%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP011^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 : Wed Sep 30 08:06:19 AM UTC 2026
% Result : Theorem 248.53s 121.92s
% Output : Refutation 250.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 13
% Syntax : Number of formulae : 684 ( 287 unt; 0 typ; 3 def)
% Number of atoms : 4622 ( 939 equ; 0 cnn)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 16577 ( 768 ~; 844 |; 129 &;14826 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 297 ( 297 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 7 con; 0-5 aty)
% Number of variables : 2332 ( 514 ^;1805 !; 10 ?;2332 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(c_2Ebool_2EF_decl,type,
c_2Ebool_2EF: $o ).
thf(c_2Eoption_2EIS__NONE_decl,type,
c_2Eoption_2EIS__NONE:
!>[TA: $tType] : ( ( tyop_2Eoption_2Eoption @ TA ) > $o ) ).
thf(c_2Eoption_2EIS__SOME_decl,type,
c_2Eoption_2EIS__SOME:
!>[TA: $tType] : ( ( tyop_2Eoption_2Eoption @ TA ) > $o ) ).
thf(c_2Eoption_2ENONE_decl,type,
c_2Eoption_2ENONE:
!>[TA: $tType] : ( tyop_2Eoption_2Eoption @ TA ) ).
thf(c_2Eoption_2EOPTION__JOIN_decl,type,
c_2Eoption_2EOPTION__JOIN:
!>[TA: $tType] : ( ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) > ( tyop_2Eoption_2Eoption @ TA ) ) ).
thf(c_2Eoption_2EOPTION__MAP_decl,type,
c_2Eoption_2EOPTION__MAP:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( tyop_2Eoption_2Eoption @ TB ) > ( tyop_2Eoption_2Eoption @ TA ) ) ).
thf(c_2Eoption_2EOPTREL_decl,type,
c_2Eoption_2EOPTREL:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > ( tyop_2Eoption_2Eoption @ TB ) > ( tyop_2Eoption_2Eoption @ TA ) > $o ) ).
thf(c_2Eoption_2ESOME_decl,type,
c_2Eoption_2ESOME:
!>[TA: $tType] : ( TA > ( tyop_2Eoption_2Eoption @ TA ) ) ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $o ).
thf(c_2Eoption_2ETHE_decl,type,
c_2Eoption_2ETHE:
!>[TA: $tType] : ( ( tyop_2Eoption_2Eoption @ TA ) > TA ) ).
thf(c_2Eoption_2Eoption__CASE_decl,type,
c_2Eoption_2Eoption__CASE:
!>[TA: $tType,TB: $tType] : ( ( tyop_2Eoption_2Eoption @ TB ) > TA > ( TB > TA ) > TA ) ).
thf(sk1_decl,type,
sk1: skt1 ).
thf(sk2_decl,type,
sk2: skt1 ).
thf(sk3_decl,type,
sk3: skt1 > skt1 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1] :
~ ! [B: skt1,C: skt1 > skt1 > $o] :
( ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ C @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ C @ ( c_2Eoption_2ESOME @ skt1 @ B ) @ ( c_2Eoption_2ENONE @ skt1 ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ C @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ A ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ C @ ( c_2Eoption_2ESOME @ skt1 @ B ) @ ( c_2Eoption_2ESOME @ skt1 @ A ) )
= ( C @ B @ A ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1] :
~ ! [B: skt1 > skt1 > $o] :
( ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ B @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ B @ ( c_2Eoption_2ESOME @ skt1 @ A ) @ ( c_2Eoption_2ENONE @ skt1 ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ B @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ B @ ( c_2Eoption_2ESOME @ skt1 @ A ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
= ( B @ A @ sk1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt1 > skt1 > $o] :
~ ( ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ A @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ A @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ A @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ A @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
= ( A @ sk2 @ sk1 ) ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: TA,C: TA > TA > $o] :
( ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ESOME @ TA @ B ) @ ( c_2Eoption_2ENONE @ TA ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ESOME @ TA @ A ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ESOME @ TA @ B ) @ ( c_2Eoption_2ESOME @ TA @ A ) )
= ( C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient__option_2EOPTION__REL__def) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: TA,C: TA > TA > $o] :
( ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ESOME @ TA @ B ) @ ( c_2Eoption_2ENONE @ TA ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ESOME @ TA @ A ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ESOME @ TA @ B ) @ ( c_2Eoption_2ESOME @ TA @ A ) )
= ( C @ B @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ! [TA: $tType,A: TA,B: TA,C: TA > TA > $o] :
( ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ESOME @ TA @ B ) @ ( c_2Eoption_2ENONE @ TA ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ESOME @ TA @ A ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EOPTREL @ TA @ TA @ C @ ( c_2Eoption_2ESOME @ TA @ B ) @ ( c_2Eoption_2ESOME @ TA @ A ) )
= ( C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
( ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
!= c_2Ebool_2ET )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
!= c_2Ebool_2EF )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= c_2Ebool_2EF )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
( ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
!= c_2Ebool_2ET )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
!= c_2Ebool_2EF )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= c_2Ebool_2EF )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
| A )
= c_2Ebool_2ET )
& ( ( A
| c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| A )
= A )
& ( ( A
| c_2Ebool_2EF )
= A )
& ( ( A
| A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CLAUSES) ).
thf(15,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
| A )
= c_2Ebool_2ET )
& ( ( A
| c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| A )
= A )
& ( ( A
| c_2Ebool_2EF )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
( ( ( c_2Ebool_2ET
| $true )
= c_2Ebool_2ET )
& ( ( $true
| c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| $true )
= $true )
& ( ( $true
| c_2Ebool_2EF )
= $true ) ),
inference(instance,[status(thm)],[15]) ).
thf(17,plain,
c_2Ebool_2ET,
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
( ( ( c_2Ebool_2ET
| $false )
= c_2Ebool_2ET )
& ( ( $false
| c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| $false )
= $false )
& ( ( $false
| c_2Ebool_2EF )
= $false ) ),
inference(instance,[status(thm)],[15]) ).
thf(19,plain,
~ c_2Ebool_2EF,
inference(simp,[status(thm)],[18]) ).
thf(117,plain,
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[14,17,19]) ).
thf(119,plain,
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(bool_ext,[status(thm)],[117]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: tyop_2Eoption_2Eoption @ TB,C: TA] :
( ! [D: TB,E: TB] :
( ( ( c_2Eoption_2ESOME @ TB @ D )
= ( c_2Eoption_2ESOME @ TB @ E ) )
= ( D = E ) )
& ! [D: TB] :
( ( c_2Eoption_2ETHE @ TB @ ( c_2Eoption_2ESOME @ TB @ D ) )
= D )
& ! [D: TB] :
( ( c_2Eoption_2ENONE @ TB )
!= ( c_2Eoption_2ESOME @ TB @ D ) )
& ! [D: TB] :
( ( c_2Eoption_2ESOME @ TB @ D )
!= ( c_2Eoption_2ENONE @ TB ) )
& ! [D: TB] :
( ( c_2Eoption_2EIS__SOME @ TB @ ( c_2Eoption_2ESOME @ TB @ D ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EIS__SOME @ TB @ ( c_2Eoption_2ENONE @ TB ) )
= c_2Ebool_2EF )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__NONE @ TB @ D )
= ( D
= ( c_2Eoption_2ENONE @ TB ) ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( ~ ( c_2Eoption_2EIS__SOME @ TB @ D ) )
= ( D
= ( c_2Eoption_2ENONE @ TB ) ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ TB @ D )
=> ( ( c_2Eoption_2ESOME @ TB @ ( c_2Eoption_2ETHE @ TB @ D ) )
= D ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ TB ) @ D @ ( c_2Eoption_2ENONE @ TB ) @ ( c_2Eoption_2ESOME @ TB ) )
= D )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ TB ) @ D @ D @ ( c_2Eoption_2ESOME @ TB ) )
= D )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__NONE @ TB @ D )
=> ( ( c_2Eoption_2Eoption__CASE @ TB @ TA @ D @ C @ A )
= C ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ TB @ D )
=> ( ( c_2Eoption_2Eoption__CASE @ TB @ TA @ D @ C @ A )
= ( A @ ( c_2Eoption_2ETHE @ TB @ D ) ) ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ TB @ D )
=> ( ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ TB ) @ D @ B @ ( c_2Eoption_2ESOME @ TB ) )
= D ) )
& ! [D: TA,E: TB > TA] :
( ( c_2Eoption_2Eoption__CASE @ TB @ TA @ ( c_2Eoption_2ENONE @ TB ) @ D @ E )
= D )
& ! [D: TB,E: TA,F: TB > TA] :
( ( c_2Eoption_2Eoption__CASE @ TB @ TA @ ( c_2Eoption_2ESOME @ TB @ D ) @ E @ F )
= ( F @ D ) )
& ! [D: TB > TA,E: TB] :
( ( c_2Eoption_2EOPTION__MAP @ TB @ TA @ D @ ( c_2Eoption_2ESOME @ TB @ E ) )
= ( c_2Eoption_2ESOME @ TA @ ( D @ E ) ) )
& ! [D: TB > TA] :
( ( c_2Eoption_2EOPTION__MAP @ TB @ TA @ D @ ( c_2Eoption_2ENONE @ TB ) )
= ( c_2Eoption_2ENONE @ TA ) )
& ( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
= ( c_2Eoption_2ENONE @ TB ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ D ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES) ).
thf(20,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: tyop_2Eoption_2Eoption @ TB,C: TA] :
( ! [D: TB,E: TB] :
( ( ( c_2Eoption_2ESOME @ TB @ D )
= ( c_2Eoption_2ESOME @ TB @ E ) )
= ( D = E ) )
& ! [D: TB] :
( ( c_2Eoption_2ETHE @ TB @ ( c_2Eoption_2ESOME @ TB @ D ) )
= D )
& ! [D: TB] :
( ( c_2Eoption_2ENONE @ TB )
!= ( c_2Eoption_2ESOME @ TB @ D ) )
& ! [D: TB] :
( ( c_2Eoption_2ESOME @ TB @ D )
!= ( c_2Eoption_2ENONE @ TB ) )
& ! [D: TB] :
( ( c_2Eoption_2EIS__SOME @ TB @ ( c_2Eoption_2ESOME @ TB @ D ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EIS__SOME @ TB @ ( c_2Eoption_2ENONE @ TB ) )
= c_2Ebool_2EF )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__NONE @ TB @ D )
= ( D
= ( c_2Eoption_2ENONE @ TB ) ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( ~ ( c_2Eoption_2EIS__SOME @ TB @ D ) )
= ( D
= ( c_2Eoption_2ENONE @ TB ) ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ TB @ D )
=> ( ( c_2Eoption_2ESOME @ TB @ ( c_2Eoption_2ETHE @ TB @ D ) )
= D ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ TB ) @ D @ ( c_2Eoption_2ENONE @ TB ) @ ( c_2Eoption_2ESOME @ TB ) )
= D )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ TB ) @ D @ D @ ( c_2Eoption_2ESOME @ TB ) )
= D )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__NONE @ TB @ D )
=> ( ( c_2Eoption_2Eoption__CASE @ TB @ TA @ D @ C @ A )
= C ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ TB @ D )
=> ( ( c_2Eoption_2Eoption__CASE @ TB @ TA @ D @ C @ A )
= ( A @ ( c_2Eoption_2ETHE @ TB @ D ) ) ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ TB @ D )
=> ( ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ TB ) @ D @ B @ ( c_2Eoption_2ESOME @ TB ) )
= D ) )
& ! [D: TA,E: TB > TA] :
( ( c_2Eoption_2Eoption__CASE @ TB @ TA @ ( c_2Eoption_2ENONE @ TB ) @ D @ E )
= D )
& ! [D: TB,E: TA,F: TB > TA] :
( ( c_2Eoption_2Eoption__CASE @ TB @ TA @ ( c_2Eoption_2ESOME @ TB @ D ) @ E @ F )
= ( F @ D ) )
& ! [D: TB > TA,E: TB] :
( ( c_2Eoption_2EOPTION__MAP @ TB @ TA @ D @ ( c_2Eoption_2ESOME @ TB @ E ) )
= ( c_2Eoption_2ESOME @ TA @ ( D @ E ) ) )
& ! [D: TB > TA] :
( ( c_2Eoption_2EOPTION__MAP @ TB @ TA @ D @ ( c_2Eoption_2ENONE @ TB ) )
= ( c_2Eoption_2ENONE @ TA ) )
& ( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
= ( c_2Eoption_2ENONE @ TB ) )
& ! [D: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
! [TA: $tType,TB: $tType,Z: tyop_2Eoption_2Eoption @ TA,Y: TA > TB,X: TA,W: TA > TB,V: TA > TB,U: TB,T: TA,S: TA > TB,R: TB,Q: tyop_2Eoption_2Eoption @ TA,P: tyop_2Eoption_2Eoption @ TA,O: tyop_2Eoption_2Eoption @ TA,N: tyop_2Eoption_2Eoption @ TA,M: tyop_2Eoption_2Eoption @ TA,L: tyop_2Eoption_2Eoption @ TA,K: tyop_2Eoption_2Eoption @ TA,J: tyop_2Eoption_2Eoption @ TA,I: TA,H: TA,G: TA,F: TA,E: TA,D: TA,C: TB,B: tyop_2Eoption_2Eoption @ TA,A: TA > TB] :
( ( ( ( c_2Eoption_2ESOME @ TA @ D )
= ( c_2Eoption_2ESOME @ TA @ E ) )
= ( D = E ) )
& ( ( c_2Eoption_2ETHE @ TA @ ( c_2Eoption_2ESOME @ TA @ F ) )
= F )
& ( ( c_2Eoption_2ENONE @ TA )
!= ( c_2Eoption_2ESOME @ TA @ G ) )
& ( ( c_2Eoption_2ESOME @ TA @ H )
!= ( c_2Eoption_2ENONE @ TA ) )
& ( ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ I ) )
= c_2Ebool_2ET )
& ( ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ENONE @ TA ) )
= c_2Ebool_2EF )
& ( ( c_2Eoption_2EIS__NONE @ TA @ J )
= ( J
= ( c_2Eoption_2ENONE @ TA ) ) )
& ( ( ~ ( c_2Eoption_2EIS__SOME @ TA @ K ) )
= ( K
= ( c_2Eoption_2ENONE @ TA ) ) )
& ( ~ ( c_2Eoption_2EIS__SOME @ TA @ L )
| ( ( c_2Eoption_2ESOME @ TA @ ( c_2Eoption_2ETHE @ TA @ L ) )
= L ) )
& ( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ M @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ESOME @ TA ) )
= M )
& ( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ N @ N @ ( c_2Eoption_2ESOME @ TA ) )
= N )
& ( ~ ( c_2Eoption_2EIS__NONE @ TA @ O )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ O @ C @ A )
= C ) )
& ( ~ ( c_2Eoption_2EIS__SOME @ TA @ P )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ P @ C @ A )
= ( A @ ( c_2Eoption_2ETHE @ TA @ P ) ) ) )
& ( ~ ( c_2Eoption_2EIS__SOME @ TA @ Q )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ Q @ B @ ( c_2Eoption_2ESOME @ TA ) )
= Q ) )
& ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ ( c_2Eoption_2ENONE @ TA ) @ R @ S )
= R )
& ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ ( c_2Eoption_2ESOME @ TA @ T ) @ U @ V )
= ( V @ T ) )
& ( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ W @ ( c_2Eoption_2ESOME @ TA @ X ) )
= ( c_2Eoption_2ESOME @ TB @ ( W @ X ) ) )
& ( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ Y @ ( c_2Eoption_2ENONE @ TA ) )
= ( c_2Eoption_2ENONE @ TB ) )
& ( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
= ( c_2Eoption_2ENONE @ TA ) )
& ( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ Z ) )
= Z ) ),
inference(cnf,[status(esa)],[20]) ).
