%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT196_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 08:27:32 AM UTC 2026
% Result : Theorem 78.26s 59.05s
% Output : Refutation 79.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 93
% Syntax : Number of formulae : 188 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 2329 ( 187 equ; 0 cnn)
% Maximal formula atoms : 77 ( 12 avg)
% Number of connectives : 9735 ( 111 ~; 14 |; 75 &;9303 @)
% ( 17 <=>; 215 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 13 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 10 con; 0-6 aty)
% Number of variables : 918 ( 0 ^; 905 !; 13 ?; 918 :)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(arrow_159774573e_indi_type,type,
arrow_159774573e_indi: $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(arrow_1158827142_above_decl,type,
arrow_1158827142_above: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) > arrow_411405190le_alt > arrow_411405190le_alt > ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) ).
thf(arrow_319942042_below_decl,type,
arrow_319942042_below: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) > arrow_411405190le_alt > arrow_411405190le_alt > ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) ).
thf(arrow_276188178_mkbot_decl,type,
arrow_276188178_mkbot: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) > arrow_411405190le_alt > ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) ).
thf(arrow_424895264_mktop_decl,type,
arrow_424895264_mktop: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) > arrow_411405190le_alt > ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(in_rel_decl,type,
in_rel:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) ) > TB > TA > $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] : ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ fun ) ) ).
thf(product_apfst_decl,type,
product_apfst:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ product_prod ) ) > ( TA @ ( TB @ product_prod ) ) ) ).
thf(product_apsnd_decl,type,
product_apsnd:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ product_prod ) ) > ( TB @ ( TA @ product_prod ) ) ) ).
thf(product_curry_decl,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) ) > ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) ) ).
thf(produc1605651328_split_decl,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TA @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) ) ).
thf(product_prod_case_decl,type,
product_prod_case:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TA @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) ) ).
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(product_scomp_decl,type,
product_scomp:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TB @ ( TC @ product_prod ) @ ( TD @ fun ) ) > ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TA @ ( TD @ 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(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(lex_prod_decl,type,
lex_prod:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ ( TB @ product_prod ) @ fun ) ) > ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > ( bool @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ 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(f_decl,type,
f: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) ) > ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) ).
thf(p_decl,type,
p: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) ).
thf(a_decl,type,
a: arrow_411405190le_alt ).
thf(b_decl,type,
b: arrow_411405190le_alt ).
thf(i_decl,type,
i: arrow_159774573e_indi ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ ( TA @ product_apsnd ) ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( TB @ ( TC @ product_Pair ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_apsnd__conv) ).
thf(289,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ ( TA @ product_apsnd ) ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( TB @ ( TC @ product_Pair ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: TD @ ( TB @ fun ) @ ( TC @ fun ),C: TB @ ( TC @ product_prod ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TD @ ( TB @ ( TC @ ( TA @ product_scomp ) ) ) ) ) @ ( TD @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( B @ ( TD @ ( TB @ ( TC @ product_prod_case ) ) @ ( TD @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TD @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TD @ ( TB @ ( TC @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_scomp__apply) ).
thf(275,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: TD @ ( TB @ fun ) @ ( TC @ fun ),C: TB @ ( TC @ product_prod ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TD @ ( TB @ ( TC @ ( TA @ product_scomp ) ) ) ) ) @ ( TD @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( B @ ( TD @ ( TB @ ( TC @ product_prod_case ) ) @ ( TD @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TD @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TD @ ( TB @ ( TC @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(58,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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prod__cases4) ).
thf(335,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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(66,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 ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_32_prod__induct3) ).
thf(362,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 ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( 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)],[66]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TA @ ( TB @ ( TC @ product_apfst ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_apfst__conv) ).
thf(446,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TA @ ( TB @ ( TC @ product_apfst ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(6,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(101,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: TB @ ( TC @ fun ),C: TA @ ( TB @ product_prod )] :
( ( C
= ( A @ ( B @ ( TA @ ( TB @ ( TC @ product_apfst ) ) ) ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ( C
!= ( E @ ( D @ ( B @ ( TB @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_apfst__convE) ).
thf(347,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: TB @ ( TC @ fun ),C: TA @ ( TB @ product_prod )] :
( ( C
= ( A @ ( B @ ( TA @ ( TB @ ( TC @ product_apfst ) ) ) ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ( C
!= ( E @ ( D @ ( B @ ( TB @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_splitD) ).
