%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : HEN002-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 12:58:30 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   8 unt;   0 nHn;   9 RR)
%            Number of literals    :   17 (  12 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(quotient_less_equal1,axiom,
    ( ~ less_equal(X,Y)
    | divide(X,Y) = zero ) ).

cnf(zero_is_smallest,axiom,
    less_equal(zero,X) ).

cnf(prove_zero_over_a_is_zero,negated_conjecture,
    divide(zero,a) != zero ).

cnf(refute_0_0,plain,
    less_equal(zero,X_6),
    inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_6))]]) ).

cnf(refute_0_1,plain,
    ( ~ less_equal(zero,X_6)
    | divide(zero,X_6) = zero ),
    inference(subst,[],[quotient_less_equal1:[bind(X,$fot(zero)),bind(Y,$fot(X_6))]]) ).

cnf(refute_0_2,plain,
    divide(zero,X_6) = zero,
    inference(resolve,[$cnf( less_equal(zero,X_6) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    divide(zero,a) = zero,
    inference(subst,[],[refute_0_2:[bind(X_6,$fot(a))]]) ).

cnf(refute_0_4,plain,
    ( divide(zero,a) != zero
    | zero != zero
    | divide(zero,a) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(divide(zero,a),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_5,plain,
    ( zero != zero
    | divide(zero,a) = zero ),
    inference(resolve,[$cnf( $equal(divide(zero,a),zero) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    zero != zero,
    inference(resolve,[$cnf( $equal(divide(zero,a),zero) )],[refute_0_5,prove_zero_over_a_is_zero]) ).

cnf(refute_0_7,plain,
    zero = zero,
    introduced(tautology,[refl,[$fot(zero)]]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_7,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : HEN002-4 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n007.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 : Fri Jul  1 13:27:39 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------