%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP169^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:02 AM UTC 2026
% Result : Theorem 115.31s 45.14s
% Output : Refutation 116.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 243
% Syntax : Number of formulae : 634 ( 276 unt; 0 typ; 13 def)
% Number of atoms : 2451 (1155 equ; 18 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 14387 ( 348 ~; 257 |; 947 &;12464 @)
% ( 0 <=>; 371 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 398 ( 398 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 54 usr; 16 con; 0-4 aty)
% Number of variables : 2493 ( 519 ^;1576 !; 385 ?;2493 :)
% ( 0 !>; 0 ?*; 0 @-; 13 @+)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(real_int_type,type,
real_int: $tType ).
thf(traffic_type,type,
traffic: $tType ).
thf(nat_int_type,type,
nat_int: $tType ).
thf(real_type,type,
real: $tType ).
thf(cars_type,type,
cars: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(wellorder_decl,type,
wellorder:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(strict2144017051up_add_decl,type,
strict2144017051up_add:
!>[TA: $tType] : $o ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(len_decl,type,
len: ( cars > traffic > cars > real ) > ( view_ext @ product_unit ) > traffic > cars > real_int ).
thf(move_decl,type,
move: traffic > traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) ).
thf(nat_card_decl,type,
nat_card: nat_int > nat ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(real_length_decl,type,
real_length: real_int > real ).
thf(regular_regular_decl,type,
regular_regular: cars > traffic > cars > real ).
thf(restrict_decl,type,
restrict: ( view_ext @ product_unit ) > ( cars > nat_int ) > cars > nat_int ).
thf(abstract_decl,type,
abstract: traffic > traffic > $o ).
thf(clm_decl,type,
clm: traffic > cars > nat_int ).
thf(create_claim_decl,type,
create_claim: traffic > cars > nat > traffic > $o ).
thf(create_reservation_decl,type,
create_reservation: traffic > cars > traffic > $o ).
thf(res_decl,type,
res: traffic > cars > nat_int ).
thf(withdraw_claim_decl,type,
withdraw_claim: traffic > cars > traffic > $o ).
thf(withdraw_reservation_decl,type,
withdraw_reservation: traffic > cars > nat > traffic > $o ).
thf(ext_decl,type,
ext:
!>[TA: $tType] : ( ( view_ext @ TA ) > real_int ) ).
thf(hchop_decl,type,
hchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
thf(lan_decl,type,
lan:
!>[TA: $tType] : ( ( view_ext @ TA ) > nat_int ) ).
thf(own_decl,type,
own:
!>[TA: $tType] : ( ( view_ext @ TA ) > cars ) ).
thf(vchop_decl,type,
vchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
thf(c_decl,type,
c: cars ).
thf(d_decl,type,
d: cars ).
thf(e_decl,type,
e: cars ).
thf(thesis_decl,type,
thesis: $o ).
thf(ts_decl,type,
ts: traffic ).
thf(ts2_decl,type,
ts2: traffic ).
thf(ts_a_decl,type,
ts_a: traffic ).
thf(ts3_decl,type,
ts3: traffic ).
thf(v_decl,type,
v: view_ext @ product_unit ).
thf(sk1_decl,type,
sk1: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) ).
thf(sk2_decl,type,
sk2: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) ).
thf(sk3_decl,type,
sk3: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) ).
thf(sk4_decl,type,
sk4: cars ).
thf(sk5_decl,type,
sk5: ( view_ext @ product_unit ) > traffic > ( traffic > ( view_ext @ product_unit ) > $o ) > ( view_ext @ product_unit ) ).
thf(sk6_decl,type,
sk6: ( view_ext @ product_unit ) > traffic > ( traffic > ( view_ext @ product_unit ) > $o ) > ( view_ext @ product_unit ) ).
thf(sk7_decl,type,
sk7: ( view_ext @ product_unit ) > traffic > ( traffic > ( view_ext @ product_unit ) > $o ) > ( view_ext @ product_unit ) ).
thf(sk8_decl,type,
sk8: ( view_ext @ product_unit ) > traffic > ( traffic > ( view_ext @ product_unit ) > $o ) > ( view_ext @ product_unit ) ).
thf(sk9_decl,type,
sk9: ( view_ext @ product_unit ) > traffic > ( traffic > ( view_ext @ product_unit ) > $o ) > ( view_ext @ product_unit ) ).
thf(sk10_decl,type,
sk10: ( view_ext @ product_unit ) > traffic > ( traffic > ( view_ext @ product_unit ) > $o ) > ( view_ext @ product_unit ) ).
thf(sk20_decl,type,
sk20: cars ).
thf(sk47_decl,type,
sk47: ( nat > $o ) > nat ).
thf(sk77_decl,type,
sk77: view_ext @ product_unit ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: view_ext @ product_unit] :
@+[B: view_ext @ product_unit] :
? [C: view_ext @ product_unit] : ( hchop @ A @ B @ C ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: view_ext @ product_unit] :
@+[B: view_ext @ product_unit] : ( hchop @ A @ ( sk1 @ A ) @ B ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: view_ext @ product_unit] :
@+[B: view_ext @ product_unit] : ( vchop @ A @ B @ A ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: cars] : ( withdraw_claim @ ts_a @ A @ ts ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: view_ext @ product_unit,B: traffic,C: traffic > ( view_ext @ product_unit ) > $o] :
@+[D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( hchop @ A @ D @ E )
& ( C @ B @ D ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: view_ext @ product_unit,B: traffic,C: traffic > ( view_ext @ product_unit ) > $o] :
@+[D: view_ext @ product_unit] : ( hchop @ A @ ( sk5 @ A @ B @ C ) @ D ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: view_ext @ product_unit,B: traffic,C: traffic > ( view_ext @ product_unit ) > $o] :
@+[D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( hchop @ A @ D @ E )
& ~ ( C @ B @ D ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: view_ext @ product_unit,B: traffic,C: traffic > ( view_ext @ product_unit ) > $o] :
@+[D: view_ext @ product_unit] : ( hchop @ A @ ( sk7 @ A @ B @ C ) @ D ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: view_ext @ product_unit,B: traffic,C: traffic > ( view_ext @ product_unit ) > $o] :
@+[D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( vchop @ A @ D @ E )
& ( C @ B @ D ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: view_ext @ product_unit,B: traffic,C: traffic > ( view_ext @ product_unit ) > $o] :
@+[D: view_ext @ product_unit] : ( vchop @ A @ ( sk9 @ A @ B @ C ) @ D ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: cars] : ( withdraw_claim @ ts_a @ A @ ts ) ) ) ).
thf(sk47_def,definition,
( sk47
= ( ^ [A: nat > $o] :
@+[B: nat] :
~ ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ~ ( A @ B )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ~ ( A @ C ) ) ) ) ) ) ).
thf(sk77_def,definition,
( sk77
= ( @+[A: view_ext @ product_unit] :
( ( ord_less_eq @ ( view_ext @ product_unit ) @ A @ ( move @ ts3 @ ts @ v ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ c )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ c )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ e )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ e )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) ) ) ) ) ).
thf(98,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_bot__nat__0_Oextremum) ).
thf(628,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(629,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(cnf,[status(esa)],[628]) ).
thf(194,axiom,
? [A: view_ext @ product_unit] :
( ( ord_less_eq @ ( view_ext @ product_unit ) @ A @ ( move @ ts3 @ ts @ v ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ c )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ c )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ e )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ e )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062) ).
thf(1015,plain,
? [A: view_ext @ product_unit] :
( ( ord_less_eq @ ( view_ext @ product_unit ) @ A @ ( move @ ts3 @ ts @ v ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ c )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ c )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ e )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ e )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(1016,plain,
( ( ord_less_eq @ ( view_ext @ product_unit ) @ sk77 @ ( move @ ts3 @ ts @ v ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ sk77 ) ) )
& ( ( len @ regular_regular @ sk77 @ ts @ c )
= ( ext @ product_unit @ sk77 ) )
& ( ( restrict @ sk77 @ ( res @ ts ) @ c )
= ( lan @ product_unit @ sk77 ) )
& ( ( nat_card @ ( lan @ product_unit @ sk77 ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ sk77 ) ) )
& ( ( len @ regular_regular @ sk77 @ ts @ e )
= ( ext @ product_unit @ sk77 ) )
& ( ( restrict @ sk77 @ ( res @ ts ) @ e )
= ( lan @ product_unit @ sk77 ) )
& ( ( nat_card @ ( lan @ product_unit @ sk77 ) )
= ( one_one @ nat ) ) ),
inference(cnf,[status(esa)],[1015]) ).
thf(1020,plain,
( ( restrict @ sk77 @ ( res @ ts ) @ e )
= ( lan @ product_unit @ sk77 ) ),
inference(cnfConj,[status(thm)],[1016]) ).
thf(1024,plain,
( ( restrict @ sk77 @ ( res @ ts ) @ e )
= ( lan @ product_unit @ sk77 ) ),
inference(lifteq,[status(thm)],[1020]) ).
thf(46,axiom,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit] : ( vchop @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_view_Overtical__chop__empty__down) ).
thf(365,plain,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit] : ( vchop @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(225,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_nat__less__induct) ).
thf(1168,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(207,axiom,
! [A: traffic,B: cars] : ( ord_less_eq @ nat @ ( nat_card @ ( clm @ A @ B ) ) @ ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_traffic_OatMostOneClm) ).
thf(1105,plain,
! [A: traffic,B: cars] : ( ord_less_eq @ nat @ ( nat_card @ ( clm @ A @ B ) ) @ ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(146,axiom,
! [A: view_ext @ product_unit,B: cars > nat_int,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ A @ B @ C ) @ ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_restriction_Orestrict__subseteq) ).
thf(846,plain,
! [A: view_ext @ product_unit,B: cars > nat_int,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ A @ B @ C ) @ ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(227,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_le0) ).
thf(1179,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(86,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( clm @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_local_Ohmlsl_Oclm__decompose) ).
thf(555,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( clm @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(164,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_bot__nat__0_Oextremum__unique) ).
thf(907,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(908,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(cnf,[status(esa)],[907]) ).
thf(909,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(lifteq,[status(thm)],[908]) ).
thf(8,axiom,
~ ! [A: cars] :
~ ( withdraw_claim @ ts_a @ A @ ts ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_Ats_H_A_092_060_094bold_062_092_060midarrow_062wdc_I_Ad_A_J_A_092_060_094bold_062_092_060rightarrow_062_Ats_H_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(246,plain,
~ ! [A: cars] :
~ ( withdraw_claim @ ts_a @ A @ ts ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(247,plain,
~ ! [A: cars] :
~ ( withdraw_claim @ ts_a @ A @ ts ),
inference(polarity_switch,[status(thm)],[246]) ).
thf(248,plain,
~ ~ ? [A: cars] : ( withdraw_claim @ ts_a @ A @ ts ),
inference(miniscope,[status(thm)],[247]) ).
thf(249,plain,
withdraw_claim @ ts_a @ sk4 @ ts,
inference(cnf,[status(esa)],[248]) ).
thf(188,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_add__gr__0) ).
thf(994,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(26,axiom,
! [TA: $tType] :
( ( strict2144017051up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_add__strict__mono) ).
thf(308,plain,
! [TA: $tType] :
( ( strict2144017051up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_gr__implies__not0) ).
thf(449,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(158,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_le__zero__eq) ).
thf(878,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(96,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_less__one) ).
thf(612,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(613,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(cnf,[status(esa)],[612]) ).
thf(614,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(lifteq,[status(thm)],[613]) ).
thf(221,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_bot__nat__0_Oextremum__strict) ).
thf(1158,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(90,axiom,
! [A: traffic,B: cars,C: nat,D: traffic,E: view_ext @ product_unit,F: cars] :
( ( ( create_claim @ A @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ D @ F )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ D ) @ F )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ A @ F )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ A ) @ F )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_hmlsl__regular_Obackwards__c__res__stab) ).
thf(582,plain,
! [A: traffic,B: cars,C: nat,D: traffic,E: view_ext @ product_unit,F: cars] :
( ( ( create_claim @ A @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ D @ F )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ D ) @ F )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ A @ F )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ A ) @ F )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(124,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ~ ? [C: cars] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_local_Ohmlsl_Ofree__no__clm) ).
thf(762,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ~ ? [C: cars] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(213,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_local_Ohmlsl_Ores__ge__zero) ).
thf(1137,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1021,plain,
( ( restrict @ sk77 @ ( res @ ts ) @ c )
= ( lan @ product_unit @ sk77 ) ),
inference(cnfConj,[status(thm)],[1016]) ).
thf(1025,plain,
( ( restrict @ sk77 @ ( res @ ts ) @ c )
= ( lan @ product_unit @ sk77 ) ),
inference(lifteq,[status(thm)],[1021]) ).
thf(1023,plain,
( ( len @ regular_regular @ sk77 @ ts @ c )
= ( ext @ product_unit @ sk77 ) ),
inference(cnfConj,[status(thm)],[1016]) ).
thf(1028,plain,
( ( len @ regular_regular @ sk77 @ ts @ c )
= ( ext @ product_unit @ sk77 ) ),
inference(lifteq,[status(thm)],[1023]) ).
thf(163,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( real_length @ ( ext @ product_unit @ B ) )
= ( zero_zero @ real ) )
=> ~ ? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_local_Ohmlsl_Oempty__no__car) ).
