iProver---3.9.4.THM-CRf.s

%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : ITP011+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 01:47:40 PM UTC 2026

% Result   : Theorem 149.62s 28.77s
% Output   : CNFRefutation 149.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   46
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  294 (  41 unt;   0 def)
%            Number of atoms       : 1124 ( 893 equ)
%            Maximal formula atoms :   33 (   3 avg)
%            Number of connectives : 1162 ( 332   ~; 705   |; 107   &)
%                                         (  12 <=>;   5  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   26 (   6 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;   9 con; 0-5 aty)
%            Number of variables   :  550 (   0 sgn 538   !;  12   ?; 344   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( ( p(s(tyop_2Emin_2Ebool,X0))
      <=> p(s(tyop_2Emin_2Ebool,X1)) )
     => s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).

fof(f3,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).

fof(f4,axiom,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).

fof(f5,axiom,
    ! [X0] :
      ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).

fof(f43,axiom,
    ! [X0] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      <=> ~ p(s(tyop_2Emin_2Ebool,X0)) )
      & ( s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0)
      <=> ~ p(s(tyop_2Emin_2Ebool,X0)) )
      & ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      <=> p(s(tyop_2Emin_2Ebool,X0)) )
      & ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0)
      <=> p(s(tyop_2Emin_2Ebool,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).

fof(f44,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( ! [X27] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(X0),X27))))) = s(tyop_2Eoption_2Eoption(X0),X27)
      & s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
      & ! [X26] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
      & ! [X24,X25] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X25))))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(X0,X25)))))
      & ! [X21,X22,X23] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X21))),s(X1,X22),s(tyop_2Emin_2Efun(X0,X1),X23))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X23),s(X0,X21)))
      & ! [X19,X20] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(X1,X19),s(tyop_2Emin_2Efun(X0,X1),X20))) = s(X1,X19)
      & ! [X18] :
          ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X18))))
         => s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X18),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X18) )
      & ! [X17] :
          ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X17))))
         => s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X17),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X17))))) )
      & ! [X16] :
          ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X16))))
         => s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X16),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,X4) )
      & ! [X15] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X15)
      & ! [X14] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X14),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X14)
      & ! [X13] :
          ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))
         => s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))) = s(tyop_2Eoption_2Eoption(X0),X13) )
      & ! [X12] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12))))
        <=> s(tyop_2Eoption_2Eoption(X0),X12) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      & ! [X11] :
          ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11))))
        <=> s(tyop_2Eoption_2Eoption(X0),X11) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      & s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      & ! [X10] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X10))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      & ! [X9] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X9))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
      & ! [X8] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X8)))
      & ! [X7] : s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7))))) = s(X0,X7)
      & ! [X5,X6] :
          ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X6)))
        <=> s(X0,X5) = s(X0,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES) ).

fof(f45,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
    <=> ( ? [X5,X6] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6))))
            & s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
            & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) )
        | ( s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
          & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2EOPTREL__def) ).

fof(f46,conjecture,
    ! [X0,X1,X2,X3] :
      ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(X0,X2))),s(X0,X1)))
      & s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      & s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      & s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient__option_2EOPTION__REL__def) ).

fof(f47,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(X0,X2))),s(X0,X1)))
        & s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
        & s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
        & s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
    inference(negated_conjecture,[status(cth)],[f46]) ).

fof(f49,plain,
    ? [X0,X1,X2,X3] :
      ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(X0,X2))),s(X0,X1)))
      | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1)))))
      | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X2))),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)))
      | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ( p(s(tyop_2Emin_2Ebool,X0))
      <~> p(s(tyop_2Emin_2Ebool,X1)) )
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f55,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ! [X27] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(X0),X27))))) = s(tyop_2Eoption_2Eoption(X0),X27)
      & s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
      & ! [X26] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
      & ! [X24,X25] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X25))))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(X0,X25)))))
      & ! [X21,X22,X23] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X21))),s(X1,X22),s(tyop_2Emin_2Efun(X0,X1),X23))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X23),s(X0,X21)))
      & ! [X19,X20] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(X1,X19),s(tyop_2Emin_2Efun(X0,X1),X20))) = s(X1,X19)
      & ! [X18] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X18))))
          | s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X18),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X18) )
      & ! [X17] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X17))))
          | s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X17),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X17))))) )
      & ! [X16] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X16))))
          | s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X16),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,X4) )
      & ! [X15] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X15)
      & ! [X14] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X14),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X14)
      & ! [X13] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))
          | s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))) = s(tyop_2Eoption_2Eoption(X0),X13) )
      & ! [X12] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12))))
        <=> s(tyop_2Eoption_2Eoption(X0),X12) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      & ! [X11] :
          ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11))))
        <=> s(tyop_2Eoption_2Eoption(X0),X11) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      & s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      & ! [X10] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X10))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      & ! [X9] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X9))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
      & ! [X8] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X8)))
      & ! [X7] : s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7))))) = s(X0,X7)
      & ! [X5,X6] :
          ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X6)))
        <=> s(X0,X5) = s(X0,X6) ) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f56,plain,
    ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1)))
    | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))
    | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0)))
    | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f49]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ( ( p(s(tyop_2Emin_2Ebool,X0))
          | p(s(tyop_2Emin_2Ebool,X1)) )
        & ( ~ p(s(tyop_2Emin_2Ebool,X0))
          | ~ p(s(tyop_2Emin_2Ebool,X1)) ) )
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f61,plain,
    ! [X0] :
      ( ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
        | ~ p(s(tyop_2Emin_2Ebool,X0)) )
      & ( p(s(tyop_2Emin_2Ebool,X0))
        | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      & ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
        | ~ p(s(tyop_2Emin_2Ebool,X0)) )
      & ( p(s(tyop_2Emin_2Ebool,X0))
        | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0) )
      & ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
        | p(s(tyop_2Emin_2Ebool,X0)) )
      & ( ~ p(s(tyop_2Emin_2Ebool,X0))
        | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      & ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
        | p(s(tyop_2Emin_2Ebool,X0)) )
      & ( ~ p(s(tyop_2Emin_2Ebool,X0))
        | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0) ) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f62,plain,
    ! [X0] :
      ( ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
        | ~ p(s(tyop_2Emin_2Ebool,X0)) )
      & ( p(s(tyop_2Emin_2Ebool,X0))
        | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      & ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
        | ~ p(s(tyop_2Emin_2Ebool,X0)) )
      & ( p(s(tyop_2Emin_2Ebool,X0))
        | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0) )
      & ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
        | p(s(tyop_2Emin_2Ebool,X0)) )
      & ( ~ p(s(tyop_2Emin_2Ebool,X0))
        | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      & ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
        | p(s(tyop_2Emin_2Ebool,X0)) )
      & ( ~ p(s(tyop_2Emin_2Ebool,X0))
        | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,X0) ) ),
    inference(flattening,[],[f61]) ).