thf(333,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(94,axiom,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( A @ ( B @ arrow_424895264_mktop ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_mktop__Lin) ).
thf(518,plain,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( A @ ( B @ arrow_424895264_mktop ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(12,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_iso__tuple__UNIV__I) ).
thf(115,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TB @ fun ) @ ( TC @ fun ),B: TB @ ( TC @ product_prod ) @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TD @ ( TB @ ( TC @ ( TA @ product_scomp ) ) ) ) ) @ ( TD @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TB @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( TD @ ( TB @ ( TC @ product_prod_case ) ) @ ( TD @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TD @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TD @ ( TB @ ( TC @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_scomp__def) ).
thf(449,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TB @ fun ) @ ( TC @ fun ),B: TB @ ( TC @ product_prod ) @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TD @ ( TB @ ( TC @ ( TA @ product_scomp ) ) ) ) ) @ ( TD @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TB @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( TD @ ( TB @ ( TC @ product_prod_case ) ) @ ( TD @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TD @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TD @ ( TB @ ( TC @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Pair__inject) ).
thf(120,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( D @ ( E @ ( C @ arrow_1158827142_above ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_in__above) ).
thf(379,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ arrow_1158827142_above ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D @ ( E @ ( C @ arrow_1158827142_above ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(60,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 ) @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) )
<=> ( B @ ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( D @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_in__inv__image) ).
thf(340,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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ inv_image ) ) ) @ ( C @ ( D @ ( TB @ ( TB @ product_Pair ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ inv_image ) ) ) @ ( C @ ( D @ ( TB @ ( TB @ product_Pair ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) )
=> ( B @ ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( D @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod ),B: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ~ ! [C: TB,D: TA] :
( ( A
= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( D @ ( C @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_splitE) ).
thf(153,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod ),B: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ~ ! [C: TB,D: TA] :
( ( A
= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( D @ ( C @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ top_top @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ top_top ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_top__apply) ).
thf(185,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)],[29]) ).
thf(55,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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_total__on__def) ).
thf(320,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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( 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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',fact_43_in__inv__imagep) ).
thf(372,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)],[69]) ).
thf(10,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(110,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_internal__split__conv) ).
thf(344,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_prod_Oexhaust) ).
thf(357,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_split__conv) ).
thf(376,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(84,axiom,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( A @ ( B @ arrow_276188178_mkbot ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_mkbot__Lin) ).
thf(485,plain,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( A @ ( B @ arrow_276188178_mkbot ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(93,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(514,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)],[93]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_PairE) ).
thf(280,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_prod_Orecs) ).
thf(265,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( 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)],[41]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ ( TA @ product_prod ),B: TC @ ( TB @ fun ) @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun ),D: TB @ ( TA @ product_prod )] :
( ! [E: TA,F: TB] :
( ( ( F @ ( E @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) )
= D )
=> ( ( F @ ( E @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) )
= ( F @ ( E @ ( B @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ) )
=> ( ( A = D )
=> ( ( A @ ( C @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) )
= ( D @ ( B @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_split__cong) ).
thf(292,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ ( TA @ product_prod ),B: TC @ ( TB @ fun ) @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun ),D: TB @ ( TA @ product_prod )] :
( ! [E: TA,F: TB] :
( ( ( F @ ( E @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) )
= D )
=> ( ( F @ ( E @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) )
= ( F @ ( E @ ( B @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ) )
=> ( ( A = D )
=> ( ( A @ ( C @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) )
= ( D @ ( B @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(77,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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_split__paired__All) ).
thf(452,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( 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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_prod_Osimps_I2_J) ).
thf(117,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(270,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(34,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( B @ ( C @ ( A @ arrow_1158827142_above ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_above__Lin) ).
thf(201,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( B @ ( C @ ( A @ arrow_1158827142_above ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',fact_47_trans__inv__image) ).
thf(102,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)],[7]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) @ ( D @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_splitD_H) ).
thf(467,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) @ ( D @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(79,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 ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_notin__Lin__iff) ).
thf(461,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 ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(30,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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TE @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ fun ) @ ( TF @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_prod__cases6) ).
thf(188,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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TE @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ fun ) @ ( TF @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_curryI) ).
thf(169,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ trans ) )
=> ( ( A @ ( TA @ trans ) )
=> ( A @ ( B @ ( TA @ ( TB @ lex_prod ) ) ) @ ( TA @ ( TB @ product_prod ) @ trans ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_trans__lex__prod) ).
