TSTP Solution File: ALG379-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ALG379-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n019.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  : 300s
% DateTime : Tue Sep  6 16:10:01 EDT 2022

% Result   : Unsatisfiable 0.60s 0.68s
% Output   : Proof 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   63 (  16 unt;  14 typ;   0 def)
%            Number of atoms       :  301 ( 155 equ)
%            Maximal formula atoms :   16 (   6 avg)
%            Number of connectives :  456 ( 220   ~; 207   |;   0   &)
%                                         (  29 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of FOOLs       :   16 (  16 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   9   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :  105 (  95   !;   0   ?; 105   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_HOL_Ozero__class_Ozero_type,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(tc_RealDef_Oreal_type,type,
    tc_RealDef_Oreal: $i ).

tff(c_HOL_Ominus__class_Ominus_type,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(c_HOL_Ouminus__class_Ouminus_type,type,
    c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).

tff(v_s_____type,type,
    v_s____: $i ).

tff(c_RealVector_Onorm__class_Onorm_type,type,
    c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).

tff(tc_Complex_Ocomplex_type,type,
    tc_Complex_Ocomplex: $i ).

tff(c_Polynomial_Opoly_type,type,
    c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).

tff(v_z_____type,type,
    v_z____: $i ).

tff(v_p_type,type,
    v_p: $i ).

tff(class_Int_Onumber__ring_type,type,
    class_Int_Onumber__ring: $i > $o ).

tff(class_Ring__and__Field_Oidom_type,type,
    class_Ring__and__Field_Oidom: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__group__add__abs_type,type,
    class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).

tff(c_HOL_Oabs__class_Oabs_type,type,
    c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(1,plain,
    ( class_Int_Onumber__ring(tc_RealDef_Oreal)
  <=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).

tff(3,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ( class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
  <=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,axiom,
    class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

tff(6,plain,
    class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    ( ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
  <=> ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,axiom,
    c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(9,plain,
    c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [V_x: $i,T_a: $i,V_y: $i] :
      refl(
        ( ( ( V_x = V_y )
          | ~ class_Int_Onumber__ring(T_a)
          | ~ class_Ring__and__Field_Oidom(T_a)
          | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      <=> ( ( V_x = V_y )
          | ~ class_Int_Onumber__ring(T_a)
          | ~ class_Ring__and__Field_Oidom(T_a)
          | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [V_x: $i,T_a: $i,V_y: $i] :
        ( ( V_x = V_y )
        | ~ class_Int_Onumber__ring(T_a)
        | ~ class_Ring__and__Field_Oidom(T_a)
        | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
  <=> ! [V_x: $i,T_a: $i,V_y: $i] :
        ( ( V_x = V_y )
        | ~ class_Int_Onumber__ring(T_a)
        | ~ class_Ring__and__Field_Oidom(T_a)
        | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [V_x: $i,T_a: $i,V_y: $i] :
        ( ( V_x = V_y )
        | ~ class_Int_Onumber__ring(T_a)
        | ~ class_Ring__and__Field_Oidom(T_a)
        | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
  <=> ! [V_x: $i,T_a: $i,V_y: $i] :
        ( ( V_x = V_y )
        | ~ class_Int_Onumber__ring(T_a)
        | ~ class_Ring__and__Field_Oidom(T_a)
        | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ^ [V_x: $i,T_a: $i,V_y: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ class_Ring__and__Field_Oidom(T_a)
                  | ~ class_Int_Onumber__ring(T_a) )
              <=> ( ~ class_Int_Onumber__ring(T_a)
                  | ~ class_Ring__and__Field_Oidom(T_a) ) )),
              ( ( ~ class_Ring__and__Field_Oidom(T_a)
                | ~ class_Int_Onumber__ring(T_a)
                | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
            <=> ( ~ class_Int_Onumber__ring(T_a)
                | ~ class_Ring__and__Field_Oidom(T_a)
                | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
            rewrite(
              ( ( ~ class_Int_Onumber__ring(T_a)
                | ~ class_Ring__and__Field_Oidom(T_a)
                | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
            <=> ( ~ class_Int_Onumber__ring(T_a)
                | ~ class_Ring__and__Field_Oidom(T_a)
                | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
            ( ( ~ class_Ring__and__Field_Oidom(T_a)
              | ~ class_Int_Onumber__ring(T_a)
              | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
          <=> ( ~ class_Int_Onumber__ring(T_a)
              | ~ class_Ring__and__Field_Oidom(T_a)
              | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
          ( ( ~ class_Ring__and__Field_Oidom(T_a)
            | ~ class_Int_Onumber__ring(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
            | ( V_x = V_y ) )
        <=> ( ~ class_Int_Onumber__ring(T_a)
            | ~ class_Ring__and__Field_Oidom(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
            | ( V_x = V_y ) ) )),
        rewrite(
          ( ( ~ class_Int_Onumber__ring(T_a)
            | ~ class_Ring__and__Field_Oidom(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
            | ( V_x = V_y ) )
        <=> ( ( V_x = V_y )
            | ~ class_Int_Onumber__ring(T_a)
            | ~ class_Ring__and__Field_Oidom(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
        ( ( ~ class_Ring__and__Field_Oidom(T_a)
          | ~ class_Int_Onumber__ring(T_a)
          | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
          | ( V_x = V_y ) )
      <=> ( ( V_x = V_y )
          | ~ class_Int_Onumber__ring(T_a)
          | ~ class_Ring__and__Field_Oidom(T_a)
          | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [V_x: $i,T_a: $i,V_y: $i] :
        ( ~ class_Ring__and__Field_Oidom(T_a)
        | ~ class_Int_Onumber__ring(T_a)
        | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
        | ( V_x = V_y ) )
  <=> ! [V_x: $i,T_a: $i,V_y: $i] :
        ( ( V_x = V_y )
        | ~ class_Int_Onumber__ring(T_a)
        | ~ class_Ring__and__Field_Oidom(T_a)
        | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,axiom,
    ! [V_x: $i,T_a: $i,V_y: $i] :
      ( ~ class_Ring__and__Field_Oidom(T_a)
      | ~ class_Int_Onumber__ring(T_a)
      | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
      | ( V_x = V_y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

