%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET050-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 05:23:09 EDT 2022

% Result   : Unsatisfiable 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   7 unt;   0 nHn;  11 RR)
%            Number of literals    :   16 (   0 equ;   7 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    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(ordered_pair(x__dfg,y__dfg),cross_product(u__dfg,v__dfg)),
    file('SET050-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ member(x__dfg,unordered_pair(x__dfg,y__dfg)),
    file('SET050-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET050-6.p',unknown),
    [] ).

cnf(6,axiom,
    subclass(u,universal_class),
    file('SET050-6.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ member(u,universal_class)
    | member(u,unordered_pair(u,v)) ),
    file('SET050-6.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ member(ordered_pair(u,v),cross_product(w,x))
    | member(u,w) ),
    file('SET050-6.p',unknown),
    [] ).

cnf(101,plain,
    ~ member(x__dfg,universal_class),
    inference(res,[status(thm),theory(equality)],[11,2]),
    [iquote('0:Res:11.1,2.0')] ).

cnf(105,plain,
    member(x__dfg,u__dfg),
    inference(res,[status(thm),theory(equality)],[1,16]),
    [iquote('0:Res:1.0,16.0')] ).

cnf(307,plain,
    ( ~ subclass(u__dfg,u)
    | member(x__dfg,u) ),
    inference(res,[status(thm),theory(equality)],[105,3]),
    [iquote('0:Res:105.0,3.0')] ).

cnf(334,plain,
    member(x__dfg,universal_class),
    inference(res,[status(thm),theory(equality)],[6,307]),
    [iquote('0:Res:6.0,307.0')] ).

cnf(338,plain,
    $false,
    inference(mrr,[status(thm)],[334,101]),
    [iquote('0:MRR:334.0,101.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET050-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 03:06:44 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.47  
% 0.19/0.47  SPASS V 3.9 
% 0.19/0.47  SPASS beiseite: Proof found.
% 0.19/0.47  % SZS status Theorem
% 0.19/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.47  SPASS derived 205 clauses, backtracked 0 clauses, performed 0 splits and kept 245 clauses.
% 0.19/0.47  SPASS allocated 76039 KBytes.
% 0.19/0.47  SPASS spent	0:00:00.11 on the problem.
% 0.19/0.47  		0:00:00.04 for the input.
% 0.19/0.47  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47  		0:00:00.01 for inferences.
% 0.19/0.47  		0:00:00.00 for the backtracking.
% 0.19/0.47  		0:00:00.04 for the reduction.
% 0.19/0.47  
% 0.19/0.47  
% 0.19/0.47  Here is a proof with depth 3, length 11 :
% 0.19/0.47  % SZS output start Refutation
% See solution above
% 0.19/0.47  Formulae used in the proof : prove_corollary_1_to_unordered_pair_1 prove_corollary_1_to_unordered_pair_2 subclass_members class_elements_are_sets unordered_pair2 cartesian_product1
% 0.19/0.47  
%------------------------------------------------------------------------------