%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT264_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 : n020.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 08:27:39 AM UTC 2026
% Result : Theorem 25.13s 10.76s
% Output : Refutation 26.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 119
% Syntax : Number of formulae : 240 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 3795 ( 204 equ; 0 cnn)
% Maximal formula atoms : 210 ( 15 avg)
% Number of connectives : 14438 ( 145 ~; 14 |; 93 &;13764 @)
% ( 39 <=>; 383 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 12 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 21 con; 0-5 aty)
% Number of variables : 613 ( 0 ^; 602 !; 11 ?; 613 :)
% 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(combi_decl,type,
combi:
!>[TA: $tType] : ( TA @ ( TA @ fun ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(finite_card_decl,type,
finite_card:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > nat ) ).
thf(inj_on_decl,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( bool @ ( TB @ fun ) ) > $o ) ).
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(hilbert_inv_into_decl,type,
hilbert_inv_into:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) ) > ( TA @ ( TB @ fun ) ) > TA > TB ) ).
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(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
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(39,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(272,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)],[39]) ).
thf(77,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_42_n_I3_J) ).
thf(479,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)],[77]) ).
thf(51,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_46__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(333,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)],[51]) ).
thf(83,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_18__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(518,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)],[83]) ).
thf(85,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(523,plain,
arrow_1985332922le_Lin @ ( lab @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TB @ fun ) @ top_top @ ( TA @ ( bool @ ( TB @ fun ) @ combk ) ) @ ( A @ ( TB @ ( TA @ pi ) ) ) )
= ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ top_top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Pi__UNIV) ).
thf(269,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TB @ fun ) @ top_top @ ( TA @ ( bool @ ( TB @ fun ) @ combk ) ) @ ( A @ ( TB @ ( TA @ pi ) ) ) )
= ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ top_top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(58,axiom,
n @ ( h @ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( nat @ ( arrow_159774573e_indi @ hilbert_inv_into ) ) ) ) @ ( 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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096) ).
thf(385,plain,
n @ ( h @ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( nat @ ( arrow_159774573e_indi @ hilbert_inv_into ) ) ) ) @ ( 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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(90,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_23__C1_C) ).
thf(533,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)],[90]) ).
thf(119,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_71_linorder__neqE__nat) ).
thf(715,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)],[119]) ).
thf(73,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_96_add__less__imp__less__left) ).
thf(472,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)],[73]) ).
thf(10,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_89_add__mono) ).
thf(153,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)],[10]) ).
thf(118,axiom,
~ ! [A: nat] :
( ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( lba @ ( lab @ ( B @ ( 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 ) ) ) )
=> ~ ( lba @ ( lab @ ( nat @ one_one @ ( A @ ( 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_49__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_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_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(709,plain,
~ ! [A: nat] :
( ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( lba @ ( lab @ ( B @ ( 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 ) ) ) )
=> ~ ( lba @ ( lab @ ( nat @ one_one @ ( A @ ( 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)],[118]) ).
thf(34,axiom,
nat @ ordere779506340up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(257,plain,
nat @ ordere779506340up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(80,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_45_unanimity__def) ).
thf(504,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)],[80]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_one__reorient) ).
thf(125,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)],[4]) ).
thf(12,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_59_add__le__cancel__left) ).
thf(157,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)],[12]) ).
thf(44,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_29__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(284,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)],[44]) ).
thf(45,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_44_IIA__def) ).
thf(289,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)],[45]) ).
thf(75,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(475,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(14,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_88_add__le__imp__le__right) ).
thf(164,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)],[14]) ).
thf(104,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(591,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(49,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(321,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(56,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_52_nat__add__left__cancel__less) ).
thf(376,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)],[56]) ).
thf(31,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_31_assms_I1_J) ).
thf(238,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)],[31]) ).
thf(78,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_13_in__mkbot) ).
thf(480,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)],[78]) ).
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 ) ) ) @ ( d @ ( e @ ( 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 ) ) ) @ ( d @ ( e @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(121,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 @ ( e @ ( 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(81,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_le__refl) ).
thf(514,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(107,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_19__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(602,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)],[107]) ).
thf(42,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_95_add__less__imp__less__right) ).
thf(280,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)],[42]) ).
thf(63,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_36_notin__Lin__iff) ).
thf(396,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)],[63]) ).
thf(5,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_64_add__imp__eq) ).
thf(133,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)],[5]) ).
thf(88,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_82_le__antisym) ).
thf(529,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)],[88]) ).
thf(113,axiom,
bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( h @ ( nat @ ( arrow_159774573e_indi @ inj_on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_injh) ).
thf(661,plain,
bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( h @ ( nat @ ( arrow_159774573e_indi @ inj_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(61,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_37_mktop__Lin) ).
thf(392,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)],[61]) ).
thf(115,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_72_nat__neq__iff) ).
thf(693,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)],[115]) ).
thf(40,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_73_less__not__refl) ).
thf(275,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)],[40]) ).
thf(48,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(317,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)],[48]) ).
