TSTP Solution File: ITP021+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ITP021+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n013.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 Aug 22 10:43:21 EDT 2023

% Result   : Theorem 28.03s 13.95s
% Output   : CNFRefutation 28.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   40
% Syntax   : Number of formulae    :  407 ( 175 unt;  26 typ;   0 def)
%            Number of atoms       :  798 ( 181 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  806 ( 389   ~; 393   |;   3   &)
%                                         (   2 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  12   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;  14 con; 0-4 aty)
%            Number of variables   :  211 (; 211   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ mem > p > ne > k > arr > ap > #nlpp > i > c_2Emin_2E_3D > c_2Ebool_2E_21 > c_2Ebool_2ECOND > ty_2Eextreal_2Eextreal > ind > c_2Emin_2E_3D_3D_3E > c_2Eextreal_2Eextreal__max > c_2Eextreal_2Eextreal__le > c_2Ebool_2E_7E > c_2Ebool_2E_5C_2F > c_2Ebool_2E_2F_5C > c_2Ebool_2ET > c_2Ebool_2EF > bool > #skF_5 > #skF_3 > #skF_4 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(arr,type,
    arr: ( $i * $i ) > $i ).

tff(ne,type,
    ne: $i > $o ).

tff(c_2Ebool_2EF,type,
    c_2Ebool_2EF: $i ).

tff(c_2Ebool_2ECOND,type,
    c_2Ebool_2ECOND: $i > $i ).

tff(i,type,
    i: $i > $i ).

tff(c_2Ebool_2E_21,type,
    c_2Ebool_2E_21: $i > $i ).

tff(ty_2Eextreal_2Eextreal,type,
    ty_2Eextreal_2Eextreal: $i ).

tff(c_2Eextreal_2Eextreal__max,type,
    c_2Eextreal_2Eextreal__max: $i ).

tff(bool,type,
    bool: $i ).

tff(mem,type,
    mem: ( $i * $i ) > $o ).

tff(ap,type,
    ap: ( $i * $i ) > $i ).

tff(p,type,
    p: $i > $o ).

tff(ind,type,
    ind: $i ).

tff('#skF_5',type,
    '#skF_5': $i ).

tff(c_2Emin_2E_3D_3D_3E,type,
    c_2Emin_2E_3D_3D_3E: $i ).

tff(c_2Eextreal_2Eextreal__le,type,
    c_2Eextreal_2Eextreal__le: $i ).

tff(c_2Ebool_2E_5C_2F,type,
    c_2Ebool_2E_5C_2F: $i ).

tff('#skF_3',type,
    '#skF_3': $i ).

tff(c_2Ebool_2E_7E,type,
    c_2Ebool_2E_7E: $i ).

tff(c_2Ebool_2ET,type,
    c_2Ebool_2ET: $i ).

tff(k,type,
    k: ( $i * $i ) > $i ).

tff('#skF_4',type,
    '#skF_4': $i ).

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

tff('#skF_1',type,
    '#skF_1': ( $i * $i * $i * $i ) > $i ).

tff(c_2Emin_2E_3D,type,
    c_2Emin_2E_3D: $i > $i ).

tff(c_2Ebool_2E_2F_5C,type,
    c_2Ebool_2E_2F_5C: $i ).

tff(f_112,axiom,
    ~ p(c_2Ebool_2EF),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).

tff(f_648,negated_conjecture,
    ~ ! [V0z] :
        ( mem(V0z,ty_2Eextreal_2Eextreal)
       => ! [V1x] :
            ( mem(V1x,ty_2Eextreal_2Eextreal)
           => ! [V2y] :
                ( mem(V2y,ty_2Eextreal_2Eextreal)
               => ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,V1x),V2y)),V0z))
                <=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V0z))
                    & p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V0z)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Emax__le) ).

tff(f_102,axiom,
    p(c_2Ebool_2ET),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).

tff(f_103,axiom,
    ne(ty_2Eextreal_2Eextreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Eextreal_2Eextreal) ).

tff(f_406,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
            | p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V0x)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__total) ).

tff(f_104,axiom,
    mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eextreal_2Eextreal__le) ).

tff(f_67,axiom,
    ! [A,B,F] :
      ( mem(F,arr(A,B))
     => ! [X] :
          ( mem(X,A)
         => mem(ap(F,X),B) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).

tff(f_101,axiom,
    mem(c_2Ebool_2ET,bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).

tff(f_78,axiom,
    ! [Q] :
      ( mem(Q,bool)
     => ! [R] :
          ( mem(R,bool)
         => ( ( p(Q)
            <=> p(R) )
           => ( Q = R ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',boolext) ).

tff(f_109,axiom,
    mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eextreal_2Eextreal__max) ).

tff(f_413,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ( ap(ap(c_2Eextreal_2Eextreal__max,V0x),V1y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)),V1y),V0x) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eextreal_2Eextreal__max__def) ).

tff(f_323,axiom,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [V0t1] :
          ( mem(V0t1,A_27a)
         => ! [V1t2] :
              ( mem(V1t2,A_27a)
             => ( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 )
                & ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CLAUSES) ).

tff(f_110,axiom,
    mem(c_2Ebool_2EF,bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).

tff(f_397,axiom,
    ! [V0x] :
      ( mem(V0x,ty_2Eextreal_2Eextreal)
     => ! [V1y] :
          ( mem(V1y,ty_2Eextreal_2Eextreal)
         => ! [V2z] :
              ( mem(V2z,ty_2Eextreal_2Eextreal)
             => ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
                  & p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z)) )
               => p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V2z)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__trans) ).

tff(c_40,plain,
    ~ p(c_2Ebool_2EF),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_1626,plain,
    mem('#skF_4',ty_2Eextreal_2Eextreal),
    inference(cnfTransformation,[status(thm)],[f_648]) ).

tff(c_28,plain,
    p(c_2Ebool_2ET),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_1636,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3'))
    | p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')) ),
    inference(cnfTransformation,[status(thm)],[f_648]) ).

tff(c_1641,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
    inference(splitLeft,[status(thm)],[c_1636]) ).

tff(c_30,plain,
    ne(ty_2Eextreal_2Eextreal),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_1624,plain,
    mem('#skF_5',ty_2Eextreal_2Eextreal),
    inference(cnfTransformation,[status(thm)],[f_648]) ).

tff(c_158,plain,
    ! [V1y_101,V0x_99] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_101),V0x_99))
      | p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_99),V1y_101))
      | ~ mem(V1y_101,ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_99,ty_2Eextreal_2Eextreal) ),
    inference(cnfTransformation,[status(thm)],[f_406]) ).

tff(c_32,plain,
    mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_1718,plain,
    ! [F_169,X_170,B_171,A_172] :
      ( mem(ap(F_169,X_170),B_171)
      | ~ mem(X_170,A_172)
      | ~ mem(F_169,arr(A_172,B_171)) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_1759,plain,
    ! [F_169,B_171] :
      ( mem(ap(F_169,'#skF_5'),B_171)
      | ~ mem(F_169,arr(ty_2Eextreal_2Eextreal,B_171)) ),
    inference(resolution,[status(thm)],[c_1624,c_1718]) ).

tff(c_1852,plain,
    ! [F_181,B_182] :
      ( mem(ap(F_181,'#skF_4'),B_182)
      | ~ mem(F_181,arr(ty_2Eextreal_2Eextreal,B_182)) ),
    inference(resolution,[status(thm)],[c_1626,c_1718]) ).

tff(c_26,plain,
    mem(c_2Ebool_2ET,bool),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_1696,plain,
    ! [R_165,Q_166] :
      ( ~ p(R_165)
      | ~ p(Q_166)
      | ( R_165 = Q_166 )
      | ~ mem(R_165,bool)
      | ~ mem(Q_166,bool) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_1700,plain,
    ! [Q_166] :
      ( ~ p(c_2Ebool_2ET)
      | ~ p(Q_166)
      | ( c_2Ebool_2ET = Q_166 )
      | ~ mem(Q_166,bool) ),
    inference(resolution,[status(thm)],[c_26,c_1696]) ).