fof(f70,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
        | ? [X5,X6] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6))))
            & s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
            & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) )
        | ( s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
          & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) )
      & ( ( ! [X5,X6] :
              ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6))))
              | s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
              | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) )
          & ( s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
            | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) )
        | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f71,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
        | ? [X5,X6] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6))))
            & s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
            & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) )
        | ( s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
          & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) )
      & ( ( ! [X5,X6] :
              ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6))))
              | s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
              | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) )
          & ( s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
            | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) )
        | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ) ),
    inference(flattening,[],[f70]) ).

fof(f72,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
        | ? [X7,X8] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X7))),s(X1,X8))))
            & s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X8)))
            & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7))) )
        | ( s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
          & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) )
      & ( ( ! [X5,X6] :
              ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6))))
              | s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
              | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) )
          & ( s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
            | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) )
        | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ) ),
    inference(rectify,[],[f71]) ).

fof(f73,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
        | ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,sK5(X0,X1,X2,X3,X4)))),s(X1,sK6(X0,X1,X2,X3,X4)))))
          & s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,sK6(X0,X1,X2,X3,X4))))
          & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK5(X0,X1,X2,X3,X4)))) )
        | ( s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
          & s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) )
      & ( ( ! [X5,X6] :
              ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6))))
              | s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
              | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) )
          & ( s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
            | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) )
        | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X7,sK5(X0,X1,X2,X3,X4)),skolemize(X8,sK6(X0,X1,X2,X3,X4))],[f72]) ).

fof(f74,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ! [X27] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(X0),X27))))) = s(tyop_2Eoption_2Eoption(X0),X27)
      & s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
      & ! [X26] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X26),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
      & ! [X24,X25] : s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X25))))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X24),s(X0,X25)))))
      & ! [X21,X22,X23] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X21))),s(X1,X22),s(tyop_2Emin_2Efun(X0,X1),X23))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X23),s(X0,X21)))
      & ! [X19,X20] : s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(X1,X19),s(tyop_2Emin_2Efun(X0,X1),X20))) = s(X1,X19)
      & ! [X18] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X18))))
          | s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X18),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X18) )
      & ! [X17] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X17))))
          | s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X17),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,app_2E2(s(tyop_2Emin_2Efun(X0,X1),X2),s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X17))))) )
      & ! [X16] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X16))))
          | s(X1,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X16),s(X1,X4),s(tyop_2Emin_2Efun(X0,X1),X2))) = s(X1,X4) )
      & ! [X15] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Eoption_2Eoption(X0),X15),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X15)
      & ! [X14] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(X0),X14),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(X0),X14)
      & ! [X13] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))
          | s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))) = s(tyop_2Eoption_2Eoption(X0),X13) )
      & ! [X12] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12))))
            | s(tyop_2Eoption_2Eoption(X0),X12) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
          & ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),X12)
            | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12)))) ) )
      & ! [X11] :
          ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11))))
            | s(tyop_2Eoption_2Eoption(X0),X11) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
          & ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),X11)
            | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11)))) ) )
      & s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      & ! [X10] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X10))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      & ! [X9] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X9))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
      & ! [X8] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X8)))
      & ! [X7] : s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7))))) = s(X0,X7)
      & ! [X5,X6] :
          ( ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X6)))
            | s(X0,X5) = s(X0,X6) )
          & ( s(X0,X5) != s(X0,X6)
            | s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X6))) ) ) ),
    inference(nnf_transformation,[],[f55]) ).

fof(f75,plain,
    ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1)))
    | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))
    | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0)))
    | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | p(s(tyop_2Emin_2Ebool,X1))
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0))
      | ~ p(s(tyop_2Emin_2Ebool,X1))
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f85,plain,
    ! [X0] :
      ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f86,plain,
    ! [X0] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f89,plain,
    ! [X0] :
      ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      | p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f90,plain,
    ! [X0] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0))
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f132,plain,
    ! [X0] :
      ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
    inference(cnf_transformation,[],[f5]) ).

fof(f133,plain,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
    inference(cnf_transformation,[],[f3]) ).