thf(499,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun )] :
( ( B @ ( TB @ trans ) )
=> ( ( A @ ( TA @ trans ) )
=> ( A @ ( B @ ( TA @ ( TB @ lex_prod ) ) ) @ ( TA @ ( TB @ product_prod ) @ trans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC @ ( TB @ product_prod ),C: bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( E @ ( D @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) ) )
=> ~ ( A @ ( E @ ( D @ ( C @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_splitE_H) ).
thf(193,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC @ ( TB @ product_prod ),C: bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( E @ ( D @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) ) )
=> ~ ( A @ ( E @ ( D @ ( C @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( TC @ ( TB @ ( TA @ produc1605651328_split ) ) )
= ( TC @ ( TB @ ( TA @ product_prod_case ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_internal__split__def) ).
thf(96,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( TC @ ( TB @ ( TA @ produc1605651328_split ) ) )
= ( TC @ ( TB @ ( TA @ product_prod_case ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(78,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ! [B: arrow_159774573e_indi] :
( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ total_on ) ) )
& ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ irrefl ) )
& ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ trans ) ) )
=> ! [B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( B != C )
=> ( ( i @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ f @ ( C @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(457,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ! [B: arrow_159774573e_indi] :
( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ total_on ) ) )
& ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ irrefl ) )
& ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ trans ) ) )
=> ! [B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( B != C )
=> ( ( i @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ f @ ( C @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ fun )] :
( ( TC @ ( TB @ product_Pair ) @ ( A @ ( TC @ ( TB @ product_prod ) @ ( TC @ ( TB @ ( TA @ product_scomp ) ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_scomp__Pair) ).
thf(173,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ fun )] :
( ( TC @ ( TB @ product_Pair ) @ ( A @ ( TC @ ( TB @ product_prod ) @ ( TC @ ( TB @ ( TA @ product_scomp ) ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(90,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 ) ) )
=> ( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Lin__irrefl) ).
thf(503,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 ) ) )
=> ( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_splitI) ).
thf(128,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_curryD) ).
thf(360,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_9_strict__linear__order__on__def) ).
thf(508,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)],[92]) ).
thf(22,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] : ( A @ ( B @ ( TA @ member ) ) )
=> ( ( bool @ ( TA @ fun ) @ top_top )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_UNIV__eq__I) ).
thf(166,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)],[22]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_17_Lin__def) ).
thf(161,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)],[20]) ).
thf(26,axiom,
i @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(176,plain,
i @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(74,axiom,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( A @ ( B @ arrow_424895264_mktop ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_in__mktop) ).
thf(423,plain,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) )
=> ( A @ ( B @ arrow_424895264_mktop ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A @ ( B @ arrow_424895264_mktop ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(31,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 ) @ ( TE @ ( TD @ product_prod ) @ ( TE @ fun ) @ ( TD @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TE @ aa ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ aa ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_28_prod__induct5) ).
thf(191,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 ) @ ( TE @ ( TD @ product_prod ) @ ( TE @ fun ) @ ( TD @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TE @ aa ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ aa ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( 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)],[31]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Pair__eq) ).
thf(204,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(82,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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_trans__def) ).
thf(477,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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( 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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: TB @ ( TA @ fun ) @ ( TC @ fun ),C: bool @ ( TB @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( E @ ( D @ ( B @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_splitE2) ).
thf(213,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: TB @ ( TA @ fun ) @ ( TC @ fun ),C: bool @ ( TB @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( E @ ( D @ ( B @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(83,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_UNIV__I) ).
thf(483,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(198,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)],[33]) ).
thf(56,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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_prod__cases3) ).
thf(330,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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(17,axiom,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( A @ ( B @ arrow_276188178_mkbot ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_in__mkbot) ).
thf(130,plain,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) )
=> ( A @ ( B @ arrow_276188178_mkbot ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A @ ( B @ arrow_276188178_mkbot ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_curryE) ).
thf(278,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun ),C: TA,D: TB,E: TA,F: TB] :
( ( A @ ( B @ ( TA @ ( TB @ lex_prod ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( E @ ( F @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
<=> ( ( ( A @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( TB @ ( TB @ product_Pair ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_in__lex__prod) ).
thf(306,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TB @ product_prod ) @ fun ),C: TA,D: TB,E: TA,F: TB] :
( ( ( ( ( A @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( TB @ ( TB @ product_Pair ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) ) )
=> ( A @ ( B @ ( TA @ ( TB @ lex_prod ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( E @ ( F @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ ( TB @ lex_prod ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( E @ ( F @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ product_prod ) @ member ) ) )
=> ( ( ( A @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( TB @ ( TB @ product_Pair ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(505,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)],[91]) ).