thf(41,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
= ( c_2Eoption_2ESOME @ TB @ ( A @ B ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(43,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
= ( c_2Eoption_2ESOME @ TB @ ( A @ B ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(44,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
= ( c_2Eoption_2ESOME @ TB @ ( A @ B ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(167,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TA @ $o @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
| ( ( sk3 @ sk2 @ sk1 )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[119,44]) ).
thf(179,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : ( sk3 @ sk2 @ sk1 )
@ ( c_2Eoption_2ESOME @ TA @ A ) ) ) ),
inference(pre_uni,[status(thm)],[167:[bind(A,$thf( ^ [C: TA] : ( sk3 @ sk2 @ sk1 ) )),bind(B,$thf( B ))]]) ).
thf(192,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : ( sk3 @ sk2 @ sk1 )
@ ( c_2Eoption_2ESOME @ TA @ A ) ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: tyop_2Eoption_2Eoption @ TB,C: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2EOPTREL @ TB @ TA @ A @ B @ C )
= ( ( ( B
= ( c_2Eoption_2ENONE @ TB ) )
& ( C
= ( c_2Eoption_2ENONE @ TA ) ) )
| ? [D: TB,E: TA] :
( ( B
= ( c_2Eoption_2ESOME @ TB @ D ) )
& ( C
= ( c_2Eoption_2ESOME @ TA @ E ) )
& ( A @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2EOPTREL__def) ).
thf(85,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: tyop_2Eoption_2Eoption @ TB,C: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2EOPTREL @ TB @ TA @ A @ B @ C )
= ( ( ( B
= ( c_2Eoption_2ENONE @ TB ) )
& ( C
= ( c_2Eoption_2ENONE @ TA ) ) )
| ? [D: TB,E: TA] :
( ( B
= ( c_2Eoption_2ESOME @ TB @ D ) )
& ( C
= ( c_2Eoption_2ESOME @ TA @ E ) )
& ( A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(86,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TB,B: tyop_2Eoption_2Eoption @ TA,A: TA > TB > $o] :
( ( c_2Eoption_2EOPTREL @ TA @ TB @ A @ B @ C )
= ( ( ( B
= ( c_2Eoption_2ENONE @ TA ) )
& ( C
= ( c_2Eoption_2ENONE @ TB ) ) )
| ? [D: TA,E: TB] :
( ( B
= ( c_2Eoption_2ESOME @ TA @ D ) )
& ( C
= ( c_2Eoption_2ESOME @ TB @ E ) )
& ( A @ D @ E ) ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TB,B: tyop_2Eoption_2Eoption @ TA,A: TA > TB > $o] :
( ( ( ( B
= ( c_2Eoption_2ENONE @ TA ) )
& ( C
= ( c_2Eoption_2ENONE @ TB ) ) )
| ? [D: TA,E: TB] :
( ( B
= ( c_2Eoption_2ESOME @ TA @ D ) )
& ( C
= ( c_2Eoption_2ESOME @ TB @ E ) )
& ( A @ D @ E ) ) )
= ( c_2Eoption_2EOPTREL @ TA @ TB @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(6699,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TB,B: tyop_2Eoption_2Eoption @ TA,A: TA > TB > $o] :
( ~ ( ( ( B
= ( c_2Eoption_2ENONE @ TA ) )
& ( C
= ( c_2Eoption_2ENONE @ TB ) ) )
| ? [D: TA,E: TB] :
( ( B
= ( c_2Eoption_2ESOME @ TA @ D ) )
& ( C
= ( c_2Eoption_2ESOME @ TB @ E ) )
& ( A @ D @ E ) ) )
| ( c_2Eoption_2EOPTREL @ TA @ TB @ A @ B @ C ) ),
inference(bool_ext,[status(thm)],[87]) ).
thf(6741,plain,
! [TA: $tType,TB: $tType,E: TB,D: TA,C: tyop_2Eoption_2Eoption @ TB,B: tyop_2Eoption_2Eoption @ TA,A: TA > TB > $o] :
( ( ( B
!= ( c_2Eoption_2ENONE @ TA ) )
| ( C
!= ( c_2Eoption_2ENONE @ TB ) )
| ( c_2Eoption_2EOPTREL @ TA @ TB @ A @ B @ C ) )
& ( ( B
!= ( c_2Eoption_2ESOME @ TA @ D ) )
| ( C
!= ( c_2Eoption_2ESOME @ TB @ E ) )
| ~ ( A @ D @ E )
| ( c_2Eoption_2EOPTREL @ TA @ TB @ A @ B @ C ) ) ),
inference(cnf,[status(esa)],[6699]) ).
thf(6742,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TB,B: tyop_2Eoption_2Eoption @ TA,A: TA > TB > $o] :
( ( B
!= ( c_2Eoption_2ENONE @ TA ) )
| ( C
!= ( c_2Eoption_2ENONE @ TB ) )
| ( c_2Eoption_2EOPTREL @ TA @ TB @ A @ B @ C ) ),
inference(cnfConj,[status(thm)],[6741]) ).
thf(6744,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TB,B: tyop_2Eoption_2Eoption @ TA,A: TA > TB > $o] :
( ( B
!= ( c_2Eoption_2ENONE @ TA ) )
| ( C
!= ( c_2Eoption_2ENONE @ TB ) )
| ( c_2Eoption_2EOPTREL @ TA @ TB @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[6742]) ).
thf(6745,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o] : ( c_2Eoption_2EOPTREL @ TA @ TB @ A @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[6744]) ).
thf(10916,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : ( sk3 @ sk2 @ sk1 )
@ ( c_2Eoption_2ESOME @ TA @ A ) ) ) ),
inference(rewrite,[status(thm)],[192,6745]) ).
thf(10917,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : ( sk3 @ sk2 @ sk1 )
@ ( c_2Eoption_2ESOME @ TA @ A ) ) ) ),
inference(simp,[status(thm)],[10916]) ).
thf(29,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(42,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(159,plain,
! [TA: $tType,TB: $tType,B: TB,A: TB > ( tyop_2Eoption_2Eoption @ TA )] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ TA ) @ A @ ( c_2Eoption_2ESOME @ TB @ B ) ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[42,44]) ).
thf(177,plain,
! [TA: $tType,TB: $tType,A: TB] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) ) ),
inference(pre_uni,[status(thm)],[159:[bind(A,$thf( ^ [C: TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )),bind(B,$thf( B ))]]) ).
thf(190,plain,
! [TA: $tType,TB: $tType,A: TB] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(936,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC,B: TC > ( tyop_2Eoption_2Eoption @ TA ),A: TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( B @ C ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [D: TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) )
!= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TA ) @ B @ ( c_2Eoption_2ESOME @ TC @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[190,44]) ).
thf(937,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ),
inference(pattern_uni,[status(thm)],[936:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TC] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )),bind(C,$thf( A )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( TC ))]]) ).
thf(163,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TA @ $o @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
| ( c_2Ebool_2ET
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17,44]) ).
thf(183,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : c_2Ebool_2ET
@ ( c_2Eoption_2ESOME @ TA @ A ) ) ),
inference(pre_uni,[status(thm)],[163:[bind(A,$thf( ^ [C: TA] : c_2Ebool_2ET ))]]) ).
thf(196,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : c_2Ebool_2ET
@ ( c_2Eoption_2ESOME @ TA @ A ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(247,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) ),
inference(rewrite,[status(thm)],[196,17]) ).
thf(1163,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,247]) ).
thf(1164,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) ),
inference(pattern_uni,[status(thm)],[1163:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ))]]) ).
thf(31,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ETHE @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) )
= A ),
inference(cnfConj,[status(thm)],[21]) ).
thf(49,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ETHE @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(50,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ETHE @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) )
= A ),
inference(simp,[status(thm)],[49]) ).
thf(694,plain,
! [TA: $tType,B: $o,A: TA] :
( ( ( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
= B )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[247,50]) ).
thf(695,plain,
! [TA: $tType,A: TA] :
( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) ),
inference(pattern_uni,[status(thm)],[694:[bind(A,$thf( A )),bind(B,$thf( $true ))]]) ).
thf(1878,plain,
! [TA: $tType,A: $o] :
( ( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [B: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1164,695]) ).
thf(1879,plain,
! [TA: $tType] :
( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [A: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1878:[bind(A,$thf( $true ))]]) ).
thf(27,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) )
= c_2Ebool_2ET ),
inference(cnfConj,[status(thm)],[21]) ).
thf(68,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) )
= c_2Ebool_2ET ),
inference(lifteq,[status(thm)],[27]) ).
thf(69,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) )
= c_2Ebool_2ET ),
inference(simp,[status(thm)],[68]) ).
thf(209,plain,
! [TA: $tType,A: TA] : ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) ),
inference(rewrite,[status(thm)],[69,17]) ).
thf(212,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
( ( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TB @ $o @ B @ ( c_2Eoption_2ESOME @ TB @ C ) ) )
| ( ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[209,44]) ).
thf(214,plain,
! [TA: $tType,TB: $tType,B: TB > TA,A: TB] :
( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TB @ $o
@ ^ [C: TB] : ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ ( B @ C ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) ) ),
inference(pre_uni,[status(thm)],[212:[bind(A,$thf( E @ C )),bind(B,$thf( ^ [E: TB] : ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ ( E @ E ) ) ) )),bind(C,$thf( C ))]]) ).
thf(216,plain,
! [TA: $tType,TB: $tType,B: TB > TA,A: TB] :
( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TB @ $o
@ ^ [C: TB] : ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ ( B @ C ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(15976,plain,
! [TB: $tType,A: TB] :
( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2EOPTION__MAP @ TB @ $o
@ ^ [B: TB] : $true
@ ( c_2Eoption_2ESOME @ TB @ A ) ) ),
inference(rewrite,[status(thm)],[216,209]) ).
thf(1884,plain,
! [TA: $tType,TB: $tType,A: $o] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: $o] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1164,190]) ).
thf(1885,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ),
inference(pattern_uni,[status(thm)],[1884:[bind(A,$thf( $true ))]]) ).
thf(32915,plain,
! [TB: $tType,TC: $tType,TD: $tType,A: TB] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [B: $o] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TB @ $o
@ ^ [B: TB] : $true
@ ( c_2Eoption_2ESOME @ TB @ A ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TC] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[15976,1885]) ).
thf(32916,plain,
! [TD: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) ),
inference(pattern_uni,[status(thm)],[32915:[bind(A,$thf( c_2Eoption_2ENONE @ TC )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( tyop_2Eoption_2Eoption @ TC ))]]) ).
thf(33329,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ),
inference(simp,[status(thm)],[32916]) ).
thf(24,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ESOME @ TA @ A )
!= ( c_2Eoption_2ENONE @ TA ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(51,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ESOME @ TA @ A )
!= ( c_2Eoption_2ENONE @ TA ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(52,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ESOME @ TA @ A )
!= ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[51]) ).
thf(33838,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33329,52]) ).
thf(33839,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(pattern_uni,[status(thm)],[33838:[bind(A,$thf( c_2Eoption_2ENONE @ TA ))]]) ).
thf(148,plain,
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[119]) ).
thf(151,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(7972,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ $true
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[151,6745]) ).
thf(7973,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[7972]) ).
thf(1209,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,190]) ).
thf(1210,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ),
inference(pattern_uni,[status(thm)],[1209:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ))]]) ).
thf(160,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > TC] :
( ( ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2ENONE @ TC ) )
| ( ( c_2Eoption_2ESOME @ TC @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ TC @ C ) ) ),
inference(paramod_ordered,[status(thm)],[44,52]) ).
thf(184,plain,
! [TA: $tType,TC: $tType,B: TA,A: TA > TC] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2ENONE @ TC ) ),
inference(pre_uni,[status(thm)],[160:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A @ B ))]]) ).
thf(197,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[184]) ).
thf(220,plain,
! [TA: $tType,TC: $tType,TD: $tType,D: TC,C: TC > TD,B: TA,A: TA > TD] :
( ( ( c_2Eoption_2ESOME @ TD @ ( A @ B ) )
!= ( c_2Eoption_2ENONE @ TD ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ TD @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ TC @ TD @ C @ ( c_2Eoption_2ESOME @ TC @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,197]) ).
thf(221,plain,
! [TC: $tType,TD: $tType,B: TC,A: TC > TD] :
( ( c_2Eoption_2ESOME @ TD @ ( A @ B ) )
!= ( c_2Eoption_2ENONE @ TD ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind_type(TA,$thf( TC ))]]) ).
thf(224,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA > TB] :
( ( c_2Eoption_2ESOME @ TB @ ( A @ B ) )
!= ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[221]) ).
thf(2887,plain,
! [TA: $tType,TB: $tType,TC: $tType,B: TC,A: TC > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [C: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1210,224]) ).
thf(2978,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pre_uni,[status(thm)],[2887:[bind(A,$thf( ^ [C: TC] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )),bind(B,$thf( B ))]]) ).
thf(6929,plain,
! [TA: $tType,TC: $tType,TD: $tType,B: TA,A: TA > ( tyop_2Eoption_2Eoption @ TD )] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TD ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( A @ B ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TD ) @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,2978]) ).
thf(6930,plain,
! [TD: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TD ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ),
inference(pattern_uni,[status(thm)],[6929:[bind(A,$thf( ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )),bind(B,$thf( c_2Eoption_2ENONE @ TC )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TC ))]]) ).
thf(6976,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[6930]) ).
thf(248,plain,
! [TA: $tType,B: $o,A: TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [C: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[247,247]) ).
thf(249,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [B: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( A )),bind(B,$thf( $true ))]]) ).
