%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT175_5 : TPTP v9.3.1. Released v6.0.0.
% 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 : n010.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 57.20s 12.50s
% Output : Refutation 49.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 111
% Syntax : Number of formulae : 286 ( 86 unt; 0 typ; 4 def)
% Number of atoms : 1272 ( 152 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 6400 ( 151 ~; 53 |; 58 &;5836 @)
% ( 32 <=>; 270 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 8 con; 0-6 aty)
% Number of variables : 1000 ( 9 ^; 976 !; 11 ?;1000 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(arrow_1985332922le_Lin_decl,type,
arrow_1985332922le_Lin: bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(order_1409979114der_on_decl,type,
order_1409979114der_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(order_915043626der_on_decl,type,
order_915043626der_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(order_preorder_on_decl,type,
order_preorder_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(order_215145569der_on_decl,type,
order_215145569der_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ fun ) ) ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(inv_imagep_decl,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) @ ( TB @ fun ) ) > ( TB @ ( TA @ fun ) ) > TA > TA > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( TA @ ( TB @ product_prod ) ) ) ).
thf(product_curry_decl,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) ) > TC > TB > TA ) ).
thf(produc1605651328_split_decl,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(product_prod_rec_decl,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(id_on_decl,type,
id_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) ) ).
thf(antisym_decl,type,
antisym:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(converse_decl,type,
converse:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) ) > ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) ) ) ).
thf(inv_image_decl,type,
inv_image:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ ( TB @ product_prod ) @ fun ) ) > ( TB @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) ) ).
thf(irrefl_decl,type,
irrefl:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(refl_on_decl,type,
refl_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(sym_decl,type,
sym:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(total_on_decl,type,
total_on:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(trans_decl,type,
trans:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(transitive_acyclic_decl,type,
transitive_acyclic:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > $o ) ).
thf(transitive_trancl_decl,type,
transitive_trancl:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(l_decl,type,
l: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ).
thf(sk1_decl,type,
sk1:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ product_prod ) ) > TA ) ).
thf(sk2_decl,type,
sk2:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ product_prod ) ) > TB ) ).
thf(sk36_decl,type,
sk36:
!>[TA: $tType] : TA ).
thf(sk65_decl,type,
sk65:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > TA ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [TA: $tType,TB: $tType,A: TB @ ( TA @ product_prod )] :
@+[B: TA] :
~ ! [C: TB] :
( A
!= ( C @ ( B @ ( TB @ ( TA @ product_Pair ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [TA: $tType,TB: $tType,A: TB @ ( TA @ product_prod )] :
@+[B: TB] :
~ ( ( A
!= ( B @ ( A @ ( TA @ ( TB @ sk1 ) ) @ ( TB @ ( TA @ product_Pair ) ) ) ) ) ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( ^ [TA: $tType] :
@+[A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ) ) ) ).
thf(sk65_def,definition,
( sk65
= ( ^ [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
@+[B: TA] :
~ ~ ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ).
thf(88,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( B != A )
=> ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_notin__Lin__iff) ).
thf(404,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( B != A )
=> ( ( ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_prod__cases5) ).
thf(365,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_curryE) ).
thf(352,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(3,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( A @ ( TA @ refl_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_refl__on__Id__on) ).
thf(115,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( A @ ( TA @ refl_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(120,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,axiom,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_top1I) ).
thf(202,plain,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(203,plain,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(cnf,[status(esa)],[202]) ).
thf(121,plain,
~ ( fFalse @ pp ),
inference(polarity_switch,[status(thm)],[120]) ).
thf(673,plain,
! [TA: $tType,A: TA] :
( ( ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,121]) ).
thf(674,plain,
! [TA: $tType,A: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[673]) ).
thf(677,plain,
! [TA: $tType,A: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[674]) ).
thf(83,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( D @ ( TA @ trans ) )
=> ( ( D @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( D @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( D @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_transD) ).
thf(384,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( D @ ( TA @ trans ) )
=> ( ( D @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( D @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( D @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1,conjecture,
( ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
<=> ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
<=> ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(109,plain,
~ ( ( ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
& ( ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(110,plain,
( ( ~ ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
| ~ ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
& ( ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
| ~ ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
& ( ~ ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
| ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
& ( ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
| ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(111,plain,
( ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
| ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(cnfConj,[status(thm)],[110]) ).
thf(114,plain,
( ~ ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
| ~ ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(cnfConj,[status(thm)],[110]) ).
thf(496,plain,
( ~ $true
| ( ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
!= ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
| ~ ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[114]) ).
thf(498,plain,
( ( arrow_1985332922le_Lin != arrow_1985332922le_Lin )
| ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l )
| ~ ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(simp,[status(thm)],[496]) ).
thf(499,plain,
( ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l )
| ~ ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(simp,[status(thm)],[498]) ).
thf(506,plain,
( ( ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
!= ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
| ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l )
| ~ $true
| ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,499]) ).
thf(507,plain,
( ( ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
!= ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
| ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l )
| ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(simp,[status(thm)],[506]) ).
thf(514,plain,
( ( arrow_1985332922le_Lin != arrow_1985332922le_Lin )
| ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l )
| ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l )
| ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(simp,[status(thm)],[507]) ).
thf(518,plain,
( ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l )
| ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(simp,[status(thm)],[514]) ).