tff(c_1704,plain,
    ! [Q_166] :
      ( ~ p(Q_166)
      | ( c_2Ebool_2ET = Q_166 )
      | ~ mem(Q_166,bool) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_1700]) ).

tff(c_2321,plain,
    ! [F_231] :
      ( ~ p(ap(F_231,'#skF_4'))
      | ( ap(F_231,'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_231,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_1852,c_1704]) ).

tff(c_26260,plain,
    ! [F_772] :
      ( ~ p(ap(ap(F_772,'#skF_5'),'#skF_4'))
      | ( ap(ap(F_772,'#skF_5'),'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_772,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_1759,c_2321]) ).

tff(c_26353,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_32,c_26260]) ).

tff(c_26354,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
    inference(splitLeft,[status(thm)],[c_26353]) ).

tff(c_26360,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_158,c_26354]) ).

tff(c_26369,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_26360]) ).

tff(c_36,plain,
    mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_1757,plain,
    ! [F_169,B_171] :
      ( mem(ap(F_169,'#skF_4'),B_171)
      | ~ mem(F_169,arr(ty_2Eextreal_2Eextreal,B_171)) ),
    inference(resolution,[status(thm)],[c_1626,c_1718]) ).

tff(c_1628,plain,
    mem('#skF_3',ty_2Eextreal_2Eextreal),
    inference(cnfTransformation,[status(thm)],[f_648]) ).

tff(c_1640,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3'))
    | p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')) ),
    inference(cnfTransformation,[status(thm)],[f_648]) ).

tff(c_1651,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
    inference(splitLeft,[status(thm)],[c_1640]) ).

tff(c_1882,plain,
    ! [F_183,B_184] :
      ( mem(ap(F_183,'#skF_3'),B_184)
      | ~ mem(F_183,arr(ty_2Eextreal_2Eextreal,B_184)) ),
    inference(resolution,[status(thm)],[c_1628,c_1718]) ).

tff(c_2091,plain,
    ! [F_207] :
      ( ~ p(ap(F_207,'#skF_3'))
      | ( ap(F_207,'#skF_3') = c_2Ebool_2ET )
      | ~ mem(F_207,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_1882,c_1704]) ).

tff(c_13246,plain,
    ! [F_533] :
      ( ~ p(ap(ap(F_533,'#skF_4'),'#skF_3'))
      | ( ap(ap(F_533,'#skF_4'),'#skF_3') = c_2Ebool_2ET )
      | ~ mem(F_533,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_1757,c_2091]) ).

tff(c_13317,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_32,c_13246]) ).

tff(c_13341,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2ET,
    inference(demodulation,[status(thm),theory(equality)],[c_1651,c_13317]) ).

tff(c_160,plain,
    ! [V0x_102,V1y_104] :
      ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,V0x_102),V1y_104)),V1y_104),V0x_102) = ap(ap(c_2Eextreal_2Eextreal__max,V0x_102),V1y_104) )
      | ~ mem(V1y_104,ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_102,ty_2Eextreal_2Eextreal) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_13377,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_3'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_3') )
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_13341,c_160]) ).

tff(c_13418,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_3'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1628,c_13377]) ).

tff(c_132,plain,
    ! [A_27a_72,V0t1_76,V1t2_78] :
      ( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a_72),c_2Ebool_2ET),V0t1_76),V1t2_78) = V0t1_76 )
      | ~ mem(V1t2_78,A_27a_72)
      | ~ mem(V0t1_76,A_27a_72)
      | ~ ne(A_27a_72) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_13468,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_3') = '#skF_3' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_13418,c_132]) ).

tff(c_13484,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_3') = '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1628,c_1626,c_13468]) ).

tff(c_8,plain,
    ! [F_6,X_8,B_5,A_4] :
      ( mem(ap(F_6,X_8),B_5)
      | ~ mem(X_8,A_4)
      | ~ mem(F_6,arr(A_4,B_5)) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_4158,plain,
    ! [F_319,F_320,B_321,B_322] :
      ( mem(ap(F_319,ap(F_320,'#skF_3')),B_321)
      | ~ mem(F_319,arr(B_322,B_321))
      | ~ mem(F_320,arr(ty_2Eextreal_2Eextreal,B_322)) ),
    inference(resolution,[status(thm)],[c_1882,c_8]) ).

tff(c_4239,plain,
    ! [F_320] :
      ( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_320,'#skF_3')),arr(ty_2Eextreal_2Eextreal,bool))
      | ~ mem(F_320,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(resolution,[status(thm)],[c_32,c_4158]) ).

tff(c_13516,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),arr(ty_2Eextreal_2Eextreal,bool))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_13484,c_4239]) ).

tff(c_14402,plain,
    ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitLeft,[status(thm)],[c_13516]) ).

tff(c_14405,plain,
    ~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    inference(resolution,[status(thm)],[c_1757,c_14402]) ).

tff(c_14409,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_14405]) ).

tff(c_14411,plain,
    mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitRight,[status(thm)],[c_13516]) ).

tff(c_4240,plain,
    ! [F_320] :
      ( mem(ap(c_2Eextreal_2Eextreal__max,ap(F_320,'#skF_3')),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
      | ~ mem(F_320,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(resolution,[status(thm)],[c_36,c_4158]) ).

tff(c_13513,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_13484,c_4240]) ).

tff(c_33170,plain,
    mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(demodulation,[status(thm),theory(equality)],[c_14411,c_13513]) ).

tff(c_14410,plain,
    mem(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),arr(ty_2Eextreal_2Eextreal,bool)),
    inference(splitRight,[status(thm)],[c_13516]) ).

tff(c_1878,plain,
    ! [F_181] :
      ( ~ p(ap(F_181,'#skF_4'))
      | ( ap(F_181,'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_181,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_1852,c_1704]) ).

tff(c_14494,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_14410,c_1878]) ).

tff(c_14501,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4')),
    inference(splitLeft,[status(thm)],[c_14494]) ).

tff(c_38,plain,
    mem(c_2Ebool_2EF,bool),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_1670,plain,
    ! [Q_160,R_161] :
      ( p(Q_160)
      | p(R_161)
      | ( R_161 = Q_160 )
      | ~ mem(R_161,bool)
      | ~ mem(Q_160,bool) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_1672,plain,
    ! [Q_160] :
      ( p(Q_160)
      | p(c_2Ebool_2EF)
      | ( c_2Ebool_2EF = Q_160 )
      | ~ mem(Q_160,bool) ),
    inference(resolution,[status(thm)],[c_38,c_1670]) ).

tff(c_1677,plain,
    ! [Q_160] :
      ( p(Q_160)
      | ( c_2Ebool_2EF = Q_160 )
      | ~ mem(Q_160,bool) ),
    inference(negUnitSimplification,[status(thm)],[c_40,c_1672]) ).

tff(c_1880,plain,
    ! [F_181] :
      ( p(ap(F_181,'#skF_4'))
      | ( ap(F_181,'#skF_4') = c_2Ebool_2EF )
      | ~ mem(F_181,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_1852,c_1677]) ).

tff(c_14495,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4') = c_2Ebool_2EF ) ),
    inference(resolution,[status(thm)],[c_14410,c_1880]) ).

tff(c_20249,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4') = c_2Ebool_2EF,
    inference(negUnitSimplification,[status(thm)],[c_14501,c_14495]) ).

tff(c_1762,plain,
    ! [F_175,B_176] :
      ( mem(ap(F_175,'#skF_5'),B_176)
      | ~ mem(F_175,arr(ty_2Eextreal_2Eextreal,B_176)) ),
    inference(resolution,[status(thm)],[c_1624,c_1718]) ).