thf(899,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( real_length @ ( ext @ product_unit @ B ) )
= ( zero_zero @ real ) )
=> ~ ? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(900,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( real_length @ ( ext @ product_unit @ B ) )
= ( zero_zero @ real ) )
=> ~ ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ? [C: cars] :
( ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ? [C: cars] :
( ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) ) ) ),
inference(miniscope,[status(thm)],[899]) ).
thf(901,plain,
! [D: cars,C: cars,B: view_ext @ product_unit,A: traffic] :
( ( ( ( real_length @ ( ext @ product_unit @ B ) )
!= ( zero_zero @ real ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
| ( ( len @ regular_regular @ B @ A @ C )
!= ( ext @ product_unit @ B ) )
| ( ( restrict @ B @ ( clm @ A ) @ C )
!= ( lan @ product_unit @ B ) )
| ( ( nat_card @ ( lan @ product_unit @ B ) )
!= ( one_one @ nat ) ) )
& ( ( ( real_length @ ( ext @ product_unit @ B ) )
!= ( zero_zero @ real ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
| ( ( len @ regular_regular @ B @ A @ D )
!= ( ext @ product_unit @ B ) )
| ( ( restrict @ B @ ( res @ A ) @ D )
!= ( lan @ product_unit @ B ) )
| ( ( nat_card @ ( lan @ product_unit @ B ) )
!= ( one_one @ nat ) ) ) ),
inference(cnf,[status(esa)],[900]) ).
thf(902,plain,
! [C: cars,B: view_ext @ product_unit,A: traffic] :
( ( ( real_length @ ( ext @ product_unit @ B ) )
!= ( zero_zero @ real ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
| ( ( len @ regular_regular @ B @ A @ C )
!= ( ext @ product_unit @ B ) )
| ( ( restrict @ B @ ( clm @ A ) @ C )
!= ( lan @ product_unit @ B ) )
| ( ( nat_card @ ( lan @ product_unit @ B ) )
!= ( one_one @ nat ) ) ),
inference(cnfConj,[status(thm)],[901]) ).
thf(904,plain,
! [C: cars,B: view_ext @ product_unit,A: traffic] :
( ( ( real_length @ ( ext @ product_unit @ B ) )
!= ( zero_zero @ real ) )
| ( ( len @ regular_regular @ B @ A @ C )
!= ( ext @ product_unit @ B ) )
| ( ( restrict @ B @ ( clm @ A ) @ C )
!= ( lan @ product_unit @ B ) )
| ( ( nat_card @ ( lan @ product_unit @ B ) )
!= ( one_one @ nat ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) ) ),
inference(lifteq,[status(thm)],[902]) ).
thf(2572,plain,
! [C: cars,B: view_ext @ product_unit,A: traffic] :
( ( ( real_length @ ( ext @ product_unit @ B ) )
!= ( zero_zero @ real ) )
| ( ( ext @ product_unit @ sk77 )
!= ( ext @ product_unit @ B ) )
| ( ( restrict @ B @ ( clm @ A ) @ C )
!= ( lan @ product_unit @ B ) )
| ( ( nat_card @ ( lan @ product_unit @ B ) )
!= ( one_one @ nat ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
| ( ( len @ regular_regular @ sk77 @ ts @ c )
!= ( len @ regular_regular @ B @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1028,904]) ).
thf(2573,plain,
( ( ( real_length @ ( ext @ product_unit @ sk77 ) )
!= ( zero_zero @ real ) )
| ( ( ext @ product_unit @ sk77 )
!= ( ext @ product_unit @ sk77 ) )
| ( ( restrict @ sk77 @ ( clm @ ts ) @ c )
!= ( lan @ product_unit @ sk77 ) )
| ( ( nat_card @ ( lan @ product_unit @ sk77 ) )
!= ( one_one @ nat ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ sk77 ) ) ) ),
inference(pattern_uni,[status(thm)],[2572:[bind(A,$thf( ts )),bind(B,$thf( sk77 )),bind(C,$thf( c ))]]) ).
thf(2588,plain,
( ( ( real_length @ ( ext @ product_unit @ sk77 ) )
!= ( zero_zero @ real ) )
| ( ( restrict @ sk77 @ ( clm @ ts ) @ c )
!= ( lan @ product_unit @ sk77 ) )
| ( ( nat_card @ ( lan @ product_unit @ sk77 ) )
!= ( one_one @ nat ) )
| ~ ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ sk77 ) ) ) ),
inference(simp,[status(thm)],[2573]) ).
thf(1018,plain,
( ( nat_card @ ( lan @ product_unit @ sk77 ) )
= ( one_one @ nat ) ),
inference(cnfConj,[status(thm)],[1016]) ).
thf(1027,plain,
( ( nat_card @ ( lan @ product_unit @ sk77 ) )
= ( one_one @ nat ) ),
inference(lifteq,[status(thm)],[1018]) ).
thf(1017,plain,
ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ sk77 ) ),
inference(cnfConj,[status(thm)],[1016]) ).
thf(2598,plain,
( ( ( real_length @ ( ext @ product_unit @ sk77 ) )
!= ( zero_zero @ real ) )
| ( ( restrict @ sk77 @ ( clm @ ts ) @ c )
!= ( lan @ product_unit @ sk77 ) )
| ( ( one_one @ nat )
!= ( one_one @ nat ) )
| ~ $true ),
inference(rewrite,[status(thm)],[2588,1027,1017]) ).
thf(2599,plain,
( ( ( real_length @ ( ext @ product_unit @ sk77 ) )
!= ( zero_zero @ real ) )
| ( ( restrict @ sk77 @ ( clm @ ts ) @ c )
!= ( lan @ product_unit @ sk77 ) ) ),
inference(simp,[status(thm)],[2598]) ).
thf(2602,plain,
( ( ( real_length @ ( ext @ product_unit @ sk77 ) )
!= ( zero_zero @ real ) )
| ( ( lan @ product_unit @ sk77 )
!= ( lan @ product_unit @ sk77 ) )
| ( ( restrict @ sk77 @ ( res @ ts ) @ c )
!= ( restrict @ sk77 @ ( clm @ ts ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[1025,2599]) ).
thf(2603,plain,
( ( ( real_length @ ( ext @ product_unit @ sk77 ) )
!= ( zero_zero @ real ) )
| ( ( restrict @ sk77 @ ( res @ ts ) @ c )
!= ( restrict @ sk77 @ ( clm @ ts ) @ c ) ) ),
inference(simp,[status(thm)],[2602]) ).
thf(2605,plain,
( ( ( real_length @ ( ext @ product_unit @ sk77 ) )
!= ( zero_zero @ real ) )
| ( sk77 != sk77 )
| ( ( res @ ts )
!= ( clm @ ts ) )
| ( c != c ) ),
inference(simp,[status(thm)],[2603]) ).
thf(2607,plain,
( ( ( real_length @ ( ext @ product_unit @ sk77 ) )
!= ( zero_zero @ real ) )
| ( ( res @ ts )
!= ( clm @ ts ) ) ),
inference(simp,[status(thm)],[2605]) ).
thf(78,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( ( vchop @ A @ B @ C )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) ) )
=> ( ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( zero_zero @ nat ) )
| ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_view_Overtical__chop__singleton) ).
thf(533,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( ( vchop @ A @ B @ C )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) ) )
=> ( ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( zero_zero @ nat ) )
| ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(130,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_view_Overtical__chop__leq1) ).
thf(797,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(135,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( ( len @ regular_regular @ A @ B @ C )
= ( ext @ product_unit @ A ) )
& ( hchop @ A @ D @ E ) )
=> ( ( len @ regular_regular @ E @ B @ C )
= ( ext @ product_unit @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_hmlsl_Olen__view__hchop__right) ).
thf(814,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( ( len @ regular_regular @ A @ B @ C )
= ( ext @ product_unit @ A ) )
& ( hchop @ A @ D @ E ) )
=> ( ( len @ regular_regular @ E @ B @ C )
= ( ext @ product_unit @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(109,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit,F: nat] :
( ( ( vchop @ A @ B @ C )
& ( vchop @ C @ D @ E )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= F ) )
=> ( ord_less_eq @ nat @ F @ ( nat_card @ ( lan @ product_unit @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_view_Overtical__chop__width__mon) ).
thf(698,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit,F: nat] :
( ( ( vchop @ A @ B @ C )
& ( vchop @ C @ D @ E )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= F ) )
=> ( ord_less_eq @ nat @ F @ ( nat_card @ ( lan @ product_unit @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(166,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit,F: cars > nat_int,G: cars] :
( ( ( vchop @ A @ B @ C )
& ( vchop @ C @ D @ E )
& ( ( nat_card @ ( restrict @ D @ F @ G ) )
= ( one_one @ nat ) ) )
=> ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( restrict @ A @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_restriction_Orestriction__card__mon__trans) ).
thf(913,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit,F: cars > nat_int,G: cars] :
( ( ( vchop @ A @ B @ C )
& ( vchop @ C @ D @ E )
& ( ( nat_card @ ( restrict @ D @ F @ G ) )
= ( one_one @ nat ) ) )
=> ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( restrict @ A @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(10,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ~ ? [D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( hchop @ C @ D @ E )
& ( A @ B @ D ) )
=> ? [D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( hchop @ C @ D @ E )
& ~ ( A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_local_Ohmlsl_Ohchop__neg1) ).
thf(253,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ~ ? [D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( hchop @ C @ D @ E )
& ( A @ B @ D ) )
=> ? [D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( hchop @ C @ D @ E )
& ~ ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(254,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ( hchop @ C @ ( sk5 @ C @ B @ A ) @ ( sk6 @ C @ B @ A ) )
| ( hchop @ C @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) ) )
& ( ( hchop @ C @ ( sk5 @ C @ B @ A ) @ ( sk6 @ C @ B @ A ) )
| ~ ( A @ B @ ( sk7 @ C @ B @ A ) ) )
& ( ( A @ B @ ( sk5 @ C @ B @ A ) )
| ( hchop @ C @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) ) )
& ( ( A @ B @ ( sk5 @ C @ B @ A ) )
| ~ ( A @ B @ ( sk7 @ C @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[253]) ).
thf(257,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( A @ B @ ( sk5 @ C @ B @ A ) )
| ( hchop @ C @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(232,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1968,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( hchop @ C @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) )
| ~ $true
| ( ( A @ B @ ( sk5 @ C @ B @ A ) )
!= thesis ) ),
inference(paramod_ordered,[status(thm)],[257,232]) ).
thf(1969,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( hchop @ C @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) )
| ( ( A @ B @ ( sk5 @ C @ B @ A ) )
!= thesis ) ),
inference(simp,[status(thm)],[1968]) ).
thf(2022,plain,
! [B: view_ext @ product_unit,A: traffic] :
( hchop @ B
@ ( sk7 @ B @ A
@ ^ [C: traffic,D: view_ext @ product_unit] : thesis )
@ ( sk8 @ B @ A
@ ^ [C: traffic,D: view_ext @ product_unit] : thesis ) ),
inference(pre_uni,[status(thm)],[1969:[bind(A,$thf( ^ [D: traffic] : ^ [E: view_ext @ product_unit] : thesis ))]]) ).
thf(2096,plain,
! [B: view_ext @ product_unit,A: traffic] :
( hchop @ B
@ ( sk7 @ B @ A
@ ^ [C: traffic,D: view_ext @ product_unit] : thesis )
@ ( sk8 @ B @ A
@ ^ [C: traffic,D: view_ext @ product_unit] : thesis ) ),
inference(simp,[status(thm)],[2022]) ).
thf(2137,plain,
! [B: view_ext @ product_unit,A: traffic] :
( hchop @ B
@ ( sk7 @ B @ A
@ ^ [C: traffic,D: view_ext @ product_unit] : $false )
@ ( sk8 @ B @ A
@ ^ [C: traffic,D: view_ext @ product_unit] : $false ) ),
inference(rewrite,[status(thm)],[2096,232]) ).
thf(256,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( hchop @ C @ ( sk5 @ C @ B @ A ) @ ( sk6 @ C @ B @ A ) )
| ~ ( A @ B @ ( sk7 @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(2140,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: view_ext @ product_unit,A: traffic] :
( ( hchop @ E @ ( sk5 @ E @ D @ C ) @ ( sk6 @ E @ D @ C ) )
| ~ $true
| ( ( hchop @ B
@ ( sk7 @ B @ A
@ ^ [F: traffic,G: view_ext @ product_unit] : $false )
@ ( sk8 @ B @ A
@ ^ [F: traffic,G: view_ext @ product_unit] : $false ) )
!= ( C @ D @ ( sk7 @ E @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[2137,256]) ).
thf(2141,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: view_ext @ product_unit,A: traffic] :
( ( hchop @ E @ ( sk5 @ E @ D @ C ) @ ( sk6 @ E @ D @ C ) )
| ( ( hchop @ B
@ ( sk7 @ B @ A
@ ^ [F: traffic,G: view_ext @ product_unit] : $false )
@ ( sk8 @ B @ A
@ ^ [F: traffic,G: view_ext @ product_unit] : $false ) )
!= ( C @ D @ ( sk7 @ E @ D @ C ) ) ) ),
inference(simp,[status(thm)],[2140]) ).