thf(548,plain,
( ( ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
!= ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
| ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l )
| ~ $true
| ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l ) ),
inference(paramod_ordered,[status(thm)],[518,499]) ).
thf(549,plain,
( ( ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
!= ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
| ( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l ) ),
inference(simp,[status(thm)],[548]) ).
thf(550,plain,
( ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) )
!= l ),
inference(pattern_uni,[status(thm)],[549:[]]) ).
thf(13,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_1409979114der_on ) ) )
<=> ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_linear__order__on__def) ).
thf(142,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) )
=> ( A @ ( B @ ( TA @ order_1409979114der_on ) ) ) )
& ( ( A @ ( B @ ( TA @ order_1409979114der_on ) ) )
=> ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(117,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(118,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(cnf,[status(esa)],[117]) ).
thf(119,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(lifteq,[status(thm)],[118]) ).
thf(72,axiom,
( arrow_1985332922le_Lin
= ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Lin__def) ).
thf(350,plain,
( arrow_1985332922le_Lin
= ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(351,plain,
( ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ collect ) )
= arrow_1985332922le_Lin ),
inference(lifteq,[status(thm)],[350]) ).
thf(569,plain,
! [A: bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun )] :
( ( ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ collect ) )
!= ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ collect ) ) )
| ( A = arrow_1985332922le_Lin ) ),
inference(paramod_ordered,[status(thm)],[119,351]) ).
thf(570,plain,
( ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) )
= arrow_1985332922le_Lin ),
inference(pattern_uni,[status(thm)],[569:[bind(A,$thf( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ order_215145569der_on ) ))]]) ).
thf(15,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ trans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_trans__Id__on) ).
thf(156,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ trans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(157,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ trans ) ),
inference(cnf,[status(esa)],[156]) ).
thf(7,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ sym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_sym__Id__on) ).
thf(125,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ sym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(69,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [B: TA] :
~ ( A @ ( TA @ transitive_trancl ) @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_acyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_acyclicI) ).
thf(344,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [B: TA] :
~ ( A @ ( TA @ transitive_trancl ) @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_acyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_prod__induct6) ).
thf(325,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_internal__split__conv) ).
thf(228,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(179,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(48,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ sym ) )
<=> ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_sym__def) ).
thf(253,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) )
=> ( A @ ( TA @ sym ) ) )
& ( ( A @ ( TA @ sym ) )
=> ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(71,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_trancl ) @ ( TA @ ( TA @ converse ) ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_trancl__converseD) ).
thf(348,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_trancl ) @ ( TA @ ( TA @ converse ) ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Pair__eq) ).
thf(147,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(132,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(85,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ irrefl ) )
<=> ! [B: TA] :
~ ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_irrefl__def) ).
thf(394,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ! [B: TA] :
~ ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ irrefl ) ) )
& ( ( A @ ( TA @ irrefl ) )
=> ! [B: TA] :
~ ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(395,plain,
! [TA: $tType,B: TA,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ( A @ ( TA @ irrefl ) )
| ( A @ ( A @ ( TA @ sk65 ) @ ( A @ ( TA @ sk65 ) @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) )
& ( ~ ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ~ ( A @ ( TA @ irrefl ) ) ) ),
inference(cnf,[status(esa)],[394]) ).
thf(396,plain,
! [TA: $tType,B: TA,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ~ ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ~ ( A @ ( TA @ irrefl ) ) ),
inference(cnfConj,[status(thm)],[395]) ).
thf(116,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( A @ ( TA @ refl_on ) ) ),
inference(cnf,[status(esa)],[115]) ).
thf(46,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] : ( A @ ( B @ ( TA @ member ) ) )
=> ( ( bool @ ( TA @ fun ) @ top_top )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_UNIV__eq__I) ).
thf(248,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] : ( A @ ( B @ ( TA @ member ) ) )
=> ( ( bool @ ( TA @ fun ) @ top_top )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_prod_Orecs) ).
thf(439,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(42,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ transitive_acyclic ) )
<=> ! [B: TA] :
~ ( A @ ( TA @ transitive_trancl ) @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_acyclic__def) ).
thf(233,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ! [B: TA] :
~ ( A @ ( TA @ transitive_trancl ) @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_acyclic ) ) )
& ( ( A @ ( TA @ transitive_acyclic ) )
=> ! [B: TA] :
~ ( A @ ( TA @ transitive_trancl ) @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(100,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ transitive_acyclic ) )
<=> ( A @ ( TA @ transitive_acyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_acyclic__converse) ).
thf(452,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ( A @ ( TA @ transitive_acyclic ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ transitive_acyclic ) ) )
& ( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ transitive_acyclic ) )
=> ( A @ ( TA @ transitive_acyclic ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(82,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ order_1409979114der_on ) ) )
<=> ( A @ ( B @ ( TA @ order_1409979114der_on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_linear__order__on__converse) ).
thf(380,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TA @ order_1409979114der_on ) ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ order_1409979114der_on ) ) ) )
& ( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ order_1409979114der_on ) ) )
=> ( A @ ( B @ ( TA @ order_1409979114der_on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_trancl ) @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_trancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_trancl__trans) ).
thf(424,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_trancl ) @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_trancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ refl_on ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( B @ ( A @ ( A @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_refl__onD) ).
thf(192,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ refl_on ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( B @ ( A @ ( A @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_PairE) ).
thf(137,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(104,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(467,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TB @ ( TA @ converse ) ) @ ( TA @ ( TB @ converse ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_converse__converse) ).