fof(f135,plain,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f141,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
      | s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK5(X0,X1,X2,X3,X4))))
      | s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
      | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,sK5(X0,X1,X2,X3,X4)))),s(X1,sK6(X0,X1,X2,X3,X4)))))
      | s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f143,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
      | s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,sK6(X0,X1,X2,X3,X4))))
      | s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f144,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
      | s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK5(X0,X1,X2,X3,X4))))
      | s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f145,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,X5))),s(X1,X6))))
      | s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X6)))
      | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X5)))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f146,plain,
    ! [X2,X3,X0,X1,X4] :
      ( s(tyop_2Eoption_2Eoption(X1),X4) != s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0)
      | s(tyop_2Eoption_2Eoption(X0),X3) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f148,plain,
    ! [X0] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0))),
    inference(cnf_transformation,[],[f74]) ).

fof(f158,plain,
    ! [X0,X13] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))
      | s(tyop_2Eoption_2Eoption(X0),X13) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X13))))) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f159,plain,
    ! [X0,X12] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12))))
      | s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(X0),X12) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f160,plain,
    ! [X0,X12] :
      ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),X12)
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X12)))) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f161,plain,
    ! [X0,X11] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11))))
      | s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(X0),X11) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f162,plain,
    ! [X0,X11] :
      ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),X11)
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X11)))) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f163,plain,
    ! [X0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))),
    inference(cnf_transformation,[],[f74]) ).

fof(f164,plain,
    ! [X10,X0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X10))))),
    inference(cnf_transformation,[],[f74]) ).

fof(f165,plain,
    ! [X0,X9] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X9))),
    inference(cnf_transformation,[],[f74]) ).

fof(f167,plain,
    ! [X0,X7] : s(X0,X7) = s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X7))))),
    inference(cnf_transformation,[],[f74]) ).

tcf(c_49,negated_conjecture,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) ) ),
    inference(cnf_transformation,[],[f75]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) )
      | ~ p(s(tyop_2Emin_2Ebool,X1))
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(cnf_transformation,[],[f81]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(cnf_transformation,[],[f80]) ).

tcf(c_57,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(cnf_transformation,[],[f90]) ).

tcf(c_58,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(cnf_transformation,[],[f89]) ).

tcf(c_61,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(cnf_transformation,[],[f86]) ).

tcf(c_62,plain,
    ! [X0: $i] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(cnf_transformation,[],[f85]) ).

tcf(c_79,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(cnf_transformation,[],[f132]) ).

tcf(c_80,plain,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
    inference(cnf_transformation,[],[f133]) ).

tcf(c_82,plain,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
    inference(cnf_transformation,[],[f135]) ).

tcf(c_86,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool)),X4),s(tyop_2Eoption_2Eoption(X0),X1),s(tyop_2Eoption_2Eoption(X2),X3))))
      | ( s(tyop_2Eoption_2Eoption(X2),X3) != s(tyop_2Eoption_2Eoption(X2),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(X0),X1) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) ),
    inference(cnf_transformation,[],[f146]) ).

tcf(c_87,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X3,tyop_2Emin_2Ebool)),X6),s(tyop_2Eoption_2Eoption(X0),X2),s(tyop_2Eoption_2Eoption(X3),X5))))
      | ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X3,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X3,tyop_2Emin_2Ebool)),X6),s(X0,X1))),s(X3,X4))))
      | ( s(tyop_2Eoption_2Eoption(X3),c_2Eoption_2ESOME_2E1(s(X3,X4))) != s(tyop_2Eoption_2Eoption(X3),X5) )
      | ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))) != s(tyop_2Eoption_2Eoption(X0),X2) ) ),
    inference(cnf_transformation,[],[f145]) ).

tcf(c_88,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK5(X0,X1,X2,X3,X4)))) = s(tyop_2Eoption_2Eoption(X0),X3) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ),
    inference(cnf_transformation,[],[f144]) ).

tcf(c_89,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,sK6(X0,X1,X2,X3,X4)))) = s(tyop_2Eoption_2Eoption(X1),X4) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ),
    inference(cnf_transformation,[],[f143]) ).

tcf(c_90,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(X0,sK5(X0,X1,X2,X3,X4)))),s(X1,sK6(X0,X1,X2,X3,X4)))))
      | ( s(tyop_2Eoption_2Eoption(X0),X3) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ),
    inference(cnf_transformation,[],[f142]) ).

tcf(c_91,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X1),X4) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK5(X0,X1,X2,X3,X4)))) = s(tyop_2Eoption_2Eoption(X0),X3) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ),
    inference(cnf_transformation,[],[f141]) ).

tcf(c_96,plain,
    ! [X0: $i,X1: $i] : s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(X0,X1),
    inference(cnf_transformation,[],[f167]) ).

tcf(c_98,plain,
    ! [X0: $i,X1: $i] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),
    inference(cnf_transformation,[],[f165]) ).

tcf(c_99,plain,
    ! [X0: $i,X1: $i] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
    inference(cnf_transformation,[],[f164]) ).

tcf(c_100,plain,
    ! [X0: $i] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
    inference(cnf_transformation,[],[f163]) ).

tcf(c_101,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))
      | ( s(tyop_2Eoption_2Eoption(X0),X1) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) ),
    inference(cnf_transformation,[],[f162]) ).

tcf(c_102,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))) ),
    inference(cnf_transformation,[],[f161]) ).

tcf(c_103,plain,
    ! [X0: $i,X1: $i] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))
      | ( s(tyop_2Eoption_2Eoption(X0),X1) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) ),
    inference(cnf_transformation,[],[f160]) ).

tcf(c_104,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))
      | ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) ),
    inference(cnf_transformation,[],[f159]) ).

