%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT176_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 : Sun Sep 27 08:27:30 AM UTC 2026
% Result : Theorem 168.29s 121.29s
% Output : Refutation 166.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 76 ( 11 unt; 0 typ; 6 def)
% Number of atoms : 926 ( 71 equ; 0 cnn)
% Maximal formula atoms : 104 ( 12 avg)
% Number of connectives : 3502 ( 166 ~; 179 |; 37 &;3098 @)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 11 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 12 con; 0-4 aty)
% Number of variables : 87 ( 0 ^; 77 !; 4 ?; 87 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ fun ) ) ).
thf(trans_decl,type,
trans:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(l_decl,type,
l: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: arrow_411405190le_alt ).
thf(sk3_decl,type,
sk3: arrow_411405190le_alt ).
thf(sk4_decl,type,
sk4: arrow_411405190le_alt ).
thf(sk5_decl,type,
sk5: arrow_411405190le_alt ).
thf(sk6_decl,type,
sk6: arrow_411405190le_alt ).
thf(sk7_decl,type,
sk7: arrow_411405190le_alt ).
thf(sk2_def,definition,
( sk2
= ( @+[A: arrow_411405190le_alt] : ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: arrow_411405190le_alt] :
~ ! [B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: arrow_411405190le_alt] :
~ ( ( sk3 != A )
=> ( ( l @ ( sk3 @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( sk3 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: arrow_411405190le_alt] : ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: arrow_411405190le_alt] :
~ ! [B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: arrow_411405190le_alt] :
~ ( ( sk6 != A )
=> ( ( l @ ( A @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk6 @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) )
<=> ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) )
<=> ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(83,plain,
~ ( ( ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) )
=> ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) ) )
& ( ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) )
=> ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(84,plain,
~ ( ( ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ~ ? [A: arrow_411405190le_alt] : ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) )
=> ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ~ ? [A: arrow_411405190le_alt] : ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) ) )
& ( ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ~ ? [A: arrow_411405190le_alt] : ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) )
=> ( ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( A != B )
=> ( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
& ~ ? [A: arrow_411405190le_alt] : ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( l @ ( arrow_411405190le_alt @ trans ) ) ) ) ),
inference(miniscope,[status(thm)],[83]) ).
thf(85,plain,
! [F: arrow_411405190le_alt,E: arrow_411405190le_alt,D: arrow_411405190le_alt,C: arrow_411405190le_alt,B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( ~ ( l @ ( sk7 @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) )
| sk1 )
& ( ~ ( l @ ( sk6 @ ( sk7 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) )
| sk1 )
& ( ( sk6 != sk7 )
| ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) )
| sk1 )
& ( ( l @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( F @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( E = F )
| sk1 )
& ( ~ ( l @ ( D @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1 )
& ( ( l @ ( arrow_411405190le_alt @ trans ) )
| sk1 )
& ( ~ sk1
| ~ ( l @ ( sk3 @ ( sk4 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk2 @ ( sk2 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) ) )
& ( ~ sk1
| ~ ( l @ ( sk4 @ ( sk3 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk2 @ ( sk2 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) ) )
& ( ~ sk1
| ( sk3 != sk4 )
| ( l @ ( sk2 @ ( sk2 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) ) )
& ( ~ sk1
| ( l @ ( C @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( B = C ) )
& ( ~ sk1
| ~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ~ sk1
| ( l @ ( arrow_411405190le_alt @ trans ) ) ) ),
inference(cnf,[status(esa)],[84]) ).
thf(86,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ~ sk1
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(100,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ~ sk1
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(101,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ~ sk1
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = B ) ),
inference(simp,[status(thm)],[100]) ).
thf(89,plain,
( ~ sk1
| ~ ( l @ ( sk3 @ ( sk4 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk2 @ ( sk2 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(95,plain,
! [A: arrow_411405190le_alt] :
( ~ sk1
| ~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(400,plain,
! [A: arrow_411405190le_alt] :
( ( ( l @ ( sk2 @ ( sk2 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ~ sk1
| ~ $true
| ~ sk1
| ~ ( l @ ( sk3 @ ( sk4 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) ) ),
inference(paramod_ordered,[status(thm)],[89,95]) ).
thf(401,plain,
! [A: arrow_411405190le_alt] :
( ( ( l @ ( sk2 @ ( sk2 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ~ sk1
| ~ ( l @ ( sk3 @ ( sk4 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) ) ),
inference(simp,[status(thm)],[400]) ).
thf(402,plain,
( ~ sk1
| ~ ( l @ ( sk3 @ ( sk4 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) ) ),
inference(pattern_uni,[status(thm)],[401:[bind(A,$thf( sk2 ))]]) ).
thf(97,plain,
( ( l @ ( arrow_411405190le_alt @ trans ) )
| sk1 ),
inference(cnfConj,[status(thm)],[85]) ).