thf(197,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TB @ ( TA @ converse ) ) @ ( TA @ ( TB @ converse ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(107,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_UNIV__def) ).
thf(487,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(488,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(cnf,[status(esa)],[487]) ).
thf(489,plain,
! [TA: $tType] :
( ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ top_top ) ),
inference(lifteq,[status(thm)],[488]) ).
thf(565,plain,
! [TB: $tType,A: bool @ ( TB @ fun )] :
( ( ( A @ ( TB @ collect ) )
!= ( fTrue @ ( TB @ ( bool @ combk ) ) @ ( TB @ collect ) ) )
| ( A
= ( bool @ ( TB @ fun ) @ top_top ) ) ),
inference(paramod_ordered,[status(thm)],[119,489]) ).
thf(566,plain,
! [TB: $tType] :
( ( fTrue @ ( TB @ ( bool @ combk ) ) )
= ( bool @ ( TB @ fun ) @ top_top ) ),
inference(pattern_uni,[status(thm)],[565:[bind(A,$thf( fTrue @ ( TB @ ( bool @ combk ) ) ))]]) ).
thf(573,plain,
! [TA: $tType] :
( ( fTrue @ ( TA @ ( bool @ combk ) ) )
= ( bool @ ( TA @ fun ) @ top_top ) ),
inference(simp,[status(thm)],[566]) ).
thf(582,plain,
( ( ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top )
!= ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top ) )
| ( ( fTrue @ ( arrow_411405190le_alt @ ( bool @ combk ) ) @ ( arrow_411405190le_alt @ order_215145569der_on ) )
= arrow_1985332922le_Lin ) ),
inference(paramod_ordered,[status(thm)],[573,570]) ).
thf(583,plain,
( ( fTrue @ ( arrow_411405190le_alt @ ( bool @ combk ) ) @ ( arrow_411405190le_alt @ order_215145569der_on ) )
= arrow_1985332922le_Lin ),
inference(pattern_uni,[status(thm)],[582:[]]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( C @ ( TA @ antisym ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C @ ( B @ ( A @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_antisymD) ).
thf(456,plain,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( C @ ( TA @ antisym ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C @ ( B @ ( A @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ sym ) )
=> ( A @ ( B @ ( TA @ ( TB @ inv_image ) ) ) @ ( TA @ sym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_sym__inv__image) ).
thf(188,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ sym ) )
=> ( A @ ( B @ ( TA @ ( TB @ inv_image ) ) ) @ ( TA @ sym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(75,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_trancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_r__r__into__trancl) ).
thf(356,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_trancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_prod_Oexhaust) ).
thf(122,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(123,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ product_prod )] :
( A
= ( A @ ( TA @ ( TB @ sk2 ) ) @ ( A @ ( TA @ ( TB @ sk1 ) ) @ ( TB @ ( TA @ product_Pair ) ) ) ) ),
inference(cnf,[status(esa)],[122]) ).
thf(124,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ product_prod )] :
( ( A @ ( TA @ ( TB @ sk2 ) ) @ ( A @ ( TA @ ( TB @ sk1 ) ) @ ( TB @ ( TA @ product_Pair ) ) ) )
= A ),
inference(lifteq,[status(thm)],[123]) ).
thf(105,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_215145569der_on ) @ ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( TA @ irrefl ) )
& ( A @ ( TA @ trans ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_strict__linear__order__on__def) ).
thf(471,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( TA @ irrefl ) )
& ( A @ ( TA @ trans ) ) )
=> ( A @ ( B @ ( TA @ order_215145569der_on ) @ ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ order_215145569der_on ) @ ( bool @ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ total_on ) ) )
& ( A @ ( TA @ irrefl ) )
& ( A @ ( TA @ trans ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(57,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_UNIV__I) ).
thf(298,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(299,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(cnf,[status(esa)],[298]) ).
thf(645,plain,
! [TA: $tType,TB: $tType,C: TB,B: bool @ ( TB @ ( TB @ product_prod ) @ fun ),A: TA] :
( ( ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) )
!= ( B @ ( C @ ( C @ ( TB @ ( TB @ product_Pair ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) ) )
| ~ $true
| ~ ( B @ ( TB @ irrefl ) ) ),
inference(paramod_ordered,[status(thm)],[299,396]) ).
thf(646,plain,
! [TA: $tType,TB: $tType,C: TB,B: bool @ ( TB @ ( TB @ product_prod ) @ fun ),A: TA] :
( ( ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) )
!= ( B @ ( C @ ( C @ ( TB @ ( TB @ product_Pair ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) ) )
| ~ ( B @ ( TB @ irrefl ) ) ),
inference(simp,[status(thm)],[645]) ).
thf(647,plain,
! [TB: $tType] :
~ ( bool @ ( TB @ ( TB @ product_prod ) @ fun ) @ top_top @ ( TB @ irrefl ) ),
inference(pattern_uni,[status(thm)],[646:[bind(A,$thf( E @ ( E @ ( TB @ ( TB @ product_Pair ) ) ) )),bind(B,$thf( bool @ ( TB @ ( TB @ product_prod ) @ fun ) @ top_top )),bind(C,$thf( E )),bind_type(TA,$thf( TB @ ( TB @ product_prod ) ))]]) ).
