%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM023-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n010.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 12:24:10 EDT 2022

% Result   : Unsatisfiable 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   5 RR)
%            Number of literals    :   10 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    7 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(adding_zero,axiom,
    equalish(add(A,n0),A) ).

cnf(smaller_number,axiom,
    ( ~ equalish(add(successor(A),B),C)
    | less(B,C) ) ).

cnf(prove_zero_is_less_than_all_successors,negated_conjecture,
    ~ less(n0,successor(a)) ).

cnf(refute_0_0,plain,
    equalish(add(successor(X_74),n0),successor(X_74)),
    inference(subst,[],[adding_zero:[bind(A,$fot(successor(X_74)))]]) ).

cnf(refute_0_1,plain,
    ( ~ equalish(add(successor(X_74),n0),successor(X_74))
    | less(n0,successor(X_74)) ),
    inference(subst,[],[smaller_number:[bind(A,$fot(X_74)),bind(B,$fot(n0)),bind(C,$fot(successor(X_74)))]]) ).

cnf(refute_0_2,plain,
    less(n0,successor(X_74)),
    inference(resolve,[$cnf( equalish(add(successor(X_74),n0),successor(X_74)) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    less(n0,successor(a)),
    inference(subst,[],[refute_0_2:[bind(X_74,$fot(a))]]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( less(n0,successor(a)) )],[refute_0_3,prove_zero_is_less_than_all_successors]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM023-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n010.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 : Wed Jul  6 03:19:17 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36  
% 0.12/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36  
%------------------------------------------------------------------------------