%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT261_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : 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 08:27:38 AM UTC 2026
% Result : Theorem 21.31s 8.26s
% Output : Refutation 22.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 118
% Syntax : Number of formulae : 238 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 2953 ( 204 equ; 0 cnn)
% Maximal formula atoms : 210 ( 12 avg)
% Number of connectives : 11538 ( 137 ~; 19 |; 82 &;10883 @)
% ( 38 <=>; 379 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 11 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 21 con; 0-5 aty)
% Number of variables : 624 ( 0 ^; 624 !; 0 ?; 624 :)
% 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(nat_type,type,
nat: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_decl,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_decl,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
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 @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) ).
thf(arrow_276188178_mkbot_decl,type,
arrow_276188178_mkbot: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) ).
thf(arrow_424895264_mktop_decl,type,
arrow_424895264_mktop: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_411405190le_alt @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ 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(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(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ fun ) ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( TA @ ( TB @ product_prod ) ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( 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(lab_decl,type,
lab: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ).
thf(lba_decl,type,
lba: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ).
thf(p_decl,type,
p: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) ).
thf(a_decl,type,
a: arrow_411405190le_alt ).
thf(b_decl,type,
b: arrow_411405190le_alt ).
thf(c_decl,type,
c: arrow_411405190le_alt ).
thf(d_decl,type,
d: arrow_411405190le_alt ).
thf(e_decl,type,
e: arrow_411405190le_alt ).
thf(h_decl,type,
h: nat @ ( arrow_159774573e_indi @ fun ) ).
thf(n_decl,type,
n: nat ).
thf(60,axiom,
~ ! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( A @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(365,plain,
~ ! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( A @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(42,axiom,
! [A: nat] : ( arrow_610318064e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_PiProf) ).
thf(275,plain,
! [A: nat] : ( arrow_610318064e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( 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)],[42]) ).
thf(109,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( B != A )
=> ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_notin__Lin__iff) ).
thf(654,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)],[109]) ).
thf(71,axiom,
! [A: arrow_159774573e_indi] :
( ( ( ~ ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
!= n )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_276188178_mkbot @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( e @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_1158827142_above @ ( 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 ) ) ) @ ( e @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
& ( ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_424895264_mktop @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( e @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
<=> ( ( ~ ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( lba @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( lab @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096) ).
thf(409,plain,
! [A: arrow_159774573e_indi] :
( ( ( ( ~ ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( lba @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( lab @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ~ ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
!= n )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_276188178_mkbot @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( e @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_1158827142_above @ ( 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 ) ) ) @ ( e @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
& ( ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_424895264_mktop @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( e @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
& ( ( ( ~ ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
!= n )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_276188178_mkbot @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( e @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_1158827142_above @ ( 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 ) ) ) @ ( e @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
& ( ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_424895264_mktop @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( e @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ~ ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( lba @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( lab @ ( 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)],[71]) ).
thf(1,conjecture,
e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( 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 @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( 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 @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(120,plain,
~ ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( 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 @ ( 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)],[2]) ).
thf(72,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(440,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(25,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__096c_A_126_061_Ad_096) ).
thf(202,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(70,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(408,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add__le__imp__le__right) ).
thf(170,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(100,axiom,
~ ( lba @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(614,plain,
~ ( lba @ ( 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)],[100]) ).
thf(119,axiom,
! [A: arrow_159774573e_indi] :
( ( A @ ( p @ ( 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 ) ) )
<=> ( ( ~ ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
!= n )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_276188178_mkbot @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_1158827142_above @ ( 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 ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
& ( ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_424895264_mktop @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096) ).
thf(677,plain,
! [A: arrow_159774573e_indi] :
( ( ( ( ~ ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
!= n )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_276188178_mkbot @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_1158827142_above @ ( 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 ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
& ( ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_424895264_mktop @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( d @ ( c @ ( 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 ) ) ) @ ( d @ ( c @ ( 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 ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( ( ~ ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
!= n )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_276188178_mkbot @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) )
= n )
=> ( e @ ( c @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_1158827142_above @ ( 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 ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
& ( ( n @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( e @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( arrow_424895264_mktop @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ 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)],[119]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_eq__imp__le) ).
thf(385,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(79,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 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_11_in__mktop) ).
thf(472,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 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A @ ( B @ ( arrow_424895264_mktop @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( 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)],[79]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
=> ~ ( ( A @ ( C @ ( nat @ ord_less_eq ) ) )
=> ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_add__leE) ).
thf(404,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
=> ~ ( ( A @ ( C @ ( nat @ ord_less_eq ) ) )
=> ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',fact_42_unanimity__def) ).
thf(185,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)],[22]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_nat__add__commute) ).
thf(288,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_41_IIA__def) ).
thf(301,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)],[51]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__add__left__cancel) ).
thf(565,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(35,axiom,
f @ arrow_2069624013nimity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_u) ).