thf(2144,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( hchop @ B
@ ( sk5 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk6 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( D @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( E @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( G @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( F @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2141:[bind(A,$thf( J @ D @ ( sk7 @ E @ D @ ^ [K: traffic] : ^ [L: view_ext @ product_unit] : ( hchop @ ( F @ K @ L ) @ ( sk7 @ ( L @ K @ L ) @ ( M @ K @ L ) @ ^ [M: traffic] : ^ [N: view_ext @ product_unit] : $false ) @ ( sk8 @ ( I @ K @ L ) @ ( J @ K @ L ) @ ^ [M: traffic] : ^ [N: view_ext @ product_unit] : $false ) ) ) )),bind(B,$thf( F @ D @ ( sk7 @ E @ D @ ^ [K: traffic] : ^ [L: view_ext @ product_unit] : ( hchop @ ( F @ K @ L ) @ ( sk7 @ ( L @ K @ L ) @ ( M @ K @ L ) @ ^ [M: traffic] : ^ [N: view_ext @ product_unit] : $false ) @ ( sk8 @ ( I @ K @ L ) @ ( J @ K @ L ) @ ^ [M: traffic] : ^ [N: view_ext @ product_unit] : $false ) ) ) )),bind(C,$thf( ^ [K: traffic] : ^ [L: view_ext @ product_unit] : ( hchop @ ( F @ K @ L ) @ ( sk7 @ ( L @ K @ L ) @ ( M @ K @ L ) @ ^ [M: traffic] : ^ [N: view_ext @ product_unit] : $false ) @ ( sk8 @ ( I @ K @ L ) @ ( J @ K @ L ) @ ^ [M: traffic] : ^ [N: view_ext @ product_unit] : $false ) ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(2145,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( hchop @ B
@ ( sk5 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk6 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( D @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( E @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( G @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( F @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2144:[]]) ).
thf(2146,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( hchop @ B
@ ( sk5 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk6 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( D @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( E @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( G @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( F @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) ) ),
inference(simp,[status(thm)],[2145]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_measure__induct__rule) ).
thf(930,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(160,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_gr0I) ).
thf(883,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(884,plain,
! [A: nat] :
( ( A
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(cnf,[status(esa)],[883]) ).
thf(885,plain,
! [A: nat] :
( ( A
= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(lifteq,[status(thm)],[884]) ).
thf(24,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( hchop @ C @ D @ E )
& ( A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_local_Ohmlsl_Ohchop__weaken1) ).
thf(301,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( hchop @ C @ D @ E )
& ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(2400,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( hchop @ B
@ ( sk5 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk6 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( D @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( E @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( G @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( F @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( D @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[2146]) ).
thf(2404,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( hchop @ B
@ ( sk5 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk6 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( D @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( E @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( G @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( F @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( D @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2400:[]]) ).
thf(2405,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( hchop @ B
@ ( sk5 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk6 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( D @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( E @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( G @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) )
| ( ( F @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
!= ( D @ A
@ ( sk7 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[2404:[]]) ).
thf(198,axiom,
! [A: view_ext @ product_unit] :
( ? [B: view_ext @ product_unit] :
( ? [C: view_ext @ product_unit] : ( vchop @ A @ B @ C )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( plus_plus @ nat @ ( zero_zero @ nat ) @ ( one_one @ nat ) ) ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat_card @ ( lan @ product_unit @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_local_Ohmlsl_Owidth__ge) ).
thf(1055,plain,
! [A: view_ext @ product_unit] :
( ? [B: view_ext @ product_unit] :
( ? [C: view_ext @ product_unit] : ( vchop @ A @ B @ C )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( plus_plus @ nat @ ( zero_zero @ nat ) @ ( one_one @ nat ) ) ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat_card @ ( lan @ product_unit @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(127,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_not__less__zero) ).
thf(784,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(785,plain,
! [TA: $tType,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(cnf,[status(esa)],[784]) ).
thf(177,axiom,
! [A: view_ext @ product_unit,B: cars > nat_int,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ A @ B @ C ) @ ( lan @ product_unit @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_restriction_Orestrict__view) ).
thf(949,plain,
! [A: view_ext @ product_unit,B: cars > nat_int,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ A @ B @ C ) @ ( lan @ product_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_less__not__refl2) ).
thf(539,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(540,plain,
! [B: nat,A: nat] :
( ~ ( ord_less @ nat @ A @ B )
| ( B != A ) ),
inference(cnf,[status(esa)],[539]) ).
thf(541,plain,
! [B: nat,A: nat] :
( ( B != A )
| ~ ( ord_less @ nat @ A @ B ) ),
inference(lifteq,[status(thm)],[540]) ).
thf(542,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(simp,[status(thm)],[541]) ).
thf(110,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( nat_card @ ( lan @ product_unit @ B ) )
!= ( one_one @ nat ) )
=> ~ ? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_local_Ohmlsl_Otwo__lanes__no__car) ).
thf(702,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( nat_card @ ( lan @ product_unit @ B ) )
!= ( one_one @ nat ) )
=> ~ ? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_trans__le__add1) ).
thf(751,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(136,axiom,
abstract @ ts3 @ ts2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_abs) ).
thf(817,plain,
abstract @ ts3 @ ts2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(203,axiom,
! [A: traffic,B: view_ext @ product_unit] :
? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
=> ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [D: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ D ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ D )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ D )
= ( bot_bot @ nat_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_local_Ohmlsl_Ores__not__free) ).
thf(1087,plain,
! [A: traffic,B: view_ext @ product_unit] :
? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
=> ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [D: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ D ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ D )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ D )
= ( bot_bot @ nat_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(156,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ G ) ) )
& ( ( len @ regular_regular @ G @ B @ A )
= ( ext @ product_unit @ G ) )
& ( ( restrict @ G @ ( res @ B ) @ A )
= ( lan @ product_unit @ G ) )
& ( ( nat_card @ ( lan @ product_unit @ G ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_local_Ohmlsl_Ono__clm__before__res2) ).
thf(870,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ G ) ) )
& ( ( len @ regular_regular @ G @ B @ A )
= ( ext @ product_unit @ G ) )
& ( ( restrict @ G @ ( res @ B ) @ A )
= ( lan @ product_unit @ G ) )
& ( ( nat_card @ ( lan @ product_unit @ G ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(74,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_infinite__descent0) ).
thf(486,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(487,plain,
! [A: nat > $o] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ~ ( A @ B )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ~ ( A @ C ) ) ) )
=> ! [B: nat] : ( A @ B ) ) ),
inference(miniscope,[status(thm)],[486]) ).
thf(488,plain,
! [C: nat,B: nat,A: nat > $o] :
( ( ~ ( A @ ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ A ) )
| ( A @ C ) )
& ( ~ ( A @ ( zero_zero @ nat ) )
| ~ ( A @ ( sk47 @ A ) )
| ( A @ C ) )
& ( ~ ( A @ ( zero_zero @ nat ) )
| ~ ( ord_less @ nat @ B @ ( sk47 @ A ) )
| ( A @ B )
| ( A @ C ) ) ),
inference(cnf,[status(esa)],[487]) ).
thf(489,plain,
! [B: nat,A: nat > $o] :
( ~ ( A @ ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[488]) ).
thf(492,plain,
! [A: nat] :
( ( ( zero_zero @ nat )
!= ( zero_zero @ nat ) )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
| ( ( zero_zero @ nat )
= A ) ),
inference(replace_leibeq,[status(thm)],[489:[bind(A,$thf( (=) @ nat @ ( zero_zero @ nat ) ))]]) ).
thf(495,plain,
! [A: nat] :
( ( ( zero_zero @ nat )
!= ( zero_zero @ nat ) )
| ( ( zero_zero @ nat )
= A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) ) ),
inference(lifteq,[status(thm)],[492]) ).
thf(496,plain,
! [A: nat] :
( ( ( zero_zero @ nat )
= A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(119,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_not__add__less1) ).
thf(748,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(749,plain,
~ ? [A: nat,B: nat] : ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(miniscope,[status(thm)],[748]) ).
thf(750,plain,
! [B: nat,A: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(cnf,[status(esa)],[749]) ).
thf(1440,plain,
! [C: nat,B: nat,A: nat] :
( ( A
!= ( zero_zero @ nat ) )
| ( ( ord_less @ nat @ A @ ( one_one @ nat ) )
!= ( ord_less @ nat @ ( plus_plus @ nat @ B @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[614,750]) ).
thf(1441,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( one_one @ nat ) @ A )
!= ( zero_zero @ nat ) ),
inference(pattern_uni,[status(thm)],[1440:[bind(A,$thf( plus_plus @ nat @ ( one_one @ nat ) @ E )),bind(B,$thf( one_one @ nat )),bind(C,$thf( E ))]]) ).
thf(1450,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( one_one @ nat ) @ A )
!= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[1441]) ).
thf(1461,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( one_one @ nat ) @ A )
!= ( zero_zero @ nat ) ),
inference(simp,[status(thm)],[1450]) ).
thf(1570,plain,
! [B: nat,A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
| ( ( zero_zero @ nat )
!= ( zero_zero @ nat ) )
| ( A
!= ( plus_plus @ nat @ ( one_one @ nat ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[496,1461]) ).
thf(1571,plain,
! [B: nat,A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
| ( A
!= ( plus_plus @ nat @ ( one_one @ nat ) @ B ) ) ),
inference(simp,[status(thm)],[1570]) ).
thf(1572,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ),
inference(pattern_uni,[status(thm)],[1571:[bind(A,$thf( plus_plus @ nat @ ( one_one @ nat ) @ D )),bind(B,$thf( D ))]]) ).
thf(159,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_nat__le__iff__add) ).
thf(881,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(32,axiom,
? [A: cars] : ( withdraw_claim @ ts_a @ A @ ts ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_wd__clm_Ohyps_I2_J) ).
thf(324,plain,
? [A: cars] : ( withdraw_claim @ ts_a @ A @ ts ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(325,plain,
withdraw_claim @ ts_a @ sk20 @ ts,
inference(cnf,[status(esa)],[324]) ).
thf(21,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ? [F: view_ext @ product_unit] :
( ? [G: view_ext @ product_unit] : ( hchop @ E @ F @ G )
& ( A @ B @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_local_Ohmlsl_Ohchop__weaken) ).
thf(289,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ? [F: view_ext @ product_unit] :
( ? [G: view_ext @ product_unit] : ( hchop @ E @ F @ G )
& ( A @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ nat_int @ ( restrict @ C @ D @ E ) @ ( restrict @ A @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_restriction_Orestriction__mon2) ).
thf(316,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ nat_int @ ( restrict @ C @ D @ E ) @ ( restrict @ A @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(72,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Nat_Oadd__0__right) ).
thf(473,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(474,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(cnf,[status(esa)],[473]) ).
thf(475,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(lifteq,[status(thm)],[474]) ).
thf(5,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ G @ H @ I )
& ( B @ D @ H )
& ( C @ D @ I ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ F @ H @ I )
& ( A @ D @ H )
& ( B @ D @ I ) )
& ( C @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_local_Ohmlsl_Ohchop__assoc) ).
thf(238,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ G @ H @ I )
& ( B @ D @ H )
& ( C @ D @ I ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ F @ H @ I )
& ( A @ D @ H )
& ( B @ D @ I ) )
& ( C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(174,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_add__is__0) ).
thf(937,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(133,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_local_Ohmlsl_Ofree__ge__zero) ).
thf(806,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(42,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(353,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(138,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ G ) ) )
& ( ( len @ regular_regular @ G @ B @ A )
= ( ext @ product_unit @ G ) )
& ( ( restrict @ G @ ( clm @ B ) @ A )
= ( lan @ product_unit @ G ) )
& ( ( nat_card @ ( lan @ product_unit @ G ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_local_Ohmlsl_Oclm__sing__not__interrupted) ).
thf(821,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ G ) ) )
& ( ( len @ regular_regular @ G @ B @ A )
= ( ext @ product_unit @ G ) )
& ( ( restrict @ G @ ( clm @ B ) @ A )
= ( lan @ product_unit @ G ) )
& ( ( nat_card @ ( lan @ product_unit @ G ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(13,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( vchop @ C @ D @ E )
& ( A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_local_Ohmlsl_Ov__chop__weaken1) ).
thf(263,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit] : ( vchop @ C @ D @ E )
& ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(264,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ~ ( A @ B @ C )
| ( vchop @ C @ ( sk9 @ C @ B @ A ) @ ( sk10 @ C @ B @ A ) ) )
& ( ~ ( A @ B @ C )
| ( A @ B @ ( sk9 @ C @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[263]) ).
thf(265,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ~ ( A @ B @ C )
| ( vchop @ C @ ( sk9 @ C @ B @ A ) @ ( sk10 @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[264]) ).
thf(2665,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: view_ext @ product_unit,A: traffic] :
( ~ $true
| ( vchop @ E @ ( sk9 @ E @ D @ C ) @ ( sk10 @ E @ D @ C ) )
| ( ( hchop @ B
@ ( sk7 @ B @ A
@ ^ [F: traffic,G: view_ext @ product_unit] : $false )
@ ( sk8 @ B @ A
@ ^ [F: traffic,G: view_ext @ product_unit] : $false ) )
!= ( C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2137,265]) ).
thf(2666,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: view_ext @ product_unit,A: traffic] :
( ( vchop @ E @ ( sk9 @ E @ D @ C ) @ ( sk10 @ E @ D @ C ) )
| ( ( hchop @ B
@ ( sk7 @ B @ A
@ ^ [F: traffic,G: view_ext @ product_unit] : $false )
@ ( sk8 @ B @ A
@ ^ [F: traffic,G: view_ext @ product_unit] : $false ) )
!= ( C @ D @ E ) ) ),
inference(simp,[status(thm)],[2665]) ).
