%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT223_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 : n004.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 08:27:35 AM UTC 2026
% Result : Theorem 51.69s 37.18s
% Output : Refutation 52.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 115
% Syntax : Number of formulae : 232 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 2650 ( 215 equ; 0 cnn)
% Maximal formula atoms : 138 ( 11 avg)
% Number of connectives : 10533 ( 164 ~; 33 |; 91 &;9933 @)
% ( 36 <=>; 276 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 12 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 17 con; 0-6 aty)
% Number of variables : 905 ( 0 ^; 872 !; 33 ?; 905 :)
% 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(arrow_1958449194le_IIA_decl,type,
arrow_1958449194le_IIA: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ) > $o ).
thf(arrow_1985332922le_Lin_decl,type,
arrow_1985332922le_Lin: bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) ).
thf(arrow_610318064e_Prof_decl,type,
arrow_610318064e_Prof: bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ 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 @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) ).
thf(arrow_987702531ctator_decl,type,
arrow_987702531ctator: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ) > arrow_159774573e_indi > $o ).
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(arrow_2069624013nimity_decl,type,
arrow_2069624013nimity: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ) > $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combi_decl,type,
combi:
!>[TA: $tType] : ( TA @ ( TA @ fun ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(pi_decl,type,
pi:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) ) > ( bool @ ( TA @ fun ) @ ( TB @ fun ) ) > ( bool @ ( TA @ ( TB @ fun ) @ fun ) ) ) ).
thf(distinct_decl,type,
distinct:
!>[TA: $tType] : ( ( TA @ list ) > $o ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(lexord_decl,type,
lexord:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > ( bool @ ( TA @ list @ ( TA @ list @ product_prod ) @ fun ) ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_all_decl,type,
list_all:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(partition_decl,type,
partition:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > ( TA @ list @ ( TA @ list @ product_prod ) ) ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( TA @ ( TB @ product_prod ) ) ) ).
thf(product_curry_decl,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) ) > TC > TB > TA ) ).
thf(produc1605651328_split_decl,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(product_prod_rec_decl,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fdisj_decl,type,
fdisj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) ) ).
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 ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ).
thf(p1_decl,type,
p1: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ 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(c_decl,type,
c: arrow_411405190le_alt ).
thf(72,axiom,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_alt3) ).
thf(417,plain,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Pi__I_H) ).
thf(570,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(73,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 ) @ member ) ) )
<=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_in__mkbot) ).
thf(419,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 ) @ 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 ) @ member ) ) ) )
& ( ( A @ ( B @ arrow_276188178_mkbot ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ member ) ) ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(30,axiom,
arrow_610318064e_Prof @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__096P_H_A_058_AProf_096) ).
thf(214,plain,
arrow_610318064e_Prof @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_prod__induct5) ).
thf(555,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(352,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(408,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(99,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(582,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)],[99]) ).
thf(32,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 ) @ member ) ) )
<=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ member ) ) )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_in__above) ).
thf(217,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 ) @ member ) ) ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ 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 ) @ 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 ) @ member ) ) )
=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ member ) ) )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(47,axiom,
! [A: arrow_159774573e_indi] :
( ( A @ ( 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 ) @ member ) ) )
<=> ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096) ).
thf(308,plain,
! [A: arrow_159774573e_indi] :
( ( ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( 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 ) @ member ) ) ) )
& ( ( A @ ( 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 ) @ member ) ) )
=> ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
arrow_610318064e_Prof @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096) ).
thf(269,plain,
arrow_610318064e_Prof @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(85,axiom,
! [A: arrow_159774573e_indi] :
( ( A @ ( 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 ) @ member ) ) )
<=> ( A @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_iff) ).
thf(533,plain,
! [A: arrow_159774573e_indi] :
( ( ( A @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( 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 ) @ member ) ) ) )
& ( ( A @ ( 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 ) @ member ) ) )
=> ( A @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_split__paired__All) ).
thf(550,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_list_Oinject) ).
thf(142,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_splice_Osimps_I3_J) ).
thf(153,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(51,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
=> ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__C1_C) ).
thf(325,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(35,axiom,
~ ! [A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(261,plain,
~ ! [A: arrow_411405190le_alt] :
~ ( arrow_411405190le_alt @ nil @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(17,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_list_Osimps_I3_J) ).
thf(164,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(179,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_curryI) ).
thf(591,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_prod__induct4) ).
thf(623,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_list_Osimps_I5_J) ).
thf(253,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(96,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 ) ) )
=> ( arrow_610318064e_Prof @ ( A @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_const__Lin__Prof) ).