tff(c_2038,plain,
    ! [F_202] :
      ( ~ p(ap(F_202,'#skF_5'))
      | ( ap(F_202,'#skF_5') = c_2Ebool_2ET )
      | ~ mem(F_202,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_1762,c_1704]) ).

tff(c_23928,plain,
    ! [F_721] :
      ( ~ p(ap(ap(F_721,'#skF_4'),'#skF_5'))
      | ( ap(ap(F_721,'#skF_4'),'#skF_5') = c_2Ebool_2ET )
      | ~ mem(F_721,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_1757,c_2038]) ).

tff(c_24043,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_32,c_23928]) ).

tff(c_24044,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
    inference(splitLeft,[status(thm)],[c_24043]) ).

tff(c_24450,plain,
    ! [F_735] :
      ( ~ p(ap(ap(F_735,'#skF_5'),'#skF_4'))
      | ( ap(ap(F_735,'#skF_5'),'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_735,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_1759,c_2321]) ).

tff(c_24565,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_32,c_24450]) ).

tff(c_24566,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
    inference(splitLeft,[status(thm)],[c_24565]) ).

tff(c_24572,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_158,c_24566]) ).

tff(c_24581,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_24572]) ).

tff(c_24583,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24044,c_24581]) ).

tff(c_24584,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET,
    inference(splitRight,[status(thm)],[c_24565]) ).

tff(c_24623,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_24584,c_160]) ).

tff(c_24666,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1626,c_24623]) ).

tff(c_24767,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4' )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_24666,c_132]) ).

tff(c_24777,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1624,c_24767]) ).

tff(c_3496,plain,
    ! [F_294,F_295,B_296,B_297] :
      ( mem(ap(F_294,ap(F_295,'#skF_4')),B_296)
      | ~ mem(F_294,arr(B_297,B_296))
      | ~ mem(F_295,arr(ty_2Eextreal_2Eextreal,B_297)) ),
    inference(resolution,[status(thm)],[c_1852,c_8]) ).

tff(c_3547,plain,
    ! [F_295] :
      ( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_295,'#skF_4')),arr(ty_2Eextreal_2Eextreal,bool))
      | ~ mem(F_295,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(resolution,[status(thm)],[c_32,c_3496]) ).

tff(c_24821,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_24777,c_3547]) ).

tff(c_24976,plain,
    ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitLeft,[status(thm)],[c_24821]) ).

tff(c_24979,plain,
    ~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    inference(resolution,[status(thm)],[c_1759,c_24976]) ).

tff(c_24983,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_24979]) ).

tff(c_24984,plain,
    mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
    inference(splitRight,[status(thm)],[c_24821]) ).

tff(c_1790,plain,
    ! [F_175] :
      ( p(ap(F_175,'#skF_5'))
      | ( ap(F_175,'#skF_5') = c_2Ebool_2EF )
      | ~ mem(F_175,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_1762,c_1677]) ).

tff(c_25159,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF ) ),
    inference(resolution,[status(thm)],[c_24984,c_1790]) ).

tff(c_25183,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF,
    inference(negUnitSimplification,[status(thm)],[c_24044,c_25159]) ).

tff(c_25225,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_25183,c_160]) ).

tff(c_25270,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_25225]) ).

tff(c_130,plain,
    ! [A_27a_72,V0t1_76,V1t2_78] :
      ( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a_72),c_2Ebool_2EF),V0t1_76),V1t2_78) = V1t2_78 )
      | ~ mem(V1t2_78,A_27a_72)
      | ~ mem(V0t1_76,A_27a_72)
      | ~ ne(A_27a_72) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_25888,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_25270,c_130]) ).

tff(c_25898,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_25888]) ).

tff(c_5409,plain,
    ! [V0x_381,V2z_382,V1y_383] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_381),V2z_382))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_383),V2z_382))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_381),V1y_383))
      | ~ mem(V2z_382,ty_2Eextreal_2Eextreal)
      | ~ mem(V1y_383,ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_381,ty_2Eextreal_2Eextreal) ),
    inference(cnfTransformation,[status(thm)],[f_397]) ).

tff(c_5417,plain,
    ! [V0x_381] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_381),'#skF_3'))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_381),'#skF_4'))
      | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
      | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_381,ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_1651,c_5409]) ).

tff(c_5429,plain,
    ! [V0x_384] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_384),'#skF_3'))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_384),'#skF_4'))
      | ~ mem(V0x_384,ty_2Eextreal_2Eextreal) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1628,c_5417]) ).

tff(c_1630,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3'))
    | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
    | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3')) ),
    inference(cnfTransformation,[status(thm)],[f_648]) ).

tff(c_1694,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_1651,c_1641,c_1630]) ).

tff(c_5438,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_4'))
    | ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_5429,c_1694]) ).

tff(c_5490,plain,
    ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal),
    inference(splitLeft,[status(thm)],[c_5438]) ).

tff(c_5494,plain,
    ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(resolution,[status(thm)],[c_1759,c_5490]) ).

tff(c_5497,plain,
    ~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    inference(resolution,[status(thm)],[c_1757,c_5494]) ).

tff(c_5501,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_5497]) ).

tff(c_5503,plain,
    mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal),
    inference(splitRight,[status(thm)],[c_5438]) ).

tff(c_4435,plain,
    ! [V1y_328,V0x_329] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_328),V0x_329))
      | p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_329),V1y_328))
      | ~ mem(V1y_328,ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_329,ty_2Eextreal_2Eextreal) ),
    inference(cnfTransformation,[status(thm)],[f_406]) ).

tff(c_4443,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')))
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
    | ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_4435,c_1694]) ).

tff(c_4449,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')))
    | ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),ty_2Eextreal_2Eextreal) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1628,c_4443]) ).

tff(c_5530,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'))),
    inference(demodulation,[status(thm),theory(equality)],[c_5503,c_4449]) ).

tff(c_25906,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4')),
    inference(demodulation,[status(thm),theory(equality)],[c_25898,c_5530]) ).

tff(c_25912,plain,
    p(c_2Ebool_2EF),
    inference(demodulation,[status(thm),theory(equality)],[c_20249,c_25906]) ).

tff(c_25914,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_40,c_25912]) ).

tff(c_25915,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
    inference(splitRight,[status(thm)],[c_24043]) ).

tff(c_25955,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_25915,c_160]) ).

tff(c_25994,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_25955]) ).

tff(c_26043,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_25994,c_132]) ).

tff(c_26059,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_26043]) ).

tff(c_26070,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_26059,c_1694]) ).

tff(c_26076,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1641,c_26070]) ).

tff(c_26077,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_4') = c_2Ebool_2ET,
    inference(splitRight,[status(thm)],[c_14494]) ).

tff(c_26188,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_3') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_4') )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_26077,c_160]) ).

tff(c_26235,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_3') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_1628,c_1626,c_26188]) ).

tff(c_32233,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_4') = '#skF_4' )
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_26235,c_132]) ).

tff(c_32243,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_4') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1628,c_32233]) ).

tff(c_32610,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_32243,c_3547]) ).

tff(c_36288,plain,
    mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
    inference(demodulation,[status(thm),theory(equality)],[c_33170,c_32610]) ).

tff(c_1788,plain,
    ! [F_175] :
      ( ~ p(ap(F_175,'#skF_5'))
      | ( ap(F_175,'#skF_5') = c_2Ebool_2ET )
      | ~ mem(F_175,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_1762,c_1704]) ).

tff(c_36321,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_36288,c_1788]) ).

tff(c_36344,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
    inference(demodulation,[status(thm),theory(equality)],[c_26369,c_36321]) ).

tff(c_36421,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_36344,c_160]) ).

tff(c_36466,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_36421]) ).

tff(c_37051,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_36466,c_132]) ).