thf(654,plain,
! [TA: $tType] :
~ ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) @ top_top @ ( TA @ irrefl ) ),
inference(simp,[status(thm)],[647]) ).
thf(21,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(173,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(8,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_preorder_on ) ) )
<=> ( ( A @ ( TA @ trans ) )
& ( A @ ( B @ ( TA @ refl_on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_preorder__on__def) ).
thf(127,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( TA @ trans ) )
& ( A @ ( B @ ( TA @ refl_on ) ) ) )
=> ( A @ ( B @ ( TA @ order_preorder_on ) ) ) )
& ( ( A @ ( B @ ( TA @ order_preorder_on ) ) )
=> ( ( A @ ( TA @ trans ) )
& ( A @ ( B @ ( TA @ refl_on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(128,plain,
! [TA: $tType,B: bool @ ( TA @ fun ),A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ( A @ ( B @ ( TA @ order_preorder_on ) ) )
| ~ ( A @ ( TA @ trans ) )
| ~ ( A @ ( B @ ( TA @ refl_on ) ) ) )
& ( ( A @ ( TA @ trans ) )
| ~ ( A @ ( B @ ( TA @ order_preorder_on ) ) ) )
& ( ( A @ ( B @ ( TA @ refl_on ) ) )
| ~ ( A @ ( B @ ( TA @ order_preorder_on ) ) ) ) ),
inference(cnf,[status(esa)],[127]) ).
thf(129,plain,
! [TA: $tType,B: bool @ ( TA @ fun ),A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ refl_on ) ) )
| ~ ( A @ ( B @ ( TA @ order_preorder_on ) ) ) ),
inference(cnfConj,[status(thm)],[128]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
<=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_in__inv__imagep) ).
thf(371,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_prod__cases6) ).
thf(237,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(45,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ order_preorder_on ) ) )
<=> ( A @ ( B @ ( TA @ order_preorder_on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_preorder__on__converse) ).
thf(244,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TA @ order_preorder_on ) ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ order_preorder_on ) ) ) )
& ( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ order_preorder_on ) ) )
=> ( A @ ( B @ ( TA @ order_preorder_on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(51,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ) @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ! [E: TA,F: TA] :
( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( F @ ( E @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [E: TA,F: TA,G: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( F @ ( E @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( TA @ transitive_trancl ) @ ( G @ ( F @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( G @ ( F @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( G @ ( E @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) )
=> ( C @ ( D @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_trancl__trans__induct) ).
thf(266,plain,
! [TA: $tType,A: bool @ ( TA @ fun ) @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ! [E: TA,F: TA] :
( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( F @ ( E @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [E: TA,F: TA,G: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( F @ ( E @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( TA @ transitive_trancl ) @ ( G @ ( F @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( G @ ( F @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( G @ ( E @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) )
=> ( C @ ( D @ ( A @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(77,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) )
=> ( A @ ( TA @ trans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_transI) ).
thf(360,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) )
=> ( A @ ( TA @ trans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(62,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ total_on ) ) )
<=> ( A @ ( B @ ( TA @ total_on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_total__on__converse) ).
thf(311,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TA @ total_on ) ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ total_on ) ) ) )
& ( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ total_on ) ) )
=> ( A @ ( B @ ( TA @ total_on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TB,D: TB] :
( ( A @ ( B @ ( TB @ ( TA @ inv_image ) ) ) @ ( C @ ( D @ ( TB @ ( TB @ product_Pair ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) )
<=> ( B @ ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( D @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_in__inv__image) ).
thf(398,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TB,D: TB] :
( ( ( B @ ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( D @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ inv_image ) ) ) @ ( C @ ( D @ ( TB @ ( TB @ product_Pair ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ inv_image ) ) ) @ ( C @ ( D @ ( TB @ ( TB @ product_Pair ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) )
=> ( B @ ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( D @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_prod__cases3) ).
thf(430,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(19,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ order_915043626der_on ) ) )
<=> ( ( A @ ( TA @ antisym ) )
& ( A @ ( B @ ( TA @ order_preorder_on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_partial__order__on__def) ).
thf(166,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( TA @ antisym ) )
& ( A @ ( B @ ( TA @ order_preorder_on ) ) ) )
=> ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) )
& ( ( A @ ( B @ ( TA @ order_915043626der_on ) ) )
=> ( ( A @ ( TA @ antisym ) )
& ( A @ ( B @ ( TA @ order_preorder_on ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: TB,C: TA] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TB @ ( TA @ converse ) ) @ ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_converseI) ).
thf(264,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: TB,C: TA] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TB @ ( TA @ converse ) ) @ ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_split__paired__All) ).
thf(375,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(64,axiom,
! [TA: $tType] :
? [A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_UNIV__witness) ).
thf(323,plain,
! [TA: $tType] :
? [A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(324,plain,
! [TA: $tType] : ( bool @ ( TA @ fun ) @ top_top @ ( TA @ sk36 @ ( TA @ member ) ) ),
inference(cnf,[status(esa)],[323]) ).
thf(578,plain,
! [TB: $tType] :
( ( ( bool @ ( TB @ fun ) @ top_top )
!= ( bool @ ( TB @ fun ) @ top_top ) )
| ( fTrue @ ( TB @ ( bool @ combk ) ) @ ( TB @ sk36 @ ( TB @ member ) ) ) ),
inference(paramod_ordered,[status(thm)],[573,324]) ).