thf(257,plain,
f @ arrow_2069624013nimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(68,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 )
=> ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_26_pairwise__neutrality) ).
thf(389,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 )
=> ( ( 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)],[68]) ).
thf(93,axiom,
arrow_610318064e_Prof @ ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096) ).
thf(587,plain,
arrow_610318064e_Prof @ ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(103,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__lessD1) ).
thf(619,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_add__le__cancel__left) ).
thf(164,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(95,axiom,
arrow_1985332922le_Lin @ ( lab @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096Lab_A_058_ALin_096) ).
thf(591,plain,
arrow_1985332922le_Lin @ ( lab @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__strict__left__mono) ).
thf(376,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__left__imp__eq) ).
thf(121,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',fact_31_const__Lin__Prof) ).
thf(353,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)],[56]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_linorder__neqE__nat) ).
thf(280,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(75,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__antisym) ).
thf(453,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_add__left__cancel) ).
thf(133,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(110,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(660,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(33,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_less__add__eq__less) ).
thf(243,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(111,axiom,
arrow_1985332922le_Lin @ ( lba @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096Lba_A_058_ALin_096) ).
thf(661,plain,
arrow_1985332922le_Lin @ ( lba @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__strict__mono) ).
thf(381,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Pair__inject) ).
thf(233,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)],[30]) ).
thf(74,axiom,
lba @ ( lab @ ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( 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 ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_n_I3_J) ).
thf(452,plain,
lba @ ( lab @ ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( 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 ) ) ) @ ( 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)],[74]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',fact_32_Lin__irrefl) ).
thf(583,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)],[91]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_trans__less__add2) ).
thf(456,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Pair__eq) ).
thf(224,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)],[29]) ).
thf(11,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(156,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__right__cancel) ).
thf(141,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__left__mono) ).
thf(124,plain,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(115,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add__leD2) ).
thf(669,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__strict__right__mono) ).
thf(205,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(84,axiom,
~ ( lab @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(541,plain,
~ ( lab @ ( 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)],[84]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__not__refl2) ).
thf(558,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(112,axiom,
! [A: nat] :
( ( n @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_18_n_I2_J) ).
thf(662,plain,
! [A: nat] :
( ( n @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( 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)],[112]) ).
thf(102,axiom,
lab @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(618,plain,
lab @ ( 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)],[102]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_one__reorient) ).
thf(148,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(264,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(161,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
<=> ( ( B != A )
& ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_nat__less__le) ).
thf(573,plain,
! [A: nat,B: nat] :
( ( ( ( B != A )
& ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( B != A )
& ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(73,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_nat__add__right__cancel) ).
thf(444,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_le__eq__less__or__eq) ).
thf(601,plain,
! [A: nat,B: nat] :
( ( ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add__mono) ).
thf(180,plain,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(49,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_not__add__less1) ).
thf(296,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(87,axiom,
lba @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(562,plain,
lba @ ( 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)],[87]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_le__neq__implies__less) ).
thf(291,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(611,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)],[99]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__right__mono) ).
thf(159,plain,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_nat__add__left__commute) ).
thf(672,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add__right__imp__eq) ).
thf(172,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',fact_30_assms_I1_J) ).
thf(274,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)],[41]) ).
thf(107,axiom,
( ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( 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 @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( lba @ ( lab @ ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( 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 ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096) ).
thf(649,plain,
( ( ( lba @ ( lab @ ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( 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 ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( 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 @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( 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 @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( lba @ ( lab @ ( nat @ one_one @ ( n @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( 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 ) ) ) @ ( 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)],[107]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_trans__less__add1) ).
thf(616,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_less__or__eq__imp__le) ).
thf(535,plain,
! [A: nat,B: nat] :
( ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(8,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(140,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(104,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 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_10_in__mkbot) ).
thf(621,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 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A @ ( B @ ( arrow_276188178_mkbot @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ aa ) ) ) @ ( 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)],[104]) ).
thf(24,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 ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( 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 ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_PW) ).
thf(198,plain,
( ( ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( 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 ) ) ) @ ( d @ ( c @ ( 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 ) ) ) @ ( d @ ( c @ ( 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 ) ) ) @ ( d @ ( c @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( e @ ( p @ ( arrow_276188178_mkbot @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( e @ ( c @ ( p @ ( arrow_1158827142_above @ ( 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 ) ) ) ) @ ( n @ ( h @ ( nat @ fequal @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( e @ ( p @ ( arrow_424895264_mktop @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ 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 @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( n @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combs ) ) ) ) @ ( 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 ) ) ) @ ( 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)],[24]) ).
thf(53,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(330,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(6,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24__096a_A_126_061_Ab_096) ).
thf(130,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__less__mono1) ).
thf(563,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_nat__le__linear) ).