tff(c_37067,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_37051]) ).

tff(c_37078,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_37067,c_1694]) ).

tff(c_37085,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1641,c_37078]) ).

tff(c_37086,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET,
    inference(splitRight,[status(thm)],[c_26353]) ).

tff(c_4433,plain,
    ! [V1y_101] :
      ( ~ mem(V1y_101,ty_2Eextreal_2Eextreal)
      | p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_101),V1y_101)) ),
    inference(factorization,[status(thm),theory(equality)],[c_158]) ).

tff(c_37116,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_37086,c_160]) ).

tff(c_37159,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1626,c_37116]) ).

tff(c_40311,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4' )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_37159,c_132]) ).

tff(c_40321,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1624,c_40311]) ).

tff(c_40356,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_40321,c_3547]) ).

tff(c_41558,plain,
    ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitLeft,[status(thm)],[c_40356]) ).

tff(c_41561,plain,
    ~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    inference(resolution,[status(thm)],[c_1759,c_41558]) ).

tff(c_41565,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_41561]) ).

tff(c_41566,plain,
    mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
    inference(splitRight,[status(thm)],[c_40356]) ).

tff(c_41637,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_41566,c_1878]) ).

tff(c_41648,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4')),
    inference(splitLeft,[status(thm)],[c_41637]) ).

tff(c_41667,plain,
    ~ mem('#skF_4',ty_2Eextreal_2Eextreal),
    inference(resolution,[status(thm)],[c_4433,c_41648]) ).

tff(c_41673,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_41667]) ).

tff(c_41674,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET,
    inference(splitRight,[status(thm)],[c_41637]) ).

tff(c_41646,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_41566,c_1788]) ).

tff(c_41884,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
    inference(splitLeft,[status(thm)],[c_41646]) ).

tff(c_41645,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF ) ),
    inference(resolution,[status(thm)],[c_41566,c_1790]) ).

tff(c_41888,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF,
    inference(negUnitSimplification,[status(thm)],[c_41884,c_41645]) ).

tff(c_41919,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_41888,c_160]) ).

tff(c_41964,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_41919]) ).

tff(c_42213,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_41964,c_130]) ).

tff(c_42223,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_42213]) ).

tff(c_5502,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_4')),
    inference(splitRight,[status(thm)],[c_5438]) ).

tff(c_42232,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4')),
    inference(demodulation,[status(thm),theory(equality)],[c_42223,c_5502]) ).

tff(c_42240,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_41674,c_42232]) ).

tff(c_42241,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
    inference(splitRight,[status(thm)],[c_41646]) ).

tff(c_42272,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_42241,c_160]) ).

tff(c_42317,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_42272]) ).

tff(c_42378,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_42317,c_132]) ).

tff(c_42394,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_42378]) ).

tff(c_42409,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
    inference(demodulation,[status(thm),theory(equality)],[c_42394,c_5502]) ).

tff(c_42416,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_37086,c_42409]) ).

tff(c_42418,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
    inference(splitRight,[status(thm)],[c_1640]) ).

tff(c_42485,plain,
    ! [F_1083,X_1084,B_1085,A_1086] :
      ( mem(ap(F_1083,X_1084),B_1085)
      | ~ mem(X_1084,A_1086)
      | ~ mem(F_1083,arr(A_1086,B_1085)) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_42526,plain,
    ! [F_1083,B_1085] :
      ( mem(ap(F_1083,'#skF_5'),B_1085)
      | ~ mem(F_1083,arr(ty_2Eextreal_2Eextreal,B_1085)) ),
    inference(resolution,[status(thm)],[c_1624,c_42485]) ).

tff(c_42648,plain,
    ! [F_1095,B_1096] :
      ( mem(ap(F_1095,'#skF_3'),B_1096)
      | ~ mem(F_1095,arr(ty_2Eextreal_2Eextreal,B_1096)) ),
    inference(resolution,[status(thm)],[c_1628,c_42485]) ).

tff(c_42462,plain,
    ! [R_1077,Q_1078] :
      ( ~ p(R_1077)
      | ~ p(Q_1078)
      | ( R_1077 = Q_1078 )
      | ~ mem(R_1077,bool)
      | ~ mem(Q_1078,bool) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_42466,plain,
    ! [Q_1078] :
      ( ~ p(c_2Ebool_2ET)
      | ~ p(Q_1078)
      | ( c_2Ebool_2ET = Q_1078 )
      | ~ mem(Q_1078,bool) ),
    inference(resolution,[status(thm)],[c_26,c_42462]) ).

tff(c_42470,plain,
    ! [Q_1078] :
      ( ~ p(Q_1078)
      | ( c_2Ebool_2ET = Q_1078 )
      | ~ mem(Q_1078,bool) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_42466]) ).

tff(c_42831,plain,
    ! [F_1119] :
      ( ~ p(ap(F_1119,'#skF_3'))
      | ( ap(F_1119,'#skF_3') = c_2Ebool_2ET )
      | ~ mem(F_1119,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_42648,c_42470]) ).

tff(c_53809,plain,
    ! [F_1456] :
      ( ~ p(ap(ap(F_1456,'#skF_5'),'#skF_3'))
      | ( ap(ap(F_1456,'#skF_5'),'#skF_3') = c_2Ebool_2ET )
      | ~ mem(F_1456,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_42526,c_42831]) ).

tff(c_53880,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_32,c_53809]) ).

tff(c_53902,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3') = c_2Ebool_2ET,
    inference(demodulation,[status(thm),theory(equality)],[c_1641,c_53880]) ).

tff(c_53934,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_3'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_3') )
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_53902,c_160]) ).

tff(c_53977,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_3'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_3'),
    inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1628,c_53934]) ).

tff(c_54019,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_3') = '#skF_3' )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_53977,c_132]) ).

tff(c_54047,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_3') = '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1628,c_1624,c_54019]) ).

tff(c_44847,plain,
    ! [F_1237,F_1238,B_1239,B_1240] :
      ( mem(ap(F_1237,ap(F_1238,'#skF_3')),B_1239)
      | ~ mem(F_1237,arr(B_1240,B_1239))
      | ~ mem(F_1238,arr(ty_2Eextreal_2Eextreal,B_1240)) ),
    inference(resolution,[status(thm)],[c_42648,c_8]) ).

tff(c_44922,plain,
    ! [F_1238] :
      ( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_1238,'#skF_3')),arr(ty_2Eextreal_2Eextreal,bool))
      | ~ mem(F_1238,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(resolution,[status(thm)],[c_32,c_44847]) ).

tff(c_54073,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),arr(ty_2Eextreal_2Eextreal,bool))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_54047,c_44922]) ).

tff(c_54258,plain,
    ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitLeft,[status(thm)],[c_54073]) ).

tff(c_54355,plain,
    ~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    inference(resolution,[status(thm)],[c_42526,c_54258]) ).

tff(c_54359,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_54355]) ).

tff(c_54361,plain,
    mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitRight,[status(thm)],[c_54073]) ).

tff(c_46916,plain,
    ! [V0x_1324,V2z_1325,V1y_1326] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),V2z_1325))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_1326),V2z_1325))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),V1y_1326))
      | ~ mem(V2z_1325,ty_2Eextreal_2Eextreal)
      | ~ mem(V1y_1326,ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_1324,ty_2Eextreal_2Eextreal) ),
    inference(cnfTransformation,[status(thm)],[f_397]) ).

tff(c_50968,plain,
    ! [V0x_1409,V0x_1410,V1y_1411] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1409),V0x_1410))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1409),V1y_1411))
      | ~ mem(V0x_1409,ty_2Eextreal_2Eextreal)
      | p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1410),V1y_1411))
      | ~ mem(V1y_1411,ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_1410,ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_158,c_46916]) ).

