%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET196+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 05:24:56 EDT 2022

% Result   : Theorem 0.18s 0.43s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   6 unt;   2 nHn;  10 RR)
%            Number of literals    :   14 (   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    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ~ subset(intersection(skc3,skc2),skc3),
    file('SET196+3.p',unknown),
    [] ).

cnf(3,axiom,
    equal(intersection(u,v),intersection(v,u)),
    file('SET196+3.p',unknown),
    [] ).

cnf(4,axiom,
    ( subset(u,v)
    | member(skf2(v,u),u) ),
    file('SET196+3.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET196+3.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ member(skf2(u,v),u)
    | subset(w,u) ),
    file('SET196+3.p',unknown),
    [] ).

cnf(14,plain,
    ~ subset(intersection(skc2,skc3),skc3),
    inference(rew,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Rew:3.0,2.0')] ).

cnf(16,plain,
    ~ member(skf2(skc3,u),skc3),
    inference(res,[status(thm),theory(equality)],[7,14]),
    [iquote('0:Res:7.1,14.0')] ).

cnf(26,plain,
    ( subset(intersection(u,v),w)
    | member(skf2(w,intersection(u,v)),v) ),
    inference(res,[status(thm),theory(equality)],[4,6]),
    [iquote('0:Res:4.1,6.0')] ).

cnf(34,plain,
    subset(intersection(u,skc3),skc3),
    inference(res,[status(thm),theory(equality)],[26,16]),
    [iquote('0:Res:26.1,16.0')] ).

cnf(39,plain,
    $false,
    inference(unc,[status(thm)],[34,14]),
    [iquote('0:UnC:34.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET196+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n020.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 : Mon Jul 11 05:08:58 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.43  
% 0.18/0.43  SPASS V 3.9 
% 0.18/0.43  SPASS beiseite: Proof found.
% 0.18/0.43  % SZS status Theorem
% 0.18/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.43  SPASS derived 23 clauses, backtracked 0 clauses, performed 0 splits and kept 23 clauses.
% 0.18/0.43  SPASS allocated 85275 KBytes.
% 0.18/0.43  SPASS spent	0:00:00.09 on the problem.
% 0.18/0.43  		0:00:00.03 for the input.
% 0.18/0.43  		0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43  		0:00:00.00 for inferences.
% 0.18/0.43  		0:00:00.00 for the backtracking.
% 0.18/0.43  		0:00:00.00 for the reduction.
% 0.18/0.43  
% 0.18/0.43  
% 0.18/0.43  Here is a proof with depth 2, length 10 :
% 0.18/0.43  % SZS output start Refutation
% See solution above
% 0.18/0.43  Formulae used in the proof : prove_intersection_is_subset commutativity_of_intersection subset_defn intersection_defn
% 0.18/0.43  
%------------------------------------------------------------------------------