thf(579,plain,
! [TB: $tType] : ( fTrue @ ( TB @ ( bool @ combk ) ) @ ( TB @ sk36 @ ( TB @ member ) ) ),
inference(pattern_uni,[status(thm)],[578:[]]) ).
thf(584,plain,
! [TA: $tType] : ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ sk36 @ ( TA @ member ) ) ),
inference(simp,[status(thm)],[579]) ).
thf(22,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ antisym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_antisym__Id__on) ).
thf(176,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ antisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(87,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_trancl ) @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_trancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_trancl__into__trancl2) ).
thf(402,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_trancl ) @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_trancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ inv_image ) ) ) @ ( TA @ ( TA @ converse ) ) )
= ( A @ ( B @ ( TB @ ( TB @ converse ) ) @ ( TA @ ( TB @ inv_image ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_converse__inv__image) ).
thf(291,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ inv_image ) ) ) @ ( TA @ ( TA @ converse ) ) )
= ( A @ ( B @ ( TB @ ( TB @ converse ) ) @ ( TA @ ( TB @ inv_image ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(34,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B = C ) ) )
=> ( A @ ( TA @ antisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_antisymI) ).
thf(204,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B = C ) ) )
=> ( A @ ( TA @ antisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(17,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ transitive_acyclic ) )
<=> ( A @ ( TA @ transitive_trancl ) @ ( TA @ irrefl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_acyclic__irrefl) ).
thf(159,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ( A @ ( TA @ transitive_trancl ) @ ( TA @ irrefl ) )
=> ( A @ ( TA @ transitive_acyclic ) ) )
& ( ( A @ ( TA @ transitive_acyclic ) )
=> ( A @ ( TA @ transitive_trancl ) @ ( TA @ irrefl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(679,plain,
! [TB: $tType,A: TB] :
( ( ( bool @ ( TB @ fun ) @ top_top )
!= ( bool @ ( TB @ fun ) @ top_top ) )
| ( ( A @ ( fTrue @ ( TB @ ( bool @ combk ) ) @ ( bool @ ( TB @ aa ) ) ) )
!= fFalse ) ),
inference(paramod_ordered,[status(thm)],[573,677]) ).
thf(680,plain,
! [TB: $tType,A: TB] :
( ( A @ ( fTrue @ ( TB @ ( bool @ combk ) ) @ ( bool @ ( TB @ aa ) ) ) )
!= fFalse ),
inference(pattern_uni,[status(thm)],[679:[]]) ).
thf(681,plain,
! [TA: $tType,A: TA] :
( ( A @ ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( bool @ ( TA @ aa ) ) ) )
!= fFalse ),
inference(simp,[status(thm)],[680]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: TC @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_curry__conv) ).
thf(219,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: TC @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(106,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ total_on ) ) )
<=> ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ! [D: TA] :
( ( B @ ( D @ ( TA @ member ) ) )
=> ( ( C != D )
=> ( ( A @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_total__on__def) ).
thf(477,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ! [D: TA] :
( ( B @ ( D @ ( TA @ member ) ) )
=> ( ( C != D )
=> ( ( A @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ) )
=> ( A @ ( B @ ( TA @ total_on ) ) ) )
& ( ( A @ ( B @ ( TA @ total_on ) ) )
=> ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ! [D: TA] :
( ( B @ ( D @ ( TA @ member ) ) )
=> ( ( C != D )
=> ( ( A @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(16,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(158,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(492,plain,
( ( ( fTrue @ pp )
!= ( fFalse @ pp ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[158,121]) ).
thf(493,plain,
( ( fTrue @ pp )
!= ( fFalse @ pp ) ),
inference(simp,[status(thm)],[492]) ).
thf(494,plain,
fTrue != fFalse,
inference(simp,[status(thm)],[493]) ).
thf(12,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ sym ) )
=> ( A @ ( TA @ transitive_trancl ) @ ( TA @ sym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_sym__trancl) ).
thf(140,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ sym ) )
=> ( A @ ( TA @ transitive_trancl ) @ ( TA @ sym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(36,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_trancl ) @ ( TA @ ( TA @ converse ) ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_trancl__converseI) ).
thf(213,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_trancl ) @ ( TA @ ( TA @ converse ) ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(666,plain,
! [TB: $tType] :
( ( ( bool @ ( TB @ ( TB @ product_prod ) @ fun ) @ top_top )
!= ( bool @ ( TB @ ( TB @ product_prod ) @ fun ) @ top_top ) )
| ~ ( fTrue @ ( TB @ ( TB @ product_prod ) @ ( bool @ combk ) ) @ ( TB @ irrefl ) ) ),
inference(paramod_ordered,[status(thm)],[573,654]) ).
thf(667,plain,
! [TB: $tType] :
~ ( fTrue @ ( TB @ ( TB @ product_prod ) @ ( bool @ combk ) ) @ ( TB @ irrefl ) ),
inference(pattern_uni,[status(thm)],[666:[]]) ).
thf(668,plain,
! [TA: $tType] :
~ ( fTrue @ ( TA @ ( TA @ product_prod ) @ ( bool @ combk ) ) @ ( TA @ irrefl ) ),
inference(simp,[status(thm)],[667]) ).
thf(44,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) )
=> ( A @ ( TA @ sym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_symI) ).
thf(240,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) )
=> ( A @ ( TA @ sym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ refl_on ) ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( D @ ( B @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_refl__onD1) ).
