%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET236-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 05:25:12 EDT 2022

% Result   : Unsatisfiable 4.27s 4.44s
% Output   : Refutation 4.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   13 (   6 unt;   1 nHn;  13 RR)
%            Number of literals    :   21 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    subclass(x__dfg,cross_product(universal_class,universal_class)),
    file('SET236-6.p',unknown),
    [] ).

cnf(2,axiom,
    member(ordered_pair(first(not_subclass_element(x__dfg,y__dfg)),second(not_subclass_element(x__dfg,y__dfg))),y__dfg),
    file('SET236-6.p',unknown),
    [] ).

cnf(3,axiom,
    ~ subclass(x__dfg,y__dfg),
    file('SET236-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET236-6.p',unknown),
    [] ).

cnf(5,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET236-6.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET236-6.p',unknown),
    [] ).

cnf(20,axiom,
    ( ~ member(u,cross_product(v,w))
    | equal(ordered_pair(first(u),second(u)),u) ),
    file('SET236-6.p',unknown),
    [] ).

cnf(118,plain,
    ~ member(not_subclass_element(x__dfg,y__dfg),y__dfg),
    inference(res,[status(thm),theory(equality)],[6,3]),
    [iquote('0:Res:6.1,3.0')] ).

cnf(119,plain,
    member(not_subclass_element(x__dfg,y__dfg),x__dfg),
    inference(res,[status(thm),theory(equality)],[5,3]),
    [iquote('0:Res:5.1,3.0')] ).

cnf(121,plain,
    ( ~ member(u,x__dfg)
    | member(u,cross_product(universal_class,universal_class)) ),
    inference(res,[status(thm),theory(equality)],[1,4]),
    [iquote('0:Res:1.0,4.0')] ).

cnf(769,plain,
    ( ~ member(u,x__dfg)
    | equal(ordered_pair(first(u),second(u)),u) ),
    inference(res,[status(thm),theory(equality)],[121,20]),
    [iquote('0:Res:121.1,20.0')] ).

cnf(15521,plain,
    ( ~ member(not_subclass_element(x__dfg,y__dfg),x__dfg)
    | member(not_subclass_element(x__dfg,y__dfg),y__dfg) ),
    inference(spr,[status(thm),theory(equality)],[769,2]),
    [iquote('0:SpR:769.1,2.0')] ).

cnf(15579,plain,
    $false,
    inference(mrr,[status(thm)],[15521,119,118]),
    [iquote('0:MRR:15521.0,15521.1,119.0,118.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET236-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jul 11 10:00:34 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 4.27/4.44  
% 4.27/4.44  SPASS V 3.9 
% 4.27/4.44  SPASS beiseite: Proof found.
% 4.27/4.44  % SZS status Theorem
% 4.27/4.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 4.27/4.44  SPASS derived 12406 clauses, backtracked 409 clauses, performed 5 splits and kept 5994 clauses.
% 4.27/4.44  SPASS allocated 89745 KBytes.
% 4.27/4.44  SPASS spent	0:00:03.98 on the problem.
% 4.27/4.44  		0:00:00.04 for the input.
% 4.27/4.44  		0:00:00.00 for the FLOTTER CNF translation.
% 4.27/4.44  		0:00:00.16 for inferences.
% 4.27/4.44  		0:00:00.13 for the backtracking.
% 4.27/4.44  		0:00:03.55 for the reduction.
% 4.27/4.44  
% 4.27/4.44  
% 4.27/4.44  Here is a proof with depth 3, length 13 :
% 4.27/4.44  % SZS output start Refutation
% See solution above
% 4.27/4.44  Formulae used in the proof : prove_cross_product_property11_1 prove_cross_product_property11_2 prove_cross_product_property11_3 subclass_members not_subclass_members1 not_subclass_members2 cartesian_product4
% 4.27/4.44  
%------------------------------------------------------------------------------