%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET234-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 05:25:11 EDT 2022

% Result   : Unsatisfiable 4.21s 4.44s
% Output   : Refutation 4.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   5 unt;   3 nHn;  10 RR)
%            Number of literals    :   15 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 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,
    member(ordered_pair(first(not_subclass_element(cross_product(x__dfg,y__dfg),z__dfg)),second(not_subclass_element(cross_product(x__dfg,y__dfg),z__dfg))),z__dfg),
    file('SET234-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ subclass(cross_product(x__dfg,y__dfg),z__dfg),
    file('SET234-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET234-6.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET234-6.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ member(u,cross_product(v,w))
    | equal(ordered_pair(first(u),second(u)),u) ),
    file('SET234-6.p',unknown),
    [] ).

cnf(1150,plain,
    ( subclass(cross_product(u,v),w)
    | equal(ordered_pair(first(not_subclass_element(cross_product(u,v),w)),second(not_subclass_element(cross_product(u,v),w))),not_subclass_element(cross_product(u,v),w)) ),
    inference(res,[status(thm),theory(equality)],[4,19]),
    [iquote('0:Res:4.1,19.0')] ).

cnf(15763,plain,
    ( subclass(cross_product(x__dfg,y__dfg),z__dfg)
    | member(not_subclass_element(cross_product(x__dfg,y__dfg),z__dfg),z__dfg) ),
    inference(spr,[status(thm),theory(equality)],[1150,1]),
    [iquote('0:SpR:1150.1,1.0')] ).

cnf(15798,plain,
    member(not_subclass_element(cross_product(x__dfg,y__dfg),z__dfg),z__dfg),
    inference(mrr,[status(thm)],[15763,2]),
    [iquote('0:MRR:15763.0,2.0')] ).

cnf(15812,plain,
    subclass(cross_product(x__dfg,y__dfg),z__dfg),
    inference(res,[status(thm),theory(equality)],[15798,5]),
    [iquote('0:Res:15798.0,5.0')] ).

cnf(15813,plain,
    $false,
    inference(mrr,[status(thm)],[15812,2]),
    [iquote('0:MRR:15812.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET234-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.13/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jul 11 07:12:15 EDT 2022
% 0.19/0.35  % CPUTime  : 
% 4.21/4.44  
% 4.21/4.44  SPASS V 3.9 
% 4.21/4.44  SPASS beiseite: Proof found.
% 4.21/4.44  % SZS status Theorem
% 4.21/4.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 4.21/4.44  SPASS derived 12580 clauses, backtracked 464 clauses, performed 5 splits and kept 6260 clauses.
% 4.21/4.44  SPASS allocated 89755 KBytes.
% 4.21/4.44  SPASS spent	0:00:03.99 on the problem.
% 4.21/4.44  		0:00:00.04 for the input.
% 4.21/4.44  		0:00:00.00 for the FLOTTER CNF translation.
% 4.21/4.44  		0:00:00.14 for inferences.
% 4.21/4.44  		0:00:00.30 for the backtracking.
% 4.21/4.44  		0:00:03.41 for the reduction.
% 4.21/4.44  
% 4.21/4.44  
% 4.21/4.44  Here is a proof with depth 3, length 10 :
% 4.21/4.44  % SZS output start Refutation
% See solution above
% 4.21/4.44  Formulae used in the proof : prove_cross_product_property9_1 prove_cross_product_property9_2 not_subclass_members1 not_subclass_members2 cartesian_product4
% 4.21/4.44  
%------------------------------------------------------------------------------