thf(261,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > ( tyop_2Eoption_2Eoption @ $o ),A: TA] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[247,224]) ).
thf(275,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) ),
inference(pre_uni,[status(thm)],[261:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TB] : ( c_2Eoption_2ESOME @ $o @ $true ) )),bind(C,$thf( C ))]]) ).
thf(1178,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,275]) ).
thf(1179,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) ),
inference(pattern_uni,[status(thm)],[1178:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ))]]) ).
thf(7,axiom,
! [TA: $tType,A: TA] :
( ( A = A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(88,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(213,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > TC] :
( ( c_2Eoption_2EIS__SOME @ TC @ ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
| ( ( c_2Eoption_2ESOME @ TC @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ TC @ C ) ) ),
inference(paramod_ordered,[status(thm)],[44,209]) ).
thf(215,plain,
! [TA: $tType,TC: $tType,B: TA,A: TA > TC] : ( c_2Eoption_2EIS__SOME @ TC @ ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) ),
inference(pre_uni,[status(thm)],[213:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A @ B ))]]) ).
thf(217,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA > TB] : ( c_2Eoption_2EIS__SOME @ TB @ ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(26,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ~ ( c_2Eoption_2EIS__SOME @ TA @ A )
| ( ( c_2Eoption_2ESOME @ TA @ ( c_2Eoption_2ETHE @ TA @ A ) )
= A ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(72,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ TA @ ( c_2Eoption_2ETHE @ TA @ A ) )
= A )
| ~ ( c_2Eoption_2EIS__SOME @ TA @ A ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(73,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ TA @ ( c_2Eoption_2ETHE @ TA @ A ) )
= A )
| ~ ( c_2Eoption_2EIS__SOME @ TA @ A ) ),
inference(simp,[status(thm)],[72]) ).
thf(929,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC,B: TC > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ),A: TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [D: TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[190,224]) ).
thf(959,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(pre_uni,[status(thm)],[929:[bind(A,$thf( F @ C )),bind(B,$thf( ^ [E: TC] : ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ TA ) @ ^ [F: TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) @ ( c_2Eoption_2ESOME @ TB @ ( F @ E ) ) ) )),bind(C,$thf( C ))]]) ).
thf(4530,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ A )
| ( A
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ A ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,959]) ).
thf(4607,plain,
! [TB: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(simp,[status(thm)],[4530]) ).
thf(4724,plain,
! [TA: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ),
inference(simp,[status(thm)],[4607]) ).
thf(6177,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB )] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( A
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ A ) )
!= ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,4724]) ).
thf(6185,plain,
! [TB: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) )
!= ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ) ),
inference(simp,[status(thm)],[6177]) ).
thf(6199,plain,
! [TA: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) ) ),
inference(simp,[status(thm)],[6185]) ).
thf(2836,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1210,52]) ).
thf(2837,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ),
inference(pattern_uni,[status(thm)],[2836:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(39,plain,
! [TA: $tType,TB: $tType,C: TA > TB,B: TB,A: TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C )
= ( C @ A ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(45,plain,
! [TA: $tType,TB: $tType,C: TA > TB,B: TB,A: TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C )
= ( C @ A ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(46,plain,
! [TA: $tType,TB: $tType,C: TA > TB,B: TB,A: TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C )
= ( C @ A ) ),
inference(simp,[status(thm)],[45]) ).
thf(342,plain,
! [TA: $tType,C: TA > $o,B: $o,A: TA] :
( ~ ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C )
| ( ( C @ A )
!= c_2Ebool_2EF ) ),
inference(paramod_ordered,[status(thm)],[46,19]) ).
thf(417,plain,
! [TA: $tType,B: $o,A: TA] :
~ ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : c_2Ebool_2EF ),
inference(pre_uni,[status(thm)],[342:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : c_2Ebool_2EF ))]]) ).
thf(44999,plain,
! [TA: $tType,B: $o,A: TA] :
~ ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : $false ),
inference(rewrite,[status(thm)],[417,19]) ).
thf(2867,plain,
! [TB: $tType,TC: $tType] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
!= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,1210]) ).
thf(2868,plain,
! [TB: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2867:[]]) ).
thf(3017,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ),
inference(simp,[status(thm)],[2868]) ).
thf(30,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) )
= A ),
inference(cnfConj,[status(thm)],[21]) ).
thf(78,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) )
= A ),
inference(lifteq,[status(thm)],[30]) ).
thf(79,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) )
= A ),
inference(simp,[status(thm)],[78]) ).
thf(5954,plain,
! [TA: $tType,TC: $tType,A: tyop_2Eoption_2Eoption @ TC] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= A )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3017,79]) ).
thf(5955,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TC ) ),
inference(pattern_uni,[status(thm)],[5954:[bind(A,$thf( c_2Eoption_2ENONE @ TC ))]]) ).
thf(5999,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[5955]) ).
thf(6214,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TD
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
= ( c_2Eoption_2ENONE @ TD ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,5999]) ).
thf(6215,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TD
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
= ( c_2Eoption_2ENONE @ TD ) ),
inference(pattern_uni,[status(thm)],[6214:[]]) ).
thf(6295,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
= ( c_2Eoption_2ENONE @ TC ) ),
inference(simp,[status(thm)],[6215]) ).
thf(1191,plain,
! [TA: $tType,TC: $tType,B: tyop_2Eoption_2Eoption @ TA,A: ( tyop_2Eoption_2Eoption @ TA ) > TC] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ TC @ A @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ TC ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[937,197]) ).
thf(1192,plain,
! [TA: $tType,TC: $tType,A: ( tyop_2Eoption_2Eoption @ TA ) > TC] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ TC @ A @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ TC ) ),
inference(pattern_uni,[status(thm)],[1191:[bind(A,$thf( A )),bind(B,$thf( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ))]]) ).
thf(1240,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Eoption_2Eoption @ TA ) > TB] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ TB @ A @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[1192]) ).
thf(9542,plain,
! [TA: $tType,TC: $tType,TD: $tType,C: ( tyop_2Eoption_2Eoption @ TC ) > TD,B: TA,A: TA > TD] :
( ( ( c_2Eoption_2ESOME @ TD @ ( A @ B ) )
!= ( c_2Eoption_2ENONE @ TD ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ TD @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ TD @ C @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,1240]) ).
thf(9543,plain,
! [TC: $tType,TD: $tType,A: ( tyop_2Eoption_2Eoption @ TC ) > TD] :
( ( c_2Eoption_2ESOME @ TD @ ( A @ ( c_2Eoption_2ENONE @ TC ) ) )
!= ( c_2Eoption_2ENONE @ TD ) ),
inference(pattern_uni,[status(thm)],[9542:[bind(A,$thf( A )),bind(B,$thf( c_2Eoption_2ENONE @ TC )),bind(C,$thf( A )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TC ))]]) ).
thf(9572,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Eoption_2Eoption @ TA ) > TB] :
( ( c_2Eoption_2ESOME @ TB @ ( A @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[9543]) ).
thf(250,plain,
! [TA: $tType,B: $o,A: TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[247,52]) ).
thf(251,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( A )),bind(B,$thf( $true ))]]) ).
thf(2853,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1210,251]) ).
thf(2854,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[2853:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(3428,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3017,247]) ).
thf(3429,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) ),
inference(pattern_uni,[status(thm)],[3428:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(38,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( c_2Eoption_2ESOME @ TA @ A )
= ( c_2Eoption_2ESOME @ TA @ B ) )
= ( A = B ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(60,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( c_2Eoption_2ESOME @ TA @ A )
= ( c_2Eoption_2ESOME @ TA @ B ) )
= ( A = B ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(61,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( c_2Eoption_2ESOME @ TA @ A )
= ( c_2Eoption_2ESOME @ TA @ B ) )
= ( A = B ) ),
inference(simp,[status(thm)],[60]) ).
thf(34,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2EIS__NONE @ TA @ A )
= ( A
= ( c_2Eoption_2ENONE @ TA ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(64,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2EIS__NONE @ TA @ A )
= ( A
= ( c_2Eoption_2ENONE @ TA ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(65,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2EIS__NONE @ TA @ A )
= ( A
= ( c_2Eoption_2ENONE @ TA ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(1184,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= A )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,50]) ).
thf(1185,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[1184:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ))]]) ).
thf(3485,plain,
! [TA: $tType,TC: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,1185]) ).
thf(3486,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ),
inference(pattern_uni,[status(thm)],[3485:[]]) ).
thf(3582,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(simp,[status(thm)],[3486]) ).
thf(7515,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,3582]) ).
thf(7516,plain,
! [TD: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ),
inference(pattern_uni,[status(thm)],[7515:[bind_type(TA,$thf( TC ))]]) ).
thf(7608,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[7516]) ).
thf(9613,plain,
! [TA: $tType,TB: $tType,B: ( tyop_2Eoption_2Eoption @ TB ) > $o,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ TA @ A ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( A
= ( c_2Eoption_2ENONE @ TA ) )
!= ( B @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,9572]) ).
thf(9687,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Eoption_2Eoption @ TB ) > ( tyop_2Eoption_2Eoption @ TA )] :
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ TA @ ( A @ ( c_2Eoption_2ENONE @ TB ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[9613:[bind(A,$thf( C @ ( c_2Eoption_2ENONE @ TB ) )),bind(B,$thf( ^ [D: tyop_2Eoption_2Eoption @ TB] : ( ( C @ D ) = ( c_2Eoption_2ENONE @ TA ) ) ))]]) ).
thf(9756,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Eoption_2Eoption @ TB ) > ( tyop_2Eoption_2Eoption @ TA )] :
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ TA @ ( A @ ( c_2Eoption_2ENONE @ TB ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[9687]) ).
thf(11289,plain,
! [TB: $tType,TC: $tType,A: ( tyop_2Eoption_2Eoption @ TC ) > ( tyop_2Eoption_2Eoption @ TB )] :
( ( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ TB @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
!= ( A @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[7608,9756]) ).
thf(11338,plain,
! [TB: $tType] :
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ TB @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[11289:[bind(A,$thf( ^ [B: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ))]]) ).
thf(11389,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ TA @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[11338]) ).
thf(12110,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( A
= ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EIS__NONE @ TA @ A )
!= ( c_2Eoption_2EIS__NONE @ TB @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,11389]) ).
thf(12111,plain,
! [TB: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
= ( c_2Eoption_2ENONE @ TB ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[12110:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )),bind_type(TA,$thf( TB ))]]) ).
thf(12159,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
= ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[12111]) ).
thf(13811,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ TA @ A )
= ( c_2Eoption_2ESOME @ TA @ B ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( A = B )
!= ( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
= ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,12159]) ).
thf(13812,plain,
! [TB: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[13811:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )),bind(B,$thf( c_2Eoption_2ENONE @ TB )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TB ))]]) ).
thf(13874,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[13812]) ).
thf(316,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( sk3 @ sk2 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
| ( ( C @ A )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[46,117]) ).
thf(382,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( sk3 @ sk2
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(pre_uni,[status(thm)],[316:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk1 ))]]) ).
thf(31238,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( sk3 @ sk2
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[382,6745]) ).
thf(31239,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( sk3 @ sk2
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[31238]) ).
thf(232,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC,C: TC > ( tyop_2Eoption_2Eoption @ TB ),B: TA,A: TA > TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ TB @ ( A @ B ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[44,224]) ).
thf(242,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC > TA,B: TC > TA > TB,A: TC] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ TB @ ( B @ A @ ( C @ A ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ),
inference(pre_uni,[status(thm)],[232:[bind(A,$thf( E @ D )),bind(B,$thf( G @ D )),bind(C,$thf( ^ [G: TC] : ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ ( E @ G ) @ ( c_2Eoption_2ESOME @ TA @ ( G @ G ) ) ) )),bind(D,$thf( D ))]]) ).
thf(243,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC > TA,B: TC > TA > TB,A: TC] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ TB @ ( B @ A @ ( C @ A ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(17210,plain,
! [TA: $tType,TB: $tType,TD: $tType,D: TD > TB,C: TD > TB > ( tyop_2Eoption_2Eoption @ $o ),B: TD,A: TA] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [E: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( C @ B @ ( D @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[247,243]) ).
thf(17433,plain,
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) ) ),
inference(pre_uni,[status(thm)],[17210:[bind(A,$thf( G @ B @ ( D @ B ) )),bind(B,$thf( B )),bind(C,$thf( ^ [F: TD] : ^ [G: TB] : ( c_2Eoption_2EOPTION__MAP @ TA @ $o @ ^ [H: TA] : $true @ ( c_2Eoption_2ESOME @ TA @ ( G @ F @ G ) ) ) )),bind(D,$thf( D ))]]) ).
thf(273,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > TC] :
( ( ( c_2Eoption_2EOPTION__MAP @ TC @ $o
@ ^ [D: TC] : $true
@ ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) )
| ( ( c_2Eoption_2ESOME @ TC @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ TC @ C ) ) ),
inference(paramod_ordered,[status(thm)],[44,247]) ).
thf(281,plain,
! [TA: $tType,TC: $tType,B: TA,A: TA > TC] :
( ( c_2Eoption_2EOPTION__MAP @ TC @ $o
@ ^ [C: TC] : $true
@ ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) ),
inference(pre_uni,[status(thm)],[273:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A @ B ))]]) ).
thf(288,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TB @ $o
@ ^ [C: TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) ),
inference(simp,[status(thm)],[281]) ).
thf(269,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > ( tyop_2Eoption_2Eoption @ $o ),A: TA] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o ) @ B @ ( c_2Eoption_2ESOME @ TB @ C ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[247,44]) ).
thf(274,plain,
! [TA: $tType,TB: $tType,B: TB > TA,A: TB] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o )
@ ^ [C: TB] :
( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ ( B @ C ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) ) ),
inference(pre_uni,[status(thm)],[269:[bind(A,$thf( F @ C )),bind(B,$thf( ^ [E: TB] : ( c_2Eoption_2EOPTION__MAP @ TA @ $o @ ^ [F: TA] : $true @ ( c_2Eoption_2ESOME @ TA @ ( F @ E ) ) ) )),bind(C,$thf( C ))]]) ).
thf(284,plain,
! [TA: $tType,TB: $tType,B: TB > TA,A: TB] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o )
@ ^ [C: TB] :
( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ ( B @ C ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(22111,plain,
! [TA: $tType,TB: $tType,TD: $tType,C: ( tyop_2Eoption_2Eoption @ TD ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ),B: TB > TA,A: TB] :
( ( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o )
@ ^ [D: TB] :
( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [E: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ ( B @ D ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) )
!= ( C @ ( c_2Eoption_2ENONE @ TD ) ) ) ),
inference(paramod_ordered,[status(thm)],[284,9756]) ).