tff(c_50978,plain,
    ! [V0x_1410] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),V0x_1410))
      | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
      | p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1410),'#skF_3'))
      | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_1410,ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_1641,c_50968]) ).

tff(c_50987,plain,
    ! [V0x_1410] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),V0x_1410))
      | p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1410),'#skF_3'))
      | ~ mem(V0x_1410,ty_2Eextreal_2Eextreal) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1628,c_1624,c_50978]) ).

tff(c_42618,plain,
    ! [F_1093,B_1094] :
      ( mem(ap(F_1093,'#skF_4'),B_1094)
      | ~ mem(F_1093,arr(ty_2Eextreal_2Eextreal,B_1094)) ),
    inference(resolution,[status(thm)],[c_1626,c_42485]) ).

tff(c_42804,plain,
    ! [F_1115] :
      ( ~ p(ap(F_1115,'#skF_4'))
      | ( ap(F_1115,'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_1115,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_42618,c_42470]) ).

tff(c_54743,plain,
    ! [F_1470] :
      ( ~ p(ap(ap(F_1470,'#skF_5'),'#skF_4'))
      | ( ap(ap(F_1470,'#skF_5'),'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_1470,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_42526,c_42804]) ).

tff(c_54836,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_32,c_54743]) ).

tff(c_54847,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
    inference(splitLeft,[status(thm)],[c_54836]) ).

tff(c_54850,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_50987,c_54847]) ).

tff(c_54859,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_54850]) ).

tff(c_54861,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42418,c_54859]) ).

tff(c_54862,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4') = c_2Ebool_2ET,
    inference(splitRight,[status(thm)],[c_54836]) ).

tff(c_54892,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_54862,c_160]) ).

tff(c_54936,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_5') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1626,c_54892]) ).

tff(c_55290,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4' )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_54936,c_132]) ).

tff(c_55318,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),'#skF_4') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1624,c_55290]) ).

tff(c_43411,plain,
    ! [F_1174,F_1175,B_1176,B_1177] :
      ( mem(ap(F_1174,ap(F_1175,'#skF_4')),B_1176)
      | ~ mem(F_1174,arr(B_1177,B_1176))
      | ~ mem(F_1175,arr(ty_2Eextreal_2Eextreal,B_1177)) ),
    inference(resolution,[status(thm)],[c_42618,c_8]) ).

tff(c_43455,plain,
    ! [F_1175] :
      ( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_1175,'#skF_4')),arr(ty_2Eextreal_2Eextreal,bool))
      | ~ mem(F_1175,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(resolution,[status(thm)],[c_32,c_43411]) ).

tff(c_55347,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_55318,c_43455]) ).

tff(c_55366,plain,
    mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
    inference(demodulation,[status(thm),theory(equality)],[c_54361,c_55347]) ).

tff(c_42439,plain,
    ! [Q_1074,R_1075] :
      ( p(Q_1074)
      | p(R_1075)
      | ( R_1075 = Q_1074 )
      | ~ mem(R_1075,bool)
      | ~ mem(Q_1074,bool) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_42441,plain,
    ! [Q_1074] :
      ( p(Q_1074)
      | p(c_2Ebool_2EF)
      | ( c_2Ebool_2EF = Q_1074 )
      | ~ mem(Q_1074,bool) ),
    inference(resolution,[status(thm)],[c_38,c_42439]) ).

tff(c_42446,plain,
    ! [Q_1074] :
      ( p(Q_1074)
      | ( c_2Ebool_2EF = Q_1074 )
      | ~ mem(Q_1074,bool) ),
    inference(negUnitSimplification,[status(thm)],[c_40,c_42441]) ).

tff(c_42676,plain,
    ! [F_1095] :
      ( p(ap(F_1095,'#skF_3'))
      | ( ap(F_1095,'#skF_3') = c_2Ebool_2EF )
      | ~ mem(F_1095,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_42648,c_42446]) ).

tff(c_55559,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2EF ) ),
    inference(resolution,[status(thm)],[c_55366,c_42676]) ).

tff(c_55578,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2EF,
    inference(negUnitSimplification,[status(thm)],[c_42418,c_55559]) ).

tff(c_42588,plain,
    ! [F_1091,B_1092] :
      ( mem(ap(F_1091,'#skF_5'),B_1092)
      | ~ mem(F_1091,arr(ty_2Eextreal_2Eextreal,B_1092)) ),
    inference(resolution,[status(thm)],[c_1624,c_42485]) ).

tff(c_42616,plain,
    ! [F_1091] :
      ( p(ap(F_1091,'#skF_5'))
      | ( ap(F_1091,'#skF_5') = c_2Ebool_2EF )
      | ~ mem(F_1091,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_42588,c_42446]) ).

tff(c_55573,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF ) ),
    inference(resolution,[status(thm)],[c_55366,c_42616]) ).

tff(c_55896,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF,
    inference(splitLeft,[status(thm)],[c_55573]) ).

tff(c_55925,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_55896,c_160]) ).

tff(c_55971,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_55925]) ).

tff(c_57292,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_55971,c_130]) ).

tff(c_57320,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_57292]) ).

tff(c_42417,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3')),
    inference(splitRight,[status(thm)],[c_1640]) ).

tff(c_57328,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_57320,c_42417]) ).

tff(c_57330,plain,
    p(c_2Ebool_2EF),
    inference(demodulation,[status(thm),theory(equality)],[c_55578,c_57328]) ).

tff(c_57332,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_40,c_57330]) ).

tff(c_57333,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
    inference(splitRight,[status(thm)],[c_55573]) ).

tff(c_46926,plain,
    ! [V0x_1324] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),'#skF_3'))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),'#skF_5'))
      | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
      | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_1324,ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_1641,c_46916]) ).

tff(c_46935,plain,
    ! [V0x_1324] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),'#skF_3'))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1324),'#skF_5'))
      | ~ mem(V0x_1324,ty_2Eextreal_2Eextreal) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1624,c_1628,c_46926]) ).

tff(c_57339,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_57333,c_46935]) ).

tff(c_57347,plain,
    p(c_2Ebool_2EF),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_55578,c_57339]) ).

tff(c_57349,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_40,c_57347]) ).

tff(c_57351,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
    inference(splitRight,[status(thm)],[c_1636]) ).

tff(c_57428,plain,
    ! [F_1523,X_1524,B_1525,A_1526] :
      ( mem(ap(F_1523,X_1524),B_1525)
      | ~ mem(X_1524,A_1526)
      | ~ mem(F_1523,arr(A_1526,B_1525)) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_57470,plain,
    ! [F_1523,B_1525] :
      ( mem(ap(F_1523,'#skF_3'),B_1525)
      | ~ mem(F_1523,arr(ty_2Eextreal_2Eextreal,B_1525)) ),
    inference(resolution,[status(thm)],[c_1628,c_57428]) ).

tff(c_60262,plain,
    ! [V1y_1683,V0x_1684] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_1683),V0x_1684))
      | p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1684),V1y_1683))
      | ~ mem(V1y_1683,ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_1684,ty_2Eextreal_2Eextreal) ),
    inference(cnfTransformation,[status(thm)],[f_406]) ).

tff(c_60266,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5'))
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_60262,c_57351]) ).

tff(c_60273,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_1628,c_1624,c_60266]) ).

tff(c_57471,plain,
    ! [F_1527,B_1528] :
      ( mem(ap(F_1527,'#skF_5'),B_1528)
      | ~ mem(F_1527,arr(ty_2Eextreal_2Eextreal,B_1528)) ),
    inference(resolution,[status(thm)],[c_1624,c_57428]) ).

