%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM025-2 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n019.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 : Mon Jul 18 12:24:11 EDT 2022

% Result   : Unsatisfiable 0.18s 0.37s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   10 (   6 unt;   4 nHn;   5 RR)
%            Number of literals    :   16 (   0 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :    9 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(transitivity_of_less,axiom,
    ( greater_or_equalish(A,B)
    | greater_or_equalish(C,A)
    | ~ greater_or_equalish(C,B) ) ).

cnf(no_number_less_than_itself,axiom,
    greater_or_equalish(A,A) ).

cnf(a_less_than_b,hypothesis,
    ~ greater_or_equalish(a,b) ).

cnf(prove_b_not_less_than_a,negated_conjecture,
    ~ greater_or_equalish(b,a) ).

cnf(refute_0_0,plain,
    greater_or_equalish(X_99,X_99),
    inference(subst,[],[no_number_less_than_itself:[bind(A,$fot(X_99))]]) ).

cnf(refute_0_1,plain,
    ( ~ greater_or_equalish(X_99,X_99)
    | greater_or_equalish(X_98,X_99)
    | greater_or_equalish(X_99,X_98) ),
    inference(subst,[],[transitivity_of_less:[bind(A,$fot(X_98)),bind(B,$fot(X_99)),bind(C,$fot(X_99))]]) ).

cnf(refute_0_2,plain,
    ( greater_or_equalish(X_98,X_99)
    | greater_or_equalish(X_99,X_98) ),
    inference(resolve,[$cnf( greater_or_equalish(X_99,X_99) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( greater_or_equalish(a,b)
    | greater_or_equalish(b,a) ),
    inference(subst,[],[refute_0_2:[bind(X_98,$fot(b)),bind(X_99,$fot(a))]]) ).

cnf(refute_0_4,plain,
    greater_or_equalish(a,b),
    inference(resolve,[$cnf( greater_or_equalish(b,a) )],[refute_0_3,prove_b_not_less_than_a]) ).

cnf(refute_0_5,plain,
    $false,
    inference(resolve,[$cnf( greater_or_equalish(a,b) )],[refute_0_4,a_less_than_b]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : NUM025-2 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jul  7 02:55:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.37  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.37  
% 0.18/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.37  
%------------------------------------------------------------------------------