[status(thm),theory(equality)],[14,57]),
    [iquote('0:Rew:14.0,57.0')] ).

cnf(59,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[58]),
    [iquote('0:Obv:58.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 08:24:55 EDT 2022
% 0.13/0.33  % 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 45 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.19/0.43  SPASS allocated 85124 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  		0:00:00.02 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 2, length 14 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : t124_zfmisc_1 commutativity_k3_xboole_0 t28_xboole_1 t123_zfmisc_1
% 0.19/0.43  
%------------------------------------------------------------------------------