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_39_above__Lin) ).
thf(188,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(76,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(476,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)],[76]) ).
thf(92,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_40_Pair__inject) ).
thf(547,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)],[92]) ).
thf(111,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_41_in__above) ).
thf(622,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)],[111]) ).
thf(69,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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__096c_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_096) ).
thf(457,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)],[69]) ).
thf(16,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_91_add__right__mono) ).
thf(173,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)],[16]) ).
thf(79,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(503,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)],[79]) ).
thf(109,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_25_pairwise__neutrality) ).
thf(605,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)],[109]) ).
thf(102,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_79_nat__le__linear) ).
thf(586,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)],[102]) ).
thf(114,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 ) ) ) @ ( d @ ( e @ ( 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 @ ( e @ ( 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 @ ( e @ ( 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 )
=> ( lba @ ( a @ ( b @ ( 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 )
=> ( 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_16__096ALL_Ai_O_A_Ie_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_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096) ).
thf(662,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 )
=> ( lba @ ( a @ ( b @ ( 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 )
=> ( lab @ ( a @ ( b @ ( 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 @ ( e @ ( 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 @ ( e @ ( 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 @ ( e @ ( 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 @ ( e @ ( 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 @ ( e @ ( 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 @ ( e @ ( 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 )
=> ( lba @ ( a @ ( b @ ( 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 )
=> ( 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)],[114]) ).
thf(120,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(718,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)],[120]) ).
thf(15,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_54_add__left__cancel) ).
thf(166,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)],[15]) ).
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_62_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(19,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(180,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(100,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_7__096P_A_058_AProf_096) ).
thf(584,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)],[100]) ).
thf(98,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_34_const__Lin__Prof) ).
thf(577,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)],[98]) ).
thf(99,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_47_split__paired__Ex) ).
thf(579,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)],[99]) ).
thf(24,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_76_nat__add__left__commute) ).
thf(191,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)],[24]) ).
thf(64,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 ) ) ) @ ( d @ ( e @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( lba @ ( lab @ ( 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 @ 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_9__096_Ie_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_Ad_J_A_061_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096) ).
thf(402,plain,
( ( ( lba @ ( lab @ ( 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 @ 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 ) ) )
=> ( 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 @ ( e @ ( 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 @ ( e @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( lba @ ( lab @ ( 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 @ 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)],[64]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(382,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(97,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_20_split__paired__All) ).
thf(572,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)],[97]) ).
thf(116,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_nat__add__commute) ).
thf(704,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(108,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(604,plain,
arrow_1985332922le_Lin @ ( lba @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(65,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_10__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(406,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)],[65]) ).
thf(29,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_69_less__not__refl2) ).
thf(219,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)],[29]) ).
thf(68,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_14_in__mktop) ).
thf(434,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)],[68]) ).
thf(110,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_51_nat__add__left__cancel__le) ).
thf(616,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)],[110]) ).
thf(53,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_94_add__strict__mono) ).
thf(367,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)],[53]) ).
thf(106,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_56_nat__add__left__cancel) ).
thf(594,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)],[106]) ).
thf(84,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(520,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)],[84]) ).
thf(11,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_87_add__le__imp__le__left) ).
thf(155,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)],[11]) ).
thf(26,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_30__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(198,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)],[26]) ).
thf(71,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( A @ ( TA @ ( TA @ pi ) ) ) @ ( TA @ combi @ ( TA @ ( TA @ fun ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_funcset__id) ).
thf(462,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( A @ ( TA @ ( TA @ pi ) ) ) @ ( TA @ combi @ ( TA @ ( TA @ fun ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( D @ ( TA @ ( TB @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TB @ member ) ) )
=> ( B @ ( A @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_funcset__mem) ).
thf(278,plain,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( D @ ( TA @ ( TB @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TB @ member ) ) )
=> ( B @ ( A @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(30,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_26__C3_C) ).
thf(223,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)],[30]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) )
=> ~ ( C @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_PiE) ).
thf(394,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) )
=> ~ ( C @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(96,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_21_Pair__eq) ).
thf(563,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)],[96]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Pi__mem) ).
thf(267,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(66,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(431,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(112,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__096c_A_126_061_Ad_096) ).
thf(658,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(82,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_38_mkbot__Lin) ).
thf(516,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)],[82]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_eq__imp__le) ).
thf(553,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(70,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(458,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)],[70]) ).
thf(25,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(194,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)],[25]) ).
thf(87,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_68_less__not__refl3) ).
thf(525,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)],[87]) ).
thf(94,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(557,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)],[94]) ).
thf(43,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_8_n_I2_J) ).
thf(282,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)],[43]) ).
