%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET676+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 05:28:01 EDT 2022

% Result   : Theorem 0.21s 0.46s
% 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    :   14 (   0 equ;   8 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ilf_type(u,set_type),
    file('SET676+3.p',unknown),
    [] ).

cnf(10,axiom,
    ~ ilf_type(cross_product(skc1,skc1),identity_relation_of_type(skc1)),
    file('SET676+3.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ ilf_type(u,set_type)
    | ~ ilf_type(v,set_type)
    | ilf_type(cross_product(u,v),relation_type(u,v)) ),
    file('SET676+3.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ ilf_type(u,relation_type(v,v))
    | ~ ilf_type(v,set_type)
    | ~ ilf_type(u,set_type)
    | ilf_type(u,identity_relation_of_type(v)) ),
    file('SET676+3.p',unknown),
    [] ).

cnf(51,plain,
    ilf_type(cross_product(u,v),relation_type(u,v)),
    inference(mrr,[status(thm)],[21,2]),
    [iquote('0:MRR:21.0,21.1,2.0,2.0')] ).

cnf(59,plain,
    ( ~ ilf_type(u,relation_type(v,v))
    | ilf_type(u,identity_relation_of_type(v)) ),
    inference(mrr,[status(thm)],[27,2]),
    [iquote('0:MRR:27.1,27.2,2.0,2.0')] ).

cnf(70,plain,
    ~ ilf_type(cross_product(skc1,skc1),relation_type(skc1,skc1)),
    inference(res,[status(thm),theory(equality)],[59,10]),
    [iquote('0:Res:59.1,10.0')] ).

cnf(71,plain,
    $false,
    inference(mrr,[status(thm)],[70,51]),
    [iquote('0:MRR:70.0,51.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET676+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.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 12:32:16 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.21/0.46  
% 0.21/0.46  SPASS V 3.9 
% 0.21/0.46  SPASS beiseite: Proof found.
% 0.21/0.46  % SZS status Theorem
% 0.21/0.46  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.46  SPASS derived 1 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.21/0.46  SPASS allocated 97791 KBytes.
% 0.21/0.46  SPASS spent	0:00:00.10 on the problem.
% 0.21/0.46  		0:00:00.03 for the input.
% 0.21/0.46  		0:00:00.04 for the FLOTTER CNF translation.
% 0.21/0.46  		0:00:00.00 for inferences.
% 0.21/0.46  		0:00:00.00 for the backtracking.
% 0.21/0.46  		0:00:00.00 for the reduction.
% 0.21/0.46  
% 0.21/0.46  
% 0.21/0.46  Here is a proof with depth 1, length 8 :
% 0.21/0.46  % SZS output start Refutation
% See solution above
% 0.21/0.46  Formulae used in the proof : p19 prove_relset_1_41 p1 p4
% 0.21/0.46  
%------------------------------------------------------------------------------