%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET203-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 05:25:01 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   8 unt;   0 nHn;  13 RR)
%            Number of literals    :   20 (   0 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   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(1,axiom,
    member(u__dfg,x__dfg),
    file('SET203-6.p',unknown),
    [] ).

cnf(2,axiom,
    member(v__dfg,y__dfg),
    file('SET203-6.p',unknown),
    [] ).

cnf(3,axiom,
    ~ member(ordered_pair(u__dfg,v__dfg),cross_product(universal_class,universal_class)),
    file('SET203-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET203-6.p',unknown),
    [] ).

cnf(7,axiom,
    subclass(u,universal_class),
    file('SET203-6.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ member(u,v)
    | ~ member(w,x)
    | member(ordered_pair(w,u),cross_product(x,v)) ),
    file('SET203-6.p',unknown),
    [] ).

cnf(118,plain,
    ( ~ subclass(y__dfg,u)
    | member(v__dfg,u) ),
    inference(res,[status(thm),theory(equality)],[2,4]),
    [iquote('0:Res:2.0,4.1')] ).

cnf(125,plain,
    ( ~ subclass(x__dfg,u)
    | member(u__dfg,u) ),
    inference(res,[status(thm),theory(equality)],[1,4]),
    [iquote('0:Res:1.0,4.1')] ).

cnf(132,plain,
    ( ~ member(v__dfg,universal_class)
    | ~ member(u__dfg,universal_class) ),
    inference(res,[status(thm),theory(equality)],[19,3]),
    [iquote('0:Res:19.2,3.0')] ).

cnf(156,plain,
    member(u__dfg,universal_class),
    inference(res,[status(thm),theory(equality)],[7,125]),
    [iquote('0:Res:7.0,125.0')] ).

cnf(157,plain,
    ~ member(v__dfg,universal_class),
    inference(mrr,[status(thm)],[132,156]),
    [iquote('0:MRR:132.1,156.0')] ).

cnf(159,plain,
    member(v__dfg,universal_class),
    inference(res,[status(thm),theory(equality)],[7,118]),
    [iquote('0:Res:7.0,118.0')] ).

cnf(160,plain,
    $false,
    inference(mrr,[status(thm)],[159,157]),
    [iquote('0:MRR:159.0,157.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET203-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.13/0.13  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n029.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 06:08:46 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.43  
% 0.20/0.43  SPASS V 3.9 
% 0.20/0.43  SPASS beiseite: Proof found.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.43  SPASS derived 36 clauses, backtracked 0 clauses, performed 0 splits and kept 140 clauses.
% 0.20/0.43  SPASS allocated 75810 KBytes.
% 0.20/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.43  		0:00:00.04 for the input.
% 0.20/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43  		0:00:00.00 for inferences.
% 0.20/0.43  		0:00:00.00 for the backtracking.
% 0.20/0.43  		0:00:00.01 for the reduction.
% 0.20/0.43  
% 0.20/0.43  
% 0.20/0.43  Here is a proof with depth 2, length 13 :
% 0.20/0.43  % SZS output start Refutation
% See solution above
% 0.20/0.43  Formulae used in the proof : prove_corollary_to_X_product_property1_1 prove_corollary_to_X_product_property1_2 prove_corollary_to_X_product_property1_3 subclass_members class_elements_are_sets cartesian_product3
% 0.20/0.43  
%------------------------------------------------------------------------------