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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_irrefl__def) ).
thf(487,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ( ! [B: TA] :
~ ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( TA @ irrefl ) ) )
& ( ( A @ ( TA @ irrefl ) )
=> ! [B: TA] :
~ ( A @ ( B @ ( B @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(11,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(112,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ fun ),D: TC] :
( ( A @ ( B @ ( C @ ( bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( TC @ member ) ) )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( D @ ( TC @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_mem__splitI) ).
thf(355,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ fun ),D: TC] :
( ( A @ ( B @ ( C @ ( bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( TC @ member ) ) )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( D @ ( TC @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1,conjecture,
p @ f @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(2,negated_conjecture,
~ ( p @ f @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(95,plain,
~ ( p @ f @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(40,axiom,
? [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] : ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_linear__alt) ).
thf(263,plain,
? [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] : ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(59,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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( D @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( D @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_transD) ).
thf(338,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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( D @ ( A @ ( B @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( D @ ( A @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ fun ),B: TC,C: TB @ ( TA @ product_prod )] :
( ! [D: TA,E: TB] :
( ( C
= ( E @ ( D @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) ) )
=> ( E @ ( D @ ( A @ ( bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( B @ ( TC @ member ) ) ) )
=> ( C @ ( A @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ ( B @ ( TC @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_mem__splitI2) ).
thf(177,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ fun ),B: TC,C: TB @ ( TA @ product_prod )] :
( ! [D: TA,E: TB] :
( ( C
= ( E @ ( D @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) ) )
=> ( E @ ( D @ ( A @ ( bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( B @ ( TC @ member ) ) ) )
=> ( C @ ( A @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ ( B @ ( TC @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(28,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( B @ ( C @ ( A @ arrow_319942042_below ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_below__Lin) ).
thf(182,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( B @ ( C @ ( A @ arrow_319942042_below ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(4,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(99,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( D @ ( E @ ( C @ arrow_319942042_below ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_in__below) ).
thf(218,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ arrow_319942042_below ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D @ ( E @ ( C @ arrow_319942042_below ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(8,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(104,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(39,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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) )
=> ( A @ ( TA @ trans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_transI) ).
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 ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( ( A @ ( D @ ( C @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TA @ product_Pair ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) )
=> ( A @ ( TA @ trans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ ( TC @ fun ) @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TC @ ( TA @ product_Pair ) @ ( TC @ ( TA @ product_prod ) @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ ( TA @ ( TC @ product_scomp ) ) ) ) ) )
= ( B @ ( A @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Pair__scomp) ).
thf(158,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB @ ( TC @ fun ) @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TC @ ( TA @ product_Pair ) @ ( TC @ ( TA @ product_prod ) @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ ( TA @ ( TC @ product_scomp ) ) ) ) ) )
= ( B @ ( A @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(24,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 ) @ ( TF @ ( TE @ product_prod ) @ ( TF @ fun ) @ ( TE @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TF @ aa ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ aa ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_26_prod__induct6) ).
thf(171,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 ) @ ( TF @ ( TE @ product_prod ) @ ( TF @ fun ) @ ( TE @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TF @ aa ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ aa ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( 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)],[24]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ fun ),C: TB] :
( ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod_case ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TB @ member ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( E @ ( D @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mem__splitE) ).
thf(418,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ fun ),C: TB] :
( ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod_case ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TB @ member ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( E @ ( D @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TC @ ( TB @ ( TA @ product_curry ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_split__curry) ).
thf(272,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TC @ ( TB @ ( TA @ product_curry ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(49,axiom,
! [TA: $tType] :
? [A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_UNIV__witness) ).
thf(287,plain,
! [TA: $tType] :
? [A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(52,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ! [B: arrow_159774573e_indi] :
( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ total_on ) ) )
& ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ irrefl ) )
& ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ trans ) ) )
=> ( ( A @ f @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ total_on ) ) )
& ( A @ f @ ( arrow_411405190le_alt @ irrefl ) )
& ( A @ f @ ( arrow_411405190le_alt @ trans ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(300,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ! [B: arrow_159774573e_indi] :
( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ total_on ) ) )
& ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ irrefl ) )
& ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ trans ) ) )
=> ( ( A @ f @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ total_on ) ) )
& ( A @ f @ ( arrow_411405190le_alt @ irrefl ) )
& ( A @ f @ ( arrow_411405190le_alt @ trans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod )] :
( ! [C: TA,D: TB] :
( ( B
= ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) ) )
=> ( D @ ( C @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_splitI2) ).
