TSTP Solution File: SCT264_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT264_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:51:26 EDT 2023
% Result : Theorem 20.39s 8.89s
% Output : Refutation 21.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 170
% Syntax : Number of formulae : 291 ( 53 unt; 51 typ; 0 def)
% Number of atoms : 3795 ( 204 equ; 0 cnn)
% Maximal formula atoms : 210 ( 15 avg)
% Number of connectives : 14606 ( 145 ~; 14 |; 93 &;13932 @)
% ( 39 <=>; 383 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 12 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 21 con; 0-5 aty)
% Number of variables : 651 ( 0 ^; 602 !; 11 ?; 651 :)
% ( 38 !>; 0 ?*; 0 @-; 0 @+)
% 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_type,type,
one:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(arrow_1958449194le_IIA_type,type,
arrow_1958449194le_IIA: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(arrow_1985332922le_Lin_type,type,
arrow_1985332922le_Lin: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ).
thf(arrow_610318064e_Prof_type,type,
arrow_610318064e_Prof: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ).
thf(arrow_1158827142_above_type,type,
arrow_1158827142_above: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) ).
thf(arrow_276188178_mkbot_type,type,
arrow_276188178_mkbot: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ).
thf(arrow_424895264_mktop_type,type,
arrow_424895264_mktop: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ).
thf(arrow_2069624013nimity_type,type,
arrow_2069624013nimity: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combi_type,type,
combi:
!>[TA: $tType] : ( fun @ TA @ TA ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(finite_card_type,type,
finite_card:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > nat ) ).
thf(inj_on_type,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > ( fun @ TB @ bool ) > $o ) ).
thf(pi_type,type,
pi:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ bool ) > ( fun @ TB @ ( fun @ TA @ bool ) ) > ( fun @ ( fun @ TB @ TA ) @ bool ) ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(hilbert_inv_into_type,type,
hilbert_inv_into:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ bool ) > ( fun @ TB @ TA ) > TA > TB ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( fun @ bool @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(f_type,type,
f: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(lab_type,type,
lab: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ).
thf(lba_type,type,
lba: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ).
thf(p_type,type,
p: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(a_type,type,
a: arrow_411405190le_alt ).
thf(b_type,type,
b: arrow_411405190le_alt ).
thf(c_type,type,
c: arrow_411405190le_alt ).
thf(d_type,type,
d: arrow_411405190le_alt ).
thf(e_type,type,
e: arrow_411405190le_alt ).
thf(h_type,type,
h: fun @ arrow_159774573e_indi @ nat ).
thf(n_type,type,
n: nat ).
thf(65,axiom,
! [A: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
<=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ e ) ) )
& ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
!= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) ) ) ) ) ),
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(384,plain,
! [A: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ e ) ) )
& ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
!= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) ) ) ) ) )
& ( ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ e ) ) )
& ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
!= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( member @ ( fun @ TB @ TA ) @ D @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) )
=> ( ( member @ TB @ A @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_funcset__mem) ).
thf(266,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( member @ ( fun @ TB @ TA ) @ D @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) )
=> ( ( member @ TB @ A @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(106,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nat__add__left__cancel) ).
thf(562,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(24,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_nat__add__left__commute) ).
thf(186,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
<=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_add__le__cancel__right) ).
thf(138,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ C @ A ) )
& ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(347,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(116,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_nat__add__commute) ).
thf(666,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(54,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__less__cancel__left) ).
thf(352,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) )
<=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_nat__add__left__cancel__le) ).
thf(582,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) )
=> ( ord_less_eq @ nat @ B @ A ) )
& ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(45,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_1958449194le_IIA @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_IIA__def) ).
thf(276,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_1958449194le_IIA @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) )
=> ( arrow_1958449194le_IIA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(74,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) @ arrow_610318064e_Prof,
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(449,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(34,axiom,
ordere779506340up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(247,plain,
ordere779506340up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(72,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat__add__right__cancel) ).
thf(440,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(66,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(408,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(17,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__left__mono) ).
thf(170,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(47,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
=> ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Lin__irrefl) ).
thf(301,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
=> ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool] :
( ( pi @ TA @ TB @ A @ ( combk @ ( fun @ TB @ bool ) @ TA @ ( top_top @ ( fun @ TB @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ TA @ TB ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Pi__UNIV) ).
thf(257,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool] :
( ( pi @ TA @ TB @ A @ ( combk @ ( fun @ TB @ bool ) @ TA @ ( top_top @ ( fun @ TB @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ TA @ TB ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(61,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ B ) @ A ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_mktop__Lin) ).
thf(372,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ B ) @ A ) @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(111,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ C ) @ E ) @ D ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_in__above) ).