tcf(c_105,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))) = s(tyop_2Eoption_2Eoption(X0),X1) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))) ),
    inference(cnf_transformation,[],[f158]) ).

tcf(c_115,plain,
    ! [X0: $i] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),
    inference(cnf_transformation,[],[f148]) ).

tcf(c_193,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))) ),
    inference(prop_impl_just,[status(thm)],[c_104]) ).

tcf(c_194,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))
      | ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) ),
    inference(renaming,[status(thm)],[c_193]) ).

tcf(c_199,plain,
    ! [X0: $i,X1: $i] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))) ),
    inference(prop_impl_just,[status(thm)],[c_102,c_103]) ).

tcf(c_201,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))) ),
    inference(prop_impl_just,[status(thm)],[c_104,c_101]) ).

tcf(c_293,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X2),X4))))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X2,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),X3),s(tyop_2Eoption_2Eoption(X2),X4),s(tyop_2Eoption_2Eoption(X0),X1))))
      | ( s(tyop_2Eoption_2Eoption(X0),X1) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) ),
    inference(bin_hyper_res,[status(thm)],[c_86,c_194]) ).

tcf(c_614,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))) ),
    inference(prop_impl_just,[status(thm)],[c_104]) ).

tcf(c_615,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))
      | ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) ) ),
    inference(renaming,[status(thm)],[c_614]) ).

tcf(c_620,plain,
    ! [X0: $i,X1: $i] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))) ),
    inference(prop_impl_just,[status(thm)],[c_199]) ).

tcf(c_622,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))) ),
    inference(prop_impl_just,[status(thm)],[c_201]) ).

tcf(c_712,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X1),X4))))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X3))))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4)))) ),
    inference(bin_hyper_res,[status(thm)],[c_293,c_615]) ).

tcf(c_1020,plain,
    ! [X0: $i] : X0 = X0,
    theory(equality) ).

tcf(c_1022,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X2 = X0 )
      | ( X2 != X1 )
      | ( X0 != X1 ) ),
    theory(equality) ).

tcf(c_1029,plain,
    ! [X0: $i,X1: $i] :
      ( p(X0)
      | ~ p(X1)
      | ( X0 != X1 ) ),
    theory(equality) ).

tcf(c_1853,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_61,c_57]) ).

tcf(c_1862,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))))
      | ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_100,c_58]) ).

tcf(c_1864,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
    | ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(light_normalisation,[status(thm)],[c_1862,c_100]) ).

tcf(c_1865,plain,
    s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
    inference(forward_subsumption_resolution,[status(thm)],[c_1864,c_82]) ).

tcf(c_1883,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Ebool,X0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_96,c_61]) ).

tcf(c_1931,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(superposition,[status(thm)],[c_53,c_57]) ).

tcf(c_1986,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_1853,c_49]) ).

tcf(c_2004,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(superposition,[status(thm)],[c_1853,c_1853]) ).

tcf(c_2056,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_1853,c_1986]) ).

tcf(c_2112,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(superposition,[status(thm)],[c_61,c_52]) ).

tcf(c_2348,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0)))) ),
    inference(instantiation,[status(thm)],[c_57]) ).

tcf(c_2463,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(superposition,[status(thm)],[c_1931,c_2112]) ).

tcf(c_2465,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(superposition,[status(thm)],[c_61,c_2112]) ).

tcf(c_2689,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)))) ),
    inference(instantiation,[status(thm)],[c_105]) ).

tcf(c_2965,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))))
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),X4))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(instantiation,[status(thm)],[c_61]) ).

tcf(c_4492,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))))
    | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0)))) ),
    inference(instantiation,[status(thm)],[c_712]) ).

tcf(c_5121,plain,
    ( ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
    | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0)))) ),
    inference(instantiation,[status(thm)],[c_2689]) ).

tcf(c_9231,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_2465,c_1986]) ).

tcf(c_9234,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_2465,c_2056]) ).

tcf(c_9469,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,X1) ) ),
    inference(superposition,[status(thm)],[c_2465,c_58]) ).

tcf(c_9489,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_2465,c_49]) ).

tcf(c_9509,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_2465,c_2465]) ).

tcf(c_9607,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9469,c_1865]) ).

tcf(c_11190,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_1853,c_9489]) ).

tcf(c_11192,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_2465,c_9489]) ).

tcf(c_11193,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_2004,c_9489]) ).

tcf(c_11246,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_1853,c_9231]) ).

tcf(c_12895,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_2465,c_9607]) ).

tcf(c_13098,plain,
    s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))))) != s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),
    inference(instantiation,[status(thm)],[c_98]) ).

tcf(c_13682,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_11192,c_2348,c_4492,c_5121,c_11192,c_13098]) ).

tcf(c_13683,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(renaming,[status(thm)],[c_13682]) ).

tcf(c_13702,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_1853,c_13683]) ).

tcf(c_13905,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_11193,c_2348,c_4492,c_5121,c_11190,c_13098]) ).

tcf(c_13906,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(renaming,[status(thm)],[c_13905]) ).

tcf(c_13925,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_2465,c_13906]) ).

tcf(c_15472,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(equality_resolution,[status(thm)],[c_13702]) ).

tcf(c_15799,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(equality_resolution,[status(thm)],[c_13925]) ).

tcf(c_17332,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_9234,c_2348,c_4492,c_5121,c_9234,c_13098]) ).

tcf(c_17349,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_1853,c_17332]) ).

tcf(c_17374,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_11246,c_2348,c_4492,c_5121,c_11246,c_13098]) ).