thf(87,plain,
( ~ sk1
| ( l @ ( arrow_411405190le_alt @ trans ) ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(392,plain,
( ( sk1 != sk1 )
| ~ $true
| ( l @ ( arrow_411405190le_alt @ trans ) )
| ( l @ ( arrow_411405190le_alt @ trans ) ) ),
inference(paramod_ordered,[status(thm)],[97,87]) ).
thf(393,plain,
( ( sk1 != sk1 )
| ( l @ ( arrow_411405190le_alt @ trans ) ) ),
inference(simp,[status(thm)],[392]) ).
thf(394,plain,
l @ ( arrow_411405190le_alt @ trans ),
inference(pattern_uni,[status(thm)],[393:[]]) ).
thf(413,plain,
( ~ sk1
| ~ ( l @ ( sk3 @ ( sk4 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[402,394]) ).
thf(414,plain,
( ~ sk1
| ~ ( l @ ( sk3 @ ( sk4 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
inference(simp,[status(thm)],[413]) ).
thf(1294,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( sk3 @ ( sk4 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ~ sk1
| ~ $true
| ~ sk1
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[101,414]) ).
thf(1295,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( sk3 @ ( sk4 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ~ sk1
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1294]) ).
thf(1296,plain,
( ~ sk1
| ( l @ ( sk4 @ ( sk3 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[1295:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(88,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = B )
| sk1 ),
inference(cnfConj,[status(thm)],[85]) ).
thf(98,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1
| ( A = B ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(99,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1
| ( A = B ) ),
inference(simp,[status(thm)],[98]) ).
thf(93,plain,
( ~ ( l @ ( sk6 @ ( sk7 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) )
| sk1 ),
inference(cnfConj,[status(thm)],[85]) ).
thf(437,plain,
( ~ ( l @ ( sk6 @ ( sk7 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ $true
| sk1 ),
inference(rewrite,[status(thm)],[93,394]) ).
thf(438,plain,
( ~ ( l @ ( sk6 @ ( sk7 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1 ),
inference(simp,[status(thm)],[437]) ).
thf(92,plain,
! [A: arrow_411405190le_alt] :
( ~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1 ),
inference(cnfConj,[status(thm)],[85]) ).
thf(104,plain,
! [A: arrow_411405190le_alt] :
( ~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1 ),
inference(simp,[status(thm)],[92]) ).
thf(457,plain,
! [A: arrow_411405190le_alt] :
( ( ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ~ $true
| sk1
| ~ ( l @ ( sk6 @ ( sk7 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1 ),
inference(paramod_ordered,[status(thm)],[438,104]) ).
thf(458,plain,
! [A: arrow_411405190le_alt] :
( ( ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ~ ( l @ ( sk6 @ ( sk7 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1 ),
inference(simp,[status(thm)],[457]) ).
thf(459,plain,
( ~ ( l @ ( sk6 @ ( sk7 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[458:[bind(A,$thf( sk5 ))]]) ).
thf(871,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( sk6 @ ( sk7 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ~ $true
| sk1
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[99,459]) ).
thf(872,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( ( l @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( sk6 @ ( sk7 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ( l @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1
| ( A = B ) ),
inference(simp,[status(thm)],[871]) ).
thf(873,plain,
( ( l @ ( sk7 @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1
| ( sk7 = sk6 ) ),
inference(pattern_uni,[status(thm)],[872:[bind(A,$thf( sk7 )),bind(B,$thf( sk6 ))]]) ).
thf(96,plain,
( ~ ( l @ ( sk7 @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) )
| sk1 ),
inference(cnfConj,[status(thm)],[85]) ).
thf(431,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( sk1 != sk1 )
| ~ $true
| ~ ( l @ ( B @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
inference(paramod_ordered,[status(thm)],[104,95]) ).
thf(432,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ( sk1 != sk1 )
| ~ ( l @ ( B @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
inference(simp,[status(thm)],[431]) ).
thf(433,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ~ ( l @ ( B @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
inference(pattern_uni,[status(thm)],[432:[]]) ).
thf(491,plain,
! [B: arrow_411405190le_alt,A: arrow_411405190le_alt] :
( ~ $true
| ( ( l @ ( B @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[433]) ).
thf(492,plain,
! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( B ))]]) ).
thf(494,plain,
! [A: arrow_411405190le_alt] :
~ ( l @ ( A @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(simp,[status(thm)],[492]) ).
thf(567,plain,
( ~ ( l @ ( sk7 @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| $false
| ~ $true
| sk1 ),
inference(rewrite,[status(thm)],[96,394,494]) ).
thf(568,plain,
( ~ ( l @ ( sk7 @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| sk1 ),
inference(simp,[status(thm)],[567]) ).