thf(574,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 ) ) )
=> ( arrow_610318064e_Prof @ ( A @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(42,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_complete__Lin) ).
thf(280,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(111,axiom,
arrow_610318064e_Prof @ ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096) ).
thf(634,plain,
arrow_610318064e_Prof @ ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_list_Osimps_I4_J) ).
thf(132,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(65,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 ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_below__Lin) ).
thf(396,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 ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
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 ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_internal__split__conv) ).
thf(411,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(36,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_26_mkbot__Lin) ).
thf(265,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)],[36]) ).
thf(83,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_third__alt) ).
thf(527,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: arrow_411405190le_alt] : ( arrow_411405190le_alt @ nil @ ( C @ ( arrow_411405190le_alt @ cons ) ) @ ( A @ ( arrow_411405190le_alt @ cons ) ) @ ( B @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1,conjecture,
! [A: arrow_159774573e_indi] :
( ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( A @ ( 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 ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: arrow_159774573e_indi] :
( ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( A @ ( 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 ) @ member ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(117,plain,
~ ! [A: arrow_159774573e_indi] :
( ( ( A @ ( 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 ) @ member ) ) )
=> ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( 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 ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_prod__cases6) ).
thf(270,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( B != A )
=> ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_notin__Lin__iff) ).
thf(302,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( B != A )
=> ( ( ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(92,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(561,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) )
=> ~ ( C @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_PiE) ).
thf(630,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) )
=> ~ ( C @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(79,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(484,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(26,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 ) @ member ) ) )
=> ~ ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Lin__irrefl) ).
thf(197,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 ) @ member ) ) )
=> ~ ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(107,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ list] :
~ ( A @ ( TA @ lexord ) @ ( TA @ nil @ ( B @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_lexord__Nil__right) ).
thf(625,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ list] :
~ ( A @ ( TA @ lexord ) @ ( TA @ nil @ ( B @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(98,axiom,
( ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_bc) ).
thf(578,plain,
( ( ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(49,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_all ) ) )
<=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_list__all__simps_I1_J) ).
thf(317,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_all ) ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_all ) ) )
=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(114,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ list] :
( ( A @ ( TA @ lexord ) @ ( B @ ( TA @ nil @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
<=> ? [C: TA,D: TA @ list] :
( B
= ( D @ ( C @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_lexord__Nil__left) ).
thf(650,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ list] :
( ( ? [C: TA,D: TA @ list] :
( B
= ( D @ ( C @ ( TA @ cons ) ) ) )
=> ( A @ ( TA @ lexord ) @ ( B @ ( TA @ nil @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) ) )
& ( ( A @ ( TA @ lexord ) @ ( B @ ( TA @ nil @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
=> ? [C: TA,D: TA @ list] :
( B
= ( D @ ( C @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(14,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_list_Oexhaust) ).
thf(156,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( TA @ distinct ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_distinct__insert) ).
thf(188,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( B @ ( TA @ distinct ) )
=> ( B @ ( A @ ( TA @ insert ) ) @ ( TA @ distinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(103,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_ex1 ) ) )
<=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_list__ex1__simps_I2_J) ).
thf(593,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_ex1 ) ) )
=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_split__paired__Ex) ).
thf(256,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: TC @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_curry__conv) ).
thf(488,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: TC @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(3,axiom,
! [TA: $tType,A: TA] : ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_distinct__singleton) ).
thf(124,plain,
! [TA: $tType,A: TA] : ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(54,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(339,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_prod__induct3) ).
thf(212,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(77,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( A @ arrow_1958449194le_IIA )
<=> ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
=> ( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_IIA__def) ).
thf(457,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) )
=> ( A @ arrow_1958449194le_IIA ) )
& ( ( A @ arrow_1958449194le_IIA )
=> ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_list_Osimps_I2_J) ).
thf(129,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(94,axiom,
arrow_411405190le_alt @ nil @ ( c @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_dist) ).
thf(569,plain,
arrow_411405190le_alt @ nil @ ( c @ ( arrow_411405190le_alt @ cons ) ) @ ( b @ ( arrow_411405190le_alt @ cons ) ) @ ( a @ ( arrow_411405190le_alt @ cons ) ) @ ( arrow_411405190le_alt @ distinct ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(115,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 ) @ member ) ) )
<=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_in__mktop) ).
thf(657,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 ) @ 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 ) @ member ) ) ) )
& ( ( A @ ( B @ arrow_424895264_mktop ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ member ) ) ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(84,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(530,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)],[84]) ).
thf(44,axiom,
( ( p @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_ab) ).