thf(22370,plain,
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[22111:[bind(A,$thf( F @ ( c_2Eoption_2ENONE @ TD ) )),bind(B,$thf( I @ ( c_2Eoption_2ENONE @ TD ) )),bind(C,$thf( ^ [F: tyop_2Eoption_2Eoption @ TD] : ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o ) @ ^ [G: TB] : ( c_2Eoption_2EOPTION__MAP @ TA @ $o @ ^ [H: TA] : $true @ ( c_2Eoption_2ESOME @ TA @ ( I @ F @ G ) ) ) @ ( c_2Eoption_2ESOME @ TB @ ( F @ F ) ) ) ))]]) ).
thf(21994,plain,
! [TA: $tType,TB: $tType,TC: $tType,TE: $tType,E: TE > TC,D: TE > TC > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ),C: TE,B: TB > TA,A: TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o )
@ ^ [F: TB] :
( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [G: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ ( B @ F ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) )
!= ( D @ C @ ( E @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[284,243]) ).
thf(22352,plain,
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) ) ) ),
inference(pre_uni,[status(thm)],[21994:[bind(A,$thf( H @ C @ ( E @ C ) )),bind(B,$thf( K @ C @ ( E @ C ) )),bind(C,$thf( C )),bind(D,$thf( ^ [H: TE] : ^ [I: TC] : ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o ) @ ^ [J: TB] : ( c_2Eoption_2EOPTION__MAP @ TA @ $o @ ^ [K: TA] : $true @ ( c_2Eoption_2ESOME @ TA @ ( K @ H @ I @ J ) ) ) @ ( c_2Eoption_2ESOME @ TB @ ( H @ H @ I ) ) ) )),bind(E,$thf( E ))]]) ).
thf(334,plain,
! [TA: $tType,C: TA > skt1 > skt1 > $o,B: skt1 > skt1 > $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( C @ A )
!= sk3 ) ),
inference(paramod_ordered,[status(thm)],[46,119]) ).
thf(391,plain,
! [TA: $tType,B: skt1 > skt1 > $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk3 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[334:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk3 ))]]) ).
thf(35451,plain,
! [TA: $tType,B: skt1 > skt1 > $o,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk3 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[391,6745]) ).
thf(35452,plain,
! [TA: $tType,B: skt1 > skt1 > $o,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk3 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[35451]) ).
thf(26139,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC,C: TC > ( tyop_2Eoption_2Eoption @ $o ),B: TB > TA,A: TB] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ $o ) @ $o
@ ^ [E: tyop_2Eoption_2Eoption @ $o] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o )
@ ^ [E: TB] :
( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [F: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ ( B @ E ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) )
!= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ $o ) @ C @ ( c_2Eoption_2ESOME @ TC @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[284,288]) ).
thf(26140,plain,
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ $o ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ $o] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) ),
inference(pattern_uni,[status(thm)],[26139:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( ^ [F: TC] : ( c_2Eoption_2EOPTION__MAP @ TA @ $o @ ^ [G: TA] : $true @ ( c_2Eoption_2ESOME @ TA @ ( G @ F ) ) ) )),bind(D,$thf( A )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( TC ))]]) ).
thf(1831,plain,
! [TA: $tType,A: $o] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [B: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1164,251]) ).
thf(1832,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [A: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[1831:[bind(A,$thf( $true ))]]) ).
thf(11273,plain,
! [TA: $tType,TC: $tType,A: ( tyop_2Eoption_2Eoption @ TC ) > ( tyop_2Eoption_2Eoption @ $o )] :
( ( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ $o @ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( A @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1164,9756]) ).
thf(11321,plain,
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ $o @ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[11273:[bind(A,$thf( ^ [B: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o @ ^ [C: tyop_2Eoption_2Eoption @ TA] : $true @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ))]]) ).
thf(33822,plain,
! [TB: $tType] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
!= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,33329]) ).
thf(33823,plain,
! [TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ),
inference(pattern_uni,[status(thm)],[33822:[]]) ).
thf(34397,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ),
inference(simp,[status(thm)],[33823]) ).
thf(40,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ A @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ESOME @ TA ) )
= A ),
inference(cnfConj,[status(thm)],[21]) ).
thf(70,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ A @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ESOME @ TA ) )
= A ),
inference(lifteq,[status(thm)],[40]) ).
thf(71,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ A @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ESOME @ TA ) )
= A ),
inference(simp,[status(thm)],[70]) ).
thf(222,plain,
! [TA: $tType,TC: $tType,TD: $tType,D: TC,C: TC > TD,B: TA,A: TA > TC] :
( ( ( c_2Eoption_2EOPTION__MAP @ TC @ TD @ C @ ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
!= ( c_2Eoption_2ENONE @ TD ) )
| ( ( c_2Eoption_2ESOME @ TC @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ TC @ D ) ) ),
inference(paramod_ordered,[status(thm)],[44,197]) ).
thf(223,plain,
! [TA: $tType,TC: $tType,TD: $tType,C: TC > TD,B: TA,A: TA > TC] :
( ( c_2Eoption_2EOPTION__MAP @ TC @ TD @ C @ ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
!= ( c_2Eoption_2ENONE @ TD ) ),
inference(pre_uni,[status(thm)],[222:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A @ B ))]]) ).
thf(225,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC,B: TA,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TB @ TC @ C @ ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
!= ( c_2Eoption_2ENONE @ TC ) ),
inference(simp,[status(thm)],[223]) ).
thf(16718,plain,
! [TB: $tType,TC: $tType,TE: $tType,D: $o > TE,C: TC,B: TC > $o,A: TB] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ TE @ D @ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ TE ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TB @ $o
@ ^ [E: TB] : $true
@ ( c_2Eoption_2ESOME @ TB @ A ) )
!= ( c_2Eoption_2EOPTION__MAP @ TC @ $o @ B @ ( c_2Eoption_2ESOME @ TC @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[15976,225]) ).
thf(16719,plain,
! [TE: $tType,A: $o > TE] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ TE @ A @ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ TE ) ),
inference(pattern_uni,[status(thm)],[16718:[bind(A,$thf( A )),bind(B,$thf( ^ [E: TC] : $true )),bind(C,$thf( A )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( TC ))]]) ).
thf(16771,plain,
! [TA: $tType,A: $o > TA] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ TA @ A @ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[16719]) ).
thf(19311,plain,
! [TA: $tType,TC: $tType,C: $o > TC,B: TA,A: TA > TC] :
( ( ( c_2Eoption_2ESOME @ TC @ ( A @ B ) )
!= ( c_2Eoption_2ENONE @ TC ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ $o @ TC @ C @ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,16771]) ).
thf(19312,plain,
! [TC: $tType,A: $o > TC] :
( ( c_2Eoption_2ESOME @ TC @ ( A @ $true ) )
!= ( c_2Eoption_2ENONE @ TC ) ),
inference(pattern_uni,[status(thm)],[19311:[bind(A,$thf( A )),bind(B,$thf( $true )),bind(C,$thf( A )),bind_type(TA,$thf( $o ))]]) ).
thf(19357,plain,
! [TA: $tType,A: $o > TA] :
( ( c_2Eoption_2ESOME @ TA @ ( A @ $true ) )
!= ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[19312]) ).
thf(19554,plain,
! [TA: $tType,B: $o > ( tyop_2Eoption_2Eoption @ TA ),A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ A @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ESOME @ TA ) )
!= ( B @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[71,19357]) ).
thf(19718,plain,
! [TA: $tType,A: $o > ( tyop_2Eoption_2Eoption @ TA )] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( A @ $true ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(pre_uni,[status(thm)],[19554:[bind(A,$thf( C @ $true )),bind(B,$thf( ^ [D: $o] : ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ ( C @ D ) @ ( c_2Eoption_2ENONE @ TA ) @ ( c_2Eoption_2ESOME @ TA ) ) ))]]) ).
thf(19750,plain,
! [TA: $tType,A: $o > ( tyop_2Eoption_2Eoption @ TA )] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( A @ $true ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(simp,[status(thm)],[19718]) ).
thf(35140,plain,
! [TA: $tType,A: $o > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( A @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[34397,19750]) ).
thf(35154,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(pre_uni,[status(thm)],[35140:[bind(A,$thf( ^ [B: $o] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ))]]) ).
thf(339,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) )
| ( ( C @ A )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[46,119]) ).
thf(401,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) ),
inference(pre_uni,[status(thm)],[339:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk1 ))]]) ).
thf(38796,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) ),
inference(rewrite,[status(thm)],[401,6745]) ).
thf(38797,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) ),
inference(simp,[status(thm)],[38796]) ).
thf(332,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( C @ A )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[46,119]) ).
thf(371,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[332:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk2 ))]]) ).
thf(27619,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[371,6745]) ).
thf(27620,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[27619]) ).
thf(3482,plain,
! [TA: $tType,TB: $tType,TC: $tType,B: TC,A: TC > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [C: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3017,224]) ).
thf(3557,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pre_uni,[status(thm)],[3482:[bind(A,$thf( ^ [C: TC] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )),bind(B,$thf( B ))]]) ).
thf(11272,plain,
! [TA: $tType,TB: $tType,TD: $tType,A: ( tyop_2Eoption_2Eoption @ TD ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( A @ ( c_2Eoption_2ENONE @ TD ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,9756]) ).
thf(11363,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[11272:[bind(A,$thf( ^ [B: tyop_2Eoption_2Eoption @ TD] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ))]]) ).
thf(312,plain,
! [TA: $tType,C: TA > ( tyop_2Eoption_2Eoption @ skt1 ),B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) )
!= ( sk3 @ sk2 @ sk1 ) )
| ( ( C @ A )
!= ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46,117]) ).
thf(387,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[312:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ))]]) ).
thf(31509,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[387,6745]) ).
thf(31510,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[31509]) ).
thf(118,plain,
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(bool_ext,[status(thm)],[117]) ).
thf(366,plain,
! [TA: $tType,C: TA > $o,B: $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C )
| ( ( C @ A )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46,118]) ).
thf(390,plain,
! [TA: $tType,B: $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( sk3 @ sk2 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[366:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : ( sk3 @ sk2 @ sk1 ) ))]]) ).
thf(33506,plain,
! [TA: $tType,B: $o,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( sk3 @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[390,6745]) ).
thf(33507,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[33506]) ).
thf(169,plain,
! [TA: $tType,TC: $tType,TD: $tType,D: TC,C: TC > TD,B: TA,A: TA > TC] :
( ( ( c_2Eoption_2EOPTION__MAP @ TC @ TD @ C @ ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2ESOME @ TD @ ( C @ D ) ) )
| ( ( c_2Eoption_2ESOME @ TC @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ TC @ D ) ) ),
inference(paramod_ordered,[status(thm)],[44,44]) ).
thf(176,plain,
! [TA: $tType,TC: $tType,TD: $tType,C: TC > TD,B: TA,A: TA > TC] :
( ( c_2Eoption_2EOPTION__MAP @ TC @ TD @ C @ ( c_2Eoption_2EOPTION__MAP @ TA @ TC @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2ESOME @ TD @ ( C @ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[169:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A @ B ))]]) ).
thf(189,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB > TC,B: TA,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TB @ TC @ C @ ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2ESOME @ TC @ ( C @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(301,plain,
! [TA: $tType,TB: $tType,C: TB > ( tyop_2Eoption_2Eoption @ TA ),B: tyop_2Eoption_2Eoption @ TA,A: TB] :
( ( ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ TB @ A ) @ B @ C )
= ( c_2Eoption_2ENONE @ TA ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
!= ( C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42,46]) ).
thf(376,plain,
! [TA: $tType,TB: $tType,B: tyop_2Eoption_2Eoption @ TA,A: TB] :
( ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ TB @ A ) @ B
@ ^ [C: TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(pre_uni,[status(thm)],[301:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ))]]) ).
thf(11,axiom,
( ! [A: $o] :
( ( ~ ~ A )
= A )
& ( ( ~ c_2Ebool_2ET ) = c_2Ebool_2EF )
& ( ( ~ c_2Ebool_2EF ) = c_2Ebool_2ET ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).
thf(106,plain,
( ( ( ~ c_2Ebool_2ET ) = c_2Ebool_2EF )
& ( ( ~ c_2Ebool_2EF ) = c_2Ebool_2ET ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1827,plain,
! [TA: $tType,A: $o] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [B: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1164,275]) ).
thf(1828,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [A: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) ),
inference(pattern_uni,[status(thm)],[1827:[bind(A,$thf( $true ))]]) ).
thf(262,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > ( tyop_2Eoption_2Eoption @ $o ),A: TA] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[247,224]) ).
thf(280,plain,
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) ),
inference(pre_uni,[status(thm)],[262:[bind(A,$thf( F @ C )),bind(B,$thf( ^ [E: TB] : ( c_2Eoption_2EOPTION__MAP @ TA @ $o @ ^ [F: TA] : $true @ ( c_2Eoption_2ESOME @ TA @ ( F @ E ) ) ) )),bind(C,$thf( C ))]]) ).
thf(164,plain,
! [TA: $tType,B: TA,A: TA > skt1] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1 @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2ESOME @ skt1 @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[44,119]) ).
thf(175,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[164:[bind(A,$thf( ^ [C: TA] : sk1 ))]]) ).
thf(188,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[175]) ).
thf(1195,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,188]) ).
thf(1196,plain,
! [TA: $tType] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1195:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ))]]) ).
thf(1429,plain,
! [TA: $tType] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1196]) ).
thf(1460,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( sk3 != sk3 )
| ( ( c_2Eoption_2ESOME @ skt1 @ sk2 )
!= ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(simp,[status(thm)],[1429]) ).
thf(1504,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(simp,[status(thm)],[1460]) ).
thf(6872,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ $true
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(rewrite,[status(thm)],[1504,6745]) ).
thf(6873,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(simp,[status(thm)],[6872]) ).
thf(7212,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1210,6873]) ).
thf(7213,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[7212:[]]) ).
thf(7324,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(simp,[status(thm)],[7213]) ).
thf(38461,plain,
! [TA: $tType,TC: $tType,TD: $tType,B: TA,A: TA > ( tyop_2Eoption_2Eoption @ TD )] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TD ) @ skt1
@ ^ [C: tyop_2Eoption_2Eoption @ TD] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( A @ B ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TD ) @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,7324]) ).
thf(38462,plain,
! [TD: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TD ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TD] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[38461:[bind(A,$thf( ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )),bind(B,$thf( c_2Eoption_2ENONE @ TC )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TC ))]]) ).
thf(38717,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(simp,[status(thm)],[38462]) ).
thf(8,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
& A )
= A )
& ( ( A
& c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF
& A )
= c_2Ebool_2EF )
& ( ( A
& c_2Ebool_2EF )
= c_2Ebool_2EF )
& ( ( A
& A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CLAUSES) ).