tff(c_57382,plain,
    ! [R_1514,Q_1515] :
      ( ~ p(R_1514)
      | ~ p(Q_1515)
      | ( R_1514 = Q_1515 )
      | ~ mem(R_1514,bool)
      | ~ mem(Q_1515,bool) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_57386,plain,
    ! [Q_1515] :
      ( ~ p(c_2Ebool_2ET)
      | ~ p(Q_1515)
      | ( c_2Ebool_2ET = Q_1515 )
      | ~ mem(Q_1515,bool) ),
    inference(resolution,[status(thm)],[c_26,c_57382]) ).

tff(c_57390,plain,
    ! [Q_1515] :
      ( ~ p(Q_1515)
      | ( c_2Ebool_2ET = Q_1515 )
      | ~ mem(Q_1515,bool) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_57386]) ).

tff(c_57744,plain,
    ! [F_1558] :
      ( ~ p(ap(F_1558,'#skF_5'))
      | ( ap(F_1558,'#skF_5') = c_2Ebool_2ET )
      | ~ mem(F_1558,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_57471,c_57390]) ).

tff(c_68861,plain,
    ! [F_1879] :
      ( ~ p(ap(ap(F_1879,'#skF_3'),'#skF_5'))
      | ( ap(ap(F_1879,'#skF_3'),'#skF_5') = c_2Ebool_2ET )
      | ~ mem(F_1879,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_57470,c_57744]) ).

tff(c_68932,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_32,c_68861]) ).

tff(c_68956,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_3'),'#skF_5') = c_2Ebool_2ET,
    inference(demodulation,[status(thm),theory(equality)],[c_60273,c_68932]) ).

tff(c_68998,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_3') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_68956,c_160]) ).

tff(c_69043,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_3') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1628,c_1624,c_68998]) ).

tff(c_69099,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_5') = '#skF_5' )
    | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_69043,c_132]) ).

tff(c_69109,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),'#skF_5') = '#skF_5',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1628,c_69099]) ).

tff(c_59432,plain,
    ! [F_1653,F_1654,B_1655,B_1656] :
      ( mem(ap(F_1653,ap(F_1654,'#skF_5')),B_1655)
      | ~ mem(F_1653,arr(B_1656,B_1655))
      | ~ mem(F_1654,arr(ty_2Eextreal_2Eextreal,B_1656)) ),
    inference(resolution,[status(thm)],[c_57471,c_8]) ).

tff(c_59493,plain,
    ! [F_1654] :
      ( mem(ap(c_2Eextreal_2Eextreal__max,ap(F_1654,'#skF_5')),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
      | ~ mem(F_1654,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(resolution,[status(thm)],[c_36,c_59432]) ).

tff(c_69144,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__max,'#skF_5'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_69109,c_59493]) ).

tff(c_69320,plain,
    ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitLeft,[status(thm)],[c_69144]) ).

tff(c_69404,plain,
    ~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    inference(resolution,[status(thm)],[c_57470,c_69320]) ).

tff(c_69408,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_69404]) ).

tff(c_69410,plain,
    mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitRight,[status(thm)],[c_69144]) ).

tff(c_59495,plain,
    ! [F_1654] :
      ( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_1654,'#skF_5')),arr(ty_2Eextreal_2Eextreal,bool))
      | ~ mem(F_1654,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(resolution,[status(thm)],[c_32,c_59432]) ).

tff(c_69135,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),arr(ty_2Eextreal_2Eextreal,bool))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_3'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_69109,c_59495]) ).

tff(c_69453,plain,
    mem(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),arr(ty_2Eextreal_2Eextreal,bool)),
    inference(demodulation,[status(thm),theory(equality)],[c_69410,c_69135]) ).

tff(c_57591,plain,
    ! [F_1535,B_1536] :
      ( mem(ap(F_1535,'#skF_3'),B_1536)
      | ~ mem(F_1535,arr(ty_2Eextreal_2Eextreal,B_1536)) ),
    inference(resolution,[status(thm)],[c_1628,c_57428]) ).

tff(c_57405,plain,
    ! [Q_1520,R_1521] :
      ( p(Q_1520)
      | p(R_1521)
      | ( R_1521 = Q_1520 )
      | ~ mem(R_1521,bool)
      | ~ mem(Q_1520,bool) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_57407,plain,
    ! [Q_1520] :
      ( p(Q_1520)
      | p(c_2Ebool_2EF)
      | ( c_2Ebool_2EF = Q_1520 )
      | ~ mem(Q_1520,bool) ),
    inference(resolution,[status(thm)],[c_38,c_57405]) ).

tff(c_57412,plain,
    ! [Q_1520] :
      ( p(Q_1520)
      | ( c_2Ebool_2EF = Q_1520 )
      | ~ mem(Q_1520,bool) ),
    inference(negUnitSimplification,[status(thm)],[c_40,c_57407]) ).

tff(c_57617,plain,
    ! [F_1535] :
      ( p(ap(F_1535,'#skF_3'))
      | ( ap(F_1535,'#skF_3') = c_2Ebool_2EF )
      | ~ mem(F_1535,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_57591,c_57412]) ).

tff(c_69469,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3') = c_2Ebool_2EF ) ),
    inference(resolution,[status(thm)],[c_69453,c_57617]) ).

tff(c_69492,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3') = c_2Ebool_2EF,
    inference(negUnitSimplification,[status(thm)],[c_57351,c_69469]) ).

tff(c_57352,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
    inference(splitLeft,[status(thm)],[c_1640]) ).

tff(c_61310,plain,
    ! [V0x_1739,V2z_1740,V1y_1741] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1739),V2z_1740))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_1741),V2z_1740))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1739),V1y_1741))
      | ~ mem(V2z_1740,ty_2Eextreal_2Eextreal)
      | ~ mem(V1y_1741,ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_1739,ty_2Eextreal_2Eextreal) ),
    inference(cnfTransformation,[status(thm)],[f_397]) ).

tff(c_61322,plain,
    ! [V0x_1739] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1739),'#skF_3'))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1739),'#skF_4'))
      | ~ mem('#skF_3',ty_2Eextreal_2Eextreal)
      | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
      | ~ mem(V0x_1739,ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_57352,c_61310]) ).

tff(c_61550,plain,
    ! [V0x_1746] :
      ( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1746),'#skF_3'))
      | ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x_1746),'#skF_4'))
      | ~ mem(V0x_1746,ty_2Eextreal_2Eextreal) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1628,c_61322]) ).

tff(c_61555,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4'))
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_61550,c_57351]) ).

tff(c_61561,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_4')),
    inference(demodulation,[status(thm),theory(equality)],[c_1624,c_61555]) ).

tff(c_61564,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(resolution,[status(thm)],[c_158,c_61561]) ).

tff(c_61570,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_61564]) ).

tff(c_57467,plain,
    ! [F_1523,B_1525] :
      ( mem(ap(F_1523,'#skF_4'),B_1525)
      | ~ mem(F_1523,arr(ty_2Eextreal_2Eextreal,B_1525)) ),
    inference(resolution,[status(thm)],[c_1626,c_57428]) ).

tff(c_57561,plain,
    ! [F_1533,B_1534] :
      ( mem(ap(F_1533,'#skF_4'),B_1534)
      | ~ mem(F_1533,arr(ty_2Eextreal_2Eextreal,B_1534)) ),
    inference(resolution,[status(thm)],[c_1626,c_57428]) ).

tff(c_57863,plain,
    ! [F_1563] :
      ( p(ap(F_1563,'#skF_4'))
      | ( ap(F_1563,'#skF_4') = c_2Ebool_2EF )
      | ~ mem(F_1563,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_57561,c_57412]) ).

tff(c_74887,plain,
    ! [F_1980] :
      ( p(ap(ap(F_1980,'#skF_4'),'#skF_4'))
      | ( ap(ap(F_1980,'#skF_4'),'#skF_4') = c_2Ebool_2EF )
      | ~ mem(F_1980,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_57467,c_57863]) ).

tff(c_75007,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2EF ) ),
    inference(resolution,[status(thm)],[c_32,c_74887]) ).

