%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM021-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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 12:24:09 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   24 (   8 unt;   6 nHn;  24 RR)
%            Number of literals    :   48 (   0 equ;  19 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   17 (   1 sgn)

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

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

cnf(less_lemma,axiom,
    ( ~ less(A,B)
    | equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B) ) ).

cnf(divides_only_less_or_equal,axiom,
    ( ~ divides(A,B)
    | less(A,B)
    | equalish(A,B) ) ).

cnf(transitivity,axiom,
    ( ~ equalish(X,Y)
    | ~ equalish(Y,Z)
    | equalish(X,Z) ) ).

cnf(b_less_than_c,hypothesis,
    less(b,c) ).

cnf(b_greater_equal_a,hypothesis,
    ~ less(b,a) ).

cnf(impossible_c_divides_a,negated_conjecture,
    divides(c,a) ).

cnf(refute_0_0,plain,
    ( ~ equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),a)
    | less(b,a) ),
    inference(subst,[],[smaller_number:[bind(A,$fot(predecessor_of_1st_minus_2nd(c,b))),bind(B,$fot(b)),bind(C,$fot(a))]]) ).

cnf(refute_0_1,plain,
    ( ~ less(b,c)
    | equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),c) ),
    inference(subst,[],[less_lemma:[bind(A,$fot(b)),bind(B,$fot(c))]]) ).

cnf(refute_0_2,plain,
    equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),c),
    inference(resolve,[$cnf( less(b,c) )],[b_less_than_c,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ divides(c,a)
    | equalish(c,a)
    | less(c,a) ),
    inference(subst,[],[divides_only_less_or_equal:[bind(A,$fot(c)),bind(B,$fot(a))]]) ).

cnf(refute_0_4,plain,
    ( equalish(c,a)
    | less(c,a) ),
    inference(resolve,[$cnf( divides(c,a) )],[impossible_c_divides_a,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ less(X_240,c)
    | ~ less(c,a)
    | less(X_240,a) ),
    inference(subst,[],[transitivity_of_less:[bind(A,$fot(c)),bind(B,$fot(a)),bind(C,$fot(X_240))]]) ).

cnf(refute_0_6,plain,
    ( ~ less(X_240,c)
    | equalish(c,a)
    | less(X_240,a) ),
    inference(resolve,[$cnf( less(c,a) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ less(b,c)
    | equalish(c,a)
    | less(b,a) ),
    inference(subst,[],[refute_0_6:[bind(X_240,$fot(b))]]) ).

cnf(refute_0_8,plain,
    ( equalish(c,a)
    | less(b,a) ),
    inference(resolve,[$cnf( less(b,c) )],[b_less_than_c,refute_0_7]) ).

cnf(refute_0_9,plain,
    equalish(c,a),
    inference(resolve,[$cnf( less(b,a) )],[refute_0_8,b_greater_equal_a]) ).

cnf(refute_0_10,plain,
    ( ~ equalish(X_245,c)
    | ~ equalish(c,a)
    | equalish(X_245,a) ),
    inference(subst,[],[transitivity:[bind(X,$fot(X_245)),bind(Y,$fot(c)),bind(Z,$fot(a))]]) ).

cnf(refute_0_11,plain,
    ( ~ equalish(X_245,c)
    | equalish(X_245,a) ),
    inference(resolve,[$cnf( equalish(c,a) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),c)
    | equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),a) ),
    inference(subst,[],[refute_0_11:[bind(X_245,$fot(add(successor(predecessor_of_1st_minus_2nd(c,b)),b)))]]) ).

cnf(refute_0_13,plain,
    equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),a),
    inference(resolve,[$cnf( equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),c) )],[refute_0_2,refute_0_12]) ).

cnf(refute_0_14,plain,
    less(b,a),
    inference(resolve,[$cnf( equalish(add(successor(predecessor_of_1st_minus_2nd(c,b)),b),a) )],[refute_0_13,refute_0_0]) ).

cnf(refute_0_15,plain,
    $false,
    inference(resolve,[$cnf( less(b,a) )],[refute_0_14,b_greater_equal_a]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM021-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n015.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 : Tue Jul  5 20:14:48 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.48  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48  
% 0.19/0.48  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.48  
%------------------------------------------------------------------------------