thf(296,plain,
( ( ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( p @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( p @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(75,axiom,
! [A: arrow_159774573e_indi,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( A @ ( B @ arrow_987702531ctator ) )
<=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dictator__def) ).
thf(444,plain,
! [A: arrow_159774573e_indi,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) ) ) )
=> ( A @ ( B @ arrow_987702531ctator ) ) )
& ( ( A @ ( B @ arrow_987702531ctator ) )
=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(104,axiom,
! [A: arrow_159774573e_indi] :
( ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096) ).
thf(601,plain,
! [A: arrow_159774573e_indi] :
( ( ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(19,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_not__Cons__self2) ).
thf(176,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(24,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_insert__Nil) ).
thf(191,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(43,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( A @ arrow_2069624013nimity )
<=> ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( E @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_unanimity__def) ).
thf(286,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( E @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( A @ arrow_2069624013nimity ) )
& ( ( A @ arrow_2069624013nimity )
=> ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( E @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(62,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(382,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)],[62]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_neq__Nil__conv) ).
thf(181,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_prod__induct6) ).
thf(350,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_not__Cons__self) ).
thf(159,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_curryD) ).
thf(399,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( D @ ( TA @ ( TB @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TB @ member ) ) )
=> ( B @ ( A @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_funcset__mem) ).
thf(267,plain,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( D @ ( TA @ ( TB @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TB @ member ) ) )
=> ( B @ ( A @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(18,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
<=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( A @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( C != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_distinct__length__2__or__more) ).
thf(167,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( A @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( C != B ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( A @ ( C @ ( TA @ cons ) ) @ ( TA @ distinct ) )
& ( C != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
f @ arrow_1958449194le_IIA,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_assms_I3_J) ).
thf(135,plain,
f @ arrow_1958449194le_IIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Pair__inject) ).
thf(563,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(16,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_list__ex1__simps_I1_J) ).
thf(162,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(680,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(87,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( A @ ( TA @ ( TA @ pi ) ) ) @ ( TA @ combi @ ( TA @ ( TA @ fun ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_funcset__id) ).
thf(548,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( A @ ( TA @ ( TA @ pi ) ) ) @ ( TA @ combi @ ( TA @ ( TA @ fun ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(61,axiom,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_list__nonempty__induct) ).
thf(374,plain,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ! [E: TA] :
( ( D @ ( E @ ( TA @ member ) ) )
=> ( ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ member ) ) )
<=> ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Pi__cong) ).
thf(342,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ! [E: TA] :
( ( D @ ( E @ ( TA @ member ) ) )
=> ( ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ member ) ) ) )
& ( ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(58,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
=> ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__C2_C) ).
thf(355,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(25,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_splice_Osimps_I2_J) ).
thf(194,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_prod_Orecs) ).
thf(557,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TA @ ( TB @ product_prod ) @ fun ),B: TB,C: TA] :
( ( C @ ( B @ ( A @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) ) ) )
= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_curry__def) ).
thf(414,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TA @ ( TB @ product_prod ) @ fun ),B: TB,C: TA] :
( ( C @ ( B @ ( A @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) ) ) )
= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(199,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(5,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ distinct ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_distinct_Osimps_I1_J) ).
thf(127,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ distinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(97,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(576,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(113,axiom,
! [A: arrow_159774573e_indi,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ) )
=> ( ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
=> ( A @ ( B @ arrow_987702531ctator ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_dictatorI) ).
thf(643,plain,
! [A: arrow_159774573e_indi,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ) )
=> ( ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
=> ( A @ ( B @ arrow_987702531ctator ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_prod_Oexhaust) ).
thf(585,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(59,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096a_A_126_061_Ab_096) ).
thf(370,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(52,axiom,
arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_assms_I1_J) ).
thf(336,plain,
arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(63,axiom,
( ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_ac) ).
thf(386,plain,
( ( ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(314,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_PairE) ).
thf(627,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Pair__eq) ).
thf(539,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(78,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA] :
~ ( B @ ( C @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( B @ ( TA @ lexord ) @ ( A @ ( A @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_lexord__irreflexive) ).
thf(482,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA] :
~ ( B @ ( C @ ( C @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
=> ~ ( B @ ( TA @ lexord ) @ ( A @ ( A @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(28,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ list,C: TA,D: TA @ list,E: TA] :
( ( A @ ( TA @ lexord ) @ ( B @ ( C @ ( TA @ cons ) ) @ ( D @ ( E @ ( TA @ cons ) ) @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
<=> ( ( ( A @ ( TA @ lexord ) @ ( B @ ( D @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_lexord__cons__cons) ).