thf(89,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
& A )
= A )
& ( ( A
& c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF
& A )
= c_2Ebool_2EF )
& ( ( A
& c_2Ebool_2EF )
= c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17242,plain,
! [TA: $tType,TB: $tType,TD: $tType,C: TD > TB,B: TD > TB > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ),A: TD] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( B @ A @ ( C @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[937,243]) ).
thf(17442,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) ),
inference(pre_uni,[status(thm)],[17242:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TD] : ^ [E: TB] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )),bind(C,$thf( C ))]]) ).
thf(7714,plain,
! [TA: $tType,TC: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1210,7608]) ).
thf(7715,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ),
inference(pattern_uni,[status(thm)],[7714:[]]) ).
thf(7764,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(simp,[status(thm)],[7715]) ).
thf(28183,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1210,7764]) ).
thf(28184,plain,
! [TD: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ),
inference(pattern_uni,[status(thm)],[28183:[bind_type(TA,$thf( TC ))]]) ).
thf(28320,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[28184]) ).
thf(35135,plain,
! [TB: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,28320]) ).
thf(35136,plain,
! [TB: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[35135:[]]) ).
thf(35341,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[35136]) ).
thf(43398,plain,
! [TB: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,35341]) ).
thf(43399,plain,
! [TB: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[43398:[]]) ).
thf(43507,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[43399]) ).
thf(43562,plain,
! [TA: $tType,TC: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,43507]) ).
thf(43563,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ),
inference(pattern_uni,[status(thm)],[43562:[]]) ).
thf(43713,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(simp,[status(thm)],[43563]) ).
thf(46668,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,43713]) ).
thf(46669,plain,
! [TD: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ),
inference(pattern_uni,[status(thm)],[46668:[bind_type(TA,$thf( TC ))]]) ).
thf(46858,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[46669]) ).
thf(1314,plain,
! [TA: $tType,TB: $tType,B: TB,A: TB > ( tyop_2Eoption_2Eoption @ TA )] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1185,224]) ).
thf(1326,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(pre_uni,[status(thm)],[1314:[bind(A,$thf( ^ [C: TB] : ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )),bind(B,$thf( B ))]]) ).
thf(5952,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) )
!= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,1326]) ).
thf(5996,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(simp,[status(thm)],[5952]) ).
thf(6020,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(simp,[status(thm)],[5996]) ).
thf(17832,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) )] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) @ A )
| ( A
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) @ ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) @ A ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,17442]) ).
thf(17883,plain,
! [TB: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ) ),
inference(simp,[status(thm)],[17832]) ).
thf(17919,plain,
! [TA: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(simp,[status(thm)],[17883]) ).
thf(34125,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= A )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33329,50]) ).
thf(34126,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(pattern_uni,[status(thm)],[34125:[bind(A,$thf( c_2Eoption_2ENONE @ TA ))]]) ).
thf(39183,plain,
! [TA: $tType,TC: $tType,B: TA,A: TA > ( tyop_2Eoption_2Eoption @ TC )] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( A @ B ) ) )
= ( c_2Eoption_2ENONE @ TC ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TC ) @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [C: $o] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,34126]) ).
thf(39184,plain,
! [TC: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ) )
= ( c_2Eoption_2ENONE @ TC ) ),
inference(pattern_uni,[status(thm)],[39183:[bind(A,$thf( ^ [C: $o] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )),bind(B,$thf( $true )),bind_type(TA,$thf( $o ))]]) ).
thf(39299,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[39184]) ).
thf(11284,plain,
! [TA: $tType,TC: $tType,A: ( tyop_2Eoption_2Eoption @ TC ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )] :
( ( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( A @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[937,9756]) ).
thf(11322,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[11284:[bind(A,$thf( ^ [B: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) ))]]) ).
thf(11831,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( A
= ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EIS__NONE @ TA @ A )
!= ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,11322]) ).
thf(11832,plain,
! [TB: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[11831:[bind(A,$thf( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TB ))]]) ).
thf(11888,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[11832]) ).
thf(13467,plain,
! [TA: $tType,TB: $tType,B: TA,A: TA] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ TA @ A )
= ( c_2Eoption_2ESOME @ TA @ B ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( A = B )
!= ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,11888]) ).
thf(13468,plain,
! [TB: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[13467:[bind(A,$thf( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )),bind(B,$thf( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ))]]) ).
thf(13519,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[13468]) ).
thf(3417,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3017,251]) ).
thf(3418,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[3417:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(363,plain,
! [TA: $tType,C: TA > skt1 > skt1 > $o,B: skt1 > skt1 > $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ( ( C @ A )
!= sk3 ) ),
inference(paramod_ordered,[status(thm)],[46,118]) ).
thf(426,plain,
! [TA: $tType,B: skt1 > skt1 > $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk3 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[363:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk3 ))]]) ).
thf(50746,plain,
! [TA: $tType,B: skt1 > skt1 > $o,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk3 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[426,6745]) ).
thf(50747,plain,
! [TA: $tType,B: skt1 > skt1 > $o,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk3 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[50746]) ).
thf(6114,plain,
! [TB: $tType,B: tyop_2Eoption_2Eoption @ TB,A: tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB )] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A )
| ( A
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[73,6020]) ).
thf(6115,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB )] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A )
| ( A
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[6114:[bind(A,$thf( C )),bind(B,$thf( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB ) @ C ))]]) ).
thf(6124,plain,
! [TA: $tType] :
~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(simp,[status(thm)],[6115]) ).
thf(331,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( C @ A )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[46,119]) ).
thf(421,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[331:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk1 ))]]) ).
thf(45955,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[421,6745]) ).
thf(45956,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[45955]) ).
thf(226,plain,
! [TA: $tType,TB: $tType,B: TB,A: TB > ( tyop_2Eoption_2Eoption @ TA )] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
!= ( A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[42,224]) ).
thf(239,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(pre_uni,[status(thm)],[226:[bind(A,$thf( ^ [C: TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )),bind(B,$thf( B ))]]) ).
thf(490,plain,
! [TA: $tType,TC: $tType,B: TA,A: TA > ( tyop_2Eoption_2Eoption @ TC )] :
( ( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TC ) @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,239]) ).
thf(493,plain,
! [TA: $tType,TC: $tType,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [B: TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ),
inference(pre_uni,[status(thm)],[490:[bind(A,$thf( ^ [C: TA] : ( c_2Eoption_2ENONE @ TC ) ))]]) ).
thf(496,plain,
! [TA: $tType,TB: $tType,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ),
inference(simp,[status(thm)],[493]) ).
thf(1837,plain,
! [TA: $tType,TC: $tType,A: $o] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [B: $o] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1164,496]) ).
thf(1838,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ),
inference(pattern_uni,[status(thm)],[1837:[bind(A,$thf( $true ))]]) ).
thf(1920,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ),
inference(simp,[status(thm)],[1838]) ).
thf(161,plain,
! [TA: $tType,B: TA,A: TA > skt1] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1 @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
!= ( sk3 @ sk2 @ sk1 ) )
| ( ( c_2Eoption_2ESOME @ skt1 @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[44,117]) ).
thf(186,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[161:[bind(A,$thf( ^ [C: TA] : sk1 ))]]) ).
thf(199,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(14247,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[199,6745]) ).
thf(14248,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[14247]) ).
thf(338,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) @ sk1 )
| ( ( C @ A )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[46,119]) ).
thf(422,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 )
@ sk1 ) ),
inference(pre_uni,[status(thm)],[338:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk2 ))]]) ).
thf(47055,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 )
@ sk1 ) ),
inference(rewrite,[status(thm)],[422,6745]) ).
thf(47056,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 )
@ sk1 ) ),
inference(simp,[status(thm)],[47055]) ).
thf(311,plain,
! [TA: $tType,C: TA > skt1 > skt1 > $o,B: skt1 > skt1 > $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) )
| ( ( C @ A )
!= sk3 ) ),
inference(paramod_ordered,[status(thm)],[46,117]) ).
thf(404,plain,
! [TA: $tType,B: skt1 > skt1 > $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk3 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[311:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk3 ))]]) ).
thf(40443,plain,
! [TA: $tType,B: skt1 > skt1 > $o,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk3 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[404,6745]) ).
thf(40444,plain,
! [TA: $tType,B: skt1 > skt1 > $o,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( skt1 > skt1 > $o ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk3 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[40443]) ).
thf(46915,plain,
! [TB: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,46858]) ).
thf(46916,plain,
! [TB: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[46915:[]]) ).
thf(47034,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[46916]) ).
thf(265,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ $o @ B @ ( c_2Eoption_2ESOME @ TB @ C ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ ( B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[247,44]) ).
thf(276,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ $o
@ ^ [C: TB] : $true
@ ( c_2Eoption_2ESOME @ TB @ B ) ) ),
inference(pre_uni,[status(thm)],[265:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TB] : $true ))]]) ).
thf(285,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ $o
@ ^ [C: TB] : $true
@ ( c_2Eoption_2ESOME @ TB @ B ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(741,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
( ( c_2Eoption_2ETHE @ $o @ ( c_2Eoption_2ESOME @ $o @ $true ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( c_2Eoption_2EOPTION__MAP @ TB @ $o
@ ^ [C: TB] : $true
@ ( c_2Eoption_2ESOME @ TB @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[247,695]) ).
thf(742,plain,
c_2Eoption_2ETHE @ $o @ ( c_2Eoption_2ESOME @ $o @ $true ),
inference(pattern_uni,[status(thm)],[741:[bind(A,$thf( A )),bind(B,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(11288,plain,
! [TA: $tType,TB: $tType,TD: $tType,A: ( tyop_2Eoption_2Eoption @ TD ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( A @ ( c_2Eoption_2ENONE @ TD ) ) ) ),
inference(paramod_ordered,[status(thm)],[1210,9756]) ).
thf(11336,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[11288:[bind(A,$thf( ^ [B: tyop_2Eoption_2Eoption @ TD] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ))]]) ).
thf(31788,plain,
! [TA: $tType,TC: $tType,TD: $tType,B: TA,A: TA > ( tyop_2Eoption_2Eoption @ TD )] :
( ( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( A @ B ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TD ) @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,11336]) ).
thf(31789,plain,
! [TD: $tType] :
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[31788:[bind(A,$thf( ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )),bind(B,$thf( c_2Eoption_2ENONE @ TC )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TC ))]]) ).
thf(31873,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[31789]) ).
thf(31937,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( A
= ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EIS__NONE @ TA @ A )
!= ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,31873]) ).
thf(31938,plain,
! [TB: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[31937:[bind(A,$thf( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TB ))]]) ).
thf(32006,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[31938]) ).
thf(2913,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1210,209]) ).
thf(2914,plain,
! [TA: $tType,TB: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ),
inference(pattern_uni,[status(thm)],[2913:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(3192,plain,
! [TB: $tType,TC: $tType] :
( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
!= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,2914]) ).
thf(3193,plain,
! [TB: $tType,TC: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[3192:[]]) ).
thf(3268,plain,
! [TA: $tType,TB: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ),
inference(simp,[status(thm)],[3193]) ).
thf(3452,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,3268]) ).
thf(3453,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3452:[]]) ).
thf(3632,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(simp,[status(thm)],[3453]) ).
thf(120,plain,
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[118]) ).
thf(121,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(7364,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ $true
| ~ ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[121,6745]) ).
thf(7365,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ),
inference(simp,[status(thm)],[7364]) ).
thf(36,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ A @ A @ ( c_2Eoption_2ESOME @ TA ) )
= A ),
inference(cnfConj,[status(thm)],[21]) ).
thf(76,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ A @ A @ ( c_2Eoption_2ESOME @ TA ) )
= A ),
inference(lifteq,[status(thm)],[36]) ).
thf(77,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ A @ A @ ( c_2Eoption_2ESOME @ TA ) )
= A ),
inference(simp,[status(thm)],[76]) ).
thf(3527,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= A )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3017,50]) ).
thf(3528,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(pattern_uni,[status(thm)],[3527:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(4085,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
= ( c_2Eoption_2ENONE @ TD ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,3528]) ).
thf(4086,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
= ( c_2Eoption_2ENONE @ TD ) ),
inference(pattern_uni,[status(thm)],[4085:[]]) ).
thf(4167,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
= ( c_2Eoption_2ENONE @ TC ) ),
inference(simp,[status(thm)],[4086]) ).
thf(252,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Eoption_2EIS__SOME @ $o
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[247,209]) ).
thf(253,plain,
! [TA: $tType,A: TA] :
( c_2Eoption_2EIS__SOME @ $o
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( A )),bind(B,$thf( $true ))]]) ).
thf(1841,plain,
! [TA: $tType,A: $o] :
( ( c_2Eoption_2EIS__SOME @ $o
@ ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [B: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1164,253]) ).
thf(1842,plain,
! [TA: $tType] :
( c_2Eoption_2EIS__SOME @ $o
@ ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [A: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1841:[bind(A,$thf( $true ))]]) ).
thf(171,plain,
! [TA: $tType,B: TA,A: TA > skt1] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1 @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2ESOME @ skt1 @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[44,118]) ).
thf(181,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[171:[bind(A,$thf( ^ [C: TA] : sk1 ))]]) ).
thf(194,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[181]) ).
thf(11891,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[194,6745]) ).
thf(11892,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk1
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[11891]) ).
thf(3431,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,2837]) ).
thf(3432,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ),
inference(pattern_uni,[status(thm)],[3431:[]]) ).
thf(3611,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ),
inference(simp,[status(thm)],[3432]) ).
thf(10,axiom,
c_2Ebool_2ET,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(105,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3510,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,2914]) ).
thf(3511,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3510:[]]) ).
thf(3587,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(simp,[status(thm)],[3511]) ).
thf(6858,plain,
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[117,6745]) ).
thf(6859,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[6858]) ).
thf(3507,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3017,695]) ).
thf(3508,plain,
! [TA: $tType,TB: $tType] :
( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3507:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(19529,plain,
! [TA: $tType,B: $o > $o,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ TA @ A ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( A
= ( c_2Eoption_2ENONE @ TA ) )
!= ( B @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[65,19357]) ).
thf(19644,plain,
! [TA: $tType,A: $o > ( tyop_2Eoption_2Eoption @ TA )] :
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ TA @ ( A @ $true ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[19529:[bind(A,$thf( C @ $true )),bind(B,$thf( ^ [D: $o] : ( ( C @ D ) = ( c_2Eoption_2ENONE @ TA ) ) ))]]) ).
thf(19775,plain,
! [TA: $tType,A: $o > ( tyop_2Eoption_2Eoption @ TA )] :
( ( c_2Eoption_2ESOME @ $o @ ( c_2Eoption_2EIS__NONE @ TA @ ( A @ $true ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[19644]) ).