tff(c_75008,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2EF,
    inference(splitLeft,[status(thm)],[c_75007]) ).

tff(c_60260,plain,
    ! [V1y_101] :
      ( ~ mem(V1y_101,ty_2Eextreal_2Eextreal)
      | p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_101),V1y_101)) ),
    inference(factorization,[status(thm),theory(equality)],[c_158]) ).

tff(c_75051,plain,
    ( ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | p(c_2Ebool_2EF) ),
    inference(superposition,[status(thm),theory(equality)],[c_75008,c_60260]) ).

tff(c_75094,plain,
    p(c_2Ebool_2EF),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_75051]) ).

tff(c_75096,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_40,c_75094]) ).

tff(c_75097,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4')),
    inference(splitRight,[status(thm)],[c_75007]) ).

tff(c_57977,plain,
    ! [F_1575] :
      ( ~ p(ap(F_1575,'#skF_4'))
      | ( ap(F_1575,'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_1575,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_57561,c_57390]) ).

tff(c_75472,plain,
    ! [F_1990] :
      ( ~ p(ap(ap(F_1990,'#skF_4'),'#skF_4'))
      | ( ap(ap(F_1990,'#skF_4'),'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_1990,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_57467,c_57977]) ).

tff(c_75563,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_32,c_75472]) ).

tff(c_75594,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET,
    inference(demodulation,[status(thm),theory(equality)],[c_75097,c_75563]) ).

tff(c_75637,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_75594,c_160]) ).

tff(c_75681,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1626,c_75637]) ).

tff(c_75833,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') = '#skF_4' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_75681,c_132]) ).

tff(c_75843,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1626,c_75833]) ).

tff(c_58459,plain,
    ! [F_1620,F_1621,B_1622,B_1623] :
      ( mem(ap(F_1620,ap(F_1621,'#skF_4')),B_1622)
      | ~ mem(F_1620,arr(B_1623,B_1622))
      | ~ mem(F_1621,arr(ty_2Eextreal_2Eextreal,B_1623)) ),
    inference(resolution,[status(thm)],[c_57561,c_8]) ).

tff(c_58506,plain,
    ! [F_1621] :
      ( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_1621,'#skF_4')),arr(ty_2Eextreal_2Eextreal,bool))
      | ~ mem(F_1621,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(resolution,[status(thm)],[c_32,c_58459]) ).

tff(c_75922,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_75843,c_58506]) ).

tff(c_76069,plain,
    ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitLeft,[status(thm)],[c_75922]) ).

tff(c_76072,plain,
    ~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    inference(resolution,[status(thm)],[c_57467,c_76069]) ).

tff(c_76076,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_76072]) ).

tff(c_76077,plain,
    mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
    inference(splitRight,[status(thm)],[c_75922]) ).

tff(c_57499,plain,
    ! [F_1527] :
      ( ~ p(ap(F_1527,'#skF_5'))
      | ( ap(F_1527,'#skF_5') = c_2Ebool_2ET )
      | ~ mem(F_1527,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_57471,c_57390]) ).

tff(c_76103,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_76077,c_57499]) ).

tff(c_76129,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
    inference(demodulation,[status(thm),theory(equality)],[c_61570,c_76103]) ).

tff(c_76203,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_76129,c_160]) ).

tff(c_76252,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_76203]) ).

tff(c_76546,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_76252,c_132]) ).

tff(c_76556,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_76546]) ).

tff(c_57350,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5')),'#skF_3')),
    inference(splitRight,[status(thm)],[c_1636]) ).

tff(c_76564,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_76556,c_57350]) ).

tff(c_76566,plain,
    p(c_2Ebool_2EF),
    inference(demodulation,[status(thm),theory(equality)],[c_69492,c_76564]) ).

tff(c_76568,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_40,c_76566]) ).

tff(c_76570,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
    inference(splitRight,[status(thm)],[c_1640]) ).

tff(c_76645,plain,
    ! [F_2032,X_2033,B_2034,A_2035] :
      ( mem(ap(F_2032,X_2033),B_2034)
      | ~ mem(X_2033,A_2035)
      | ~ mem(F_2032,arr(A_2035,B_2034)) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_76684,plain,
    ! [F_2032,B_2034] :
      ( mem(ap(F_2032,'#skF_4'),B_2034)
      | ~ mem(F_2032,arr(ty_2Eextreal_2Eextreal,B_2034)) ),
    inference(resolution,[status(thm)],[c_1626,c_76645]) ).

tff(c_79994,plain,
    ! [V1y_101] :
      ( ~ mem(V1y_101,ty_2Eextreal_2Eextreal)
      | p(ap(ap(c_2Eextreal_2Eextreal__le,V1y_101),V1y_101)) ),
    inference(factorization,[status(thm),theory(equality)],[c_158]) ).

tff(c_76809,plain,
    ! [F_2046,B_2047] :
      ( mem(ap(F_2046,'#skF_4'),B_2047)
      | ~ mem(F_2046,arr(ty_2Eextreal_2Eextreal,B_2047)) ),
    inference(resolution,[status(thm)],[c_1626,c_76645]) ).

tff(c_76599,plain,
    ! [R_2023,Q_2024] :
      ( ~ p(R_2023)
      | ~ p(Q_2024)
      | ( R_2023 = Q_2024 )
      | ~ mem(R_2023,bool)
      | ~ mem(Q_2024,bool) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_76603,plain,
    ! [Q_2024] :
      ( ~ p(c_2Ebool_2ET)
      | ~ p(Q_2024)
      | ( c_2Ebool_2ET = Q_2024 )
      | ~ mem(Q_2024,bool) ),
    inference(resolution,[status(thm)],[c_26,c_76599]) ).

tff(c_76607,plain,
    ! [Q_2024] :
      ( ~ p(Q_2024)
      | ( c_2Ebool_2ET = Q_2024 )
      | ~ mem(Q_2024,bool) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_76603]) ).

tff(c_77046,plain,
    ! [F_2074] :
      ( ~ p(ap(F_2074,'#skF_4'))
      | ( ap(F_2074,'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_2074,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_76809,c_76607]) ).

tff(c_87882,plain,
    ! [F_2400] :
      ( ~ p(ap(ap(F_2400,'#skF_4'),'#skF_4'))
      | ( ap(ap(F_2400,'#skF_4'),'#skF_4') = c_2Ebool_2ET )
      | ~ mem(F_2400,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
    inference(resolution,[status(thm)],[c_76684,c_77046]) ).

tff(c_87975,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_32,c_87882]) ).

tff(c_87976,plain,
    ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4')),
    inference(splitLeft,[status(thm)],[c_87975]) ).

tff(c_87979,plain,
    ~ mem('#skF_4',ty_2Eextreal_2Eextreal),
    inference(resolution,[status(thm)],[c_79994,c_87976]) ).

tff(c_87985,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_87979]) ).

tff(c_87986,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_4') = c_2Ebool_2ET,
    inference(splitRight,[status(thm)],[c_87975]) ).

tff(c_88013,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_87986,c_160]) ).

tff(c_88057,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_4'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1626,c_88013]) ).

tff(c_88131,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') = '#skF_4' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_88057,c_132]) ).

tff(c_88141,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_4') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1626,c_1626,c_88131]) ).

tff(c_79430,plain,
    ! [F_2199,F_2200,B_2201,B_2202] :
      ( mem(ap(F_2199,ap(F_2200,'#skF_4')),B_2201)
      | ~ mem(F_2199,arr(B_2202,B_2201))
      | ~ mem(F_2200,arr(ty_2Eextreal_2Eextreal,B_2202)) ),
    inference(resolution,[status(thm)],[c_76809,c_8]) ).

tff(c_79508,plain,
    ! [F_2200] :
      ( mem(ap(c_2Eextreal_2Eextreal__le,ap(F_2200,'#skF_4')),arr(ty_2Eextreal_2Eextreal,bool))
      | ~ mem(F_2200,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(resolution,[status(thm)],[c_32,c_79430]) ).