thf(1093,plain,
( ( ( l @ ( sk7 @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( sk7 @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| ~ $true
| sk1
| sk1
| ( sk7 = sk6 ) ),
inference(paramod_ordered,[status(thm)],[873,568]) ).
thf(1094,plain,
( ( ( l @ ( sk7 @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
!= ( l @ ( sk7 @ ( sk6 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
| sk1
| ( sk7 = sk6 ) ),
inference(simp,[status(thm)],[1093]) ).
thf(1095,plain,
( sk1
| ( sk7 = sk6 ) ),
inference(pattern_uni,[status(thm)],[1094:[]]) ).
thf(90,plain,
( ( sk6 != sk7 )
| ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) )
| sk1 ),
inference(cnfConj,[status(thm)],[85]) ).
thf(103,plain,
( ( l @ ( sk5 @ ( sk5 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) )
| sk1
| ( sk7 != sk6 ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(706,plain,
( $false
| ~ $true
| sk1
| ( sk7 != sk6 ) ),
inference(rewrite,[status(thm)],[103,394,494]) ).
thf(707,plain,
( sk1
| ( sk7 != sk6 ) ),
inference(simp,[status(thm)],[706]) ).
thf(1142,plain,
( ( sk7 != sk7 )
| sk1
| ( sk6 != sk6 )
| sk1 ),
inference(paramod_ordered,[status(thm)],[1095,707]) ).
thf(1143,plain,
( ( sk7 != sk7 )
| sk1 ),
inference(simp,[status(thm)],[1142]) ).
thf(1144,plain,
sk1,
inference(pattern_uni,[status(thm)],[1143:[]]) ).
thf(94,plain,
( ~ sk1
| ~ ( l @ ( sk4 @ ( sk3 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( l @ ( sk2 @ ( sk2 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(515,plain,
( ~ sk1
| ~ ( l @ ( sk4 @ ( sk3 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| $false
| ~ $true ),
inference(rewrite,[status(thm)],[94,394,494]) ).
thf(516,plain,
( ~ sk1
| ~ ( l @ ( sk4 @ ( sk3 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(1435,plain,
( ~ $true
| ~ ( l @ ( sk4 @ ( sk3 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
inference(rewrite,[status(thm)],[516,1144]) ).
thf(1436,plain,
~ ( l @ ( sk4 @ ( sk3 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(simp,[status(thm)],[1435]) ).
thf(3888,plain,
( ~ $true
| $false
| ( sk4 = sk3 ) ),
inference(rewrite,[status(thm)],[1296,1144,1436]) ).
thf(3889,plain,
sk4 = sk3,
inference(simp,[status(thm)],[3888]) ).
thf(91,plain,
( ~ sk1
| ( sk3 != sk4 )
| ( l @ ( sk2 @ ( sk2 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(102,plain,
( ~ sk1
| ( l @ ( sk2 @ ( sk2 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( l @ ( arrow_411405190le_alt @ trans ) )
| ( sk4 != sk3 ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(559,plain,
( ~ sk1
| $false
| ~ $true
| ( sk4 != sk3 ) ),
inference(rewrite,[status(thm)],[102,394,494]) ).
thf(560,plain,
( ~ sk1
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[559]) ).
thf(1441,plain,
( ~ $true
| ( sk4 != sk3 ) ),
inference(rewrite,[status(thm)],[560,1144]) ).
thf(1442,plain,
sk4 != sk3,
inference(simp,[status(thm)],[1441]) ).
thf(3890,plain,
$false,
inference(simplifyReflect,[status(thm)],[3889,1442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT176_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 06:38:33 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.92/1.32 % [INFO] Parsing done (332ms).
% 1.92/1.34 % [INFO] Running in sequential loop mode.
% 2.80/1.73 % [INFO] eprover registered as external prover.
% 2.80/1.74 % [INFO] Scanning for conjecture ...
% 3.29/1.95 % [INFO] Found a conjecture (or negated_conjecture) and 80 axioms. Running axiom selection ...
% 3.76/2.08 % [INFO] Axiom selection finished. Selected 80 axioms (removed 0 axioms).
% 4.70/2.33 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.70/2.36 % [INFO] Type checking passed.
% 4.70/2.37 % [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 ...
% 6.27/2.79 % [INFO] [Domain constraints] Detected constraint on bool
% 6.27/2.80 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 168.29/121.28 % [INFO] Killing All external provers ...
% 168.29/121.28 % Time passed: 120735ms (effective reasoning time: 119934ms)
% 168.29/121.28 % 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)>
% 168.29/121.28 % Axioms used in derivation (0):
% 168.29/121.28 % No. of inferences in proof: 70
% 168.29/121.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 120735 ms resp. 119934 ms w/o parsing
% 166.36/121.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 166.36/121.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------