thf(203,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ list,C: TA,D: TA @ list,E: TA] :
( ( ( ( ( A @ ( TA @ lexord ) @ ( B @ ( D @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) )
=> ( A @ ( TA @ lexord ) @ ( B @ ( C @ ( TA @ cons ) ) @ ( D @ ( E @ ( TA @ cons ) ) @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) ) )
& ( ( A @ ( TA @ lexord ) @ ( B @ ( C @ ( TA @ cons ) ) @ ( D @ ( E @ ( TA @ cons ) ) @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
=> ( ( ( A @ ( TA @ lexord ) @ ( B @ ( D @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_prod__cases5) ).
thf(588,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(64,axiom,
! [A: arrow_159774573e_indi] :
( ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096) ).
thf(390,plain,
! [A: arrow_159774573e_indi] :
( ( ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( a @ ( b @ ( b @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( c @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Pi__mem) ).
thf(632,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Pi__I) ).
thf(401,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_splice_Osimps_I1_J) ).
thf(139,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_list__all__simps_I2_J) ).
thf(151,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(45,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(300,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(68,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ partition ) ) )
= ( TA @ nil @ ( TA @ nil @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_partition_Osimps_I1_J) ).
thf(405,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ partition ) ) )
= ( TA @ nil @ ( TA @ nil @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(23,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(190,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TA @ ( TB @ fun ),C: bool @ ( TB @ fun )] :
( ! [D: TB] :
( ( C @ ( D @ ( TB @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) )
=> ( A @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( B @ ( TA @ ( TB @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_funcsetI) ).
thf(273,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TA @ ( TB @ fun ),C: bool @ ( TB @ fun )] :
( ! [D: TB] :
( ( C @ ( D @ ( TB @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) )
=> ( A @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( B @ ( TA @ ( TB @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(60,axiom,
arrow_610318064e_Prof @ ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096) ).
thf(373,plain,
arrow_610318064e_Prof @ ( c @ ( a @ ( a @ ( b @ ( b @ ( c @ ( p @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( arrow_319942042_below @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(112,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [D: TA,E: TA] :
( ( C @ ( D @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ( D = E )
| ( C @ ( E @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) )
=> ( ( C @ ( TA @ lexord ) @ ( B @ ( A @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
| ( B = A )
| ( C @ ( TA @ lexord ) @ ( A @ ( B @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_lexord__linear) ).
thf(635,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ ( TA @ product_prod ) @ fun )] :
( ! [D: TA,E: TA] :
( ( C @ ( D @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) )
| ( D = E )
| ( C @ ( E @ ( D @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) )
=> ( ( C @ ( TA @ lexord ) @ ( B @ ( A @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
| ( B = A )
| ( C @ ( TA @ lexord ) @ ( A @ ( B @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(4,axiom,
f @ arrow_2069624013nimity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_u) ).
thf(126,plain,
f @ arrow_2069624013nimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_splice__Nil2) ).
thf(136,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_prod__cases3) ).
thf(277,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(74,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_61_linear__alt) ).
thf(442,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)],[74]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB] :
( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
<=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_pred__equals__eq2) ).
thf(607,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
& ( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) ) )
& ( ! [C: TA,D: TB] :
( ( ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
& ( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(50,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_42_above__Lin) ).
thf(322,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)],[50]) ).
thf(80,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(486,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(53,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_27_mktop__Lin) ).
thf(337,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)],[53]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_curryE) ).
thf(215,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(91,axiom,
arrow_610318064e_Prof @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096P_A_058_AProf_096) ).
thf(560,plain,
arrow_610318064e_Prof @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(82,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 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ member ) ) ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ member ) ) ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_in__below) ).
thf(491,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 ) @ member ) ) ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ member ) ) ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D @ ( E @ ( C @ ( arrow_319942042_below @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ member ) ) ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( 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 ) @ member ) ) ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_prod__cases4) ).
thf(454,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(683,plain,
$false,
inference(e,[status(thm)],[417,570,419,214,555,352,408,582,217,308,269,533,550,142,153,325,261,164,179,591,623,253,574,280,634,132,396,411,265,527,117,270,302,561,630,484,197,625,578,317,650,156,188,593,256,488,124,339,212,457,129,569,657,530,296,444,601,176,191,286,382,181,350,159,399,267,167,135,563,162,680,548,374,342,355,194,557,414,199,127,576,643,585,370,336,386,314,627,539,482,203,588,390,632,401,139,151,300,405,190,273,373,635,126,136,277,442,607,322,486,337,215,560,491,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT223_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
% 0.14/5.41 % Computer : n004.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 06:43:27 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 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
% 0.18/5.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.64/6.15 % [INFO] Parsing done (223ms).
