TSTP Solution File: SWW218+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWW218+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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 : Thu Jul 21 00:59:21 EDT 2022

% Result   : Theorem 1.54s 1.76s
% Output   : CNFRefutation 1.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   22 (   8 unt;   0 def)
%            Number of atoms       :   59 (   6 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   62 (  25   ~;  22   |;   7   &)
%                                         (   7 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   29 (   0 sgn  16   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096,axiom,
    ? [B_s] :
    ! [B_y] :
      ( ? [B_x] :
          ( ? [B_z] :
              ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
              & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) ).

fof(conj_0,hypothesis,
    ( ? [B_s] :
      ! [B_y] :
        ( ? [B_x] :
            ( ? [B_z] :
                ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
                & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) )
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
      <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) )
   => v_thesis____ ) ).

fof(conj_1,conjecture,
    v_thesis____ ).

fof(subgoal_0,plain,
    v_thesis____,
    inference(strip,[],[conj_1]) ).

fof(negate_0_0,plain,
    ~ v_thesis____,
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( v_thesis____
    | ! [B_s] :
      ? [B_y] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s)
      <=> ? [B_x] :
            ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
            & ? [B_z] :
                ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
                & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) ) ) ),
    inference(canonicalize,[],[conj_0]) ).

fof(normalize_0_1,plain,
    ? [B_s] :
    ! [B_y] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s)
    <=> ! [B_x] :
          ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
          | ! [B_z] :
              ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
              | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) ) ),
    inference(canonicalize,[],[fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096]) ).

fof(normalize_0_2,plain,
    ! [B_y] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,skolemFOFtoCNF_B_s)
    <=> ! [B_x] :
          ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
          | ! [B_z] :
              ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
              | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) ) ),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [B_y] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,skolemFOFtoCNF_B_s)
    <=> ! [B_x] :
          ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x)
          | ! [B_z] :
              ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x)
              | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ) ) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ( v_thesis____
    | ! [B_s] :
      ? [B_y] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s)
      <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,skolemFOFtoCNF_B_s) ) ),
    inference(simplify,[],[normalize_0_0,normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [B_s] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),B_s)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),skolemFOFtoCNF_B_s)
        | v_thesis____ )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),B_s)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),skolemFOFtoCNF_B_s)
        | v_thesis____ ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [B_s] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),B_s)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),skolemFOFtoCNF_B_s)
      | v_thesis____ ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [B_s] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),B_s)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),skolemFOFtoCNF_B_s)
      | v_thesis____ ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_8,plain,
    ~ v_thesis____,
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),B_s)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),skolemFOFtoCNF_B_s)
    | v_thesis____ ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_1,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(skolemFOFtoCNF_B_s),skolemFOFtoCNF_B_s)
    | v_thesis____ ),
    inference(subst,[],[refute_0_0:[bind(B_s,$fot(skolemFOFtoCNF_B_s))]]) ).

cnf(refute_0_2,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),B_s)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(B_s),skolemFOFtoCNF_B_s)
    | v_thesis____ ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_3,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(skolemFOFtoCNF_B_s),skolemFOFtoCNF_B_s)
    | v_thesis____ ),
    inference(subst,[],[refute_0_2:[bind(B_s,$fot(skolemFOFtoCNF_B_s))]]) ).

cnf(refute_0_4,plain,
    ~ v_thesis____,
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(skolemFOFtoCNF_B_s),skolemFOFtoCNF_B_s),
    inference(resolve,[$cnf( v_thesis____ )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    v_thesis____,
    inference(resolve,[$cnf( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,skolemFOFtoCNF_B_y_1(skolemFOFtoCNF_B_s),skolemFOFtoCNF_B_s) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( v_thesis____ )],[refute_0_6,refute_0_4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW218+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n021.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 : Sun Jun  5 00:42:49 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.54/1.76  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.54/1.76  
% 1.54/1.76  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.54/1.76  
%------------------------------------------------------------------------------