thf(25,plain,
! [TA: $tType] :
( ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ENONE @ TA ) )
= c_2Ebool_2EF ),
inference(cnfConj,[status(thm)],[21]) ).
thf(55,plain,
! [TA: $tType] :
( ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ENONE @ TA ) )
= c_2Ebool_2EF ),
inference(lifteq,[status(thm)],[25]) ).
thf(128,plain,
! [TA: $tType] :
~ ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ENONE @ TA ) ),
inference(rewrite,[status(thm)],[55,19]) ).
thf(34982,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34397,251]) ).
thf(34983,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[34982:[bind(A,$thf( c_2Eoption_2ENONE @ TA ))]]) ).
thf(17225,plain,
! [TA: $tType,TB: $tType,TD: $tType,C: TD > TB,B: TD > TB > ( tyop_2Eoption_2Eoption @ $o ),A: TD] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [D: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( B @ A @ ( C @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1164,243]) ).
thf(17454,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ $o ) ) ) ),
inference(pre_uni,[status(thm)],[17225:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TD] : ^ [E: TB] : ( c_2Eoption_2ESOME @ $o @ $true ) )),bind(C,$thf( C ))]]) ).
thf(3636,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TD ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,3557]) ).
thf(3637,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TD ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ),
inference(pattern_uni,[status(thm)],[3636:[]]) ).
thf(3707,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TC ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ),
inference(simp,[status(thm)],[3637]) ).
thf(367,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) @ sk1 )
| ( ( C @ A )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[46,118]) ).
thf(414,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 )
@ sk1 ) ),
inference(pre_uni,[status(thm)],[367:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk2 ))]]) ).
thf(43731,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 )
@ sk1 ) ),
inference(rewrite,[status(thm)],[414,6745]) ).
thf(43732,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 )
@ sk1 ) ),
inference(simp,[status(thm)],[43731]) ).
thf(33005,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: $o] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1885,209]) ).
thf(33006,plain,
! [TA: $tType,TB: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[33005:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(48007,plain,
! [TB: $tType,TC: $tType] :
( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
!= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,33006]) ).
thf(48008,plain,
! [TB: $tType,TC: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ) ),
inference(pattern_uni,[status(thm)],[48007:[]]) ).
thf(48176,plain,
! [TA: $tType,TB: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(simp,[status(thm)],[48008]) ).
thf(360,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ( ( C @ A )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[46,118]) ).
thf(403,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[360:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk1 ))]]) ).
thf(39726,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[403,6745]) ).
thf(39727,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[39726]) ).
thf(266,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > ( tyop_2Eoption_2Eoption @ $o ),A: TA] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o ) @ B @ ( c_2Eoption_2ESOME @ TB @ C ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[247,44]) ).
thf(278,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o )
@ ^ [C: TB] : ( c_2Eoption_2ESOME @ $o @ $true )
@ ( c_2Eoption_2ESOME @ TB @ B ) ) ),
inference(pre_uni,[status(thm)],[266:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TB] : ( c_2Eoption_2ESOME @ $o @ $true ) )),bind(C,$thf( C ))]]) ).
thf(286,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ $o )
@ ^ [C: TB] : ( c_2Eoption_2ESOME @ $o @ $true )
@ ( c_2Eoption_2ESOME @ TB @ B ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(11780,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( A
= ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EIS__NONE @ TA @ A )
!= ( c_2Eoption_2EIS__NONE @ $o @ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,11321]) ).
thf(11781,plain,
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2ENONE @ $o ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[11780:[bind(A,$thf( c_2Eoption_2ESOME @ $o @ $true )),bind_type(TA,$thf( $o ))]]) ).
thf(13394,plain,
! [TA: $tType] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ENONE @ $o ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[1164,11781]) ).
thf(13395,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ENONE @ $o ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[13394:[]]) ).
thf(35033,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= A )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34397,50]) ).
thf(35034,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(pattern_uni,[status(thm)],[35033:[bind(A,$thf( c_2Eoption_2ENONE @ TA ))]]) ).
thf(35790,plain,
! [TB: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2ENONE @ TB ) )
| ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,35034]) ).
thf(35791,plain,
! [TB: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(pattern_uni,[status(thm)],[35790:[]]) ).
thf(35941,plain,
! [TA: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[35791]) ).
thf(36462,plain,
! [TA: $tType,TC: $tType] :
( ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TC ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1210,35941]) ).
thf(36463,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TC ) ),
inference(pattern_uni,[status(thm)],[36462:[]]) ).
thf(36604,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[36463]) ).
thf(28,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TA,B: TB,A: TA > TB] :
( ~ ( c_2Eoption_2EIS__NONE @ TA @ C )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ C @ B @ A )
= B ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(58,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TA,B: TB,A: TA > TB] :
( ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ C @ B @ A )
= B )
| ~ ( c_2Eoption_2EIS__NONE @ TA @ C ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(59,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TA,B: TB,A: TA > TB] :
( ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ C @ B @ A )
= B )
| ~ ( c_2Eoption_2EIS__NONE @ TA @ C ) ),
inference(simp,[status(thm)],[58]) ).
thf(37,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ~ ( c_2Eoption_2EIS__SOME @ TA @ A ) )
= ( A
= ( c_2Eoption_2ENONE @ TA ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(53,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ~ ( c_2Eoption_2EIS__SOME @ TA @ A ) )
= ( A
= ( c_2Eoption_2ENONE @ TA ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(54,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ~ ( c_2Eoption_2EIS__SOME @ TA @ A ) )
= ( A
= ( c_2Eoption_2ENONE @ TA ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(1187,plain,
! [TA: $tType,TC: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,496]) ).
thf(1188,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ),
inference(pattern_uni,[status(thm)],[1187:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ))]]) ).
thf(1239,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ),
inference(simp,[status(thm)],[1188]) ).
thf(228,plain,
! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
( ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[209,224]) ).
thf(236,plain,
( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[228:[bind(A,$thf( E @ C )),bind(B,$thf( ^ [E: TB] : ( c_2Eoption_2EIS__SOME @ TA @ ( c_2Eoption_2ESOME @ TA @ ( E @ E ) ) ) )),bind(C,$thf( C ))]]) ).
thf(3415,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3017,275]) ).
thf(3416,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) ),
inference(pattern_uni,[status(thm)],[3415:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(170,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC,C: TC > ( tyop_2Eoption_2Eoption @ TB ),B: TA,A: TA > TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB ) @ C @ ( c_2Eoption_2ESOME @ TC @ D ) ) )
| ( ( c_2Eoption_2ESOME @ TB @ ( A @ B ) )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[44,44]) ).
thf(173,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC > TB,C: TC,B: TA,A: TA > TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [E: TC] : ( c_2Eoption_2ESOME @ TB @ ( D @ E ) )
@ ( c_2Eoption_2ESOME @ TC @ C ) ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[170:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [F: TC] : ( c_2Eoption_2ESOME @ TB @ ( E @ F ) ) ))]]) ).
thf(174,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC > TB,C: TC,B: TA,A: TA > TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [E: TC] : ( c_2Eoption_2ESOME @ TB @ ( D @ E ) )
@ ( c_2Eoption_2ESOME @ TC @ C ) ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[173:[]]) ).
thf(187,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC > TB,C: TC,B: TA,A: TA > TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [E: TC] : ( c_2Eoption_2ESOME @ TB @ ( D @ E ) )
@ ( c_2Eoption_2ESOME @ TC @ C ) ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(1805,plain,
! [TA: $tType,A: $o] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [B: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1164,247]) ).
thf(1806,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [A: $o] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) ),
inference(pattern_uni,[status(thm)],[1805:[bind(A,$thf( $true ))]]) ).
thf(35101,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= A )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34397,79]) ).
thf(35102,plain,
! [TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(pattern_uni,[status(thm)],[35101:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(35335,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[35102]) ).
thf(37403,plain,
! [TB: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2ENONE @ TB ) )
| ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,35335]) ).
thf(37404,plain,
! [TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(pattern_uni,[status(thm)],[37403:[]]) ).
thf(37557,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[37404]) ).
thf(37654,plain,
! [TA: $tType,TC: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TC ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1210,37557]) ).
thf(37655,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TC ) ),
inference(pattern_uni,[status(thm)],[37654:[]]) ).
thf(37788,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[37655]) ).
thf(3340,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1210,3268]) ).
thf(3341,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3340:[]]) ).
thf(3388,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(simp,[status(thm)],[3341]) ).
thf(14792,plain,
! [TA: $tType,TC: $tType,TD: $tType,TE: $tType,B: TA,A: TA > ( tyop_2Eoption_2Eoption @ TD )] :
( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TE )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TD ) @ ( tyop_2Eoption_2Eoption @ TE )
@ ^ [C: tyop_2Eoption_2Eoption @ TD] : ( c_2Eoption_2ENONE @ TE )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( A @ B ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TD ) @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,3388]) ).
thf(14793,plain,
! [TD: $tType,TE: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TE )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TD ) @ ( tyop_2Eoption_2Eoption @ TE )
@ ^ [A: tyop_2Eoption_2Eoption @ TD] : ( c_2Eoption_2ENONE @ TE )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[14792:[bind(A,$thf( ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )),bind(B,$thf( c_2Eoption_2ENONE @ TC )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TC ))]]) ).
thf(14874,plain,
! [TA: $tType,TB: $tType] :
( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) ) ),
inference(simp,[status(thm)],[14793]) ).
thf(15423,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Eoption_2Eoption @ TC] :
( ( ( ~ $true )
= ( A
= ( c_2Eoption_2ENONE @ TC ) ) )
| ( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) ) )
!= ( c_2Eoption_2EIS__SOME @ TC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14874,54]) ).
thf(15424,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: tyop_2Eoption_2Eoption @ TC] :
( ( A
!= ( c_2Eoption_2ENONE @ TC ) )
| ( ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) ) )
!= ( c_2Eoption_2EIS__SOME @ TC @ A ) ) ),
inference(simp,[status(thm)],[15423]) ).
thf(15425,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ),
inference(pattern_uni,[status(thm)],[15424:[bind(A,$thf( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB ) @ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( tyop_2Eoption_2Eoption @ TB ))]]) ).
thf(15455,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ),
inference(lifteq,[status(thm)],[15425]) ).
thf(35,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ENONE @ TA ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(47,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ENONE @ TA ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(48,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ENONE @ TA ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[47]) ).
thf(205,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC,B: TC > ( tyop_2Eoption_2Eoption @ TB ),A: TA > TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB ) @ B @ ( c_2Eoption_2ESOME @ TC @ C ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ENONE @ TA ) )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[48,44]) ).
thf(207,plain,
! [TA: $tType,TB: $tType,TC: $tType,B: TC > TA > TB,A: TC] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [C: TC] : ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ ( B @ C ) @ ( c_2Eoption_2ENONE @ TA ) )
@ ( c_2Eoption_2ESOME @ TC @ A ) ) ),
inference(pre_uni,[status(thm)],[205:[bind(A,$thf( D @ C )),bind(B,$thf( ^ [E: TC] : ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ ( D @ E ) @ ( c_2Eoption_2ENONE @ TA ) ) )),bind(C,$thf( C ))]]) ).
thf(208,plain,
! [TA: $tType,TB: $tType,TC: $tType,B: TC > TA > TB,A: TC] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [C: TC] : ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ ( B @ C ) @ ( c_2Eoption_2ENONE @ TA ) )
@ ( c_2Eoption_2ESOME @ TC @ A ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(13455,plain,
! [TA: $tType,TC: $tType] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,11888]) ).
thf(13456,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[13455:[]]) ).
thf(13518,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[13456]) ).
thf(3433,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,3017]) ).
thf(3434,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) ),
inference(pattern_uni,[status(thm)],[3433:[]]) ).
thf(3614,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ),
inference(simp,[status(thm)],[3434]) ).
thf(5962,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= A )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,79]) ).
thf(5963,plain,
! [TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[5962:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ))]]) ).
thf(6000,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[5963]) ).
thf(6028,plain,
! [TA: $tType,TC: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,6000]) ).
thf(6029,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ),
inference(pattern_uni,[status(thm)],[6028:[]]) ).
thf(6082,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(simp,[status(thm)],[6029]) ).
thf(8335,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,6082]) ).
thf(8336,plain,
! [TD: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ),
inference(pattern_uni,[status(thm)],[8335:[bind_type(TA,$thf( TC ))]]) ).
thf(8439,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[8336]) ).
thf(8487,plain,
! [TA: $tType,TC: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1210,8439]) ).
thf(8488,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ),
inference(pattern_uni,[status(thm)],[8487:[]]) ).
thf(8575,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(simp,[status(thm)],[8488]) ).
thf(29851,plain,
! [TB: $tType,TC: $tType,TD: $tType,A: TB] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TB @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [B: TB] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ TB @ A ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [B: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[190,8575]) ).
thf(29852,plain,
! [TD: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ),
inference(pattern_uni,[status(thm)],[29851:[bind(A,$thf( c_2Eoption_2ENONE @ TC )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( tyop_2Eoption_2Eoption @ TC ))]]) ).
thf(29947,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[29852]) ).
thf(35041,plain,
! [TB: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,29947]) ).
thf(35042,plain,
! [TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[35041:[]]) ).
thf(35319,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[35042]) ).
thf(41973,plain,
! [TB: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,35319]) ).
thf(41974,plain,
! [TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[41973:[]]) ).
thf(42201,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[41974]) ).
thf(42982,plain,
! [TA: $tType,TC: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,42201]) ).
thf(42983,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TC
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ),
inference(pattern_uni,[status(thm)],[42982:[]]) ).
thf(43209,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(simp,[status(thm)],[42983]) ).
thf(45655,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,43209]) ).
thf(45656,plain,
! [TD: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2ENONE @ TD ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ),
inference(pattern_uni,[status(thm)],[45655:[bind_type(TA,$thf( TC ))]]) ).
thf(45894,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[45656]) ).
thf(46449,plain,
! [TB: $tType] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,45894]) ).
thf(46450,plain,
! [TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[46449:[]]) ).
thf(46655,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(simp,[status(thm)],[46450]) ).
thf(297,plain,
! [TA: $tType,TB: $tType,D: TB > ( tyop_2Eoption_2Eoption @ $o ),C: tyop_2Eoption_2Eoption @ $o,B: TB,A: TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [E: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
= ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ TB @ B ) @ C @ D ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[247,46]) ).
thf(394,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ $o,B: TB,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
= ( c_2Eoption_2Eoption__CASE @ TB @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ TB @ B ) @ C
@ ^ [D: TB] : ( c_2Eoption_2ESOME @ $o @ $true ) ) ),
inference(pre_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( ^ [E: TB] : ( c_2Eoption_2ESOME @ $o @ $true ) ))]]) ).
thf(308,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) ) )
!= ( sk3 @ sk2 @ sk1 ) )
| ( ( C @ A )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[46,117]) ).
