%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET204-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 05:25:02 EDT 2022

% Result   : Unsatisfiable 0.18s 0.42s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   5 unt;   0 nHn;   9 RR)
%            Number of literals    :   14 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(ordered_pair(u__dfg,v__dfg),cross_product(x__dfg,y__dfg)),
    file('SET204-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ member(ordered_pair(v__dfg,u__dfg),cross_product(y__dfg,x__dfg)),
    file('SET204-6.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ member(ordered_pair(u,v),cross_product(w,x))
    | member(u,w) ),
    file('SET204-6.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ member(ordered_pair(u,v),cross_product(w,x))
    | member(v,x) ),
    file('SET204-6.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ member(u,v)
    | ~ member(w,x)
    | member(ordered_pair(w,u),cross_product(x,v)) ),
    file('SET204-6.p',unknown),
    [] ).

cnf(118,plain,
    member(u__dfg,x__dfg),
    inference(res,[status(thm),theory(equality)],[1,16]),
    [iquote('0:Res:1.0,16.0')] ).

cnf(119,plain,
    member(v__dfg,y__dfg),
    inference(res,[status(thm),theory(equality)],[1,17]),
    [iquote('0:Res:1.0,17.0')] ).

cnf(127,plain,
    ( ~ member(v__dfg,y__dfg)
    | ~ member(u__dfg,x__dfg) ),
    inference(res,[status(thm),theory(equality)],[18,2]),
    [iquote('0:Res:18.2,2.0')] ).

cnf(135,plain,
    $false,
    inference(mrr,[status(thm)],[127,119,118]),
    [iquote('0:MRR:127.0,127.1,119.0,118.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET204-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.11/0.33  % Computer : n028.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Mon Jul 11 03:46:13 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.18/0.42  
% 0.18/0.42  SPASS V 3.9 
% 0.18/0.42  SPASS beiseite: Proof found.
% 0.18/0.42  % SZS status Theorem
% 0.18/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.42  SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 116 clauses.
% 0.18/0.42  SPASS allocated 75769 KBytes.
% 0.18/0.42  SPASS spent	0:00:00.08 on the problem.
% 0.18/0.42  		0:00:00.04 for the input.
% 0.18/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42  		0:00:00.00 for inferences.
% 0.18/0.42  		0:00:00.00 for the backtracking.
% 0.18/0.42  		0:00:00.01 for the reduction.
% 0.18/0.42  
% 0.18/0.42  
% 0.18/0.42  Here is a proof with depth 1, length 9 :
% 0.18/0.42  % SZS output start Refutation
% See solution above
% 0.18/0.42  Formulae used in the proof : prove_cross_product_property2_1 prove_cross_product_property2_2 cartesian_product1 cartesian_product2 cartesian_product3
% 0.18/0.42  
%------------------------------------------------------------------------------