%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM837+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 12:30:48 EDT 2022

% Result   : Theorem 5.71s 5.95s
% Output   : CNFRefutation 5.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (  12 unt;   0 def)
%            Number of atoms       :   28 (  16 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   23 (  14   ~;   5   |;   1   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   22 (   1 sgn  15   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof('qe(171)',conjecture,
    ? [Vd273] : vd269 = vplus(vd268,Vd273) ).

fof('holds(conjunct1(170), 270, 0)',axiom,
    less(vd268,vd269) ).

fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
    ! [Vd198,Vd199] :
      ( less(Vd199,Vd198)
    <=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ) ).

fof(subgoal_0,plain,
    ? [Vd273] : vd269 = vplus(vd268,Vd273),
    inference(strip,[],['qe(171)']) ).

fof(negate_0_0,plain,
    ~ ? [Vd273] : vd269 = vplus(vd268,Vd273),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    less(vd268,vd269),
    inference(canonicalize,[],['holds(conjunct1(170), 270, 0)']) ).

fof(normalize_0_1,plain,
    ! [Vd198,Vd199] :
      ( ~ less(Vd199,Vd198)
    <=> ! [Vd201] : Vd198 != vplus(Vd199,Vd201) ),
    inference(canonicalize,[],['def(cond(conseq(axiom(3)), 12), 1)']) ).

fof(normalize_0_2,plain,
    ! [Vd198,Vd199] :
      ( ~ less(Vd199,Vd198)
    <=> ! [Vd201] : Vd198 != vplus(Vd199,Vd201) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [Vd198,Vd199,Vd201] :
      ( ( Vd198 != vplus(Vd199,Vd201)
        | less(Vd199,Vd198) )
      & ( ~ less(Vd199,Vd198)
        | Vd198 = vplus(Vd199,skolemFOFtoCNF_Vd201(Vd198,Vd199)) ) ),
    inference(clausify,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [Vd198,Vd199] :
      ( ~ less(Vd199,Vd198)
      | Vd198 = vplus(Vd199,skolemFOFtoCNF_Vd201(Vd198,Vd199)) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Vd273] : vd269 != vplus(vd268,Vd273),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_6,plain,
    ! [Vd273] : vd269 != vplus(vd268,Vd273),
    inference(specialize,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    less(vd268,vd269),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    ( ~ less(Vd199,Vd198)
    | Vd198 = vplus(Vd199,skolemFOFtoCNF_Vd201(Vd198,Vd199)) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_2,plain,
    ( ~ less(vd268,vd269)
    | vd269 = vplus(vd268,skolemFOFtoCNF_Vd201(vd269,vd268)) ),
    inference(subst,[],[refute_0_1:[bind(Vd198,$fot(vd269)),bind(Vd199,$fot(vd268))]]) ).

cnf(refute_0_3,plain,
    vd269 = vplus(vd268,skolemFOFtoCNF_Vd201(vd269,vd268)),
    inference(resolve,[$cnf( less(vd268,vd269) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    vd269 != vplus(vd268,Vd273),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_5,plain,
    vd269 != vplus(vd268,skolemFOFtoCNF_Vd201(vd269,vd268)),
    inference(subst,[],[refute_0_4:[bind(Vd273,$fot(skolemFOFtoCNF_Vd201(vd269,vd268)))]]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( $equal(vd269,vplus(vd268,skolemFOFtoCNF_Vd201(vd269,vd268))) )],[refute_0_3,refute_0_5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM837+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jul  7 15:09:37 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.71/5.95  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.71/5.95  
% 5.71/5.95  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.71/5.95  
%------------------------------------------------------------------------------