thf(587,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ C ) @ E ) @ D ) )
=> ( ( B != A )
& ( ( B = D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) )
& ( ( ( B != A )
& ( ( B = D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ C ) @ E ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(4,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_one__reorient) ).
thf(125,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22__C2_C) ).
thf(196,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_split__paired__All) ).
thf(542,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(13,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(157,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(104,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(559,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(25,axiom,
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_PW) ).
thf(189,plain,
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__le__imp__le__left) ).
thf(152,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(63,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( B != A )
=> ( ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_notin__Lin__iff) ).
thf(376,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( B != A )
=> ( ( ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C )
=> ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(29,axiom,
! [A: nat,B: nat] :
( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_less__not__refl2) ).
thf(211,plain,
! [A: nat,B: nat] :
( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1,conjecture,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(121,plain,
~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_add__right__imp__eq) ).
thf(147,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_add__imp__eq) ).
thf(132,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(68,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ B ) @ A ) )
<=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_in__mktop) ).
thf(411,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ B ) @ A ) )
=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) )
& ( ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(50,axiom,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ C ) @ B ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ C ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_nat__less__cases) ).
thf(307,plain,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ C ) @ B ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ C ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(33,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [F: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ F ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24__C4_C) ).
thf(233,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [F: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ F ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(35,axiom,
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) ) @ lab ) @ lba ) ) ) ),
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(248,plain,
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) ) @ lab ) @ lba ) ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) ) @ lab ) @ lba ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(43,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ A ) ) @ lab ) @ lba ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_n_I2_J) ).
thf(270,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ A ) ) @ lab ) @ lba ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(98,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) @ arrow_610318064e_Prof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_const__Lin__Prof) ).
thf(546,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) @ arrow_610318064e_Prof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(64,axiom,
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ lab ) @ lba ) ) ) ),
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(381,plain,
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ lab ) @ lba ) ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ lab ) @ lba ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(58,axiom,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ ( hilbert_inv_into @ arrow_159774573e_indi @ nat @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) @ h @ n ) ),
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(366,plain,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ d ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ ( hilbert_inv_into @ arrow_159774573e_indi @ nat @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) @ h @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Pair__eq) ).
thf(534,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ bool @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( if @ TA ) @ fFalse ) @ B ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(260,plain,
! [TA: $tType,A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ bool @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( if @ TA ) @ fFalse ) @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(14,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_add__le__imp__le__right) ).
thf(160,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(26,axiom,
~ ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ A )
=> ~ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ) ),
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(192,plain,
~ ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ A )
=> ~ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(31,axiom,
member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ f @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_assms_I1_J) ).
thf(229,plain,
member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ f @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(113,axiom,
inj_on @ arrow_159774573e_indi @ nat @ h @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_injh) ).
thf(625,plain,
inj_on @ arrow_159774573e_indi @ nat @ h @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ bool @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( if @ TA ) @ fTrue ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(493,plain,
! [TA: $tType,A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ bool @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( if @ TA ) @ fTrue ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Pair__inject) ).
thf(519,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(51,axiom,
! [A: arrow_159774573e_indi] :
( ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ e ) ) )
& ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
!= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) ) ) ) )
<=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lab ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lba ) ) ) ),
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(317,plain,
! [A: arrow_159774573e_indi] :
( ( ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ e ) ) )
& ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
!= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) ) ) ) )
=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lab ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lba ) ) ) )
& ( ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lab ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lba ) ) )
=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ e ) ) )
& ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
!= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(8,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_add__right__cancel) ).
thf(141,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
| ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_nat__le__linear) ).
thf(554,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
| ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(117,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ A ) ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add__strict__right__mono) ).
thf(669,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ A ) ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(82,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ B ) @ A ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_mkbot__Lin) ).
thf(489,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ B ) @ A ) @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(120,axiom,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lab,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(679,plain,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lab,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(112,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__096c_A_126_061_Ad_096) ).
thf(622,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(107,axiom,
~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lab ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(569,plain,
~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lab ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(109,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_pairwise__neutrality) ).
thf(572,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(87,axiom,
! [A: nat,B: nat] :
( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__not__refl3) ).
thf(498,plain,
! [A: nat,B: nat] :
( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(22,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_le__trans) ).
thf(181,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(53,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ D ) @ C ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ D @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add__strict__mono) ).
thf(350,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ D ) @ C ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ D @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(18,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27__096a_A_126_061_Ab_096) ).
thf(172,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(230,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(451,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(434,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(48,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mem__def) ).
