%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 05:30:00 EDT 2022

% Result   : Theorem 0.21s 0.45s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   12 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    in(skc5,cartesian_product2(skc6,skc7)),
    file('SET949+1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(ordered_pair(u,v),skc5),
    file('SET949+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ in(u,v)
    | ~ equal(v,cartesian_product2(w,x))
    | skP0(u,x,w) ),
    file('SET949+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ skP0(u,v,w)
    | equal(ordered_pair(skf5(w,v,u),skf4(v,u,w)),u) ),
    file('SET949+1.p',unknown),
    [] ).

cnf(19,plain,
    ( ~ equal(cartesian_product2(skc6,skc7),cartesian_product2(u,v))
    | skP0(skc5,v,u) ),
    inference(res,[status(thm),theory(equality)],[3,11]),
    [iquote('0:Res:3.0,11.0')] ).

cnf(23,plain,
    ~ skP0(skc5,u,v),
    inference(res,[status(thm),theory(equality)],[14,5]),
    [iquote('0:Res:14.1,5.0')] ).

cnf(24,plain,
    ~ equal(cartesian_product2(skc6,skc7),cartesian_product2(u,v)),
    inference(mrr,[status(thm)],[19,23]),
    [iquote('0:MRR:19.1,23.0')] ).

cnf(31,plain,
    $false,
    inference(eqr,[status(thm),theory(equality)],[24]),
    [iquote('0:EqR:24.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 13:40:55 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.21/0.45  
% 0.21/0.45  SPASS V 3.9 
% 0.21/0.45  SPASS beiseite: Proof found.
% 0.21/0.45  % SZS status Theorem
% 0.21/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.45  SPASS derived 13 clauses, backtracked 0 clauses, performed 0 splits and kept 22 clauses.
% 0.21/0.45  SPASS allocated 85306 KBytes.
% 0.21/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.21/0.45  		0:00:00.04 for the input.
% 0.21/0.45  		0:00:00.04 for the FLOTTER CNF translation.
% 0.21/0.45  		0:00:00.00 for inferences.
% 0.21/0.45  		0:00:00.00 for the backtracking.
% 0.21/0.45  		0:00:00.00 for the reduction.
% 0.21/0.45  
% 0.21/0.45  
% 0.21/0.45  Here is a proof with depth 2, length 8 :
% 0.21/0.45  % SZS output start Refutation
% See solution above
% 0.21/0.45  Formulae used in the proof : t102_zfmisc_1 d2_zfmisc_1
% 0.21/0.45  
%------------------------------------------------------------------------------