thf(2754,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( vchop @ B
@ ( sk9 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk10 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A @ B )
!= ( D @ A @ B ) )
| ( ( E @ A @ B )
!= ( G @ A @ B ) )
| ( ( C @ A @ B )
!= ( F @ A @ B ) ) ),
inference(pre_uni,[status(thm)],[2666:[bind(A,$thf( J @ D @ E )),bind(B,$thf( F @ D @ E )),bind(C,$thf( ^ [K: traffic] : ^ [L: view_ext @ product_unit] : ( hchop @ ( F @ K @ L ) @ ( sk7 @ ( L @ K @ L ) @ ( M @ K @ L ) @ ^ [M: traffic] : ^ [N: view_ext @ product_unit] : $false ) @ ( sk8 @ ( I @ K @ L ) @ ( J @ K @ L ) @ ^ [M: traffic] : ^ [N: view_ext @ product_unit] : $false ) ) )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(2757,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( vchop @ B
@ ( sk9 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk10 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A @ B )
!= ( D @ A @ B ) )
| ( ( E @ A @ B )
!= ( G @ A @ B ) )
| ( ( C @ A @ B )
!= ( F @ A @ B ) ) ),
inference(pre_uni,[status(thm)],[2754:[]]) ).
thf(2893,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( vchop @ B
@ ( sk9 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk10 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A @ B )
!= ( D @ A @ B ) )
| ( ( E @ A @ B )
!= ( G @ A @ B ) )
| ( ( C @ A @ B )
!= ( F @ A @ B ) ) ),
inference(simp,[status(thm)],[2757]) ).
thf(30,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_le__iff__add) ).
thf(319,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(320,plain,
! [TA: $tType] :
( ~ ( canoni770627133id_add @ TA )
| ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(cnf,[status(esa)],[319]) ).
thf(321,plain,
! [TA: $tType] :
( ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) )
| ~ ( canoni770627133id_add @ TA ) ),
inference(lifteq,[status(thm)],[320]) ).
thf(67,axiom,
! [A: traffic,B: cars,C: traffic,D: cars,E: view_ext @ product_unit] :
( ( ( create_reservation @ A @ B @ C )
& ( B != D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ C @ D )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ C ) @ D )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ A @ D )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ A ) @ D )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_hmlsl__regular_Obackwards__res__stab) ).
thf(453,plain,
! [A: traffic,B: cars,C: traffic,D: cars,E: view_ext @ product_unit] :
( ( ( create_reservation @ A @ B @ C )
& ( B != D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ C @ D )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ C ) @ D )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ A @ D )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ A ) @ D )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(126,axiom,
! [A: traffic,B: cars,C: nat,D: traffic,E: view_ext @ product_unit,F: cars] :
( ( ( withdraw_reservation @ A @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ D @ F )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ D ) @ F )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ A @ F )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ A ) @ F )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_hmlsl__regular_Obackwards__wdr__res__stab) ).
thf(774,plain,
! [A: traffic,B: cars,C: nat,D: traffic,E: view_ext @ product_unit,F: cars] :
( ( ( withdraw_reservation @ A @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ D @ F )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ D ) @ F )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ A @ F )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ A ) @ F )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(187,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_local_Ohmlsl_Owidth__free) ).
thf(988,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(6,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_zero__eq__add__iff__both__eq__0) ).
thf(241,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(242,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(cnf,[status(esa)],[241]) ).
thf(243,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) )
= ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) ) )
| ~ ( canoni770627133id_add @ TA ) ),
inference(lifteq,[status(thm)],[242]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_le__antisym) ).
thf(507,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(50,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_infinite__descent0__measure) ).
thf(380,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(83,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_le__add2) ).
thf(546,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(123,axiom,
c != e,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_neg) ).
thf(759,plain,
c != e,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(760,plain,
c != e,
inference(polarity_switch,[status(thm)],[759]) ).
thf(761,plain,
e != c,
inference(lifteq,[status(thm)],[760]) ).
thf(223,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( ( real_length @ ( len @ regular_regular @ A @ B @ C ) )
= ( zero_zero @ real ) )
& ( hchop @ A @ D @ E ) )
=> ( ( real_length @ ( len @ regular_regular @ E @ B @ C ) )
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_hmlsl_Olen__empty__on__subview2) ).
thf(1163,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( ( real_length @ ( len @ regular_regular @ A @ B @ C ) )
= ( zero_zero @ real ) )
& ( hchop @ A @ D @ E ) )
=> ( ( real_length @ ( len @ regular_regular @ E @ B @ C ) )
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(3008,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( vchop @ B
@ ( sk9 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk10 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A @ B )
!= ( D @ A @ B ) )
| ( ( E @ A @ B )
!= ( G @ A @ B ) )
| ( ( C @ A @ B )
!= ( C @ A @ B ) )
| ( ( F @ A @ B )
!= ( D @ A @ B ) ) ),
inference(eqfactor_ordered,[status(thm)],[2893]) ).
thf(3010,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( vchop @ B
@ ( sk9 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk10 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A @ B )
!= ( D @ A @ B ) )
| ( ( E @ A @ B )
!= ( G @ A @ B ) )
| ( ( F @ A @ B )
!= ( D @ A @ B ) ) ),
inference(pre_uni,[status(thm)],[3008:[]]) ).
thf(3011,plain,
! [G: traffic > ( view_ext @ product_unit ) > traffic,F: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),E: traffic > ( view_ext @ product_unit ) > traffic,D: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: view_ext @ product_unit,A: traffic] :
( ( vchop @ B
@ ( sk9 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) )
@ ( sk10 @ B @ A
@ ^ [H: traffic,I: view_ext @ product_unit] :
( hchop @ ( C @ H @ I )
@ ( sk7 @ ( F @ H @ I ) @ ( G @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false )
@ ( sk8 @ ( D @ H @ I ) @ ( E @ H @ I )
@ ^ [J: traffic,K: view_ext @ product_unit] : $false ) ) ) )
| ( ( C @ A @ B )
!= ( D @ A @ B ) )
| ( ( E @ A @ B )
!= ( G @ A @ B ) )
| ( ( F @ A @ B )
!= ( D @ A @ B ) ) ),
inference(pre_uni,[status(thm)],[3010:[]]) ).
thf(3,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_local_Ohmlsl_Ohchop__disj__distr1) ).
thf(233,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(450,plain,
! [B: nat,A: nat] :
( ~ ( ord_less @ nat @ A @ B )
| ( B
!= ( zero_zero @ nat ) ) ),
inference(cnf,[status(esa)],[449]) ).
thf(451,plain,
! [B: nat,A: nat] :
( ( B
!= ( zero_zero @ nat ) )
| ~ ( ord_less @ nat @ A @ B ) ),
inference(lifteq,[status(thm)],[450]) ).
thf(452,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(simp,[status(thm)],[451]) ).
thf(36,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_add__left__cancel) ).
thf(334,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(165,axiom,
! [A: view_ext @ product_unit,B: cars > nat_int,C: cars] :
( ( ( ( nat_card @ ( restrict @ A @ B @ C ) )
= ( nat_card @ ( lan @ product_unit @ A ) ) )
& ( ord_less_eq @ nat_int @ ( restrict @ A @ B @ C ) @ ( lan @ product_unit @ A ) ) )
=> ( ( restrict @ A @ B @ C )
= ( lan @ product_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_restriction_Orestrict__eq__lan__subs) ).
thf(910,plain,
! [A: view_ext @ product_unit,B: cars > nat_int,C: cars] :
( ( ( ( nat_card @ ( restrict @ A @ B @ C ) )
= ( nat_card @ ( lan @ product_unit @ A ) ) )
& ( ord_less_eq @ nat_int @ ( restrict @ A @ B @ C ) @ ( lan @ product_unit @ A ) ) )
=> ( ( restrict @ A @ B @ C )
= ( lan @ product_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(180,axiom,
monoid_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__add_8) ).
thf(957,plain,
monoid_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(139,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_local_Ohmlsl_Owidth__clm) ).
thf(825,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(178,axiom,
( ( nat_card @ ( bot_bot @ nat_int ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_card__empty__zero) ).
thf(951,plain,
( ( nat_card @ ( bot_bot @ nat_int ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(952,plain,
( ( nat_card @ ( bot_bot @ nat_int ) )
= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[951]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_le__neq__implies__less) ).
thf(392,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(23,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( hchop @ A @ B @ C )
=> ( ( restrict @ A @ D @ E )
= ( restrict @ B @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_restriction_Orestriction__stable1) ).
thf(297,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( hchop @ A @ B @ C )
=> ( ( restrict @ A @ D @ E )
= ( restrict @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_add_Oright__neutral) ).
thf(275,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(115,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( clm @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_local_Ohmlsl_Oclm__sing) ).
thf(729,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( clm @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(12,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( ( A @ D @ F )
| ( B @ D @ F ) )
& ( C @ D @ G ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( B @ D @ F )
& ( C @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_local_Ohmlsl_Ohchop__disj__distr2) ).
thf(260,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( ( A @ D @ F )
| ( B @ D @ F ) )
& ( C @ D @ G ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( B @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(153,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_view_Ohorizontal__chop__leq1) ).
thf(862,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(41,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( A @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_local_Ohmlsl_Ov__chop__weaken2) ).
thf(349,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( A @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(57,axiom,
! [A: nat,B: nat,C: traffic,D: view_ext @ product_unit] :
( ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( plus_plus @ nat @ A @ B ) )
=> ? [E: view_ext @ product_unit,F: view_ext @ product_unit] :
( ( vchop @ D @ E @ F )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= A )
& ( ( nat_card @ ( lan @ product_unit @ F ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_local_Ohmlsl_Owidth__add2) ).
thf(407,plain,
! [A: nat,B: nat,C: view_ext @ product_unit] :
( ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( plus_plus @ nat @ A @ B ) )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= A )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(99,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_zero__reorient) ).
thf(630,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(45,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ B @ D @ E ) )
=> ? [F: view_ext @ product_unit] :
( ( hchop @ A @ D @ F )
& ( hchop @ F @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_view_Ohorizontal__chop__assoc2) ).
thf(361,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ B @ D @ E ) )
=> ? [F: view_ext @ product_unit] :
( ( hchop @ A @ D @ F )
& ( hchop @ F @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(105,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Nat_Oex__has__greatest__nat) ).
thf(665,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(210,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(1128,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_less__imp__le__nat) ).
thf(710,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(145,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: traffic,D: cars] :
( ( ( ( ext @ product_unit @ A )
= ( ext @ product_unit @ B ) )
& ( ( own @ product_unit @ A )
= ( own @ product_unit @ B ) ) )
=> ( ( len @ regular_regular @ A @ C @ D )
= ( len @ regular_regular @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_hmlsl_Oext__eq__len__eq) ).
thf(842,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: traffic,D: cars] :
( ( ( ( ext @ product_unit @ A )
= ( ext @ product_unit @ B ) )
& ( ( own @ product_unit @ A )
= ( own @ product_unit @ B ) ) )
=> ( ( len @ regular_regular @ A @ C @ D )
= ( len @ regular_regular @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(167,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars] : ( ord_less_eq @ real_int @ ( len @ regular_regular @ A @ B @ C ) @ ( ext @ product_unit @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_hmlsl_Olen__sub__int) ).
thf(916,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars] : ( ord_less_eq @ real_int @ ( len @ regular_regular @ A @ B @ C ) @ ( ext @ product_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(70,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_zero__less__iff__neq__zero) ).
thf(467,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(196,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ C @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ C @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ C @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ D @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ D @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ D @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_local_Ohmlsl_Ofree__compose) ).
thf(1032,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ C @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ C @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ C @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ D @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ D @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ D @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(9,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_local_Ohmlsl_Ovchop__disj__distr1) ).
thf(250,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(251,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(252,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(lifteq,[status(thm)],[251]) ).
thf(20,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( hchop @ A @ B @ C )
=> ( ( restrict @ B @ D @ E )
= ( restrict @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_restriction_Orestriction__stable) ).
thf(285,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( hchop @ A @ B @ C )
=> ( ( restrict @ B @ D @ E )
= ( restrict @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1106,plain,
! [B: cars,A: traffic] : ( ord_less_eq @ nat @ ( nat_card @ ( clm @ A @ B ) ) @ ( one_one @ nat ) ),
inference(cnf,[status(esa)],[1105]) ).
thf(88,axiom,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq @ nat_int @ A @ B )
=> ( ord_less_eq @ nat @ ( nat_card @ A ) @ ( nat_card @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_card__subset__le) ).
thf(578,plain,
! [A: nat_int,B: nat_int] :
( ( ord_less_eq @ nat_int @ A @ B )
=> ( ord_less_eq @ nat @ ( nat_card @ A ) @ ( nat_card @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(97,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) )
=> ! [D: traffic] :
( ( create_reservation @ B @ A @ D )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ D @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ D ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_hmlsl__regular_Oreservation1) ).
thf(615,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) )
=> ! [D: traffic] :
( ( create_reservation @ B @ A @ D )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ D @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ D ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(114,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ! [D: traffic] :
( ( abstract @ B @ D )
=> ( A @ D @ ( move @ B @ D @ C ) ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_local_Ohmlsl_Oglobally__refl) ).