thf(251,plain,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ refl_on ) ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( D @ ( B @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [D: TA] :
~ ( C @ ( TA @ transitive_trancl ) @ ( D @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_irrefl__trancl__rD) ).
thf(278,plain,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [D: TA] :
~ ( C @ ( TA @ transitive_trancl ) @ ( D @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(10,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] : ( A @ ( TA @ transitive_trancl ) @ ( TA @ trans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_trans__trancl) ).
thf(135,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] : ( A @ ( TA @ transitive_trancl ) @ ( TA @ trans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ transitive_trancl ) )
= ( A @ ( TA @ transitive_trancl ) @ ( TA @ ( TA @ converse ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_trancl__converse) ).
thf(306,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ transitive_trancl ) )
= ( A @ ( TA @ transitive_trancl ) @ ( TA @ ( TA @ converse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_prod__induct3) ).
thf(490,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(94,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ trans ) )
<=> ( A @ ( TA @ trans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_trans__converse) ).
thf(426,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ( A @ ( TA @ trans ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ trans ) ) )
& ( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ trans ) )
=> ( A @ ( TA @ trans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(513,plain,
( ~ $true
| ( ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
!= ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
| ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[111]) ).
thf(516,plain,
( ( ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
!= ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
| ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(simp,[status(thm)],[513]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_prod__induct4) ).
thf(342,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(29,axiom,
bool @ top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(194,plain,
bool @ top,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(53,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ ( TA @ product_prod )] :
( ( A @ ( TA @ id_on ) @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ! [C: TA] :
( ( A @ ( C @ ( TA @ member ) ) )
=> ( B
!= ( C @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Id__onE) ).
thf(282,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ ( TA @ product_prod )] :
( ( A @ ( TA @ id_on ) @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ! [C: TA] :
( ( A @ ( C @ ( TA @ member ) ) )
=> ( B
!= ( C @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(66,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ! [E: TA] :
( ( B @ ( E @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [E: TA,F: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( E @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( F @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_trancl__induct) ).
thf(327,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ! [E: TA] :
( ( B @ ( E @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [E: TA,F: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( E @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( F @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(580,plain,
! [TB: $tType] :
( ( ( fTrue @ ( TB @ ( bool @ combk ) ) )
!= ( fTrue @ ( TB @ ( bool @ combk ) ) ) )
| ( ( bool @ ( TB @ fun ) @ top_top @ ( TB @ collect ) )
= ( bool @ ( TB @ fun ) @ top_top ) ) ),
inference(paramod_ordered,[status(thm)],[573,489]) ).
thf(581,plain,
! [TB: $tType] :
( ( bool @ ( TB @ fun ) @ top_top @ ( TB @ collect ) )
= ( bool @ ( TB @ fun ) @ top_top ) ),
inference(pattern_uni,[status(thm)],[580:[]]) ).
thf(585,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ top_top ) ),
inference(simp,[status(thm)],[581]) ).
thf(103,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ! [D: TA] :
( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( A @ ( TA @ transitive_trancl ) @ ( B @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_converse__tranclE) ).
thf(463,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ! [D: TA] :
( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( A @ ( TA @ transitive_trancl ) @ ( B @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(177,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ antisym ) ),
inference(cnf,[status(esa)],[176]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_Pair__inject) ).
thf(182,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(84,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ id_on ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
<=> ( ( A @ ( C @ ( TA @ member ) ) )
& ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Id__on__iff) ).
thf(386,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( ( ( A @ ( C @ ( TA @ member ) ) )
& ( C = B ) )
=> ( A @ ( TA @ id_on ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) )
& ( ( A @ ( TA @ id_on ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( C @ ( TA @ member ) ) )
& ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(497,plain,
( ( ( arrow_1985332922le_Lin @ ( l @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ converse ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
!= ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) )
| ~ ( arrow_1985332922le_Lin @ ( l @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(simp,[status(thm)],[496]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_curryD) ).
thf(231,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(79,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ id_on ) @ ( TA @ ( TA @ converse ) ) )
= ( A @ ( TA @ id_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_converse__Id__on) ).
thf(368,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ id_on ) @ ( TA @ ( TA @ converse ) ) )
= ( A @ ( TA @ id_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(304,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(49,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ trans ) )
<=> ! [B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_trans__def) ).
thf(258,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ! [B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) )
=> ( A @ ( TA @ trans ) ) )
& ( ( A @ ( TA @ trans ) )
=> ! [B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ trans ) )
=> ( A @ ( B @ ( TA @ ( TB @ inv_image ) ) ) @ ( TA @ trans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_trans__inv__image) ).
thf(171,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ trans ) )
=> ( A @ ( B @ ( TA @ ( TB @ inv_image ) ) ) @ ( TA @ trans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(91,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ sym ) )
<=> ( A @ ( TA @ sym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_sym__converse) ).
thf(418,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ( A @ ( TA @ sym ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ sym ) ) )
& ( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ sym ) )
=> ( A @ ( TA @ sym ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(96,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ! [D: TA] :
( ( A @ ( TA @ transitive_trancl ) @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( A @ ( B @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_tranclE) ).
thf(433,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ! [D: TA] :
( ( A @ ( TA @ transitive_trancl ) @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( A @ ( B @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(70,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_iso__tuple__UNIV__I) ).
thf(346,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(54,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ refl_on ) ) )
<=> ( A @ ( B @ ( TA @ refl_on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_refl__on__converse) ).