thf(369,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[308:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk1 ))]]) ).
thf(26563,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[369,6745]) ).
thf(26564,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[26563]) ).
thf(5,axiom,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(80,plain,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(313,plain,
! [TA: $tType,C: TA > ( tyop_2Eoption_2Eoption @ skt1 ),B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) )
| ( ( C @ A )
!= ( c_2Eoption_2ESOME @ skt1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[46,117]) ).
thf(406,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[313:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) ))]]) ).
thf(41178,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[406,6745]) ).
thf(41179,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[41178]) ).
thf(17214,plain,
! [TA: $tType,TB: $tType,TC: $tType,TE: $tType,C: TE > TC,B: TE > TC > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ),A: TE] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [D: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( B @ A @ ( C @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,243]) ).
thf(17400,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ),
inference(pre_uni,[status(thm)],[17214:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TE] : ^ [E: TC] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) )),bind(C,$thf( C ))]]) ).
thf(3454,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3017,253]) ).
thf(3455,plain,
! [TA: $tType,TB: $tType] :
( c_2Eoption_2EIS__SOME @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3454:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(1180,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,251]) ).
thf(1181,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[1180:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ))]]) ).
thf(6874,plain,
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[119,6745]) ).
thf(6875,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[6874]) ).
thf(32,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TA,B: TB,A: TA > TB] :
( ~ ( c_2Eoption_2EIS__SOME @ TA @ C )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ C @ B @ A )
= ( A @ ( c_2Eoption_2ETHE @ TA @ C ) ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(62,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TA,B: TB,A: TA > TB] :
( ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ C @ B @ A )
= ( A @ ( c_2Eoption_2ETHE @ TA @ C ) ) )
| ~ ( c_2Eoption_2EIS__SOME @ TA @ C ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(63,plain,
! [TA: $tType,TB: $tType,C: tyop_2Eoption_2Eoption @ TA,B: TB,A: TA > TB] :
( ( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ C @ B @ A )
= ( A @ ( c_2Eoption_2ETHE @ TA @ C ) ) )
| ~ ( c_2Eoption_2EIS__SOME @ TA @ C ) ),
inference(simp,[status(thm)],[62]) ).
thf(11275,plain,
! [TA: $tType,TC: $tType,A: ( tyop_2Eoption_2Eoption @ TC ) > ( tyop_2Eoption_2Eoption @ $o )] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( c_2Eoption_2EIS__NONE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( A @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1164,9756]) ).
thf(11327,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( c_2Eoption_2EIS__NONE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[11275:[bind(A,$thf( ^ [B: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ESOME @ $o @ $true ) ))]]) ).
thf(256,plain,
! [TA: $tType,TC: $tType,C: $o,B: $o > TC,A: TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ TC @ B
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( c_2Eoption_2ENONE @ TC ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ C ) ) ),
inference(paramod_ordered,[status(thm)],[247,197]) ).
thf(257,plain,
! [TA: $tType,TC: $tType,B: $o > TC,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ TC @ B
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( c_2Eoption_2ENONE @ TC ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( $true ))]]) ).
thf(282,plain,
! [TA: $tType,TB: $tType,B: $o > TB,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ TB @ B
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( c_2Eoption_2ENONE @ TB ) ),
inference(simp,[status(thm)],[257]) ).
thf(8597,plain,
! [TA: $tType,TB: $tType,A: TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [B: $o] : $true
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[247,1806]) ).
thf(8598,plain,
( ( c_2Eoption_2EOPTION__MAP @ $o @ $o
@ ^ [A: $o] : $true
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ESOME @ $o @ $true ) ),
inference(pattern_uni,[status(thm)],[8597:[bind(A,$thf( c_2Eoption_2ENONE @ TB )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TB ))]]) ).
thf(34998,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34397,695]) ).
thf(34999,plain,
! [TA: $tType] :
( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(pattern_uni,[status(thm)],[34998:[bind(A,$thf( c_2Eoption_2ENONE @ TA ))]]) ).
thf(336,plain,
! [TA: $tType,C: TA > ( tyop_2Eoption_2Eoption @ skt1 ),B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( C @ A )
!= ( c_2Eoption_2ESOME @ skt1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[46,119]) ).
thf(424,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[336:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) ))]]) ).
thf(48229,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[424,6745]) ).
thf(48230,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[48229]) ).
thf(147,plain,
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[119]) ).
thf(149,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(7617,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ $true
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) ) ) ),
inference(rewrite,[status(thm)],[149,6745]) ).
thf(7618,plain,
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) ) ) ),
inference(simp,[status(thm)],[7617]) ).
thf(22,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ TA,A: tyop_2Eoption_2Eoption @ TA] :
( ~ ( c_2Eoption_2EIS__SOME @ TA @ B )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ B @ A @ ( c_2Eoption_2ESOME @ TA ) )
= B ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(66,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ TA,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ B @ A @ ( c_2Eoption_2ESOME @ TA ) )
= B )
| ~ ( c_2Eoption_2EIS__SOME @ TA @ B ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(67,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ TA,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ TA ) @ B @ A @ ( c_2Eoption_2ESOME @ TA ) )
= B )
| ~ ( c_2Eoption_2EIS__SOME @ TA @ B ) ),
inference(simp,[status(thm)],[66]) ).
thf(335,plain,
! [TA: $tType,C: TA > ( tyop_2Eoption_2Eoption @ skt1 ),B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( C @ A )
!= ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46,119]) ).
thf(407,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[335:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ))]]) ).
thf(42649,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[407,6745]) ).
thf(42650,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[42649]) ).
thf(365,plain,
! [TA: $tType,C: TA > ( tyop_2Eoption_2Eoption @ skt1 ),B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ( ( C @ A )
!= ( c_2Eoption_2ESOME @ skt1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[46,118]) ).
thf(372,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[365:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) ))]]) ).
thf(28682,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[372,6745]) ).
thf(28683,plain,
! [TA: $tType,B: tyop_2Eoption_2Eoption @ skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2Eoption__CASE @ TA @ ( tyop_2Eoption_2Eoption @ skt1 ) @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( c_2Eoption_2ESOME @ skt1 @ sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[28682]) ).
thf(368,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) )
| ( ( C @ A )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[46,118]) ).
thf(427,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) ),
inference(pre_uni,[status(thm)],[368:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk1 ))]]) ).
thf(51472,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) ),
inference(rewrite,[status(thm)],[427,6745]) ).
thf(51473,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk1 ) ) ),
inference(simp,[status(thm)],[51472]) ).
thf(2869,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2EIS__SOME @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1210,253]) ).
thf(2870,plain,
! [TA: $tType,TB: $tType] :
( c_2Eoption_2EIS__SOME @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2869:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(1607,plain,
! [TA: $tType,TC: $tType,B: TA,A: TA > ( tyop_2Eoption_2Eoption @ TC )] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ skt1
@ ^ [C: tyop_2Eoption_2Eoption @ TC] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TC ) @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,1504]) ).
thf(1627,plain,
! [TA: $tType,TC: $tType,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ skt1
@ ^ [B: tyop_2Eoption_2Eoption @ TC] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [B: TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(pre_uni,[status(thm)],[1607:[bind(A,$thf( ^ [C: TA] : ( c_2Eoption_2ENONE @ TC ) ))]]) ).
thf(1687,plain,
! [TA: $tType,TB: $tType,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ skt1
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(simp,[status(thm)],[1627]) ).
thf(6860,plain,
! [TA: $tType,TB: $tType,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ $true
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ skt1
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(rewrite,[status(thm)],[1687,6745]) ).
thf(6861,plain,
! [TA: $tType,TB: $tType,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ skt1
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(simp,[status(thm)],[6860]) ).
thf(22683,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( A
= ( c_2Eoption_2ENONE @ TA ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EIS__NONE @ TA @ A )
!= ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,22370]) ).
thf(22684,plain,
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ $o ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[22683:[bind(A,$thf( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ $o ))]]) ).
thf(3419,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,1504]) ).
thf(3420,plain,
! [TA: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[3419:[]]) ).
thf(3599,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(simp,[status(thm)],[3420]) ).
thf(6866,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ~ $true
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(rewrite,[status(thm)],[3599,6745]) ).
thf(6867,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : sk1
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ skt1 ) ) ),
inference(simp,[status(thm)],[6866]) ).
thf(13405,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ TA @ A )
= ( c_2Eoption_2ESOME @ TA @ B ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( A = B )
!= ( ( c_2Eoption_2ESOME @ $o @ $true )
= ( c_2Eoption_2ENONE @ $o ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,11781]) ).
thf(13406,plain,
( ( c_2Eoption_2ESOME @ $o
@ ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ESOME @ $o @ $true ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ $o ) @ ( c_2Eoption_2ENONE @ $o ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[13405:[bind(A,$thf( c_2Eoption_2ESOME @ $o @ $true )),bind(B,$thf( c_2Eoption_2ENONE @ $o )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ $o ))]]) ).
thf(314,plain,
! [TA: $tType,C: TA > $o,B: $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
| ( ( C @ A )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46,117]) ).
thf(425,plain,
! [TA: $tType,B: $o,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( sk3 @ sk2 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(pre_uni,[status(thm)],[314:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : ( sk3 @ sk2 @ sk1 ) ))]]) ).
thf(48790,plain,
! [TA: $tType,B: $o,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( sk3 @ sk2 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[425,6745]) ).
thf(48791,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : ( sk3 @ sk2 @ sk1 ) )
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[48790]) ).
thf(48891,plain,
! [TA: $tType,TC: $tType,E: $o,D: TC,C: tyop_2Eoption_2Eoption @ TA,B: $o,A: TA > $o] :
( ~ ( c_2Eoption_2EIS__NONE @ TA @ C )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( B
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) )
| ( ( c_2Eoption_2Eoption__CASE @ TA @ $o @ C @ B @ A )
!= ( c_2Eoption_2Eoption__CASE @ TC @ $o @ ( c_2Eoption_2ESOME @ TC @ D ) @ E
@ ^ [F: TC] : ( sk3 @ sk2 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[59,48791]) ).
thf(48892,plain,
! [TC: $tType,B: TC,A: $o] :
( ~ ( c_2Eoption_2EIS__NONE @ TC @ ( c_2Eoption_2ESOME @ TC @ B ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( A
!= ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[48891:[bind(A,$thf( ^ [F: TC] : ( sk3 @ sk2 @ sk1 ) )),bind(B,$thf( B )),bind(C,$thf( c_2Eoption_2ESOME @ TC @ F )),bind(D,$thf( F )),bind(E,$thf( B )),bind_type(TA,$thf( TC ))]]) ).
thf(49128,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EIS__NONE @ TA @ ( c_2Eoption_2ESOME @ TA @ A ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) ) ),
inference(simp,[status(thm)],[48892]) ).
thf(34194,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: $o] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= A )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33329,79]) ).
thf(34195,plain,
! [TB: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TB
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2ENONE @ TB ) ),
inference(pattern_uni,[status(thm)],[34194:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(34500,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[34195]) ).
thf(40212,plain,
! [TA: $tType,TC: $tType,B: TA,A: TA > ( tyop_2Eoption_2Eoption @ TC )] :
( ( ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( A @ B ) ) )
= ( c_2Eoption_2ENONE @ TC ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TC ) @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [C: $o] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,34500]) ).
thf(40213,plain,
! [TC: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ) )
= ( c_2Eoption_2ENONE @ TC ) ),
inference(pattern_uni,[status(thm)],[40212:[bind(A,$thf( ^ [C: $o] : ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) )),bind(B,$thf( $true )),bind_type(TA,$thf( $o ))]]) ).
thf(40360,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
= ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[40213]) ).
thf(16576,plain,
! [TA: $tType,TC: $tType,TD: $tType,B: TA,A: TA > ( tyop_2Eoption_2Eoption @ TD )] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TD ) @ $o
@ ^ [C: tyop_2Eoption_2Eoption @ TD] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( A @ B ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ ( tyop_2Eoption_2Eoption @ TD ) @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[44,2854]) ).
thf(16577,plain,
! [TD: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TD ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TD] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TD ) @ ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pattern_uni,[status(thm)],[16576:[bind(A,$thf( ^ [C: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2EOPTION__JOIN @ TD @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ) )),bind(B,$thf( c_2Eoption_2ENONE @ TC )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TC ))]]) ).
thf(16635,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(simp,[status(thm)],[16577]) ).
thf(34940,plain,
! [TB: $tType,TC: $tType] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,1239]) ).
thf(34941,plain,
! [TB: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ),
inference(pattern_uni,[status(thm)],[34940:[]]) ).
thf(35296,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ),
inference(simp,[status(thm)],[34941]) ).
thf(34977,plain,
! [TA: $tType,TC: $tType,A: ( tyop_2Eoption_2Eoption @ TC ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )] :
( ( ( c_2Eoption_2ESOME @ $o
@ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TA )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( A @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,9756]) ).
thf(35197,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ $o
@ ( c_2Eoption_2EIS__NONE @ ( tyop_2Eoption_2Eoption @ TA )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
!= ( c_2Eoption_2ENONE @ $o ) ),
inference(pre_uni,[status(thm)],[34977:[bind(A,$thf( ^ [B: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ))]]) ).
thf(9661,plain,
! [TA: $tType,TB: $tType,B: ( tyop_2Eoption_2Eoption @ TB ) > ( tyop_2Eoption_2Eoption @ TA ),A: tyop_2Eoption_2Eoption @ TA] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) )
!= ( B @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,9572]) ).
thf(9679,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Eoption_2Eoption @ TB ) > ( tyop_2Eoption_2Eoption @ TA )] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( A @ ( c_2Eoption_2ENONE @ TB ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(pre_uni,[status(thm)],[9661:[bind(A,$thf( D @ ( c_2Eoption_2ENONE @ TB ) )),bind(B,$thf( ^ [D: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( D @ D ) ) ) ))]]) ).
thf(9755,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Eoption_2Eoption @ TB ) > ( tyop_2Eoption_2Eoption @ TA )] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( A @ ( c_2Eoption_2ENONE @ TB ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(simp,[status(thm)],[9679]) ).
thf(23,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TB] :
( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ ( c_2Eoption_2ENONE @ TA ) @ A @ B )
= A ),
inference(cnfConj,[status(thm)],[21]) ).
thf(74,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TB] :
( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ ( c_2Eoption_2ENONE @ TA ) @ A @ B )
= A ),
inference(lifteq,[status(thm)],[23]) ).
thf(75,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TB] :
( ( c_2Eoption_2Eoption__CASE @ TA @ TB @ ( c_2Eoption_2ENONE @ TA ) @ A @ B )
= A ),
inference(simp,[status(thm)],[74]) ).