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_65_add__right__imp__eq) ).
thf(150,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)],[9]) ).
thf(117,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_92_add__strict__right__mono) ).
thf(707,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)],[117]) ).
thf(101,axiom,
nat @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(585,plain,
nat @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(91,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_70_less__irrefl__nat) ).
thf(544,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)],[91]) ).
thf(18,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27__096a_A_126_061_Ab_096) ).
thf(177,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(182,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(46,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(314,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8,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_55_add__right__cancel) ).
thf(143,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)],[8]) ).
thf(17,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_90_add__left__mono) ).
thf(175,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)],[17]) ).
thf(59,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_61_add__less__cancel__right) ).
thf(386,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)],[59]) ).
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,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__C2_C) ).
thf(203,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)],[27]) ).
thf(86,axiom,
bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( n @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_n_I1_J) ).
thf(524,plain,
bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( n @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(28,axiom,
f @ arrow_2069624013nimity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_u) ).
thf(218,plain,
f @ arrow_2069624013nimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(103,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_77_nat__add__assoc) ).
thf(588,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)],[103]) ).
thf(35,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_43__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(258,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)],[35]) ).
thf(60,axiom,
( arrow_610318064e_Prof
= ( arrow_1985332922le_Lin @ ( arrow_159774573e_indi @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ pi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Prof__def) ).
thf(390,plain,
( arrow_610318064e_Prof
= ( arrow_1985332922le_Lin @ ( arrow_159774573e_indi @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ pi ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(22,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_81_le__trans) ).
thf(186,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)],[22]) ).
thf(7,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_60_add__le__cancel__right) ).
thf(139,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)],[7]) ).
thf(47,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_35_Lin__irrefl) ).
thf(315,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)],[47]) ).
thf(67,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_93_add__strict__left__mono) ).
thf(432,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)],[67]) ).
thf(36,axiom,
? [A: nat] :
( ( lba @ ( lab @ ( nat @ one_one @ ( A @ ( 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 ) ) )
& ! [B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( lba @ ( lab @ ( B @ ( 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 ) ) ) )
& ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_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_096) ).
thf(262,plain,
? [A: nat] :
( ( lba @ ( lab @ ( nat @ one_one @ ( A @ ( 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 ) ) )
& ! [B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( lba @ ( lab @ ( B @ ( 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 ) ) ) )
& ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(21,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_98_not__add__less2) ).
thf(183,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)],[21]) ).
thf(55,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(373,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(6,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_63_add__left__imp__eq) ).
thf(136,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)],[6]) ).
thf(74,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_15__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(474,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)],[74]) ).
thf(89,axiom,
f @ arrow_1958449194le_IIA,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I3_J) ).
thf(532,plain,
f @ arrow_1958449194le_IIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(32,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(239,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)],[32]) ).
thf(33,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_24__C4_C) ).
thf(242,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)],[33]) ).
thf(72,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_57_nat__add__right__cancel) ).
thf(464,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)],[72]) ).
thf(54,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_53_add__less__cancel__left) ).
thf(369,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)],[54]) ).
thf(50,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_67_nat__less__cases) ).
thf(322,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)],[50]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(122,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(95,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_97_not__add__less1) ).
thf(560,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)],[95]) ).
thf(105,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_28_PiProf) ).
thf(592,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)],[105]) ).
thf(52,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(364,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)],[52]) ).
thf(728,plain,
$false,
inference(e,[status(thm)],[272,479,333,518,523,269,385,533,715,472,153,709,257,504,125,157,284,289,475,164,591,321,376,238,480,121,514,602,280,396,133,529,661,392,693,275,317,188,476,547,622,457,173,503,605,586,662,718,166,161,180,584,577,579,191,402,382,572,704,604,406,219,434,616,367,594,520,155,198,462,278,223,394,563,267,431,658,516,553,458,194,525,557,282,150,707,585,544,177,182,314,143,175,386,203,524,218,588,258,390,186,139,315,432,262,183,373,136,474,532,239,242,464,369,322,122,560,592,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT264_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n020.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 06:47:48 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.31/1.24 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.80/1.77 % [INFO] Parsing done (532ms).
% 2.80/1.80 % [INFO] Running in sequential loop mode.
% 4.39/2.20 % [INFO] eprover registered as external prover.
% 4.39/2.21 % [INFO] Scanning for conjecture ...