tcf(c_17391,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_1853,c_17374]) ).

tcf(c_27913,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_15472,c_53]) ).

tcf(c_27939,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK6(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ENONE_2E0)))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(superposition,[status(thm)],[c_15472,c_89]) ).

tcf(c_28001,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_15472,c_9607]) ).

tcf(c_28335,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_27939,c_98,c_98]) ).

tcf(c_28343,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_27913,c_28335]) ).

tcf(c_28362,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_28001,c_28343]) ).

tcf(c_28368,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_28335,c_28362]) ).

tcf(c_28480,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_15799,c_53]) ).

tcf(c_28505,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK5(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0,c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(superposition,[status(thm)],[c_15799,c_91]) ).

tcf(c_28573,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_15799,c_9607]) ).

tcf(c_28907,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28505,c_98,c_98]) ).

tcf(c_28915,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_28480,c_28907]) ).

tcf(c_28934,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_28573,c_28915]) ).

tcf(c_28940,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_28907,c_28934]) ).

tcf(c_29395,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_17349,c_53]) ).

tcf(c_29420,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK5(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0,c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(superposition,[status(thm)],[c_17349,c_91]) ).

tcf(c_29489,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_17349,c_9607]) ).

tcf(c_29827,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29420,c_98,c_98]) ).

tcf(c_29835,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_29395,c_29827]) ).

tcf(c_29854,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_29489,c_29835]) ).

tcf(c_29860,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_29827,c_29854]) ).

tcf(c_29967,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_17391,c_53]) ).

tcf(c_29993,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK6(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ENONE_2E0)))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(superposition,[status(thm)],[c_17391,c_89]) ).

tcf(c_30056,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_17391,c_9607]) ).

tcf(c_30394,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_29993,c_98,c_98]) ).

tcf(c_30402,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_29967,c_30394]) ).

tcf(c_30421,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_30056,c_30402]) ).

tcf(c_30427,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_30394,c_30421]) ).

tcf(c_30771,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X1),X3))))
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X1),X3))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(instantiation,[status(thm)],[c_2965]) ).

tcf(c_35648,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_2463,c_1853]) ).

tcf(c_115134,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))))
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(instantiation,[status(thm)],[c_30771]) ).

tcf(c_131524,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_49,c_2348,c_4492,c_5121,c_13098]) ).

tcf(c_131525,negated_conjecture,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) ) ),
    inference(renaming,[status(thm)],[c_131524]) ).

tcf(c_131539,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_61,c_57]) ).

tcf(c_131548,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))))
      | ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_100,c_58]) ).

tcf(c_131550,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
    | ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(light_normalisation,[status(thm)],[c_131548,c_100]) ).

tcf(c_131551,plain,
    s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
    inference(forward_subsumption_resolution,[status(thm)],[c_131550,c_82]) ).

tcf(c_131604,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X1))
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(superposition,[status(thm)],[c_53,c_57]) ).

tcf(c_131624,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0)))))) ),
    inference(superposition,[status(thm)],[c_115,c_622]) ).

tcf(c_131628,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)))) ),
    inference(light_normalisation,[status(thm)],[c_131624,c_100,c_115]) ).

tcf(c_131629,plain,
    ! [X0: $i] : p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_131628,c_82]) ).

tcf(c_131632,plain,
    ! [X0: $i] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
    inference(superposition,[status(thm)],[c_131629,c_57]) ).

tcf(c_131652,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_131539,c_131525]) ).

tcf(c_131666,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(superposition,[status(thm)],[c_131539,c_131539]) ).

tcf(c_131702,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_131539,c_131652]) ).

tcf(c_131715,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_131539,c_131702]) ).

tcf(c_131728,plain,
    ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_131539,c_131715]) ).

tcf(c_131746,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))))
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_131728,c_58]) ).

tcf(c_131779,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(superposition,[status(thm)],[c_131746,c_52]) ).

tcf(c_131845,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),X1)))) ),
    inference(superposition,[status(thm)],[c_61,c_620]) ).

tcf(c_131966,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_61,c_131779]) ).

tcf(c_132070,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Ebool,X0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_131966,c_96]) ).

tcf(c_132233,plain,
    ! [X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) ) ),
    inference(global_subsumption_just,[status(thm)],[c_35648,c_62,c_9509,c_12895]) ).

tcf(c_132234,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(renaming,[status(thm)],[c_132233]) ).

tcf(c_132333,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( s(tyop_2Emin_2Ebool,X3) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X3) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(superposition,[status(thm)],[c_132234,c_132234]) ).

tcf(c_132353,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_132234,c_131702]) ).

tcf(c_132358,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_132234,c_131525]) ).

tcf(c_132360,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_132234,c_131715]) ).

tcf(c_132688,plain,
    ! [X0: $i,X1: $i] :
      ( p(X0)
      | ~ p(s(tyop_2Emin_2Ebool,X1))
      | ( X0 != s(tyop_2Emin_2Ebool,X1) ) ),
    inference(instantiation,[status(thm)],[c_1029]) ).

tcf(c_132772,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X4))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK5(X0,X1,X2,X3,c_2Eoption_2ESOME_2E1(s(X1,X4)))))) = s(tyop_2Eoption_2Eoption(X0),X3) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X4)))))) ),
    inference(instantiation,[status(thm)],[c_91]) ).

tcf(c_132940,plain,
    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))))
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(instantiation,[status(thm)],[c_58]) ).

tcf(c_132957,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = X1 )
      | ( X1 != X0 )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != X0 ) ),
    inference(instantiation,[status(thm)],[c_1022]) ).