thf(303,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(79,axiom,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lba,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(477,plain,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lba,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(36,axiom,
? [A: nat] :
( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ ( finite_card @ arrow_159774573e_indi @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) ) ) )
& ! [B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ B ) ) @ lab ) @ lba ) ) ) )
& ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) @ lab ) @ lba ) ) ) ),
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(251,plain,
? [A: nat] :
( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ ( finite_card @ arrow_159774573e_indi @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) ) ) )
& ! [B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ B ) ) @ lab ) @ lba ) ) ) )
& ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) @ lab ) @ lba ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(114,axiom,
! [A: arrow_159774573e_indi] :
( ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ e ) ) )
& ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
!= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) ) ) ) )
<=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lab ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lba ) ) ) ),
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(626,plain,
! [A: arrow_159774573e_indi] :
( ( ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ e ) ) )
& ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
!= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) ) ) ) )
=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lab ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lba ) ) ) )
& ( ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lab ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ lba ) ) )
=> ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_424895264_mktop @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) )
& ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( aa @ arrow_159774573e_indi @ nat @ h @ A ) ) @ n ) )
=> ( ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ e ) ) )
& ( ( ( aa @ arrow_159774573e_indi @ nat @ h @ A )
!= n )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ e @ d ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ e ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_add__less__cancel__right) ).
thf(367,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(100,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p @ arrow_610318064e_Prof,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__096P_A_058_AProf_096) ).
thf(552,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(78,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ B ) @ A ) )
<=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_in__mkbot) ).
thf(455,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ B ) @ A ) )
=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) )
& ( ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_276188178_mkbot @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(49,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(306,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(6,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_add__left__imp__eq) ).
thf(135,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(89,axiom,
arrow_1958449194le_IIA @ f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I3_J) ).
thf(505,plain,
arrow_1958449194le_IIA @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(71,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( member @ ( fun @ TA @ TA ) @ ( combi @ TA ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_funcset__id) ).
thf(438,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( member @ ( fun @ TA @ TA ) @ ( combi @ TA ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_split__paired__Ex) ).
thf(548,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ~ ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_PiE) ).
thf(374,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ~ ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ( member @ TA @ A @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Pi__mem) ).
thf(255,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ( member @ TA @ A @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(81,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_le__refl) ).
thf(487,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(91,axiom,
! [A: nat] :
~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__irrefl__nat) ).
thf(516,plain,
! [A: nat] :
~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(55,axiom,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(355,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(101,axiom,
ordere223160158up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(553,plain,
ordere223160158up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(15,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_add__left__cancel) ).
thf(162,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(95,axiom,
! [A: nat,B: nat] :
~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( plus_plus @ nat @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_not__add__less1) ).
thf(531,plain,
! [A: nat,B: nat] :
~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( plus_plus @ nat @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(10,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ D @ C )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__mono) ).
thf(150,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ D @ C )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(67,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ A @ C ) ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_add__strict__left__mono) ).
thf(409,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ A @ C ) ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(40,axiom,
! [A: nat] :
~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__not__refl) ).
thf(263,plain,
! [A: nat] :
~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(20,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(177,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,axiom,
( arrow_610318064e_Prof
= ( pi @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ arrow_159774573e_indi @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Prof__def) ).
thf(370,plain,
( arrow_610318064e_Prof
= ( pi @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ arrow_159774573e_indi @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(88,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_le__antisym) ).
thf(502,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
| ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_nat__neq__iff) ).
thf(656,plain,
! [A: nat,B: nat] :
( ( ( B != A )
=> ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
| ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ B ) ) ) )
& ( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
| ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ B ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(12,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
<=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_add__le__cancel__left) ).
thf(154,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) )
& ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(175,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(108,axiom,
member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ lba @ arrow_1985332922le_Lin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096Lba_A_058_ALin_096) ).
thf(571,plain,
member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ lba @ arrow_1985332922le_Lin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(86,axiom,
pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ n ) @ ( finite_card @ arrow_159774573e_indi @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_n_I1_J) ).
thf(497,plain,
pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ n ) @ ( finite_card @ arrow_159774573e_indi @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(75,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(450,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(118,axiom,
~ ! [A: nat] :
( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ ( finite_card @ arrow_159774573e_indi @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) ) ) )
=> ( ! [B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ B ) ) @ lab ) @ lba ) ) ) )
=> ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) @ lab ) @ lba ) ) ) ) ),
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(671,plain,
~ ! [A: nat] :
( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ ( finite_card @ arrow_159774573e_indi @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) ) ) )
=> ( ! [B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ B ) ) @ lab ) @ lba ) ) ) )
=> ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) @ lab ) @ lba ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_eq__imp__le) ).
thf(524,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(363,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(103,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_nat__add__assoc) ).