tff(c_88173,plain,
    ( mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool))
    | ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)) ),
    inference(superposition,[status(thm),theory(equality)],[c_88141,c_79508]) ).

tff(c_89048,plain,
    ~ mem(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal)),
    inference(splitLeft,[status(thm)],[c_88173]) ).

tff(c_89125,plain,
    ~ mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
    inference(resolution,[status(thm)],[c_76684,c_89048]) ).

tff(c_89129,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_89125]) ).

tff(c_89130,plain,
    mem(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),arr(ty_2Eextreal_2Eextreal,bool)),
    inference(splitRight,[status(thm)],[c_88173]) ).

tff(c_76779,plain,
    ! [F_2044,B_2045] :
      ( mem(ap(F_2044,'#skF_3'),B_2045)
      | ~ mem(F_2044,arr(ty_2Eextreal_2Eextreal,B_2045)) ),
    inference(resolution,[status(thm)],[c_1628,c_76645]) ).

tff(c_76621,plain,
    ! [Q_2028,R_2029] :
      ( p(Q_2028)
      | p(R_2029)
      | ( R_2029 = Q_2028 )
      | ~ mem(R_2029,bool)
      | ~ mem(Q_2028,bool) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_76623,plain,
    ! [Q_2028] :
      ( p(Q_2028)
      | p(c_2Ebool_2EF)
      | ( c_2Ebool_2EF = Q_2028 )
      | ~ mem(Q_2028,bool) ),
    inference(resolution,[status(thm)],[c_38,c_76621]) ).

tff(c_76628,plain,
    ! [Q_2028] :
      ( p(Q_2028)
      | ( c_2Ebool_2EF = Q_2028 )
      | ~ mem(Q_2028,bool) ),
    inference(negUnitSimplification,[status(thm)],[c_40,c_76623]) ).

tff(c_76805,plain,
    ! [F_2044] :
      ( p(ap(F_2044,'#skF_3'))
      | ( ap(F_2044,'#skF_3') = c_2Ebool_2EF )
      | ~ mem(F_2044,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_76779,c_76628]) ).

tff(c_89159,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2EF ) ),
    inference(resolution,[status(thm)],[c_89130,c_76805]) ).

tff(c_89180,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3') = c_2Ebool_2EF,
    inference(negUnitSimplification,[status(thm)],[c_76570,c_89159]) ).

tff(c_76748,plain,
    ! [F_2040,B_2041] :
      ( mem(ap(F_2040,'#skF_5'),B_2041)
      | ~ mem(F_2040,arr(ty_2Eextreal_2Eextreal,B_2041)) ),
    inference(resolution,[status(thm)],[c_1624,c_76645]) ).

tff(c_76774,plain,
    ! [F_2040] :
      ( p(ap(F_2040,'#skF_5'))
      | ( ap(F_2040,'#skF_5') = c_2Ebool_2EF )
      | ~ mem(F_2040,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_76748,c_76628]) ).

tff(c_89177,plain,
    ( p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF ) ),
    inference(resolution,[status(thm)],[c_89130,c_76774]) ).

tff(c_89303,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2EF,
    inference(splitLeft,[status(thm)],[c_89177]) ).

tff(c_89329,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_89303,c_160]) ).

tff(c_89372,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_89329]) ).

tff(c_89662,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_89372,c_130]) ).

tff(c_89672,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_89662]) ).

tff(c_89680,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_89672,c_57350]) ).

tff(c_89682,plain,
    p(c_2Ebool_2EF),
    inference(demodulation,[status(thm),theory(equality)],[c_89180,c_89680]) ).

tff(c_89684,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_40,c_89682]) ).

tff(c_89685,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5')),
    inference(splitRight,[status(thm)],[c_89177]) ).

tff(c_76776,plain,
    ! [F_2040] :
      ( ~ p(ap(F_2040,'#skF_5'))
      | ( ap(F_2040,'#skF_5') = c_2Ebool_2ET )
      | ~ mem(F_2040,arr(ty_2Eextreal_2Eextreal,bool)) ),
    inference(resolution,[status(thm)],[c_76748,c_76607]) ).

tff(c_89172,plain,
    ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5'))
    | ( ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET ) ),
    inference(resolution,[status(thm)],[c_89130,c_76776]) ).

tff(c_89772,plain,
    ap(ap(c_2Eextreal_2Eextreal__le,'#skF_4'),'#skF_5') = c_2Ebool_2ET,
    inference(demodulation,[status(thm),theory(equality)],[c_89685,c_89172]) ).

tff(c_89801,plain,
    ( ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') )
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_89772,c_160]) ).

tff(c_89844,plain,
    ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),'#skF_5'),'#skF_4') = ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_1626,c_1624,c_89801]) ).

tff(c_90058,plain,
    ( ( ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5' )
    | ~ mem('#skF_4',ty_2Eextreal_2Eextreal)
    | ~ mem('#skF_5',ty_2Eextreal_2Eextreal)
    | ~ ne(ty_2Eextreal_2Eextreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_89844,c_132]) ).

tff(c_90068,plain,
    ap(ap(c_2Eextreal_2Eextreal__max,'#skF_4'),'#skF_5') = '#skF_5',
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_1624,c_1626,c_90058]) ).

tff(c_90076,plain,
    p(ap(ap(c_2Eextreal_2Eextreal__le,'#skF_5'),'#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_90068,c_57350]) ).

tff(c_90079,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_57351,c_90076]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ITP021+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.17/0.35  % Computer : n013.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Thu Aug  3 18:56:17 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 28.03/13.95  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.03/13.98  
% 28.03/13.98  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.20/14.04  
% 28.20/14.04  Inference rules
% 28.20/14.04  ----------------------
% 28.20/14.04  #Ref     : 4
% 28.20/14.04  #Sup     : 20604
% 28.20/14.04  #Fact    : 12
% 28.20/14.04  #Define  : 0
% 28.20/14.04  #Split   : 248
% 28.20/14.04  #Chain   : 0
% 28.20/14.04  #Close   : 0
% 28.20/14.04  
% 28.20/14.04  Ordering : KBO
% 28.20/14.04  
% 28.20/14.04  Simplification rules
% 28.20/14.04  ----------------------
% 28.20/14.04  #Subsume      : 1616
% 28.20/14.04  #Demod        : 9481
% 28.20/14.04  #Tautology    : 4060
% 28.20/14.04  #SimpNegUnit  : 350
% 28.20/14.04  #BackRed      : 291
% 28.20/14.04  
% 28.20/14.04  #Partial instantiations: 0
% 28.20/14.04  #Strategies tried      : 1
% 28.20/14.04  
% 28.20/14.04  Timing (in seconds)
% 28.20/14.04  ----------------------
% 28.20/14.04  Preprocessing        : 0.90
% 28.20/14.04  Parsing              : 0.26
% 28.20/14.04  CNF conversion       : 0.09
% 28.20/14.04  Main loop            : 12.01
% 28.20/14.04  Inferencing          : 3.24
% 28.20/14.04  Reduction            : 4.50
% 28.20/14.04  Demodulation         : 3.39
% 28.20/14.04  BG Simplification    : 0.29
% 28.20/14.04  Subsumption          : 3.09
% 28.20/14.04  Abstraction          : 0.23
% 28.20/14.04  MUC search           : 0.00
% 28.20/14.04  Cooper               : 0.00
% 28.20/14.05  Total                : 13.02
% 28.20/14.05  Index Insertion      : 0.00
% 28.20/14.05  Index Deletion       : 0.00
% 28.20/14.05  Index Matching       : 0.00
% 28.20/14.05  BG Taut test         : 0.00
%------------------------------------------------------------------------------