tcf(c_133077,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_131539,c_132358]) ).

tcf(c_133164,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_132234,c_133077]) ).

tcf(c_133421,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_49,c_2348,c_4492,c_5121,c_13098]) ).

tcf(c_133422,negated_conjecture,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) ) ),
    inference(renaming,[status(thm)],[c_133421]) ).

tcf(c_133426,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | ~ p(s(tyop_2Emin_2Ebool,X1))
      | ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,X1) ) ),
    inference(instantiation,[status(thm)],[c_132688]) ).

tcf(c_133503,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_61,c_57]) ).

tcf(c_133870,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),c_2Eoption_2ENONE_2E0)))))) ),
    inference(superposition,[status(thm)],[c_115,c_622]) ).

tcf(c_133874,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
      | p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)))) ),
    inference(light_normalisation,[status(thm)],[c_133870,c_100,c_115]) ).

tcf(c_133875,plain,
    ! [X0: $i] : p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_133874,c_82]) ).

tcf(c_133878,plain,
    ! [X0: $i] : s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
    inference(superposition,[status(thm)],[c_133875,c_57]) ).

tcf(c_133998,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_133503,c_133422]) ).

tcf(c_134044,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X3))) = s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK5(X0,X1,X2,c_2Eoption_2ENONE_2E0,c_2Eoption_2ESOME_2E1(s(X1,X3)))))) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X3)))))) ),
    inference(instantiation,[status(thm)],[c_132772]) ).

tcf(c_134045,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,sK5(X0,X1,X2,c_2Eoption_2ENONE_2E0,c_2Eoption_2ESOME_2E1(s(X1,X3)))))) != s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0),
    inference(instantiation,[status(thm)],[c_98]) ).

tcf(c_134109,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_133503,c_133998]) ).

tcf(c_134189,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_133503,c_134109]) ).

tcf(c_134194,plain,
    ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))))
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(instantiation,[status(thm)],[c_62]) ).

tcf(c_134205,plain,
    ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_133503,c_134189]) ).

tcf(c_134221,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_132353,c_29860,c_132940,c_134194]) ).

tcf(c_134222,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(renaming,[status(thm)],[c_134221]) ).

tcf(c_134232,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_131702,c_134222]) ).

tcf(c_134259,plain,
    ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_131539,c_134232]) ).

tcf(c_134295,plain,
    ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_134205,c_134259]) ).

tcf(c_134296,plain,
    ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(renaming,[status(thm)],[c_134295]) ).

tcf(c_134308,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))))
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_134296,c_58]) ).

tcf(c_134456,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0)) ),
    inference(superposition,[status(thm)],[c_134308,c_52]) ).

tcf(c_134497,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_133164,c_61,c_132940,c_134194,c_134456]) ).

tcf(c_134498,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(renaming,[status(thm)],[c_134497]) ).

tcf(c_135347,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))))
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(instantiation,[status(thm)],[c_58]) ).

tcf(c_135352,plain,
    ! [X0: $i,X1: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))))
      | ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,X0))),s(sK0,X1))))
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,X1))) != s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,X0))) != s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) ) ),
    inference(instantiation,[status(thm)],[c_87]) ).

tcf(c_135397,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = X1 )
      | ( X1 != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(instantiation,[status(thm)],[c_132957]) ).

tcf(c_135405,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0))
      | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) ),
    inference(instantiation,[status(thm)],[c_52]) ).

tcf(c_137147,plain,
    ! [X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) ) ),
    inference(global_subsumption_just,[status(thm)],[c_35648,c_62,c_9509,c_12895]) ).

tcf(c_137148,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(renaming,[status(thm)],[c_137147]) ).

tcf(c_137274,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_137148,c_133422]) ).

tcf(c_137394,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_137148,c_137148]) ).

tcf(c_138325,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_104,c_131845]) ).

tcf(c_139813,plain,
    ( ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))))
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(instantiation,[status(thm)],[c_62]) ).

tcf(c_139915,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,X1) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(instantiation,[status(thm)],[c_135397]) ).

tcf(c_140557,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_133503,c_137274]) ).

tcf(c_140708,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
      | ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))) = s(tyop_2Emin_2Ebool,X2) ) ),
    inference(superposition,[status(thm)],[c_138325,c_131604]) ).

tcf(c_140739,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))) = s(tyop_2Emin_2Ebool,X2) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_140708,c_82]) ).

tcf(c_140809,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_140557,c_134498]) ).

tcf(c_140823,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_137148,c_140809]) ).

tcf(c_142427,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X4))))))
      | ~ p(s(tyop_2Emin_2Ebool,X5))
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X2),s(tyop_2Eoption_2Eoption(X0),X3),s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E1(s(X1,X4))))) != s(tyop_2Emin_2Ebool,X5) ) ),
    inference(instantiation,[status(thm)],[c_133426]) ).

tcf(c_144231,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Ebool),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Ebool,X0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_132070,c_62,c_1883,c_30427,c_135347,c_135405]) ).

tcf(c_144234,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X0) ) ),
    inference(demodulation,[status(thm)],[c_144231,c_96]) ).

tcf(c_144425,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_144234,c_131632]) ).

tcf(c_144436,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(light_normalisation,[status(thm)],[c_144425,c_131632]) ).

tcf(c_144437,plain,
    ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_144436,c_131551]) ).

tcf(c_147470,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_140823,c_133422]) ).

tcf(c_147510,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ~ p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_140823,c_62]) ).

tcf(c_151964,plain,
    ( ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
    | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK5(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0,c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
    | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) ),
    inference(instantiation,[status(thm)],[c_134044]) ).

