%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 14:33:54 EDT 2022

% Result   : Theorem 0.18s 0.51s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   8 unt;   0 nHn;  12 RR)
%            Number of literals    :   18 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    finite(skc26),
    file('SEU089+1.p',unknown),
    [] ).

cnf(2,axiom,
    finite(skc25),
    file('SEU089+1.p',unknown),
    [] ).

cnf(3,axiom,
    finite(skc24),
    file('SEU089+1.p',unknown),
    [] ).

cnf(113,axiom,
    ~ finite(cartesian_product3(skc26,skc25,skc24)),
    file('SEU089+1.p',unknown),
    [] ).

cnf(137,axiom,
    equal(cartesian_product2(cartesian_product2(u,v),w),cartesian_product3(u,v,w)),
    file('SEU089+1.p',unknown),
    [] ).

cnf(139,axiom,
    ( ~ finite(u)
    | ~ finite(v)
    | finite(cartesian_product2(v,u)) ),
    file('SEU089+1.p',unknown),
    [] ).

cnf(151,plain,
    ( ~ finite(u)
    | finite(cartesian_product2(u,skc25)) ),
    inference(res,[status(thm),theory(equality)],[2,139]),
    [iquote('0:Res:2.0,139.1')] ).

cnf(160,plain,
    finite(cartesian_product2(skc26,skc25)),
    inference(res,[status(thm),theory(equality)],[1,151]),
    [iquote('0:Res:1.0,151.0')] ).

cnf(366,plain,
    ( ~ finite(u)
    | ~ finite(cartesian_product2(v,w))
    | finite(cartesian_product3(v,w,u)) ),
    inference(spr,[status(thm),theory(equality)],[137,139]),
    [iquote('0:SpR:137.0,139.2')] ).

cnf(1006,plain,
    ( ~ finite(u)
    | finite(cartesian_product3(skc26,skc25,u)) ),
    inference(sor,[status(thm)],[366,160]),
    [iquote('0:SoR:366.1,160.0')] ).

cnf(1024,plain,
    ~ finite(skc24),
    inference(res,[status(thm),theory(equality)],[1006,113]),
    [iquote('0:Res:1006.1,113.0')] ).

cnf(1025,plain,
    $false,
    inference(ssi,[status(thm)],[1024,3]),
    [iquote('0:SSi:1024.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n025.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
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jun 19 04:24:13 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.18/0.51  
% 0.18/0.51  SPASS V 3.9 
% 0.18/0.51  SPASS beiseite: Proof found.
% 0.18/0.51  % SZS status Theorem
% 0.18/0.51  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.51  SPASS derived 800 clauses, backtracked 0 clauses, performed 0 splits and kept 524 clauses.
% 0.18/0.51  SPASS allocated 98409 KBytes.
% 0.18/0.51  SPASS spent	0:00:00.16 on the problem.
% 0.18/0.51  		0:00:00.04 for the input.
% 0.18/0.51  		0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.51  		0:00:00.01 for inferences.
% 0.18/0.51  		0:00:00.00 for the backtracking.
% 0.18/0.51  		0:00:00.04 for the reduction.
% 0.18/0.51  
% 0.18/0.51  
% 0.18/0.51  Here is a proof with depth 4, length 12 :
% 0.18/0.51  % SZS output start Refutation
% See solution above
% 0.18/0.51  Formulae used in the proof : t20_finset_1 d3_zfmisc_1 t19_finset_1
% 0.18/0.51  
%------------------------------------------------------------------------------