% 4.95/2.46 % [INFO] Found a conjecture (or negated_conjecture) and 118 axioms. Running axiom selection ...
% 5.87/2.64 % [INFO] Axiom selection finished. Selected 118 axioms (removed 0 axioms).
% 6.76/2.90 % [INFO] Problem is typed first-order (TPTP TFF).
% 6.76/2.95 % [INFO] Type checking passed.
% 6.76/2.95 % [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 ...
% 7.72/3.19 % [INFO] [Domain constraints] Detected constraint on bool
% 7.72/3.19 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 25.13/10.75 % External prover 'e' found a proof!
% 25.13/10.75 % [INFO] Killing All external provers ...
% 25.13/10.75 % Time passed: 10160ms (effective reasoning time: 8945ms)
% 25.13/10.75 % 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)>
% 25.13/10.75 % Axioms used in derivation (118): fact_31_assms_I1_J, fact_48__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_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_096, fact_33_injh, fact_47_split__paired__Ex, fact_37_mktop__Lin, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_51_nat__add__left__cancel__le, fact_80_eq__imp__le, fact_85_funcset__id, help_COMBS_1_1_U, fact_12_PW, fact_82_le__antisym, fact_88_add__le__imp__le__right, fact_72_nat__neq__iff, fact_16__096ALL_Ai_O_A_Ie_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_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096, fact_59_add__le__cancel__left, fact_95_add__less__imp__less__right, help_COMBI_1_1_U, fact_1__096Lba_A_058_ALin_096, fact_32_n_I1_J, fact_10__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_74_mem__def, fact_50_Pi__UNIV, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_14_in__mktop, fact_69_less__not__refl2, fact_61_add__less__cancel__right, fact_22__C2_C, fact_77_nat__add__assoc, fact_96_add__less__imp__less__left, fact_0__096Lab_A_058_ALin_096, fact_63_add__left__imp__eq, fact_89_add__mono, fact_94_add__strict__mono, fact_64_add__imp__eq, fact_2_assms_I3_J, fact_54_add__left__cancel, fact_46__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_41_in__above, fact_13_in__mkbot, help_COMBB_1_1_U, help_If_1_1_T, fact_79_nat__le__linear, fact_27__096a_A_126_061_Ab_096, fact_71_linorder__neqE__nat, fact_5__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact_84_Prof__def, fact_25_pairwise__neutrality, fact_86_funcset__mem, fact_60_add__le__cancel__right, fact_17__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096, fact_62_ab__semigroup__add__class_Oadd__ac_I1_J, fact_87_add__le__imp__le__left, fact_24__C4_C, fact_19__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_44_IIA__def, fact_26__C3_C, fact_45_unanimity__def, fact_6__096c_A_126_061_Ad_096, fact_34_const__Lin__Prof, fact_30__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_43__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_76_nat__add__left__commute, fact_52_nat__add__left__cancel__less, fact_36_notin__Lin__iff, fact_65_add__right__imp__eq, fact_23__C1_C, fact_39_above__Lin, fact_93_add__strict__left__mono, help_fequal_1_1_T, fact_7__096P_A_058_AProf_096, fact_55_add__right__cancel, fact_42_n_I3_J, fact_15__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_11__096c_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_096, fact_18__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_98_not__add__less2, fact_56_nat__add__left__cancel, fact_29__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_81_le__trans, help_If_3_1_T, fact_8_n_I2_J, fact_28_PiProf, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_97_not__add__less1, fact_9__096_Ie_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_Ad_J_A_061_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096, help_If_2_1_T, help_COMBK_1_1_U, fact_67_nat__less__cases, fact_83_Pi__mem, fact_40_Pair__inject, fact_90_add__left__mono, fact_4__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, help_COMBC_1_1_U, fact_70_less__irrefl__nat, fact_57_nat__add__right__cancel, fact_38_mkbot__Lin, help_fequal_2_1_T, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_58_PiE, fact_66_one__reorient, arity_Nat_Onat___Groups_Oone, fact_49__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_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_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_3_u, help_pp_1_1_U, fact_20_split__paired__All, fact_78_le__refl, fact_21_Pair__eq, fact_73_less__not__refl, fact_53_add__less__cancel__left, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_91_add__right__mono, fact_75_nat__add__commute, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_68_less__not__refl3, fact_92_add__strict__right__mono, help_pp_2_1_U, fact_35_Lin__irrefl
% 25.13/10.75 % No. of inferences in proof: 240
% 25.13/10.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10160 ms resp. 8945 ms w/o parsing
% 26.30/10.95 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.30/10.96 % [INFO] Killing All external provers ...
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