thf(556,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(69,axiom,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ),
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(433,plain,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ c @ e ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_424895264_mktop @ p ) @ e ) ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combs @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( fequal @ nat ) @ h ) @ n ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_1158827142_above @ p ) @ c ) @ e ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_159774573e_indi @ arrow_276188178_mkbot @ p ) @ e ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(80,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_2069624013nimity @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_unanimity__def) ).
thf(478,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_2069624013nimity @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) )
=> ( arrow_2069624013nimity @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(44,axiom,
~ ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ A )
=> ~ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ) ),
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(272,plain,
~ ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ A )
=> ~ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(46,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(300,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(73,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add__less__imp__less__left) ).
thf(447,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(16,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__right__mono) ).
thf(168,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ A ) @ C ) @ B ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_above__Lin) ).
thf(183,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_1158827142_above @ A ) @ C ) @ B ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,axiom,
arrow_2069624013nimity @ f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_u) ).
thf(210,plain,
arrow_2069624013nimity @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(56,axiom,
! [A: nat,B: nat,C: nat] :
( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( plus_plus @ nat @ C @ B ) ) @ ( plus_plus @ nat @ C @ A ) ) )
<=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_nat__add__left__cancel__less) ).
thf(358,plain,
! [A: nat,B: nat,C: nat] :
( ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( plus_plus @ nat @ C @ B ) ) @ ( plus_plus @ nat @ C @ A ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) ) )
& ( ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( plus_plus @ nat @ C @ B ) ) @ ( plus_plus @ nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(90,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23__C1_C) ).
thf(506,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(42,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_add__less__imp__less__right) ).
thf(268,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(528,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(21,axiom,
! [A: nat,B: nat] :
~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( plus_plus @ nat @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_not__add__less2) ).
thf(178,plain,
! [A: nat,B: nat] :
~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( plus_plus @ nat @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(122,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(30,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( D != C )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [E: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ E ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26__C3_C) ).
thf(215,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( D != C )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [E: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ E ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(105,axiom,
! [A: nat] : ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ A ) ) @ lab ) @ lba ) @ arrow_610318064e_Prof ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_PiProf) ).
thf(560,plain,
! [A: nat] : ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ A ) ) @ lab ) @ lba ) @ arrow_610318064e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_linorder__neqE__nat) ).
thf(676,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ B ) @ A ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(83,axiom,
~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lba ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(491,plain,
~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ lba ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(85,axiom,
member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ lab @ arrow_1985332922le_Lin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096Lab_A_058_ALin_096) ).
thf(496,plain,
member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ lab @ arrow_1985332922le_Lin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(77,axiom,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) ) @ lab ) @ lba ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_n_I3_J) ).
thf(454,plain,
member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ nat @ bool @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_159774573e_indi @ ( ord_less @ nat ) @ h ) @ ( plus_plus @ nat @ n @ ( one_one @ nat ) ) ) ) @ lab ) @ lba ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(680,plain,
$false,
inference(e,[status(thm)],[384,266,562,186,138,347,666,352,582,276,449,247,440,408,170,301,257,372,587,125,196,542,157,559,189,152,376,211,121,147,132,411,307,233,248,270,546,381,366,534,260,160,192,229,625,493,519,317,141,554,669,489,679,622,569,572,498,181,350,172,230,451,434,303,477,251,626,367,552,455,306,135,505,438,548,374,255,487,516,355,553,162,531,150,409,263,177,370,502,656,154,175,571,497,450,671,524,363,556,433,478,272,300,447,168,183,210,358,506,268,528,178,122,215,560,676,491,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT264_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 15:42:23 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.52/1.06 % [INFO] Parsing done (216ms).
% 1.52/1.07 % [INFO] Running in sequential loop mode.
% 2.24/1.28 % [INFO] eprover registered as external prover.
% 2.24/1.28 % [INFO] cvc4 registered as external prover.
% 2.24/1.28 % [INFO] Scanning for conjecture ...
% 2.81/1.43 % [INFO] Found a conjecture and 118 axioms. Running axiom selection ...
% 3.31/1.53 % [INFO] Axiom selection finished. Selected 118 axioms (removed 0 axioms).
% 3.76/1.68 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.98/1.70 % [INFO] Type checking passed.
% 3.98/1.70 % [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 ...
% 4.54/1.85 % [INFO] [Domain constraints] Detected constraint on bool
% 4.54/1.85 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 20.39/8.89 % External prover 'e' found a proof!
% 20.39/8.89 % [INFO] Killing All external provers ...
% 20.39/8.89 % Time passed: 8368ms (effective reasoning time: 7816ms)
% 20.39/8.89 % 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)>
% 20.39/8.89 % 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
% 20.39/8.89 % No. of inferences in proof: 240
% 20.39/8.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8368 ms resp. 7816 ms w/o parsing
% 21.06/9.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.06/9.04 % [INFO] Killing All external provers ...
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