thf(299,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(39,axiom,
nat @ ordere779506340up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(267,plain,
nat @ ordere779506340up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__less__mono) ).
thf(241,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(108,axiom,
arrow_610318064e_Prof @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__096P_A_058_AProf_096) ).
thf(653,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)],[108]) ).
thf(117,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(675,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(81,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(531,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__less__imp__less__left) ).
thf(374,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(106,axiom,
nat @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(648,plain,
nat @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat__neq__iff) ).
thf(342,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(355,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)],[57]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',fact_21__C2_C) ).
thf(458,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)],[77]) ).
thf(54,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_nat__less__cases) ).
thf(331,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__imp__eq) ).
thf(177,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_less__irrefl__nat) ).
thf(182,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_add__le__mono) ).
thf(585,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( A @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__less__cancel__right) ).
thf(370,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(18,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(175,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(97,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_nat__add__left__cancel__le) ).
thf(595,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(59,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add__leD1) ).
thf(363,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(80,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 @ ( 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 ) ) )
<=> ( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_38_in__above) ).
thf(495,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 @ ( 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_1158827142_above @ ( 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 ) ) )
=> ( ( ( 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)],[80]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(588,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_add__less__cancel__left) ).
thf(258,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(378,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)],[64]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_22__C1_C) ).
thf(246,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)],[34]) ).
thf(27,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] :
( ( D != C )
=> ( ( 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 ) ) )
=> ( ! [E: arrow_159774573e_indi] :
( ( E @ ( B @ ( 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 ) ) )
<=> ( E @ ( A @ ( 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 @ ( 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 ) ) )
<=> ( 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 ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25__C3_C) ).
thf(207,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] :
( ( D != C )
=> ( ( 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 ) ) )
=> ( ! [E: arrow_159774573e_indi] :
( ( ( E @ ( A @ ( 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 ) ) )
=> ( E @ ( B @ ( 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 ) ) ) )
& ( ( E @ ( B @ ( 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 ) ) )
=> ( E @ ( A @ ( 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 ) ) ) ) )
=> ( ( ( 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 ) ) ) @ ( D @ ( C @ ( 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 ) ) ) @ ( 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 ) ) ) @ ( 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 ) ) ) @ ( 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)],[27]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__less__imp__less__right) ).
thf(667,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__imp__le__nat) ).
thf(383,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_add__le__imp__le__left) ).
thf(168,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(37,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 ) @ ( 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 @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_mktop__Lin) ).
thf(262,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 ) @ ( 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 @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(52,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mem__def) ).
thf(326,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)],[52]) ).
thf(31,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 ) @ ( 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 @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_mkbot__Lin) ).
thf(239,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 ) @ ( 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 @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_nat__add__left__cancel__less) ).
thf(268,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_split__paired__All) ).
thf(358,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)],[58]) ).
thf(23,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 ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_36_above__Lin) ).
thf(195,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 ) @ ( 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)],[23]) ).
thf(113,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_less__not__refl) ).
thf(664,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(532,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)],[82]) ).
thf(45,axiom,
~ ! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( A @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(283,plain,
~ ! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( A @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(48,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_le__refl) ).
thf(294,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__le__cancel__right) ).
thf(126,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(105,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_less__not__refl3) ).
thf(644,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(277,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(78,axiom,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_not__add__less2) ).
thf(469,plain,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(85,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] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( 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 ) ) )
=> ( ! [F: arrow_159774573e_indi] :
( ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( F @ ( 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 ) ) ) @ ( D @ ( E @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_23__C4_C) ).
thf(543,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] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( 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 ) ) )
=> ( ! [F: arrow_159774573e_indi] :
( ( ( F @ ( 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 ) ) )
=> ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( E @ ( 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 ) ) ) @ ( D @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( 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 ) ) ) @ ( D @ ( E @ ( 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 ) ) ) @ ( D @ ( E @ ( 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)],[85]) ).
thf(118,axiom,
f @ arrow_1958449194le_IIA,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I3_J) ).
thf(676,plain,
f @ arrow_1958449194le_IIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(28,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__trans) ).
thf(222,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(96,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_nat__add__assoc) ).
thf(592,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(707,plain,
$false,
inference(e,[status(thm)],[365,275,654,409,120,440,202,408,170,614,677,385,472,404,185,288,301,565,257,389,587,619,164,591,376,121,353,280,453,133,660,243,661,381,233,452,583,456,224,156,141,124,669,205,541,558,662,618,148,264,161,573,444,601,180,296,562,291,611,159,672,172,274,649,616,535,140,621,198,330,130,563,299,267,241,653,675,531,374,648,342,355,458,331,177,182,585,370,175,595,363,495,588,258,378,246,207,667,383,168,262,326,239,268,358,195,664,532,283,294,126,644,277,469,543,676,222,592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT261_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.41 % Computer : n004.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 06:46:36 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.82/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.29 % [INFO] Parsing done (311ms).