thf(725,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ! [D: traffic] :
( ( abstract @ B @ D )
=> ( A @ D @ ( move @ B @ D @ C ) ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(204,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_not__add__less2) ).
thf(1096,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(192,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
=> ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_local_Ohmlsl_Olength__split) ).
thf(1006,plain,
! [A: view_ext @ product_unit] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
=> ? [B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_le__Suc__ex) ).
thf(420,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(151,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_le__refl) ).
thf(857,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(157,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_gr__implies__not__zero) ).
thf(874,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(215,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ B @ D @ E ) ) @ ( nat_card @ ( restrict @ A @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_restriction_Orestriction__card__mon1) ).
thf(1143,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ B @ D @ E ) ) @ ( nat_card @ ( restrict @ A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(38,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_less__eqE) ).
thf(339,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(85,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_not__gr0) ).
thf(552,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(553,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(cnf,[status(esa)],[552]) ).
thf(554,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(lifteq,[status(thm)],[553]) ).
thf(73,axiom,
! [A: traffic,B: cars,C: traffic,D: view_ext @ product_unit,E: cars] :
( ( ( withdraw_claim @ A @ B @ C )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ C @ E )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ C ) @ E )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ A @ E )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ A ) @ E )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_hmlsl__regular_Obackwards__wdc__res__stab) ).
thf(476,plain,
! [A: traffic,B: cars,C: traffic,D: view_ext @ product_unit,E: cars] :
( ( ( withdraw_claim @ A @ B @ C )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ C @ E )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ C ) @ E )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ A @ E )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ A ) @ E )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(184,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) )
=> ( ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_local_Ohmlsl_Ocar__one__lane__non__empty) ).
thf(970,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) )
=> ( ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(219,axiom,
! [A: cars,B: traffic,C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( regular_regular @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_local_Ohmlsl_Osensors__ge) ).
thf(1155,plain,
! [A: cars,B: traffic,C: cars] : ( ord_less @ real @ ( zero_zero @ real ) @ ( regular_regular @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(34,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ A @ ( clm @ B ) @ C ) @ ( clm @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_restriction_Orestrict__clm) ).
thf(328,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ A @ ( clm @ B ) @ C ) @ ( clm @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(143,axiom,
! [A: nat_int] :
( ( A
!= ( bot_bot @ nat_int ) )
= ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_card__non__empty__geq__one) ).
thf(837,plain,
! [A: nat_int] :
( ( A
!= ( bot_bot @ nat_int ) )
= ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(189,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_le__0__eq) ).
thf(997,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(212,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
=> ( ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( nat_card @ ( lan @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( nat_card @ ( lan @ product_unit @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_view_Ohorizontal__chop__width__stable) ).
thf(1131,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
=> ( ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( nat_card @ ( lan @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( nat_card @ ( lan @ product_unit @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(113,axiom,
! [A: nat,B: nat,C: traffic,D: view_ext @ product_unit] :
( ? [E: view_ext @ product_unit,F: view_ext @ product_unit] :
( ( vchop @ D @ E @ F )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= A )
& ( ( nat_card @ ( lan @ product_unit @ F ) )
= B ) )
=> ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_local_Ohmlsl_Owidth__add1) ).
thf(721,plain,
! [A: nat,B: nat,C: view_ext @ product_unit] :
( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= A )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= B ) )
=> ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(205,axiom,
! [A: nat,B: traffic,C: view_ext @ product_unit] :
( ( ( nat_card @ ( lan @ product_unit @ C ) )
= A )
= ( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= A )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_local_Ohmlsl_Owidth__hchop__stable) ).
thf(1099,plain,
! [A: nat,B: view_ext @ product_unit] :
( ( ( nat_card @ ( lan @ product_unit @ B ) )
= A )
= ( ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= A )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(185,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_plus__nat_Oadd__0) ).
thf(983,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(984,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(cnf,[status(esa)],[983]) ).
thf(985,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(lifteq,[status(thm)],[984]) ).
thf(75,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ F ) ) )
& ( ( len @ regular_regular @ F @ B @ A )
= ( ext @ product_unit @ F ) )
& ( ( restrict @ F @ ( res @ B ) @ A )
= ( lan @ product_unit @ F ) )
& ( ( nat_card @ ( lan @ product_unit @ F ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ G ) ) )
& ( ( len @ regular_regular @ G @ B @ A )
= ( ext @ product_unit @ G ) )
& ( ( restrict @ G @ ( res @ B ) @ A )
= ( lan @ product_unit @ G ) )
& ( ( nat_card @ ( lan @ product_unit @ G ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_local_Ohmlsl_Ores__at__most__two) ).
thf(503,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ F ) ) )
& ( ( len @ regular_regular @ F @ B @ A )
= ( ext @ product_unit @ F ) )
& ( ( restrict @ F @ ( res @ B ) @ A )
= ( lan @ product_unit @ F ) )
& ( ( nat_card @ ( lan @ product_unit @ F ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ G ) ) )
& ( ( len @ regular_regular @ G @ B @ A )
= ( ext @ product_unit @ G ) )
& ( ( restrict @ G @ ( res @ B ) @ A )
= ( lan @ product_unit @ G ) )
& ( ( nat_card @ ( lan @ product_unit @ G ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(93,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_neq0__conv) ).
thf(605,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(4,axiom,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit,C: view_ext @ product_unit] : ( hchop @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_view_Ohorizontal__chop1) ).
thf(236,plain,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit,C: view_ext @ product_unit] : ( hchop @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(237,plain,
! [A: view_ext @ product_unit] : ( hchop @ A @ ( sk1 @ A ) @ ( sk2 @ A ) ),
inference(cnf,[status(esa)],[236]) ).
thf(7,axiom,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit] : ( vchop @ A @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_view_Overtical__chop__empty__up) ).
thf(244,plain,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit] : ( vchop @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(266,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ~ ( A @ B @ C )
| ( A @ B @ ( sk9 @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[264]) ).
thf(100,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_local_Ohmlsl_Ores__decompose) ).
thf(633,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(55,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_trans__le__add2) ).
thf(398,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(104,axiom,
! [A: view_ext @ product_unit,B: cars > nat_int,C: cars] :
( ( ( restrict @ A @ B @ C )
= ( lan @ product_unit @ A ) )
=> ( ( nat_card @ ( restrict @ A @ B @ C ) )
= ( nat_card @ ( lan @ product_unit @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_restriction_Orestriction__eq__view__card) ).
thf(662,plain,
! [A: view_ext @ product_unit,B: cars > nat_int,C: cars] :
( ( ( restrict @ A @ B @ C )
= ( lan @ product_unit @ A ) )
=> ( ( nat_card @ ( restrict @ A @ B @ C ) )
= ( nat_card @ ( lan @ product_unit @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1022,plain,
( ( len @ regular_regular @ sk77 @ ts @ e )
= ( ext @ product_unit @ sk77 ) ),
inference(cnfConj,[status(thm)],[1016]) ).
thf(1026,plain,
( ( len @ regular_regular @ sk77 @ ts @ e )
= ( ext @ product_unit @ sk77 ) ),
inference(lifteq,[status(thm)],[1022]) ).
thf(1097,plain,
~ ? [A: nat,B: nat] : ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(miniscope,[status(thm)],[1096]) ).
thf(1098,plain,
! [B: nat,A: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(cnf,[status(esa)],[1097]) ).
thf(1885,plain,
! [B: nat,A: nat] :
( ~ $true
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
!= ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1572,1098]) ).
thf(1886,plain,
! [B: nat,A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
!= ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ) ),
inference(simp,[status(thm)],[1885]) ).
thf(1890,plain,
! [B: nat,A: nat] :
( ( ( zero_zero @ nat )
!= ( plus_plus @ nat @ A @ B ) )
| ( ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) )
!= B ) ),
inference(simp,[status(thm)],[1886]) ).
thf(1895,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
!= ( zero_zero @ nat ) ),
inference(simp,[status(thm)],[1890]) ).
thf(224,axiom,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts3 @ ts @ v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_move__stab) ).
thf(1166,plain,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts3 @ ts @ v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1167,plain,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts3 @ ts @ v ) ),
inference(lifteq,[status(thm)],[1166]) ).
thf(179,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_less__not__refl3) ).
thf(953,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(230,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_infinite__descent) ).
thf(1185,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(89,axiom,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062) ).
thf(580,plain,
( ( move @ ts3 @ ts_a @ v )
= ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(581,plain,
( ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) )
= ( move @ ts3 @ ts_a @ v ) ),
inference(lifteq,[status(thm)],[580]) ).
thf(2936,plain,
( ( move @ ts_a @ ts @ ( move @ ts3 @ ts @ v ) )
= ( move @ ts3 @ ts @ v ) ),
inference(rewrite,[status(thm)],[581,1167]) ).
thf(216,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
= ( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( clm @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_local_Ohmlsl_Oclm__dense) ).
thf(1146,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
= ( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( clm @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(2755,plain,
! [F: traffic,E: view_ext @ product_unit,D: traffic > ( view_ext @ product_unit ) > traffic,C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),A: traffic] :
( ( vchop
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false )
@ ( sk9
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false )
@ A
@ ^ [G: traffic,H: view_ext @ product_unit] :
( hchop @ ( B @ G @ H ) @ H
@ ( sk8 @ ( C @ G @ H ) @ ( D @ G @ H )
@ ^ [I: traffic,J: view_ext @ product_unit] : $false ) ) )
@ ( sk10
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false )
@ A
@ ^ [G: traffic,H: view_ext @ product_unit] :
( hchop @ ( B @ G @ H ) @ H
@ ( sk8 @ ( C @ G @ H ) @ ( D @ G @ H )
@ ^ [I: traffic,J: view_ext @ product_unit] : $false ) ) ) )
| ( ( B @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) )
!= ( C @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) ) )
| ( ( B @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) )
!= E )
| ( ( D @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) )
!= F ) ),
inference(pre_uni,[status(thm)],[2666:[bind(A,$thf( J @ D @ ( sk7 @ X @ Y @ ^ [I: traffic] : ^ [J: view_ext @ product_unit] : $false ) )),bind(B,$thf( F @ D @ ( sk7 @ X @ Y @ ^ [I: traffic] : ^ [J: view_ext @ product_unit] : $false ) )),bind(C,$thf( ^ [I: traffic] : ^ [J: view_ext @ product_unit] : ( hchop @ ( F @ I @ J ) @ J @ ( sk8 @ ( I @ I @ J ) @ ( J @ I @ J ) @ ^ [K: traffic] : ^ [L: view_ext @ product_unit] : $false ) ) )),bind(D,$thf( D )),bind(E,$thf( sk7 @ X @ Y @ ^ [H: traffic] : ^ [I: view_ext @ product_unit] : $false ))]]) ).
thf(2758,plain,
! [F: traffic,E: view_ext @ product_unit,D: traffic > ( view_ext @ product_unit ) > traffic,C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),A: traffic] :
( ( vchop
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false )
@ ( sk9
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false )
@ A
@ ^ [G: traffic,H: view_ext @ product_unit] :
( hchop @ ( B @ G @ H ) @ H
@ ( sk8 @ ( C @ G @ H ) @ ( D @ G @ H )
@ ^ [I: traffic,J: view_ext @ product_unit] : $false ) ) )
@ ( sk10
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false )
@ A
@ ^ [G: traffic,H: view_ext @ product_unit] :
( hchop @ ( B @ G @ H ) @ H
@ ( sk8 @ ( C @ G @ H ) @ ( D @ G @ H )
@ ^ [I: traffic,J: view_ext @ product_unit] : $false ) ) ) )
| ( ( B @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) )
!= ( C @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) ) )
| ( ( B @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) )
!= E )
| ( ( D @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) )
!= F ) ),
inference(pre_uni,[status(thm)],[2755:[]]) ).
thf(2894,plain,
! [F: traffic,E: view_ext @ product_unit,D: traffic > ( view_ext @ product_unit ) > traffic,C: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),B: traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ),A: traffic] :
( ( vchop
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false )
@ ( sk9
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false )
@ A
@ ^ [G: traffic,H: view_ext @ product_unit] :
( hchop @ ( B @ G @ H ) @ H
@ ( sk8 @ ( C @ G @ H ) @ ( D @ G @ H )
@ ^ [I: traffic,J: view_ext @ product_unit] : $false ) ) )
@ ( sk10
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false )
@ A
@ ^ [G: traffic,H: view_ext @ product_unit] :
( hchop @ ( B @ G @ H ) @ H
@ ( sk8 @ ( C @ G @ H ) @ ( D @ G @ H )
@ ^ [I: traffic,J: view_ext @ product_unit] : $false ) ) ) )
| ( ( B @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) )
!= ( C @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) ) )
| ( ( B @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) )
!= E )
| ( ( D @ A
@ ( sk7 @ E @ F
@ ^ [G: traffic,H: view_ext @ product_unit] : $false ) )
!= F ) ),
inference(simp,[status(thm)],[2758]) ).
thf(49,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_less__mono__imp__le__mono) ).
thf(375,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(116,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( ( real_length @ ( len @ regular_regular @ A @ B @ C ) )
= ( zero_zero @ real ) )
& ( hchop @ A @ D @ E ) )
=> ( ( real_length @ ( len @ regular_regular @ D @ B @ C ) )
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_hmlsl_Olen__empty__on__subview1) ).