thf(315,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod )] :
( ! [C: TA,D: TB] :
( ( B
= ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) ) )
=> ( D @ ( C @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB @ ( TA @ product_prod ),B: TD @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( TB @ ( TD @ ( TA @ product_apfst ) ) ) ) @ ( C @ ( TD @ ( TC @ ( TB @ product_apsnd ) ) ) ) )
= ( A @ ( C @ ( TA @ ( TC @ ( TB @ product_apsnd ) ) ) ) @ ( B @ ( TC @ ( TD @ ( TA @ product_apfst ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_apsnd__apfst__commute) ).
thf(107,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB @ ( TA @ product_prod ),B: TD @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( TB @ ( TD @ ( TA @ product_apfst ) ) ) ) @ ( C @ ( TD @ ( TC @ ( TB @ product_apsnd ) ) ) ) )
= ( A @ ( C @ ( TA @ ( TC @ ( TB @ product_apsnd ) ) ) ) @ ( B @ ( TC @ ( TD @ ( TA @ product_apfst ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,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 ) @ ( TD @ ( TC @ product_prod ) @ ( TD @ fun ) @ ( TC @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TD @ aa ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_30_prod__induct4) ).
thf(126,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 ) @ ( TD @ ( TC @ product_prod ) @ ( TD @ fun ) @ ( TC @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TD @ aa ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( 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)],[15]) ).
thf(42,axiom,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_top1I) ).
thf(268,plain,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ in_rel ) ) ) ) )
<=> ( C @ ( A @ ( B @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_in__rel__def) ).
thf(283,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( C @ ( A @ ( B @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( B @ ( C @ ( TB @ ( TA @ in_rel ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( TB @ ( TA @ in_rel ) ) ) ) )
=> ( C @ ( A @ ( B @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_curry ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_curry__split) ).
thf(415,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_curry ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(21,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 ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_curry__conv) ).
thf(163,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 ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_prod__caseI) ).
thf(501,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(68,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_UNIV__def) ).
thf(369,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod ),C: TB @ ( TA @ product_prod )] :
( ( C = B )
=> ( ( C @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) )
= ( B @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_split__weak__cong) ).
thf(254,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod ),C: TB @ ( TA @ product_prod )] :
( ( C = B )
=> ( ( C @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) )
= ( B @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(81,axiom,
! [A: arrow_159774573e_indi] :
( ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ total_on ) ) )
& ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ irrefl ) )
& ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ trans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(469,plain,
! [A: arrow_159774573e_indi] :
( ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ fun ) @ top_top @ ( arrow_411405190le_alt @ total_on ) ) )
& ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ irrefl ) )
& ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_411405190le_alt @ trans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ),C: TB @ ( TC @ product_prod )] :
( ! [D: TC,E: TB] :
( ( ( E @ ( D @ ( TB @ ( TC @ product_Pair ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ aa ) ) ) )
= C )
=> ( A @ ( E @ ( D @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( C @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_splitI2_H) ).
thf(491,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ),C: TB @ ( TC @ product_prod )] :
( ! [D: TC,E: TB] :
( ( ( E @ ( D @ ( TB @ ( TC @ product_Pair ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ aa ) ) ) )
= C )
=> ( A @ ( E @ ( D @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( C @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(87,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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TE @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_prod__cases5) ).
thf(496,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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TE @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_split__paired__Ex) ).
thf(364,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( 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 ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(5,axiom,
bool @ top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(100,plain,
bool @ top,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(520,plain,
$false,
inference(e,[status(thm)],[289,275,335,362,446,101,347,333,518,115,449,120,379,340,153,185,320,372,110,344,357,376,485,514,280,265,292,452,117,270,201,102,467,461,188,169,499,193,96,457,173,503,128,360,508,166,161,176,423,191,204,477,213,483,198,330,130,278,306,505,487,112,355,95,263,338,177,182,99,218,104,258,158,171,418,272,287,300,315,107,126,268,283,415,163,501,369,254,469,491,496,364,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT196_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/10.63 % Computer : n002.cluster.edu
% 0.15/10.63 % Model : x86_64 x86_64
% 0.15/10.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.63 % Memory : 8046.5625MB
% 0.15/10.63 % OS : Linux 6.8.0-71-generic
% 0.15/10.63 % CPULimit : 300
% 0.15/10.63 % WCLimit : 300
% 0.15/10.63 % DateTime : Sat Sep 26 06:43:02 UTC 2026
% 0.15/10.63 % CPUTime :
% 0.15/10.63 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.96/11.21 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.74/11.55 % [INFO] Parsing done (335ms).