% 1.85/1.30 % [INFO] Running in sequential loop mode.
% 2.89/1.69 % [INFO] eprover registered as external prover.
% 2.89/1.69 % [INFO] Scanning for conjecture ...
% 3.90/1.91 % [INFO] Found a conjecture (or negated_conjecture) and 117 axioms. Running axiom selection ...
% 4.38/2.07 % [INFO] Axiom selection finished. Selected 117 axioms (removed 0 axioms).
% 5.06/2.28 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.32/2.31 % [INFO] Type checking passed.
% 5.32/2.32 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.60/2.64 % [INFO] [Domain constraints] Detected constraint on bool
% 6.60/2.64 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 21.31/8.25 % External prover 'e' found a proof!
% 21.31/8.25 % [INFO] Killing All external provers ...
% 21.31/8.25 % Time passed: 7705ms (effective reasoning time: 6943ms)
% 21.31/8.25 % 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)>
% 21.31/8.26 % Axioms used in derivation (117): fact_63_nat__add__assoc, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_79_add__strict__mono, fact_22__C1_C, fact_28__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_51_add__right__imp__eq, fact_26_pairwise__neutrality, fact_62_nat__less__cases, fact_50_add__le__cancel__left, fact_96_add__leD1, fact_73_add__mono, fact_98_add__le__mono, fact_10_in__mkbot, fact_48_nat__add__right__cancel, help_COMBS_1_1_U, fact_42_unanimity__def, fact_16__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_91_le__eq__less__or__eq, fact_13__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096, fact_52_add__imp__eq, fact_12_PW, fact_18_n_I2_J, fact_7__096c_A_126_061_Ad_096, fact_1__096Lba_A_058_ALin_096, fact_36_above__Lin, fact_24__096a_A_126_061_Ab_096, fact_89_add__lessD1, fact_74_mem__def, fact_84_trans__less__add1, fact_60_less__not__refl2, fact_38_in__above, fact_71_add__le__imp__le__left, fact_46_add__right__cancel, fact_75_add__left__mono, fact_49_nat__add__left__cancel, fact_23__C4_C, fact_34_mktop__Lin, fact_29__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_0__096Lab_A_058_ALin_096, fact_87_add__less__mono, fact_76_add__right__mono, fact_68_eq__imp__le, fact_92_less__imp__le__nat, fact_2_assms_I3_J, fact_70_le__refl, fact_72_add__le__imp__le__right, help_COMBB_1_1_U, help_If_1_1_T, fact_67_le__trans, fact_30_assms_I1_J, fact_59_less__irrefl__nat, fact_11_in__mktop, fact_5__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact_64_nat__add__left__commute, fact_81_add__less__imp__less__left, fact_56_less__not__refl, fact_15__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_A_Ia_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096, fact_39_nat__add__left__cancel__le, fact_69_nat__le__linear, fact_93_le__neq__implies__less, fact_83_not__add__less2, fact_20_Pair__eq, fact_33_notin__Lin__iff, fact_41_IIA__def, fact_80_add__less__imp__less__right, fact_86_add__less__mono1, fact_32_Lin__irrefl, help_fequal_1_1_T, fact_54_ab__semigroup__add__class_Oadd__ac_I1_J, fact_19_split__paired__All, fact_35_mkbot__Lin, help_If_3_1_T, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_85_trans__less__add2, help_If_2_1_T, help_COMBK_1_1_U, fact_47_add__left__cancel, fact_4__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, help_COMBC_1_1_U, fact_31_const__Lin__Prof, help_fequal_2_1_T, fact_44_add__less__cancel__right, fact_55_one__reorient, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_6__096P_A_058_AProf_096, fact_43_add__less__cancel__left, fact_57_nat__neq__iff, arity_Nat_Onat___Groups_Oone, fact_45_add__le__cancel__right, fact_9__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096, fact_27_PiProf, fact_3_u, fact_65_nat__add__commute, fact_17__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_53_add__left__imp__eq, fact_66_le__antisym, fact_8_n_I3_J, fact_82_not__add__less1, fact_88_less__add__eq__less, fact_77_add__strict__right__mono, fact_90_nat__less__le, help_pp_1_1_U, fact_95_add__leE, fact_37_Pair__inject, fact_40_nat__add__left__cancel__less, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_94_less__or__eq__imp__le, fact_97_add__leD2, fact_58_linorder__neqE__nat, help_pp_2_1_U, fact_61_less__not__refl3, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_25__C3_C, fact_21__C2_C, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_14__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096, fact_78_add__strict__left__mono
% 21.31/8.26 % No. of inferences in proof: 238
% 21.31/8.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7705 ms resp. 6943 ms w/o parsing
% 22.29/8.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.29/8.41 % [INFO] Killing All external provers ...
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