thf(733,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( ( real_length @ ( len @ regular_regular @ A @ B @ C ) )
= ( zero_zero @ real ) )
& ( hchop @ A @ D @ E ) )
=> ( ( real_length @ ( len @ regular_regular @ D @ B @ C ) )
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(61,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_one__reorient) ).
thf(423,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(209,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_add__eq__self__zero) ).
thf(1125,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(181,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_bot__nat__0_Oextremum__uniqueI) ).
thf(958,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(19,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( vchop @ A @ B @ C )
& ( vchop @ C @ D @ E ) )
=> ? [F: view_ext @ product_unit] :
( ( vchop @ A @ F @ E )
& ( vchop @ F @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_view_Overtical__chop__assoc1) ).
thf(281,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( vchop @ A @ B @ C )
& ( vchop @ C @ D @ E ) )
=> ? [F: view_ext @ product_unit] :
( ( vchop @ A @ F @ E )
& ( vchop @ F @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
abstract @ ts3 @ ts_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_wd__clm_Ohyps_I1_J) ).
thf(259,plain,
abstract @ ts3 @ ts_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(52,axiom,
strict2144017051up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(391,plain,
strict2144017051up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(173,axiom,
wellorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(936,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(28,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ nat_int @ ( restrict @ B @ D @ E ) @ ( restrict @ A @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_restriction_Orestriction__mon1) ).
thf(313,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ nat_int @ ( restrict @ B @ D @ E ) @ ( restrict @ A @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(95,axiom,
one @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oone_10) ).
thf(611,plain,
one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1270,plain,
( ( ( one_one @ nat )
= ( zero_zero @ nat ) )
| ( ( nat_card @ ( lan @ product_unit @ sk77 ) )
!= ( nat_card @ ( bot_bot @ nat_int ) ) ) ),
inference(paramod_ordered,[status(thm)],[1027,952]) ).
thf(1272,plain,
( ( ( one_one @ nat )
= ( zero_zero @ nat ) )
| ( ( lan @ product_unit @ sk77 )
!= ( bot_bot @ nat_int ) ) ),
inference(simp,[status(thm)],[1270]) ).
thf(1445,plain,
! [B: nat,A: nat] :
( ( A
!= ( zero_zero @ nat ) )
| ( ( ord_less @ nat @ A @ ( one_one @ nat ) )
!= ( ord_less @ nat @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[614,542]) ).
thf(1446,plain,
( ( one_one @ nat )
!= ( zero_zero @ nat ) ),
inference(pattern_uni,[status(thm)],[1445:[bind(A,$thf( one_one @ nat )),bind(B,$thf( one_one @ nat ))]]) ).
thf(1453,plain,
( ( one_one @ nat )
!= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[1446]) ).
thf(1464,plain,
( ( lan @ product_unit @ sk77 )
!= ( bot_bot @ nat_int ) ),
inference(simplifyReflect,[status(thm)],[1272,1453]) ).
thf(199,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: traffic,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ( len @ regular_regular @ A @ D @ E )
= ( len @ regular_regular @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_hmlsl_Olen__stable__up) ).
thf(1058,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: traffic,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ( len @ regular_regular @ A @ D @ E )
= ( len @ regular_regular @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(208,axiom,
! [A: traffic,B: cars,C: traffic,D: view_ext @ product_unit] :
( ( ( create_reservation @ A @ B @ C )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ C @ B )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ C ) @ B )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) )
=> ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ A @ B )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ A ) @ B )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ A @ B )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ A ) @ B )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_hmlsl__regular_Obackwards__res__act) ).
thf(1107,plain,
! [A: traffic,B: cars,C: traffic,D: view_ext @ product_unit] :
( ( ( create_reservation @ A @ B @ C )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ C @ B )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ C ) @ B )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) )
=> ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ A @ B )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ A ) @ B )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ A @ B )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ A ) @ B )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1875,plain,
! [B: nat,A: nat] :
( ~ $true
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
!= ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1572,750]) ).
thf(1876,plain,
! [B: nat,A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
!= ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ) ),
inference(simp,[status(thm)],[1875]) ).
thf(1892,plain,
! [B: nat,A: nat] :
( ( ( zero_zero @ nat )
!= ( plus_plus @ nat @ A @ B ) )
| ( ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) )
!= A ) ),
inference(simp,[status(thm)],[1876]) ).
thf(1897,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) @ A )
!= ( zero_zero @ nat ) ),
inference(simp,[status(thm)],[1892]) ).
thf(169,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_local_Ohmlsl_Ono__clm__before__res) ).
thf(919,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(132,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars] : ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ A @ ( clm @ B ) @ C ) ) @ ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_restriction_Orestriction__clm__leq__one) ).
thf(804,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars] : ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ A @ ( clm @ B ) @ C ) ) @ ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(231,axiom,
! [A: view_ext @ product_unit] :
( ( ( ord_less_eq @ ( view_ext @ product_unit ) @ A @ ( move @ ts3 @ ts @ v ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ c )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ c )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ e )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ e )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1194,plain,
! [A: view_ext @ product_unit] :
( ( ( ord_less_eq @ ( view_ext @ product_unit ) @ A @ ( move @ ts3 @ ts @ v ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ c )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ c )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
& ( ( len @ regular_regular @ A @ ts @ e )
= ( ext @ product_unit @ A ) )
& ( ( restrict @ A @ ( res @ ts ) @ e )
= ( lan @ product_unit @ A ) )
& ( ( nat_card @ ( lan @ product_unit @ A ) )
= ( one_one @ nat ) ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_nat__neq__iff) ).
thf(681,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(16,axiom,
withdraw_claim @ ts_a @ d @ ts,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_d__def) ).
thf(274,plain,
withdraw_claim @ ts_a @ d @ ts,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1881,plain,
! [A: nat] :
( ~ $true
| ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
!= ( ord_less @ nat @ A @ ( zero_zero @ nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[1572,452]) ).
thf(1882,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) ) )
!= ( ord_less @ nat @ A @ ( zero_zero @ nat ) ) ),
inference(simp,[status(thm)],[1881]) ).
thf(1889,plain,
! [A: nat] :
( ( ( zero_zero @ nat )
!= A )
| ( ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) )
!= ( zero_zero @ nat ) ) ),
inference(simp,[status(thm)],[1882]) ).
thf(1894,plain,
( ( sk47 @ ( (=) @ nat @ ( zero_zero @ nat ) ) )
!= ( zero_zero @ nat ) ),
inference(simp,[status(thm)],[1889]) ).
thf(245,plain,
! [A: view_ext @ product_unit] : ( vchop @ A @ ( sk3 @ A ) @ A ),
inference(cnf,[status(esa)],[244]) ).
thf(117,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_less__eq__nat_Osimps_I1_J) ).
thf(737,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(15,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
=> ( ( own @ product_unit @ B )
= ( own @ product_unit @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_view_Ohorizontal__chop__own__trans) ).
thf(271,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
=> ( ( own @ product_unit @ B )
= ( own @ product_unit @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(193,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_less__add__eq__less) ).
thf(1011,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(59,axiom,
! [A: traffic,B: cars] : ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( res @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_traffic_OatLeastOneRes) ).
thf(418,plain,
! [A: traffic,B: cars] : ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( res @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(419,plain,
! [B: cars,A: traffic] : ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( res @ A @ B ) ) ),
inference(cnf,[status(esa)],[418]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( ! [D: traffic] :
( ( abstract @ B @ D )
=> ! [E: TB] : ( A @ D @ ( move @ B @ D @ C ) ) ) )
= ( ! [D: TA,E: traffic] :
( ( abstract @ B @ E )
=> ( A @ E @ ( move @ B @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_local_Ohmlsl_Oglobally__all__iff) ).
thf(758,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(222,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_nat__less__le) ).
thf(1161,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1162,plain,
( ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) )
= ( ord_less @ nat ) ),
inference(lifteq,[status(thm)],[1161]) ).
thf(147,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_local_Ohmlsl_Olength__meld) ).
thf(848,plain,
! [A: view_ext @ product_unit] :
( ? [B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(239,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ G @ H @ I )
& ( B @ D @ H )
& ( C @ D @ I ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ F @ H @ I )
& ( A @ D @ H )
& ( B @ D @ I ) )
& ( C @ D @ G ) ) ) ),
inference(cnf,[status(esa)],[238]) ).
thf(240,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ G @ H @ I )
& ( B @ D @ H )
& ( C @ D @ I ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ F @ H @ I )
& ( A @ D @ H )
& ( B @ D @ I ) )
& ( C @ D @ G ) ) ) ),
inference(lifteq,[status(thm)],[239]) ).
thf(195,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_local_Ohmlsl_Oclm__ge__zero) ).
thf(1029,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(217,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_bot__nat__0_Onot__eq__extremum) ).
thf(1149,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(226,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_view_Overtical__chop__leq2) ).
thf(1177,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(35,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( hchop @ A @ B @ C )
=> ( ( restrict @ A @ D @ E )
= ( restrict @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_restriction_Orestriction__stable2) ).
thf(330,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( hchop @ A @ B @ C )
=> ( ( restrict @ A @ D @ E )
= ( restrict @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(40,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( A @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_local_Ohmlsl_Ohchop__weaken2) ).
thf(345,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ( A @ B @ C )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( A @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(47,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( A @ B @ E ) )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ~ ( A @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_local_Ohmlsl_Ohchop__neg2) ).
thf(367,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ~ ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( A @ B @ E ) )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ~ ( A @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(94,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_local_Ohmlsl_Otwo__res__not__res) ).
thf(608,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(186,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_view_Ohorizontal__chop__leq2) ).
thf(986,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
=> ( ord_less_eq @ ( view_ext @ product_unit ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(190,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ C @ D @ E ) ) @ ( nat_card @ ( restrict @ A @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_restriction_Orestriction__card__mon2) ).
thf(1000,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: cars > nat_int,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ord_less_eq @ nat @ ( nat_card @ ( restrict @ C @ D @ E ) ) @ ( nat_card @ ( restrict @ A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(63,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_le__add1) ).
thf(431,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(18,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_add_Oleft__neutral) ).
thf(278,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(155,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ A @ ( res @ B ) @ C ) @ ( res @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_restriction_Orestrict__res) ).
thf(868,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars] : ( ord_less_eq @ nat_int @ ( restrict @ A @ ( res @ B ) @ C ) @ ( res @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(14,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( vchop @ A @ B @ C )
& ( vchop @ B @ D @ E ) )
=> ? [F: view_ext @ product_unit] :
( ( vchop @ A @ D @ F )
& ( vchop @ F @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_view_Overtical__chop__assoc2) ).
thf(267,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( vchop @ A @ B @ C )
& ( vchop @ B @ D @ E ) )
=> ? [F: view_ext @ product_unit] :
( ( vchop @ A @ D @ F )
& ( vchop @ F @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(149,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_less__nat__zero__code) ).
thf(851,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(206,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit,F: view_ext @ product_unit,G: view_ext @ product_unit,H: view_ext @ product_unit,I: view_ext @ product_unit,J: cars > nat_int,K: cars] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ C @ D @ E )
& ( vchop @ D @ F @ G )
& ( vchop @ G @ H @ I )
& ( ( nat_card @ ( restrict @ H @ J @ K ) )
= ( one_one @ nat ) ) )
=> ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( restrict @ A @ J @ K ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_restriction_Orestriction__card__somewhere__mon) ).
thf(1102,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit,F: view_ext @ product_unit,G: view_ext @ product_unit,H: view_ext @ product_unit,I: view_ext @ product_unit,J: cars > nat_int,K: cars] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ C @ D @ E )
& ( vchop @ D @ F @ G )
& ( vchop @ G @ H @ I )
& ( ( nat_card @ ( restrict @ H @ J @ K ) )
= ( one_one @ nat ) ) )
=> ( ord_less_eq @ nat @ ( one_one @ nat ) @ ( nat_card @ ( restrict @ A @ J @ K ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_le__trans) ).
thf(653,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(84,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( ( len @ regular_regular @ A @ B @ C )
= ( ext @ product_unit @ A ) )
& ( hchop @ A @ D @ E ) )
=> ( ( len @ regular_regular @ D @ B @ C )
= ( ext @ product_unit @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_hmlsl_Olen__view__hchop__left) ).
thf(548,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( ( len @ regular_regular @ A @ B @ C )
= ( ext @ product_unit @ A ) )
& ( hchop @ A @ D @ E ) )
=> ( ( len @ regular_regular @ D @ B @ C )
= ( ext @ product_unit @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(171,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_local_Ohmlsl_Owidth__res) ).
thf(927,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
=> ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(255,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( hchop @ C @ ( sk5 @ C @ B @ A ) @ ( sk6 @ C @ B @ A ) )
| ( hchop @ C @ ( sk7 @ C @ B @ A ) @ ( sk8 @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(134,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_le__eq__less__or__eq) ).
thf(812,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(201,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ! [D: traffic] :
( ( create_reservation @ B @ A @ D )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ D @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ D ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) )
= ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_hmlsl__regular_Oreservation) ).
thf(1081,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ! [D: traffic] :
( ( create_reservation @ B @ A @ D )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ D @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ D ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) )
= ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(39,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( vchop @ A @ B @ C )
=> ( ( own @ product_unit @ B )
= ( own @ product_unit @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_view_Overtical__chop__own__trans) ).