% 1.64/6.15 % [INFO] Running in sequential loop mode.
% 2.32/6.38 % [INFO] eprover registered as external prover.
% 2.32/6.39 % [INFO] Scanning for conjecture ...
% 3.22/6.61 % [INFO] Found a conjecture (or negated_conjecture) and 114 axioms. Running axiom selection ...
% 3.53/6.75 % [INFO] Axiom selection finished. Selected 114 axioms (removed 0 axioms).
% 4.43/7.02 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.91/7.05 % [INFO] Type checking passed.
% 4.91/7.05 % [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 ...
% 51.69/37.17 % External prover 'e' found a proof!
% 51.69/37.17 % [INFO] Killing All external provers ...
% 51.69/37.17 % Time passed: 31616ms (effective reasoning time: 31013ms)
% 51.69/37.17 % 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)>
% 51.69/37.17 % Axioms used in derivation (114): help_fdisj_1_1_U, fact_42_above__Lin, fact_94_list__all__simps_I2_J, fact_60_alt3, fact_20_assms_I3_J, fact_78_prod__induct3, fact_91_list__ex1__simps_I2_J, fact_64_splice_Osimps_I2_J, help_COMBS_1_1_U, fact_15_ab, fact_18_in__below, fact_1__096a_A_126_061_Ab_096, fact_92_lexord__cons__cons, fact_29_notin__Lin__iff, fact_57_funcsetI, fact_83_internal__split__conv, fact_95_lexord__Nil__right, help_COMBI_1_1_U, fact_23__C2_C, fact_3_iff, fact_70_prod__induct6, fact_62_Pi__cong, fact_50_list_Oexhaust, fact_21__096P_H_A_058_AProf_096, fact_38_in__above, fact_69_list_Osimps_I5_J, fact_9_Pair__eq, fact_11__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096, fact_8_split__paired__All, fact_5__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096, fact_71_prod__cases6, fact_82_prod_Oexhaust, help_fNot_2_1_U, fact_32_distinct_Osimps_I1_J, fact_67_splice__Nil2, help_fNot_1_1_U, fact_73_prod__cases5, fact_39_prod_Orecs, fact_25_const__Lin__Prof, fact_52_funcset__mem, fact_14__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096, fact_34_split__paired__Ex, fact_44_list_Osimps_I2_J, fact_77_prod__induct4, fact_51_Pi__mem, fact_43_list_Osimps_I3_J, fact_12_in__mkbot, fact_87_curryD, fact_80_pred__equals__eq2, help_COMBB_1_1_U, fact_93_list__all__simps_I1_J, fact_99_partition_Osimps_I1_J, fact_97_lexord__irreflexive, fact_45_distinct__length__2__or__more, fact_98_lexord__linear, fact_89_list__ex1__simps_I1_J, fact_85_curryI, fact_90_list__nonempty__induct, fact_10__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096, fact_55_Pi__I, fact_41_not__Cons__self, fact_35_distinct__singleton, fact_30_below__Lin, fact_36_complete__Lin, fact_74_prod__cases4, fact_46_unanimity__def, help_fequal_1_1_T, fact_17_bc, fact_24_assms_I1_J, fact_47_IIA__def, fact_22__C1_C, fact_59_distinct__insert, fact_88_curry__def, fact_76_mem__def, fact_4__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096, fact_2_dist, fact_0__096P_A_058_AProf_096, fact_54_dictator__def, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_58_insert__Nil, fact_7__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_31_Pair__inject, fact_84_curry__conv, fact_53_funcset__id, help_COMBC_1_1_U, fact_56_neq__Nil__conv, help_fequal_2_1_T, fact_48_dictatorI, fact_26_mkbot__Lin, fact_68_splice_Osimps_I1_J, fact_79_prod__cases3, fact_16_ac, fact_27_mktop__Lin, help_fdisj_3_1_U, fact_37_list_Oinject, fact_49_PiE, fact_72_prod__induct5, fact_86_curryE, help_pp_1_1_U, fact_40_not__Cons__self2, fact_66_splice_Osimps_I3_J, fact_65_list_Osimps_I4_J, fact_81_PairE, fact_13_in__mktop, fact_75_ext, fact_6__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096, help_pp_2_1_U, fact_19_u, fact_61_linear__alt, fact_28_Lin__irrefl, fact_33_third__alt, fact_63_Pi__I_H, fact_96_lexord__Nil__left
% 51.69/37.17 % No. of inferences in proof: 232
% 51.69/37.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 31616 ms resp. 31013 ms w/o parsing
% 52.47/37.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.47/37.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------