%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU140+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 14:34:16 EDT 2022

% Result   : Theorem 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   16 (  12 unt;   0 nHn;  16 RR)
%            Number of literals    :   20 (   0 equ;   7 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    subset(skc7,skc5),
    file('SEU140+1.p',unknown),
    [] ).

cnf(4,axiom,
    disjoint(skc5,skc6),
    file('SEU140+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ disjoint(skc7,skc6),
    file('SEU140+1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(set_intersection2(u,v),set_intersection2(v,u)),
    file('SEU140+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ subset(u,empty_set)
    | equal(u,empty_set) ),
    file('SEU140+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ disjoint(u,v)
    | equal(set_intersection2(u,v),empty_set) ),
    file('SEU140+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ equal(set_intersection2(u,v),empty_set)
    | disjoint(u,v) ),
    file('SEU140+1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ subset(u,v)
    | subset(set_intersection2(u,w),set_intersection2(v,w)) ),
    file('SEU140+1.p',unknown),
    [] ).

cnf(20,plain,
    equal(set_intersection2(skc5,skc6),empty_set),
    inference(res,[status(thm),theory(equality)],[4,16]),
    [iquote('0:Res:4.0,16.0')] ).

cnf(22,plain,
    subset(set_intersection2(skc7,u),set_intersection2(skc5,u)),
    inference(res,[status(thm),theory(equality)],[3,19]),
    [iquote('0:Res:3.0,19.0')] ).

cnf(23,plain,
    ~ equal(set_intersection2(skc7,skc6),empty_set),
    inference(res,[status(thm),theory(equality)],[17,7]),
    [iquote('0:Res:17.1,7.0')] ).

cnf(25,plain,
    ~ equal(set_intersection2(skc6,skc7),empty_set),
    inference(rew,[status(thm),theory(equality)],[11,23]),
    [iquote('0:Rew:11.0,23.0')] ).

cnf(37,plain,
    subset(set_intersection2(skc7,skc6),empty_set),
    inference(spr,[status(thm),theory(equality)],[20,22]),
    [iquote('0:SpR:20.0,22.0')] ).

cnf(42,plain,
    subset(set_intersection2(skc6,skc7),empty_set),
    inference(rew,[status(thm),theory(equality)],[11,37]),
    [iquote('0:Rew:11.0,37.0')] ).

cnf(44,plain,
    equal(set_intersection2(skc6,skc7),empty_set),
    inference(res,[status(thm),theory(equality)],[42,13]),
    [iquote('0:Res:42.0,13.0')] ).

cnf(45,plain,
    $false,
    inference(mrr,[status(thm)],[44,25]),
    [iquote('0:MRR:44.0,25.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SEU140+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n003.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 Jun 19 05:01:43 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 20 clauses, backtracked 0 clauses, performed 0 splits and kept 29 clauses.
% 0.19/0.42  SPASS allocated 97624 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.42  		0:00:00.03 for the input.
% 0.19/0.42  		0:00:00.02 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 3, length 16 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : t63_xboole_1 commutativity_k3_xboole_0 t3_xboole_1 d7_xboole_0 t26_xboole_1
% 0.19/0.42  
%------------------------------------------------------------------------------