%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 : Sat Jul 16 07:22:08 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (  10 unt;   0 nHn;  14 RR)
%            Number of literals    :   19 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   2 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    complete,
    file('GRA002+4.p',unknown),
    [] ).

cnf(2,axiom,
    shortest_path(skc4,skc5,skc3),
    file('GRA002+4.p',unknown),
    [] ).

cnf(12,axiom,
    less_or_equal(number_of_in(u,v),number_of_in(u,graph)),
    file('GRA002+4.p',unknown),
    [] ).

cnf(20,axiom,
    ~ less_or_equal(minus(length_of(skc3),n1),number_of_in(triangles,graph)),
    file('GRA002+4.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ shortest_path(u,v,w)
    | path(u,v,w) ),
    file('GRA002+4.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ path(u,v,w)
    | equal(minus(length_of(w),n1),number_of_in(sequential_pairs,w)) ),
    file('GRA002+4.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ complete
    | ~ shortest_path(u,v,w)
    | equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
    file('GRA002+4.p',unknown),
    [] ).

cnf(68,plain,
    ( ~ shortest_path(u,v,w)
    | equal(number_of_in(triangles,w),number_of_in(sequential_pairs,w)) ),
    inference(mrr,[status(thm)],[38,1]),
    [iquote('0:MRR:38.0,1.0')] ).

cnf(75,plain,
    equal(number_of_in(triangles,skc3),number_of_in(sequential_pairs,skc3)),
    inference(res,[status(thm),theory(equality)],[2,68]),
    [iquote('0:Res:2.0,68.0')] ).

cnf(76,plain,
    path(skc4,skc5,skc3),
    inference(res,[status(thm),theory(equality)],[2,26]),
    [iquote('0:Res:2.0,26.0')] ).

cnf(84,plain,
    less_or_equal(number_of_in(sequential_pairs,skc3),number_of_in(triangles,graph)),
    inference(spr,[status(thm),theory(equality)],[75,12]),
    [iquote('0:SpR:75.0,12.0')] ).

cnf(99,plain,
    equal(minus(length_of(skc3),n1),number_of_in(sequential_pairs,skc3)),
    inference(res,[status(thm),theory(equality)],[76,33]),
    [iquote('0:Res:76.0,33.0')] ).

cnf(100,plain,
    ~ less_or_equal(number_of_in(sequential_pairs,skc3),number_of_in(triangles,graph)),
    inference(rew,[status(thm),theory(equality)],[99,20]),
    [iquote('0:Rew:99.0,20.0')] ).

cnf(101,plain,
    $false,
    inference(mrr,[status(thm)],[100,84]),
    [iquote('0:MRR:100.0,84.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue May 31 02:28:21 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.20/0.49  
% 0.20/0.49  SPASS V 3.9 
% 0.20/0.49  SPASS beiseite: Proof found.
% 0.20/0.49  % SZS status Theorem
% 0.20/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.49  SPASS derived 25 clauses, backtracked 0 clauses, performed 0 splits and kept 82 clauses.
% 0.20/0.49  SPASS allocated 98224 KBytes.
% 0.20/0.49  SPASS spent	0:00:00.14 on the problem.
% 0.20/0.49  		0:00:00.04 for the input.
% 0.20/0.49  		0:00:00.07 for the FLOTTER CNF translation.
% 0.20/0.49  		0:00:00.00 for inferences.
% 0.20/0.49  		0:00:00.00 for the backtracking.
% 0.20/0.49  		0:00:00.00 for the reduction.
% 0.20/0.49  
% 0.20/0.49  
% 0.20/0.49  Here is a proof with depth 2, length 14 :
% 0.20/0.49  % SZS output start Refutation
% See solution above
% 0.20/0.49  Formulae used in the proof : maximal_path_length graph_has_them_all shortest_path_defn path_length_sequential_pairs triangles_and_sequential_pairs
% 0.20/0.49  
%------------------------------------------------------------------------------