tff(16,plain,
    ! [V_x: $i,T_a: $i,V_y: $i] :
      ( ( V_x = V_y )
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Ring__and__Field_Oidom(T_a)
      | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [V_x: $i,T_a: $i,V_y: $i] :
      ( ( V_x = V_y )
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Ring__and__Field_Oidom(T_a)
      | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [V_x: $i,T_a: $i,V_y: $i] :
      ( ( V_x = V_y )
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Ring__and__Field_Oidom(T_a)
      | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [V_x: $i,T_a: $i,V_y: $i] :
      ( ( V_x = V_y )
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Ring__and__Field_Oidom(T_a)
      | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
    inference(modus_ponens,[status(thm)],[18,11]) ).

tff(20,plain,
    ( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
            ( ( V_x = V_y )
            | ~ class_Int_Onumber__ring(T_a)
            | ~ class_Ring__and__Field_Oidom(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
      | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
      | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
            ( ( V_x = V_y )
            | ~ class_Int_Onumber__ring(T_a)
            | ~ class_Ring__and__Field_Oidom(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
      | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
      | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ( ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
      | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
      | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
      | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
      | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
            ( ( V_x = V_y )
            | ~ class_Int_Onumber__ring(T_a)
            | ~ class_Ring__and__Field_Oidom(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
      | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
      | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
            ( ( V_x = V_y )
            | ~ class_Int_Onumber__ring(T_a)
            | ~ class_Ring__and__Field_Oidom(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
      | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
      | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(monotonicity,[status(thm)],[21]) ).

tff(23,plain,
    ( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
            ( ( V_x = V_y )
            | ~ class_Int_Onumber__ring(T_a)
            | ~ class_Ring__and__Field_Oidom(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
      | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
      | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
            ( ( V_x = V_y )
            | ~ class_Int_Onumber__ring(T_a)
            | ~ class_Ring__and__Field_Oidom(T_a)
            | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
      | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
      | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(transitivity,[status(thm)],[22,20]) ).

tff(24,plain,
    ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
          ( ( V_x = V_y )
          | ~ class_Int_Onumber__ring(T_a)
          | ~ class_Ring__and__Field_Oidom(T_a)
          | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
    | ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
    | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
    | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
    | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(25,plain,
    ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
          ( ( V_x = V_y )
          | ~ class_Int_Onumber__ring(T_a)
          | ~ class_Ring__and__Field_Oidom(T_a)
          | ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
    | ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
    | ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
    | ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
    | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).

tff(27,plain,
    ( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
  <=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,axiom,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).

tff(29,plain,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[28,27]) ).

tff(30,plain,
    ( ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
  <=> ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,axiom,
    c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

tff(32,plain,
    c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(modus_ponens,[status(thm)],[31,30]) ).

tff(33,plain,
    ^ [V_a: $i,T_a: $i] :
      refl(
        ( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
          | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      <=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
          | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(34,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
        | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
        | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
    inference(quant_intro,[status(thm)],[33]) ).

tff(35,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
        | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
        | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ^ [V_a: $i,T_a: $i] :
      rewrite(
        ( ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
          | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
          | ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
      <=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
          | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
    inference(bind,[status(th)],]) ).

tff(37,plain,
    ( ! [V_a: $i,T_a: $i] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
        | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
        | ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
  <=> ! [V_a: $i,T_a: $i] :
        ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
        | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
        | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,axiom,
    ! [V_a: $i,T_a: $i] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
      | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
      | ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).

tff(39,plain,
    ! [V_a: $i,T_a: $i] :
      ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
      | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    ! [V_a: $i,T_a: $i] :
      ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
      | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
    inference(modus_ponens,[status(thm)],[39,35]) ).

tff(41,plain,
    ! [V_a: $i,T_a: $i] :
      ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
      | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
    inference(skolemize,[status(sab)],[40]) ).

tff(42,plain,
    ! [V_a: $i,T_a: $i] :
      ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
      | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
    inference(modus_ponens,[status(thm)],[41,34]) ).

tff(43,plain,
    ( ( ~ ! [V_a: $i,T_a: $i] :
            ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
            | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ ! [V_a: $i,T_a: $i] :
            ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
            | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ( ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ( ~ ! [V_a: $i,T_a: $i] :
            ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
            | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ ! [V_a: $i,T_a: $i] :
            ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
            | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(monotonicity,[status(thm)],[44]) ).

tff(46,plain,
    ( ( ~ ! [V_a: $i,T_a: $i] :
            ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
            | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
  <=> ( ~ ! [V_a: $i,T_a: $i] :
            ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
            | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
            | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
      | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
    inference(transitivity,[status(thm)],[45,43]) ).

tff(47,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
          | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
    | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
    | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(48,plain,
    ( ~ ! [V_a: $i,T_a: $i] :
          ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
          | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
          | ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
    | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
    | ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
    | ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    $false,
    inference(unit_resolution,[status(thm)],[48,42,32,29,26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : ALG379-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Aug 29 16:26:35 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.60/0.68  % SZS status Unsatisfiable
% 0.60/0.68  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------