tcf(c_152038,plain,
    s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) != s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),
    inference(instantiation,[status(thm)],[c_98]) ).

tcf(c_153285,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_132333,c_131525]) ).

tcf(c_159359,plain,
    s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))),
    inference(instantiation,[status(thm)],[c_1020]) ).

tcf(c_159530,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,X0) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(instantiation,[status(thm)],[c_139915]) ).

tcf(c_159577,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))))
      | ~ p(s(tyop_2Emin_2Ebool,X0))
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(instantiation,[status(thm)],[c_133426]) ).

tcf(c_160083,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_147470,c_61,c_28940,c_134194,c_147510,c_159577]) ).

tcf(c_160117,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X1),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(superposition,[status(thm)],[c_133878,c_160083]) ).

tcf(c_160564,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_160117,c_79,c_159530]) ).

tcf(c_160565,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(renaming,[status(thm)],[c_160564]) ).

tcf(c_162986,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_49,c_2348,c_4492,c_5121,c_13098]) ).

tcf(c_162987,negated_conjecture,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) ) ),
    inference(renaming,[status(thm)],[c_162986]) ).

tcf(c_163010,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))))
      | ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_100,c_58]) ).

tcf(c_163012,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
    | ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(light_normalisation,[status(thm)],[c_163010,c_100]) ).

tcf(c_163013,plain,
    s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
    inference(forward_subsumption_resolution,[status(thm)],[c_163012,c_82]) ).

tcf(c_163014,plain,
    ! [X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) ) ),
    inference(global_subsumption_just,[status(thm)],[c_137394,c_62,c_9509,c_12895]) ).

tcf(c_163015,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(renaming,[status(thm)],[c_163014]) ).

tcf(c_163054,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( s(tyop_2Emin_2Ebool,X3) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X3) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(superposition,[status(thm)],[c_163015,c_163015]) ).

tcf(c_164363,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_163054,c_162987]) ).

tcf(c_164434,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( s(tyop_2Emin_2Ebool,X4) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X3) = s(tyop_2Emin_2Ebool,X4) )
      | ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,X3) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E1(s(X0,X1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_163054,c_99]) ).

tcf(c_164778,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(light_normalisation,[status(thm)],[c_164434,c_99]) ).

tcf(c_164779,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1) ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_164778,c_163013]) ).

tcf(c_192650,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_132360,c_144437,c_160565]) ).

tcf(c_192861,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_192650,c_131652]) ).

tcf(c_195044,plain,
    s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK5(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0,c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) != s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),
    inference(instantiation,[status(thm)],[c_134045]) ).

tcf(c_201940,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X2) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_164363,c_115134,c_151964,c_152038,c_153285,c_195044]) ).

tcf(c_201975,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( s(tyop_2Emin_2Ebool,X4) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,X3) )
      | ( s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X4) )
      | ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,X3) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,X1) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_164779,c_201940]) ).

tcf(c_206939,plain,
    ! [X0: $i] :
      ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))))
      | ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,X0))),s(sK0,sK1))))
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) != s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) )
      | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,X0))) != s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) ) ),
    inference(instantiation,[status(thm)],[c_135352]) ).

tcf(c_214510,plain,
    s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),
    inference(instantiation,[status(thm)],[c_1020]) ).

tcf(c_216642,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_192861,c_1986,c_2348,c_4492,c_5121,c_13098,c_115134,c_151964,c_152038,c_192861,c_195044]) ).

tcf(c_216643,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(renaming,[status(thm)],[c_216642]) ).

tcf(c_230201,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))))
    | ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ) ),
    inference(instantiation,[status(thm)],[c_142427]) ).

tcf(c_232210,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))))
    | ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))))
    | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) != s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) )
    | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) != s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) ) ),
    inference(instantiation,[status(thm)],[c_206939]) ).

tcf(c_232894,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,X0) ) ),
    inference(global_subsumption_just,[status(thm)],[c_201975,c_80,c_61,c_28368,c_134194,c_139813,c_151964,c_152038,c_159359,c_159577,c_195044,c_214510,c_230201,c_232210]) ).

tcf(c_232959,plain,
    s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
    inference(equality_resolution,[status(thm)],[c_232894]) ).

tcf(c_235851,plain,
    ! [X0: $i,X1: $i] :
      ( ( s(tyop_2Eoption_2Eoption(X0),X1) = s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(X0),X1))) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
      | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_140739,c_131525]) ).

tcf(c_241247,plain,
    s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
    inference(global_subsumption_just,[status(thm)],[c_235851,c_80,c_151964,c_152038,c_195044,c_216643,c_230201,c_232959]) ).

tcf(c_241327,plain,
    ( ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(demodulation,[status(thm)],[c_131525,c_241247]) ).

tcf(c_241621,plain,
    ( ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
    | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK6(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))) )
    | ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
    inference(superposition,[status(thm)],[c_241247,c_89]) ).

tcf(c_241622,plain,
    ( ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
    | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK5(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) )
    | ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
    inference(superposition,[status(thm)],[c_241247,c_88]) ).

tcf(c_241660,plain,
    s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK5(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),
    inference(forward_subsumption_resolution,[status(thm)],[c_241622,c_98,c_80]) ).

tcf(c_241661,plain,
    s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK6(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))),
    inference(forward_subsumption_resolution,[status(thm)],[c_241621,c_98,c_80]) ).

tcf(c_241704,plain,
    s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) != s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),
    inference(global_subsumption_just,[status(thm)],[c_241327,c_132940,c_134194,c_232959]) ).

