%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET196-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 05:24:57 EDT 2022

% Result   : Unsatisfiable 0.99s 1.16s
% Output   : Refutation 0.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   3 unt;   3 nHn;   8 RR)
%            Number of literals    :   13 (   0 equ;   3 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    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ subclass(intersection(x__dfg,y__dfg),x__dfg),
    file('SET196-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET196-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET196-6.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET196-6.p',unknown),
    [] ).

cnf(184,plain,
    ( subclass(intersection(u,v),w)
    | member(not_subclass_element(intersection(u,v),w),u) ),
    inference(res,[status(thm),theory(equality)],[3,22]),
    [iquote('0:Res:3.1,22.0')] ).

cnf(5223,plain,
    ( subclass(intersection(u,v),u)
    | subclass(intersection(u,v),u) ),
    inference(res,[status(thm),theory(equality)],[184,4]),
    [iquote('0:Res:184.1,4.0')] ).

cnf(5227,plain,
    subclass(intersection(u,v),u),
    inference(obv,[status(thm),theory(equality)],[5223]),
    [iquote('0:Obv:5223.0')] ).

cnf(5228,plain,
    $false,
    inference(unc,[status(thm)],[5227,1]),
    [iquote('0:UnC:5227.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET196-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n015.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 : Mon Jul 11 09:39:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.99/1.16  
% 0.99/1.16  SPASS V 3.9 
% 0.99/1.16  SPASS beiseite: Proof found.
% 0.99/1.16  % SZS status Theorem
% 0.99/1.16  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.99/1.16  SPASS derived 4596 clauses, backtracked 204 clauses, performed 4 splits and kept 2331 clauses.
% 0.99/1.16  SPASS allocated 80366 KBytes.
% 0.99/1.16  SPASS spent	0:00:00.79 on the problem.
% 0.99/1.16  		0:00:00.04 for the input.
% 0.99/1.16  		0:00:00.00 for the FLOTTER CNF translation.
% 0.99/1.16  		0:00:00.05 for inferences.
% 0.99/1.16  		0:00:00.02 for the backtracking.
% 0.99/1.16  		0:00:00.63 for the reduction.
% 0.99/1.16  
% 0.99/1.16  
% 0.99/1.16  Here is a proof with depth 2, length 8 :
% 0.99/1.16  % SZS output start Refutation
% See solution above
% 0.99/1.16  Formulae used in the proof : prove_lattice_lower_bound1_1 not_subclass_members1 not_subclass_members2 intersection1
% 0.99/1.16  
%------------------------------------------------------------------------------