thf(287,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TA @ refl_on ) ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ refl_on ) ) ) )
& ( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ refl_on ) ) )
=> ( A @ ( B @ ( TA @ refl_on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(58,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ order_915043626der_on ) ) )
<=> ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_partial__order__on__converse) ).
thf(300,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TA @ order_915043626der_on ) ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ order_915043626der_on ) ) ) )
& ( ( A @ ( TA @ ( TA @ converse ) ) @ ( B @ ( TA @ order_915043626der_on ) ) )
=> ( A @ ( B @ ( TA @ order_915043626der_on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(63,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ antisym ) )
<=> ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_antisym__def) ).
thf(315,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B = C ) ) )
=> ( A @ ( TA @ antisym ) ) )
& ( ( A @ ( TA @ antisym ) )
=> ! [B: TA,C: TA] :
( ( A @ ( C @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: TA @ ( TB @ product_prod )] :
( ( A @ ( TB @ ( TA @ converse ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ member ) ) )
=> ~ ! [C: TA,D: TB] :
( ( B
= ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_converseE) ).
thf(410,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: TA @ ( TB @ product_prod )] :
( ( A @ ( TB @ ( TA @ converse ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ member ) ) )
=> ~ ! [C: TA,D: TB] :
( ( B
= ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ refl_on ) ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( D @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_refl__onD2) ).
thf(190,plain,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ refl_on ) ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( D @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_prod__induct5) ).
thf(422,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_prod__cases4) ).
thf(210,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( C @ ( TA @ sym ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( A @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_symD) ).
thf(358,plain,
! [TA: $tType,A: TA,B: TA,C: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( C @ ( TA @ sym ) )
=> ( ( C @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( A @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(30,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_trancl_Or__into__trancl) ).
thf(195,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_trancl ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(97,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ ( TA @ product_prod )] :
( ( A @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_trancl ) @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_r__into__trancl_H) ).
thf(437,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ ( TA @ product_prod )] :
( ( A @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ transitive_trancl ) @ ( B @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ top_top @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ top_top ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_top__apply) ).
thf(415,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ top_top @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ top_top ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: TA,C: TB] :
( ( A @ ( TB @ ( TA @ converse ) ) @ ( B @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ member ) ) )
<=> ( A @ ( C @ ( B @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_converse__iff) ).
thf(294,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: TA,C: TB] :
( ( ( A @ ( C @ ( B @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TB @ ( TA @ converse ) ) @ ( B @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ member ) ) ) )
& ( ( A @ ( TB @ ( TA @ converse ) ) @ ( B @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ member ) ) )
=> ( A @ ( C @ ( B @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(126,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ id_on ) @ ( TA @ sym ) ),
inference(cnf,[status(esa)],[125]) ).
thf(136,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] : ( A @ ( TA @ transitive_trancl ) @ ( TA @ trans ) ),
inference(cnf,[status(esa)],[135]) ).
thf(575,plain,
( ( arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ collect ) )
= arrow_1985332922le_Lin ),
inference(rewrite,[status(thm)],[351,570]) ).
thf(102,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( C @ ( TA @ member ) ) )
=> ( A @ ( TA @ id_on ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Id__on__eqI) ).
thf(459,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( C @ ( TA @ member ) ) )
=> ( A @ ( TA @ id_on ) @ ( B @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(23,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(178,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(99,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ! [E: TA] :
( ( B @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [E: TA,F: TA] :
( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( F @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( F @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_converse__trancl__induct) ).
thf(442,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ! [E: TA] :
( ( B @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [E: TA,F: TA] :
( ( B @ ( F @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( F @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( F @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(18,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ trans ) )
=> ( ( A @ ( TA @ transitive_trancl ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_trancl__id) ).
thf(163,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ trans ) )
=> ( ( A @ ( TA @ transitive_trancl ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_trancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Transitive__Closure_Otrancl__into__trancl) ).
thf(200,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ ( TA @ product_prod ) @ fun ),C: TA,D: TA] :
( ( B @ ( TA @ transitive_trancl ) @ ( C @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( TA @ transitive_trancl ) @ ( A @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: TA,C: TB] :
( ( A @ ( TB @ ( TA @ converse ) ) @ ( B @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ member ) ) )
=> ( A @ ( C @ ( B @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_converseD) ).
thf(354,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: TA,C: TB] :
( ( A @ ( TB @ ( TA @ converse ) ) @ ( B @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( TA @ ( TB @ product_prod ) @ member ) ) )
=> ( A @ ( C @ ( B @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_curryI) ).
thf(309,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(37,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ antisym ) )
<=> ( A @ ( TA @ antisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_antisym__converse) ).
thf(215,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ( A @ ( TA @ antisym ) )
=> ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ antisym ) ) )
& ( ( A @ ( TA @ ( TA @ converse ) ) @ ( TA @ antisym ) )
=> ( A @ ( TA @ antisym ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(39,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TA @ sym ) )
<=> ( ( A @ ( TA @ ( TA @ converse ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_sym__conv__converse__eq) ).
thf(222,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ( ( A @ ( TA @ ( TA @ converse ) ) )
= A )
=> ( A @ ( TA @ sym ) ) )
& ( ( A @ ( TA @ sym ) )
=> ( ( A @ ( TA @ ( TA @ converse ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_split__paired__Ex) ).
thf(337,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(9479,plain,
$false,
inference(e,[status(thm)],[404,365,352,115,120,677,202,384,550,142,570,157,125,344,325,228,179,253,121,348,147,132,396,116,248,439,233,452,380,117,424,192,137,467,197,583,456,156,188,356,124,489,109,471,654,173,129,371,237,244,266,360,311,398,298,430,166,264,573,375,584,176,402,291,204,350,159,681,219,477,494,323,140,213,668,240,251,278,135,299,394,306,490,426,487,516,342,194,282,327,585,463,127,177,182,386,497,231,203,368,304,258,158,114,171,418,119,433,346,287,300,315,410,190,422,210,358,195,437,415,294,126,136,575,459,178,442,163,200,111,354,309,215,222,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT175_5 : TPTP v9.3.1. Released v6.0.0.