thf(342,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( vchop @ A @ B @ C )
=> ( ( own @ product_unit @ B )
= ( own @ product_unit @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(121,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: traffic,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ( len @ regular_regular @ A @ D @ E )
= ( len @ regular_regular @ B @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_hmlsl_Olen__stable__down) ).
thf(754,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: traffic,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ( len @ regular_regular @ A @ D @ E )
= ( len @ regular_regular @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(228,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_trans__less__add1) ).
thf(1181,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(142,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zero__le) ).
thf(835,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(836,plain,
! [TA: $tType,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(cnf,[status(esa)],[835]) ).
thf(62,axiom,
! [A: view_ext @ product_unit] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
=> ? [B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_view_Ohorizontal__chop__non__empty) ).
thf(426,plain,
! [A: view_ext @ product_unit] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
=> ? [B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(108,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ~ ? [D: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ D )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ D )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ D )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ D )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_local_Ohmlsl_Otwo__res__no__car) ).
thf(690,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ~ ? [D: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ D )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ D )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ D )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ D )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(118,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ A @ B @ C ) ) )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit,F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ A @ D @ E )
& ( hchop @ E @ G @ F )
& ( ( len @ regular_regular @ G @ B @ C )
= ( ext @ product_unit @ G ) )
& ( ( real_length @ ( len @ regular_regular @ G @ B @ C ) )
= ( real_length @ ( len @ regular_regular @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_hmlsl_Olen__fills__subview) ).
thf(739,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ A @ B @ C ) ) )
=> ? [D: view_ext @ product_unit,E: view_ext @ product_unit,F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ A @ D @ E )
& ( hchop @ E @ G @ F )
& ( ( len @ regular_regular @ G @ B @ C )
= ( ext @ product_unit @ G ) )
& ( ( real_length @ ( len @ regular_regular @ G @ B @ C ) )
= ( real_length @ ( len @ regular_regular @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(112,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ~ ? [C: cars] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_local_Ohmlsl_Ofree__no__res) ).
thf(712,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ~ ? [C: cars] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(191,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_nat__add__left__cancel__le) ).
thf(1003,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(27,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_add__right__cancel) ).
thf(310,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(197,axiom,
( ( ord_less_eq @ ( view_ext @ product_unit ) )
= ( ^ [A: view_ext @ product_unit,B: view_ext @ product_unit] :
? [C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit,F: view_ext @ product_unit,G: view_ext @ product_unit,H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ B @ F @ C )
& ( hchop @ C @ D @ G )
& ( vchop @ D @ I @ E )
& ( vchop @ E @ A @ H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_view_Osomewhere__leq) ).
thf(1053,plain,
( ( ord_less_eq @ ( view_ext @ product_unit ) )
= ( ^ [A: view_ext @ product_unit,B: view_ext @ product_unit] :
? [C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit,F: view_ext @ product_unit,G: view_ext @ product_unit,H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( hchop @ B @ F @ C )
& ( hchop @ C @ D @ G )
& ( vchop @ D @ I @ E )
& ( vchop @ E @ A @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_nat__le__linear) ).
thf(840,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(68,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(463,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(71,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_add__le__mono) ).
thf(470,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less_eq @ nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_add__leD1) ).
thf(544,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less_eq @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(102,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: traffic,D: cars] :
( ( ( ord_less_eq @ real_int @ ( ext @ product_unit @ A ) @ ( ext @ product_unit @ B ) )
& ( ( own @ product_unit @ A )
= ( own @ product_unit @ B ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ A @ C @ D ) ) ) )
=> ( ord_less_eq @ real_int @ ( len @ regular_regular @ A @ C @ D ) @ ( len @ regular_regular @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_hmlsl_Oview__leq__len__leq) ).
thf(656,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: traffic,D: cars] :
( ( ( ord_less_eq @ real_int @ ( ext @ product_unit @ A ) @ ( ext @ product_unit @ B ) )
& ( ( own @ product_unit @ A )
= ( own @ product_unit @ B ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( len @ regular_regular @ A @ C @ D ) ) ) )
=> ( ord_less_eq @ real_int @ ( len @ regular_regular @ A @ C @ D ) @ ( len @ regular_regular @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(214,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_less__zeroE) ).
thf(1140,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(152,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_trans__less__add2) ).
thf(859,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(202,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_less__not__refl) ).
thf(1084,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1448,plain,
! [C: nat,B: nat,A: nat] :
( ( A
!= ( zero_zero @ nat ) )
| ( ( ord_less @ nat @ A @ ( one_one @ nat ) )
!= ( ord_less @ nat @ ( plus_plus @ nat @ B @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[614,1098]) ).
thf(1449,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( one_one @ nat ) )
!= ( zero_zero @ nat ) ),
inference(pattern_uni,[status(thm)],[1448:[bind(A,$thf( plus_plus @ nat @ D @ ( one_one @ nat ) )),bind(B,$thf( D )),bind(C,$thf( one_one @ nat ))]]) ).
thf(1457,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( one_one @ nat ) )
!= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[1449]) ).
thf(1459,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( one_one @ nat ) )
!= ( zero_zero @ nat ) ),
inference(simp,[status(thm)],[1457]) ).
thf(220,axiom,
! [TA: $tType,TB: $tType,A: traffic,B: traffic > ( view_ext @ product_unit ) > $o,C: view_ext @ product_unit] :
( ( ! [D: traffic] :
( ( abstract @ A @ D )
=> ! [E: TB] : ( B @ D @ ( move @ A @ D @ C ) ) ) )
= ( ! [D: TA,E: traffic] :
( ( abstract @ A @ E )
=> ( B @ E @ ( move @ A @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_local_Ohmlsl_Oglobally__all__iff_H) ).
thf(1157,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(125,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: traffic,E: cars] :
( ( ( hchop @ A @ B @ C )
& ( ( len @ regular_regular @ B @ D @ E )
= ( ext @ product_unit @ B ) )
& ( ( len @ regular_regular @ C @ D @ E )
= ( ext @ product_unit @ C ) ) )
=> ( ( len @ regular_regular @ A @ D @ E )
= ( ext @ product_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_hmlsl_Olen__compose__hchop) ).
thf(771,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: traffic,E: cars] :
( ( ( hchop @ A @ B @ C )
& ( ( len @ regular_regular @ B @ D @ E )
= ( ext @ product_unit @ B ) )
& ( ( len @ regular_regular @ C @ D @ E )
= ( ext @ product_unit @ C ) ) )
=> ( ( len @ regular_regular @ A @ D @ E )
= ( ext @ product_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(3099,plain,
! [D: $o,C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ~ ( A @ B @ C )
| ~ ( canoni770627133id_add @ $o )
| ~ ( ord_less @ $o @ D @ $true )
| ( ( A @ B @ ( sk9 @ C @ B @ A ) )
!= ( zero_zero @ $o ) ) ),
inference(paramod_ordered,[status(thm)],[266,785]) ).
thf(3309,plain,
! [A: $o] :
( ~ ( zero_zero @ $o )
| ~ ( canoni770627133id_add @ $o )
| ~ ( ord_less @ $o @ A @ $true ) ),
inference(pre_uni,[status(thm)],[3099:[bind(A,$thf( ^ [E: traffic] : ^ [F: view_ext @ product_unit] : ( zero_zero @ $o ) ))]]) ).
thf(3593,plain,
! [A: $o] :
( ~ ( zero_zero @ $o )
| ~ ( canoni770627133id_add @ $o )
| ~ ( ord_less @ $o @ A @ $true ) ),
inference(simp,[status(thm)],[3309]) ).
thf(200,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ! [D: traffic] :
( ( create_reservation @ B @ A @ D )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ D @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ D ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) )
=> ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_hmlsl__regular_Oreservation2) ).
thf(1062,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ! [D: traffic] :
( ( create_reservation @ B @ A @ D )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ D @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ D ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) )
=> ( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
| ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(51,axiom,
cancel_semigroup_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__semigroup__add_7) ).
thf(390,plain,
cancel_semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(56,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( vchop @ A @ B @ C )
=> ( ( ( real_length @ ( ext @ product_unit @ A ) )
= ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( real_length @ ( ext @ product_unit @ A ) )
= ( real_length @ ( ext @ product_unit @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_view_Overtical__chop__length__stable) ).
thf(401,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( vchop @ A @ B @ C )
=> ( ( ( real_length @ ( ext @ product_unit @ A ) )
= ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( real_length @ ( ext @ product_unit @ A ) )
= ( real_length @ ( ext @ product_unit @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(182,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_infinite__descent__measure) ).
thf(961,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(813,plain,
( ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) )
= ( ord_less_eq @ nat ) ),
inference(lifteq,[status(thm)],[812]) ).
thf(162,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_add__less__mono1) ).
thf(896,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(176,axiom,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit] :
( ( ( ( real_length @ ( len @ regular_regular @ A @ B @ C ) )
= ( zero_zero @ real ) )
& ( ord_less_eq @ ( view_ext @ product_unit ) @ D @ A ) )
=> ( ( real_length @ ( len @ regular_regular @ D @ B @ C ) )
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hmlsl_Olen__empty__subview) ).
thf(946,plain,
! [A: view_ext @ product_unit,B: traffic,C: cars,D: view_ext @ product_unit] :
( ( ( ( real_length @ ( len @ regular_regular @ A @ B @ C ) )
= ( zero_zero @ real ) )
& ( ord_less_eq @ ( view_ext @ product_unit ) @ D @ A ) )
=> ( ( real_length @ ( len @ regular_regular @ D @ B @ C ) )
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(258,plain,
! [C: view_ext @ product_unit,B: traffic,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( A @ B @ ( sk5 @ C @ B @ A ) )
| ~ ( A @ B @ ( sk7 @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[254]) ).
thf(128,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( clm @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_local_Ohmlsl_Oclm__compose) ).
thf(786,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( clm @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( clm @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( clm @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1285,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ~ ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) )
| ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) ) ),
inference(bool_ext,[status(thm)],[243]) ).
thf(1290,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
| ~ ( canoni770627133id_add @ TA )
| ~ ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ),
inference(lifteq,[status(thm)],[1285]) ).
thf(1292,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
| ~ ( canoni770627133id_add @ TA )
| ( A
!= ( zero_zero @ TA ) )
| ( B
!= ( zero_zero @ TA ) ) ),
inference(cnf,[status(esa)],[1290]) ).
thf(1293,plain,
! [TA: $tType,B: TA,A: TA] :
( ( A
!= ( zero_zero @ TA ) )
| ( B
!= ( zero_zero @ TA ) )
| ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
| ~ ( canoni770627133id_add @ TA ) ),
inference(lifteq,[status(thm)],[1292]) ).
thf(1294,plain,
! [TA: $tType] :
( ( ( plus_plus @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) )
| ~ ( canoni770627133id_add @ TA ) ),
inference(simp,[status(thm)],[1293]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_linorder__neqE__nat) ).
thf(536,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(234,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( ( B @ D @ G )
| ( C @ D @ G ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( B @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(64,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_ex__least__nat__le) ).
thf(433,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(77,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ C @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ C @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ C @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ D @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ D @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ D @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_local_Ohmlsl_Ofree__decompose) ).
thf(510,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
=> ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ C @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ C @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ C @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ D @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ D @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ D @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(141,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( real_length @ ( ext @ product_unit @ B ) )
= ( zero_zero @ real ) )
| ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_local_Ohmlsl_Olength__geq__zero) ).
thf(832,plain,
! [A: view_ext @ product_unit] :
( ( ( real_length @ ( ext @ product_unit @ A ) )
= ( zero_zero @ real ) )
| ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_measure__induct) ).
thf(684,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_eq__imp__le) ).
thf(800,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(65,axiom,
! [A: nat_int,B: nat_int] :
( ( ord_less @ nat_int @ A @ B )
=> ( ord_less @ nat @ ( nat_card @ A ) @ ( nat_card @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_card__subset__less) ).
thf(447,plain,
! [A: nat_int,B: nat_int] :
( ( ord_less @ nat_int @ A @ B )
=> ( ord_less @ nat @ ( nat_card @ A ) @ ( nat_card @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(183,axiom,
! [A: real,B: traffic,C: view_ext @ product_unit] :
( ( ( real_length @ ( ext @ product_unit @ C ) )
= A )
= ( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( vchop @ C @ D @ E )
& ( ( real_length @ ( ext @ product_unit @ D ) )
= A )
& ( ( real_length @ ( ext @ product_unit @ E ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_local_Ohmlsl_Olength__vchop__stable) ).
thf(967,plain,
! [A: real,B: view_ext @ product_unit] :
( ( ( real_length @ ( ext @ product_unit @ B ) )
= A )
= ( ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( vchop @ B @ C @ D )
& ( ( real_length @ ( ext @ product_unit @ C ) )
= A )
& ( ( real_length @ ( ext @ product_unit @ D ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(137,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_less__irrefl__nat) ).
thf(818,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(150,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_not__gr__zero) ).
thf(854,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(154,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
= ( ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_local_Ohmlsl_Olength__dense) ).
thf(865,plain,
! [A: view_ext @ product_unit] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ A ) ) )
= ( ? [B: view_ext @ product_unit,C: view_ext @ product_unit] :
( ( hchop @ A @ B @ C )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(48,axiom,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit,C: view_ext @ product_unit] : ( vchop @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_view_Overtical__chop1) ).