% 1.74/11.56 % [INFO] Running in sequential loop mode.
% 2.89/11.94 % [INFO] eprover registered as external prover.
% 2.89/11.95 % [INFO] Scanning for conjecture ...
% 3.45/12.13 % [INFO] Found a conjecture (or negated_conjecture) and 92 axioms. Running axiom selection ...
% 3.70/12.26 % [INFO] Axiom selection finished. Selected 92 axioms (removed 0 axioms).
% 4.86/12.55 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.25/12.60 % [INFO] Type checking passed.
% 5.25/12.61 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.29/12.89 % [INFO] [Domain constraints] Detected constraint on bool
% 6.29/12.90 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 78.26/59.04 % External prover 'e' found a proof!
% 78.26/59.04 % [INFO] Killing All external provers ...
% 78.26/59.05 % Time passed: 48271ms (effective reasoning time: 47479ms)
% 78.26/59.05 % 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)>
% 78.26/59.05 % Axioms used in derivation (92): fact_36_above__Lin, help_fTrue_1_1_T, fact_42_curryI, fact_7_trans__def, fact_68_splitI2_H, fact_50_in__rel__def, fact_23_notin__Lin__iff, fact_34_in__above, fact_29_prod__cases5, fact_32_prod__induct3, fact_62_split__curry, fact_14_split__paired__Ex, fact_35_linear__alt, fact_25_mkbot__Lin, fact_18_UNIV__eq__I, fact_55_split__conv, fact_21_PairE, fact_5_Pair__eq, fact_54_mem__splitI, fact_47_trans__inv__image, fact_80_apfst__convE, conj_3, fact_61_curry__split, fact_71_scomp__apply, fact_33_in__below, fact_37_below__Lin, fact_60_splitD, fact_49_trans__lex__prod, help_fTrue_1_1_U, fact_4_split__paired__All, fact_27_prod__cases6, fact_67_mem__splitI2, fact_58_prod_Osimps_I2_J, fact_79_scomp__Pair, fact_11_in__mkbot, fact_74_apsnd__apfst__commute, fact_10_top__apply, fact_40_internal__split__conv, conj_2, fact_78_Pair__scomp, fact_66_mem__splitE, fact_26_prod__induct6, fact_19_UNIV__witness, fact_20_prod_Oexhaust, fact_70_split__cong, fact_13_UNIV__def, fact_41_curry__conv, arity_HOL_Obool___Orderings_Otop, fact_16_prod_Orecs, fact_46_curryD, fact_59_split__weak__cong, fact_56_in__lex__prod, fact_63_splitE, fact_9_strict__linear__order__on__def, fact_76_mem__def, fact_38_mktop__Lin, fact_44_in__inv__image, help_COMBK_1_1_U, fact_39_in__mktop, fact_22_prod__cases3, fact_6_total__on__def, fact_53_splitI, fact_31_prod__cases4, fact_28_prod__induct5, fact_3_iso__tuple__UNIV__I, fact_72_apfst__conv, fact_0_irrefl__def, fact_51_apsnd__conv, fact_52_prod__caseI, conj_1, fact_64_splitI2, fact_1_top1I, fact_17_Lin__def, fact_73_scomp__def, fact_69_splitE2, fact_43_in__inv__imagep, fact_57_splitD_H, fact_48_internal__split__def, fact_77_Collect__def, fact_8_transD, fact_65_splitE_H, help_pp_1_1_U, fact_2_UNIV__I, fact_75_ext, arity_fun___Orderings_Otop, fact_15_transI, fact_45_curryE, conj_0, help_pp_2_1_U, fact_24_Lin__irrefl, fact_30_prod__induct4, fact_12_Pair__inject
% 78.26/59.05 % No. of inferences in proof: 188
% 78.26/59.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 48271 ms resp. 47479 ms w/o parsing
% 79.11/59.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 79.11/59.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------