% 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
% 0.13/0.40 % Computer : n010.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 06:38:46 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.83/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.28 % [INFO] Parsing done (284ms).
% 1.37/1.29 % [INFO] Running in sequential loop mode.
% 2.44/1.66 % [INFO] eprover registered as external prover.
% 2.44/1.67 % [INFO] Scanning for conjecture ...
% 2.83/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 106 axioms. Running axiom selection ...
% 3.02/1.92 % [INFO] Axiom selection finished. Selected 106 axioms (removed 0 axioms).
% 3.86/2.14 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.86/2.16 % [INFO] Type checking passed.
% 3.86/2.17 % [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 ...
% 5.05/2.54 % [INFO] [Domain constraints] Detected constraint on bool
% 5.05/2.54 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 56.83/12.50 % External prover 'e' found a proof!
% 56.83/12.50 % [INFO] Killing All external provers ...
% 57.20/12.50 % Time passed: 11952ms (effective reasoning time: 11204ms)
% 57.20/12.50 % 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)>
% 57.20/12.50 % Axioms used in derivation (106): fact_20_sym__inv__image, fact_23_Id__on__eqI, fact_86_Transitive__Closure_Otrancl__into__trancl, fact_73_trancl__id, fact_62_strict__linear__order__on__def, fact_87_trancl__into__trancl2, fact_40_split__paired__Ex, fact_53_PairE, fact_78_refl__on__Id__on, fact_70_acyclic__irrefl, fact_55_internal__split__conv, fact_51_prod__cases3, fact_45_prod__induct6, fact_81_r__into__trancl_H, fact_24_partial__order__on__def, fact_26_converseD, fact_31_antisymI, fact_89_trancl__converseD, fact_5_partial__order__on__converse, fact_0_converse__converse, fact_69_preorder__on__def, help_fTrue_1_1_T, fact_9_acyclic__converse, fact_37_Pair__eq, fact_67_trans__inv__image, fact_74_trans__trancl, fact_19_Id__on__iff, fact_48_prod__cases5, fact_35_iso__tuple__UNIV__I, fact_32_symI, fact_3_Lin__def, help_fTrue_1_1_U, fact_43_UNIV__eq__I, fact_41_prod_Orecs, fact_97_converse__trancl__induct, fact_68_transI, fact_21_symD, fact_30_converseE, fact_10_converse__Id__on, fact_11_sym__converse, fact_2_linear__order__on__converse, fact_8_antisym__converse, fact_15_antisym__Id__on, fact_66_trans__Id__on, fact_7_converse__inv__image, fact_80_sym__trancl, fact_95_irrefl__trancl__rD, fact_46_prod__cases6, fact_47_prod__induct5, fact_36_split__paired__All, arity_HOL_Obool___Orderings_Otop, fact_94_converse__tranclE, fact_54_prod_Oexhaust, fact_85_trancl__trans, fact_93_tranclE, fact_49_prod__cases4, fact_76_mem__def, fact_83_refl__onD1, fact_60_in__inv__imagep, fact_59_curryD, fact_64_transD, fact_58_curryE, fact_44_UNIV__witness, fact_72_refl__on__converse, help_COMBK_1_1_U, fact_84_refl__onD2, fact_18_total__on__def, fact_29_Id__onE, fact_79_trancl__converse, fact_61_irrefl__def, fact_63_trans__converse, fact_82_refl__onD, fact_33_top1I, fact_4_preorder__on__converse, fact_96_trancl__trans__induct, fact_56_curry__conv, fact_16_sym__def, fact_14_sym__Id__on, fact_13_in__inv__image, fact_17_antisym__def, fact_27_converseI, fact_38_Pair__inject, fact_77_Collect__def, fact_65_trans__def, fact_98_trancl__induct, fact_88_r__r__into__trancl, fact_91_acyclic__def, help_pp_1_1_U, fact_92_acyclicI, fact_1_notin__Lin__iff, fact_57_curryI, fact_71_trancl_Or__into__trancl, fact_39_UNIV__def, fact_75_ext, arity_fun___Orderings_Otop, fact_25_linear__order__on__def, fact_52_prod__induct3, fact_90_trancl__converseI, fact_50_prod__induct4, fact_34_UNIV__I, help_pp_2_1_U, fact_22_antisymD, fact_12_converse__iff, fact_6_total__on__converse, fact_28_sym__conv__converse__eq, fact_42_top__apply
% 57.20/12.50 % No. of inferences in proof: 282
% 57.20/12.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11952 ms resp. 11204 ms w/o parsing
% 49.19/12.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.19/12.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------