tcf(c_241741,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,X0) ) ),
    inference(superposition,[status(thm)],[c_131666,c_241704]) ).

tcf(c_242502,plain,
    ! [X0: $i] :
      ( ( s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(X0),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) )
      | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(superposition,[status(thm)],[c_241741,c_100]) ).

tcf(c_242569,plain,
    ( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) )
    | ( s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ),
    inference(light_normalisation,[status(thm)],[c_242502,c_100]) ).

tcf(c_242570,plain,
    s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK2))),s(sK0,sK1))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),
    inference(forward_subsumption_resolution,[status(thm)],[c_242569,c_131551]) ).

tcf(c_243125,plain,
    s(sK0,sK5(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))) = s(sK0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))))),
    inference(superposition,[status(thm)],[c_241660,c_96]) ).

tcf(c_243343,plain,
    s(sK0,sK5(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))) = s(sK0,sK2),
    inference(demodulation,[status(thm)],[c_243125,c_96]) ).

tcf(c_243382,plain,
    s(sK0,sK6(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))) = s(sK0,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1))))),
    inference(superposition,[status(thm)],[c_241661,c_96]) ).

tcf(c_243588,plain,
    s(sK0,sK6(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))) = s(sK0,sK1),
    inference(demodulation,[status(thm)],[c_243382,c_96]) ).

tcf(c_243598,plain,
    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(sK0,sK5(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(s(sK0,sK2)),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))),s(sK0,sK1))))
    | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
    | ~ p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),sK3),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))),s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK1)))))) ),
    inference(superposition,[status(thm)],[c_243588,c_90]) ).

tcf(c_243613,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
    | ( s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E1(s(sK0,sK2))) = s(tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ENONE_2E0) )
    | ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
    inference(light_normalisation,[status(thm)],[c_243598,c_242570,c_241247,c_243343]) ).

tcf(c_243614,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_243613,c_82,c_98,c_80]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : ITP011+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.44  % Computer : n008.cluster.edu
% 0.16/5.44  % Model    : x86_64 x86_64
% 0.16/5.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44  % Memory   : 8046.5625MB
% 0.16/5.44  % OS       : Linux 6.8.0-71-generic
% 0.16/5.44  % CPULimit : 300
% 0.16/5.44  % WCLimit  : 300
% 0.16/5.44  % DateTime : Wed Sep 23 17:36:32 UTC 2026
% 0.16/5.44  % CPUTime  : 
% 0.16/5.45  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/5.51  Running first-order theorem proving
% 0.22/5.51  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/5.52  
% 0.22/5.52  % ======== iProver multi-core TPTP/SMT =========
% 0.22/5.52  
% 0.22/5.52  % Detected problem language: tptp
% 0.22/5.54  % Proving...
% 149.62/28.77  % SZS status Started for theBenchmark.p
% 149.62/28.77  % SZS status Theorem for theBenchmark.p
% 149.62/28.77  
% 149.62/28.77  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 149.62/28.77  
% 149.62/28.77  % ------  iProver source info
% 149.62/28.77  
% 149.62/28.77  % git: date: 2026-07-19 20:42:38 +0200
% 149.62/28.77  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 149.62/28.77  % git: non_committed_changes: false
% 149.62/28.77  
% 149.62/28.77  % ------ Parsing...
% 149.62/28.77  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 149.62/28.77  
% 149.62/28.77  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 149.62/28.77  
% 149.62/28.77  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 149.62/28.77  
% 149.62/28.77  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 149.62/28.77  % ------ Proving...
% 149.62/28.77  % ------ Problem Properties 
% 149.62/28.77  
% 149.62/28.77  % 
% 149.62/28.77  % clauses                               42
% 149.62/28.77  % conjectures                           1
% 149.62/28.77  % EPR                                   0
% 149.62/28.77  % Horn                                  30
% 149.62/28.77  % unary                                 16
% 149.62/28.77  % binary                                15
% 149.62/28.77  % lits                                  81
% 149.62/28.77  % lits eq                               48
% 149.62/28.77  % fd_pure                               0
% 149.62/28.77  % fd_pseudo                             0
% 149.62/28.77  % fd_cond                               0
% 149.62/28.77  % fd_pseudo_cond                        0
% 149.62/28.77  % AC symbols                            0
% 149.62/28.77  
% 149.62/28.77  % ------ Schedule dynamic 5 is on 
% 149.62/28.77  
% 149.62/28.77  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 149.62/28.77  
% 149.62/28.77  
% 149.62/28.77  % ------ 
% 149.62/28.77  % Current options:
% 149.62/28.77  % ------ 
% 149.62/28.77  
% 149.62/28.77  
% 149.62/28.77  % 
% 149.62/28.77  
% 149.62/28.77  % ------ Proving...
% 149.62/28.77  % Proof_search_loop: time out after: 2596 full_loop iterations
% 149.62/28.77  
% 149.62/28.77  % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 149.62/28.77  
% 149.62/28.77  
% 149.62/28.77  % ------ 
% 149.62/28.77  % Current options:
% 149.62/28.77  % ------ 
% 149.62/28.77  
% 149.62/28.77  
% 149.62/28.77  % 
% 149.62/28.77  
% 149.62/28.77  % ------ Proving...
% 149.62/28.77  % 
% 149.62/28.77  
% 149.62/28.77  % SZS status Theorem for theBenchmark.p
% 149.62/28.77  
% 149.62/28.77  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 149.62/28.80  
% 149.62/28.80  
%------------------------------------------------------------------------------