thf(2911,plain,
! [TA: $tType,TB: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1210,695]) ).
thf(2912,plain,
! [TA: $tType,TB: $tType] :
( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2911:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(3502,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[3017,1239]) ).
thf(3503,plain,
! [TA: $tType,TC: $tType,TD: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TC ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TC] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ),
inference(pattern_uni,[status(thm)],[3502:[]]) ).
thf(3585,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ),
inference(simp,[status(thm)],[3503]) ).
thf(34819,plain,
! [TA: $tType,TB: $tType,TD: $tType,C: TD > TB,B: TD > TB > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ),A: TD] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [D: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( B @ A @ ( C @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[34397,243]) ).
thf(35165,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) ),
inference(pre_uni,[status(thm)],[34819:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TD] : ^ [E: TB] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )),bind(C,$thf( C ))]]) ).
thf(361,plain,
! [TA: $tType,C: TA > skt1,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C ) ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ( ( C @ A )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[46,118]) ).
thf(395,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[361:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : sk2 ))]]) ).
thf(36940,plain,
! [TA: $tType,B: skt1,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[395,6745]) ).
thf(36941,plain,
! [TA: $tType,B: skt1,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2ESOME @ skt1
@ ( c_2Eoption_2Eoption__CASE @ TA @ skt1 @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : sk2 ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[36940]) ).
thf(172,plain,
! [TA: $tType,B: TA,A: TA > skt1] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1 @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2ESOME @ skt1 @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ skt1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[44,118]) ).
thf(178,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[172:[bind(A,$thf( ^ [C: TA] : sk2 ))]]) ).
thf(191,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[178]) ).
thf(1197,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : sk2
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,191]) ).
thf(1198,plain,
! [TA: $tType] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk2
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1197:[bind(A,$thf( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ))]]) ).
thf(6870,plain,
! [TA: $tType] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk2
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[1198,6745]) ).
thf(6871,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk2
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ~ ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[6870]) ).
thf(165,plain,
! [TA: $tType,B: TA,A: TA > skt1] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1 @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 )
| ( ( c_2Eoption_2ESOME @ skt1 @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ skt1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[44,119]) ).
thf(185,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(pre_uni,[status(thm)],[165:[bind(A,$thf( ^ [C: TA] : sk2 ))]]) ).
thf(198,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[185]) ).
thf(13541,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[198,6745]) ).
thf(13542,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[13541]) ).
thf(5201,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [B: $o] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [B: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) )
!= ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[247,1920]) ).
thf(5202,plain,
! [TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ),
inference(pattern_uni,[status(thm)],[5201:[bind(A,$thf( c_2Eoption_2ENONE @ TB )),bind_type(TA,$thf( tyop_2Eoption_2Eoption @ TB ))]]) ).
thf(5268,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TA )
@ ( c_2Eoption_2ESOME @ $o @ $true ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ),
inference(simp,[status(thm)],[5202]) ).
thf(162,plain,
! [TA: $tType,B: TA,A: TA > skt1] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1 @ A @ ( c_2Eoption_2ESOME @ TA @ B ) ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) )
| ( ( c_2Eoption_2ESOME @ skt1 @ ( A @ B ) )
!= ( c_2Eoption_2ESOME @ skt1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[44,117]) ).
thf(180,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[162:[bind(A,$thf( ^ [C: TA] : sk2 ))]]) ).
thf(193,plain,
! [TA: $tType,A: TA] :
( ~ ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(11562,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[193,6745]) ).
thf(11563,plain,
! [TA: $tType,A: TA] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3
@ ( c_2Eoption_2EOPTION__MAP @ TA @ skt1
@ ^ [B: TA] : sk2
@ ( c_2Eoption_2ESOME @ TA @ A ) )
@ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
!= ( sk3 @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[11562]) ).
thf(2863,plain,
! [TA: $tType,TB: $tType,TD: $tType,A: tyop_2Eoption_2Eoption @ TB] :
( ( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [B: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1210,496]) ).
thf(2864,plain,
! [TA: $tType,TB: $tType,TD: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TD )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TD )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TD ) ) ),
inference(pattern_uni,[status(thm)],[2863:[bind(A,$thf( c_2Eoption_2ENONE @ TB ))]]) ).
thf(3015,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) )
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ),
inference(simp,[status(thm)],[2864]) ).
thf(320,plain,
! [TA: $tType,C: TA > $o,B: $o,A: TA] :
( ( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B @ C )
| ( c_2Ebool_2ET
!= ( C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17,46]) ).
thf(377,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : c_2Ebool_2ET ),
inference(pre_uni,[status(thm)],[320:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : c_2Ebool_2ET ))]]) ).
thf(29259,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eoption_2Eoption__CASE @ TA @ $o @ ( c_2Eoption_2ESOME @ TA @ A ) @ B
@ ^ [C: TA] : $true ),
inference(rewrite,[status(thm)],[377,17]) ).
thf(168,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC,C: TC > ( tyop_2Eoption_2Eoption @ TB ),B: TA,A: TA > TB] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ TB @ ( A @ B ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB ) @ C @ ( c_2Eoption_2ESOME @ TC @ D ) ) )
| ( ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ A @ ( c_2Eoption_2ESOME @ TA @ B ) )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[44,44]) ).
thf(182,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC > TA,B: TC > TA > TB,A: TC] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ TB @ ( B @ A @ ( C @ A ) ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [D: TC] : ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ ( B @ D ) @ ( c_2Eoption_2ESOME @ TA @ ( C @ D ) ) )
@ ( c_2Eoption_2ESOME @ TC @ A ) ) ),
inference(pre_uni,[status(thm)],[168:[bind(A,$thf( E @ D )),bind(B,$thf( G @ D )),bind(C,$thf( ^ [G: TC] : ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ ( E @ G ) @ ( c_2Eoption_2ESOME @ TA @ ( G @ G ) ) ) )),bind(D,$thf( D ))]]) ).
thf(195,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC > TA,B: TC > TA > TB,A: TC] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ESOME @ TB @ ( B @ A @ ( C @ A ) ) ) )
= ( c_2Eoption_2EOPTION__MAP @ TC @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [D: TC] : ( c_2Eoption_2EOPTION__MAP @ TA @ TB @ ( B @ D ) @ ( c_2Eoption_2ESOME @ TA @ ( C @ D ) ) )
@ ( c_2Eoption_2ESOME @ TC @ A ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(9,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ( ~ A ) )
& ( ( A = c_2Ebool_2EF )
= ( ~ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(94,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ( ~ A ) )
& ( ( A = c_2Ebool_2EF )
= ( ~ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(263,plain,
! [TA: $tType,TC: $tType,C: $o,B: $o > TC,A: TA] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ TC @ B
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [D: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
= ( c_2Eoption_2ESOME @ TC @ ( B @ C ) ) )
| ( ( c_2Eoption_2ESOME @ $o @ $true )
!= ( c_2Eoption_2ESOME @ $o @ C ) ) ),
inference(paramod_ordered,[status(thm)],[247,44]) ).
thf(264,plain,
! [TA: $tType,TC: $tType,B: $o > TC,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ TC @ B
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
= ( c_2Eoption_2ESOME @ TC @ ( B @ $true ) ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( $true ))]]) ).
thf(283,plain,
! [TA: $tType,TB: $tType,B: $o > TB,A: TA] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ TB @ B
@ ( c_2Eoption_2EOPTION__MAP @ TA @ $o
@ ^ [C: TA] : $true
@ ( c_2Eoption_2ESOME @ TA @ A ) ) )
= ( c_2Eoption_2ESOME @ TB @ ( B @ $true ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(32721,plain,
! [TB: $tType,TC: $tType] :
( ( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) )
| ( ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) )
!= ( c_2Eoption_2EOPTION__JOIN @ TC @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TC ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,1885]) ).
thf(32722,plain,
! [TB: $tType,TC: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TC )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TC )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TB ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TB] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TC ) @ ( c_2Eoption_2ENONE @ TC ) ) ),
inference(pattern_uni,[status(thm)],[32721:[]]) ).
thf(33461,plain,
! [TA: $tType,TB: $tType] :
( ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TB )
@ ^ [A: $o] : ( c_2Eoption_2ENONE @ TB )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ),
inference(simp,[status(thm)],[32722]) ).
thf(7023,plain,
! [TB: $tType,A: tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) )] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ A )
| ( A
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ A ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,6976]) ).
thf(7054,plain,
! [TB: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2EOPTION__JOIN @ TB @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) ) ),
inference(simp,[status(thm)],[7023]) ).
thf(7071,plain,
! [TA: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
| ( ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) ) ),
inference(simp,[status(thm)],[7054]) ).
thf(3033,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2EIS__NONE @ TA @ A )
| ( A
!= ( c_2Eoption_2ENONE @ TA ) ) ),
inference(bool_ext,[status(thm)],[65]) ).
thf(3058,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( A
!= ( c_2Eoption_2ENONE @ TA ) )
| ( c_2Eoption_2EIS__NONE @ TA @ A ) ),
inference(lifteq,[status(thm)],[3033]) ).
thf(3076,plain,
! [TA: $tType] : ( c_2Eoption_2EIS__NONE @ TA @ ( c_2Eoption_2ENONE @ TA ) ),
inference(simp,[status(thm)],[3058]) ).
thf(33799,plain,
! [TA: $tType,TB: $tType,A: ( tyop_2Eoption_2Eoption @ TB ) > ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )] :
( ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( A @ ( c_2Eoption_2ENONE @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[33329,9572]) ).
thf(34278,plain,
! [TA: $tType] :
( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) )
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) )
!= ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ),
inference(pre_uni,[status(thm)],[33799:[bind(A,$thf( ^ [B: tyop_2Eoption_2Eoption @ TB] : ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ))]]) ).
thf(4606,plain,
! [TB: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TB ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TB ) @ ( c_2Eoption_2ENONE @ TB ) ) ) ) ),
inference(simp,[status(thm)],[4530]) ).
thf(4723,plain,
! [TA: $tType] :
( ~ ( c_2Eoption_2EIS__SOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ETHE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) ) ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ TA ) ) @ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) ) ),
inference(simp,[status(thm)],[4606]) ).
thf(6856,plain,
! [TA: $tType] :
( ~ $true
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[1196,6745]) ).
thf(6857,plain,
! [TA: $tType] :
( ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 ) @ ( c_2Eoption_2ENONE @ skt1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ENONE @ skt1 ) @ ( c_2Eoption_2ESOME @ skt1 @ sk1 ) )
| ( c_2Eoption_2EOPTREL @ skt1 @ skt1 @ sk3 @ ( c_2Eoption_2ESOME @ skt1 @ sk2 )
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ skt1
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : sk1
@ ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) ) ) )
| ( sk3 @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[6856]) ).
thf(34089,plain,
! [TA: $tType,A: tyop_2Eoption_2Eoption @ TA] :
( ( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [B: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [B: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) )
| ( ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ ( c_2Eoption_2ENONE @ TA ) )
!= ( c_2Eoption_2ESOME @ ( tyop_2Eoption_2Eoption @ TA ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33329,695]) ).
thf(34090,plain,
! [TA: $tType] :
( c_2Eoption_2ETHE @ $o
@ ( c_2Eoption_2EOPTION__MAP @ ( tyop_2Eoption_2Eoption @ TA ) @ $o
@ ^ [A: tyop_2Eoption_2Eoption @ TA] : $true
@ ( c_2Eoption_2EOPTION__MAP @ $o @ ( tyop_2Eoption_2Eoption @ TA )
@ ^ [A: $o] : ( c_2Eoption_2EOPTION__JOIN @ TA @ ( c_2Eoption_2ENONE @ ( tyop_2Eoption_2Eoption @ TA ) ) )
@ ( c_2Eoption_2ESOME @ $o @ $true ) ) ) ),
inference(pattern_uni,[status(thm)],[34089:[bind(A,$thf( c_2Eoption_2ENONE @ TA ))]]) ).
thf(65041,plain,
$false,
inference(e,[status(thm)],[10917,1879,33839,7973,6976,249,1179,88,217,6199,247,2837,44999,6295,9572,2854,3017,3429,1164,13874,42,31239,17433,288,22370,22352,52,35452,26140,1832,33329,20,11321,35154,46,284,38797,27620,3557,11363,31510,33507,189,376,6745,106,1828,937,11389,4724,280,61,38717,89,243,17442,46858,6020,17919,85,39299,13519,3418,50747,12159,6124,275,45956,197,65,1920,14248,47056,1210,40444,47034,285,224,742,32006,3632,7365,225,77,4167,1842,2978,11892,3611,11888,11336,73,105,3587,6859,3508,19775,128,34983,34397,17454,3707,15976,43732,17,48176,39727,44,286,13395,36604,59,71,12,54,1239,236,3416,31873,43713,187,1806,37788,15455,208,33006,19357,9756,13518,251,3614,959,695,46655,394,7324,26564,11781,80,41179,34126,209,17400,3455,1181,6875,48,63,11327,282,45894,8598,34999,48230,7618,50,67,42650,28683,43209,51473,3388,1240,87,2870,6861,22684,6867,13406,49128,1326,40360,16635,35296,35197,9755,75,2912,3585,11322,35165,36941,6871,13542,5268,190,19,11563,3015,239,29259,79,195,16771,94,283,48791,34500,33461,7071,15,3076,1885,34278,4723,19750,6857,34090,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP011^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.24 % Computer : n016.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 19:30:50 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.11 % [INFO] Parsing done (230ms).
% 1.31/1.12 % [INFO] Running in sequential loop mode.
% 2.20/1.52 % [INFO] eprover registered as external prover.
% 2.20/1.53 % [INFO] Scanning for conjecture ...
% 2.37/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.54/1.73 % [INFO] Axiom selection finished. Selected 9 axioms (removed 9 axioms).
% 2.80/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 2.80/1.81 % [INFO] Type checking passed.
% 2.80/1.82 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 248.53/121.91 % External prover 'e' found a proof!
% 248.53/121.91 % [INFO] Killing All external provers ...
% 248.53/121.91 % Time passed: 121526ms (effective reasoning time: 120784ms)
% 248.53/121.91 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 248.53/121.91 % Axioms used in derivation (9): thm_2Ebool_2ENOT__CLAUSES, thm_2Ebool_2EREFL__CLAUSE, thm_2Ebool_2EEQ__CLAUSES, thm_2Eoption_2EOPTREL__def, thm_2Ebool_2EFALSITY, thm_2Eoption_2Eoption__CLAUSES, thm_2Ebool_2ETRUTH, thm_2Ebool_2EOR__CLAUSES, thm_2Ebool_2EAND__CLAUSES
% 248.53/121.91 % No. of inferences in proof: 681
% 248.53/121.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 121526 ms resp. 120784 ms w/o parsing
% 250.20/122.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 250.20/122.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------