thf(373,plain,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit,C: view_ext @ product_unit] : ( vchop @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(261,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( ( A @ D @ F )
| ( B @ D @ F ) )
& ( C @ D @ G ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( B @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(cnf,[status(esa)],[260]) ).
thf(262,plain,
! [E: view_ext @ product_unit,D: traffic,C: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,A: traffic > ( view_ext @ product_unit ) > $o] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( ( A @ D @ F )
| ( B @ D @ F ) )
& ( C @ D @ G ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( hchop @ E @ F @ G )
& ( B @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(25,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( vchop @ G @ H @ I )
& ( B @ D @ H )
& ( C @ D @ I ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( vchop @ F @ H @ I )
& ( A @ D @ H )
& ( B @ D @ I ) )
& ( C @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_local_Ohmlsl_Ov__chop__assoc) ).
thf(305,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( vchop @ G @ H @ I )
& ( B @ D @ H )
& ( C @ D @ I ) ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ? [H: view_ext @ product_unit,I: view_ext @ product_unit] :
( ( vchop @ F @ H @ I )
& ( A @ D @ H )
& ( B @ D @ I ) )
& ( C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit] : ( hchop @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_view_Ohorizontal__chop__empty__right) ).
thf(326,plain,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit] : ( hchop @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(44,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_add__eq__0__iff__both__eq__0) ).
thf(358,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(140,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ nat @ A @ C )
=> ~ ( ord_less_eq @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_add__leE) ).
thf(828,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ nat @ A @ C )
=> ~ ( ord_less_eq @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(129,axiom,
zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_9) ).
thf(796,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(22,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( ( A @ D @ F )
| ( B @ D @ F ) )
& ( C @ D @ G ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( B @ D @ F )
& ( C @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_local_Ohmlsl_Ovchop__disj__distr2) ).
thf(294,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic > ( view_ext @ product_unit ) > $o,C: traffic > ( view_ext @ product_unit ) > $o,D: traffic,E: view_ext @ product_unit] :
( ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( ( A @ D @ F )
| ( B @ D @ F ) )
& ( C @ D @ G ) ) )
= ( ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( A @ D @ F )
& ( C @ D @ G ) )
| ? [F: view_ext @ product_unit,G: view_ext @ product_unit] :
( ( vchop @ E @ F @ G )
& ( B @ D @ F )
& ( C @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(168,axiom,
wellorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Owellorder_11) ).
thf(918,plain,
wellorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(161,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_local_Ohmlsl_Ores__compose) ).
thf(886,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(58,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_nat__add__left__cancel__less) ).
thf(415,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(54,axiom,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
= ( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_local_Ohmlsl_Ores__dense) ).
thf(395,plain,
! [A: cars,B: traffic,C: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( len @ regular_regular @ C @ B @ A )
= ( ext @ product_unit @ C ) )
& ( ( restrict @ C @ ( res @ B ) @ A )
= ( lan @ product_unit @ C ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) ) )
= ( ? [D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( hchop @ C @ D @ E )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( len @ regular_regular @ D @ B @ A )
= ( ext @ product_unit @ D ) )
& ( ( restrict @ D @ ( res @ B ) @ A )
= ( lan @ product_unit @ D ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ E ) ) )
& ( ( len @ regular_regular @ E @ B @ A )
= ( ext @ product_unit @ E ) )
& ( ( restrict @ E @ ( res @ B ) @ A )
= ( lan @ product_unit @ E ) )
& ( ( nat_card @ ( lan @ product_unit @ E ) )
= ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_add__le__mono1) ).
thf(464,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(211,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less_eq @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_add__leD2) ).
thf(1129,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less_eq @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(218,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_gr__zeroI) ).
thf(1152,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(92,axiom,
! [A: traffic,B: view_ext @ product_unit] :
? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
=> ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [D: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ D ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ D )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ D )
= ( bot_bot @ nat_int ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_local_Ohmlsl_Oclm__not__free) ).
thf(596,plain,
! [A: traffic,B: view_ext @ product_unit] :
? [C: cars] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( len @ regular_regular @ B @ A @ C )
= ( ext @ product_unit @ B ) )
& ( ( restrict @ B @ ( clm @ A ) @ C )
= ( lan @ product_unit @ B ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) ) )
=> ~ ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [D: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ D ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ D )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ D )
= ( bot_bot @ nat_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(1019,plain,
ord_less_eq @ ( view_ext @ product_unit ) @ sk77 @ ( move @ ts3 @ ts @ v ),
inference(cnfConj,[status(thm)],[1016]) ).
thf(148,axiom,
strict2144017051up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_2) ).
thf(850,plain,
strict2144017051up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(882,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ) ),
inference(lifteq,[status(thm)],[881]) ).
thf(1268,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A )
= ( ^ [B: nat] :
? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ) ),
inference(func_ext,[status(esa)],[882]) ).
thf(87,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_not__less0) ).
thf(575,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(31,axiom,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit] : ( hchop @ A @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_view_Ohorizontal__chop__empty__left) ).
thf(322,plain,
! [A: view_ext @ product_unit] :
? [B: view_ext @ product_unit] : ( hchop @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(801,plain,
! [B: nat,A: nat] :
( ( A != B )
| ( ord_less_eq @ nat @ A @ B ) ),
inference(cnf,[status(esa)],[800]) ).
thf(802,plain,
! [B: nat,A: nat] :
( ( A != B )
| ( ord_less_eq @ nat @ A @ B ) ),
inference(lifteq,[status(thm)],[801]) ).
thf(803,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(simp,[status(thm)],[802]) ).
thf(37,axiom,
! [A: traffic,B: cars,C: traffic] :
( ( create_reservation @ A @ B @ C )
=> ( ord_less_eq @ nat_int @ ( clm @ A @ B ) @ ( res @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_traffic_Ocreate__res__subseteq2) ).
thf(337,plain,
! [A: traffic,B: cars,C: traffic] :
( ( create_reservation @ A @ B @ C )
=> ( ord_less_eq @ nat_int @ ( clm @ A @ B ) @ ( res @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(175,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_less__or__eq__imp__le) ).
thf(940,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(43,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ C @ D @ E ) )
=> ? [F: view_ext @ product_unit] :
( ( hchop @ A @ F @ E )
& ( hchop @ F @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_view_Ohorizontal__chop__assoc1) ).
thf(354,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: view_ext @ product_unit,E: view_ext @ product_unit] :
( ( ( hchop @ A @ B @ C )
& ( hchop @ C @ D @ E ) )
=> ? [F: view_ext @ product_unit] :
( ( hchop @ A @ F @ E )
& ( hchop @ F @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(170,axiom,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: traffic,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ( len @ regular_regular @ B @ D @ E )
= ( len @ regular_regular @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_hmlsl_Olen__stable) ).
thf(923,plain,
! [A: view_ext @ product_unit,B: view_ext @ product_unit,C: view_ext @ product_unit,D: traffic,E: cars] :
( ( vchop @ A @ B @ C )
=> ( ( len @ regular_regular @ B @ D @ E )
= ( len @ regular_regular @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(229,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add) ).
thf(1184,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(103,axiom,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
= ( ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ C @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ C @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ C @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ D @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ D @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ D @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_local_Ohmlsl_Ofree__dense) ).
thf(659,plain,
! [A: traffic,B: view_ext @ product_unit] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ B ) ) )
& ( ( nat_card @ ( lan @ product_unit @ B ) )
= ( one_one @ nat ) )
& ! [C: cars] :
( ( ( real_length @ ( len @ regular_regular @ B @ A @ C ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ B @ ( clm @ A ) @ C )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ B @ ( res @ A ) @ C )
= ( bot_bot @ nat_int ) ) ) ) )
= ( ? [C: view_ext @ product_unit,D: view_ext @ product_unit] :
( ( hchop @ B @ C @ D )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ C ) ) )
& ( ( nat_card @ ( lan @ product_unit @ C ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ C @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ C @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ C @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( real_length @ ( ext @ product_unit @ D ) ) )
& ( ( nat_card @ ( lan @ product_unit @ D ) )
= ( one_one @ nat ) )
& ! [E: cars] :
( ( ( real_length @ ( len @ regular_regular @ D @ A @ E ) )
= ( zero_zero @ real ) )
| ( ( ( restrict @ D @ ( clm @ A ) @ E )
= ( bot_bot @ nat_int ) )
& ( ( restrict @ D @ ( res @ A ) @ E )
= ( bot_bot @ nat_int ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(81,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(543,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(91,axiom,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ! [D: traffic] :
( ( abstract @ B @ D )
=> ( A @ D @ ( move @ B @ D @ C ) ) )
=> ! [D: traffic] :
( ( abstract @ B @ D )
=> ! [E: traffic] :
( ( abstract @ D @ E )
=> ( A @ E @ ( move @ D @ E @ ( move @ B @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_local_Ohmlsl_Oglobally__4) ).
thf(592,plain,
! [A: traffic > ( view_ext @ product_unit ) > $o,B: traffic,C: view_ext @ product_unit] :
( ! [D: traffic] :
( ( abstract @ B @ D )
=> ( A @ D @ ( move @ B @ D @ C ) ) )
=> ! [D: traffic] :
( ( abstract @ B @ D )
=> ! [E: traffic] :
( ( abstract @ D @ E )
=> ( A @ E @ ( move @ D @ E @ ( move @ B @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(4214,plain,
$false,
inference(e,[status(thm)],[629,1024,365,1168,1105,846,1179,555,909,628,249,994,308,449,878,614,1158,582,762,1137,2607,533,797,814,698,913,2146,930,885,301,2405,257,1055,785,949,542,702,751,817,1087,870,1572,881,325,289,316,475,253,238,937,806,353,821,2893,321,453,774,2137,988,243,265,507,380,546,761,1163,3011,233,452,334,910,957,825,952,392,297,275,729,260,862,349,407,630,361,665,1027,1128,710,842,324,916,467,1032,252,285,1106,578,1017,615,725,1096,1006,420,857,874,1143,1028,339,554,1461,476,970,1155,328,256,837,997,1131,721,1099,985,503,605,237,244,266,633,398,662,1026,1895,1167,953,1185,2936,750,1146,2894,375,733,904,423,1125,958,281,259,391,936,313,611,236,1464,1058,1107,1897,919,804,1194,681,274,1894,784,245,737,271,1011,419,758,1162,848,240,1029,1149,1177,330,345,367,552,983,883,1015,608,986,1000,431,278,868,267,851,1102,241,653,473,548,927,255,812,1081,342,754,1181,836,426,1166,580,690,1025,739,712,1003,263,1098,310,1053,840,463,470,951,2599,544,907,656,1140,612,859,250,1084,1459,539,1157,759,1453,771,3593,319,1062,390,401,961,813,896,748,946,258,418,786,1294,899,536,235,246,433,510,832,684,1161,800,447,967,818,854,865,373,835,262,305,326,358,828,796,294,918,886,415,395,464,1129,1152,596,1019,850,1268,575,322,486,803,337,940,354,923,1184,659,543,592,232,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP169^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 20:05:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.90/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.73/1.34 % [INFO] Parsing done (565ms).
% 2.73/1.36 % [INFO] Running in sequential loop mode.
% 4.18/1.87 % [INFO] eprover registered as external prover.
% 4.18/1.87 % [INFO] Scanning for conjecture ...
% 4.78/2.07 % [INFO] Found a conjecture (or negated_conjecture) and 278 axioms. Running axiom selection ...
% 5.35/2.29 % [INFO] Axiom selection finished. Selected 229 axioms (removed 49 axioms).
% 7.18/2.77 % [INFO] Problem is higher-order (TPTP THF).
% 7.62/2.82 % [INFO] Type checking passed.
% 7.62/2.83 % [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 ...
% 115.31/45.14 % External prover 'e' found a proof!
% 115.31/45.14 % [INFO] Killing All external provers ...
% 115.31/45.14 % Time passed: 44817ms (effective reasoning time: 43773ms)
% 115.31/45.14 % 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)>
% 115.31/45.14 % Axioms used in derivation (229): fact_127_restriction_Orestriction__card__mon2, fact_34_local_Ohmlsl_Oglobally__all__iff, fact_227_plus__nat_Oadd__0, fact_5_local_Ohmlsl_Ores__ge__zero, fact_19_local_Ohmlsl_Ohchop__weaken2, fact_59_local_Ohmlsl_Oclm__sing, fact_16_local_Ohmlsl_Ores__at__most__two, fact_180_traffic_OatLeastOneRes, fact_32_local_Ohmlsl_Oglobally__refl, fact_83_one__reorient, fact_160_less__or__eq__imp__le, tcon_Real_Oreal___Groups_Oone_10, fact_177_local_Ohmlsl_Owidth__ge, fact_41_hmlsl_Olen__stable, fact_82_view_Overtical__chop__singleton, fact_52_hmlsl_Olen__fills__subview, fact_216_add__leE, fact_77_hmlsl__regular_Obackwards__c__res__stab, fact_233_less__eqE, fact_199_add__is__0, fact_252_not__add__less1, fact_7_abs, fact_134_card__non__empty__geq__one, fact_85_view_Ohorizontal__chop__assoc1, fact_71_local_Ohmlsl_Ofree__ge__zero, fact_43_hmlsl_Olen__view__hchop__left, fact_157_less__mono__imp__le__mono, fact_222_add__le__mono, fact_65_local_Ohmlsl_Ofree__decompose, fact_187_add_Oleft__neutral, fact_174_less__eq__nat_Osimps_I1_J, fact_120_restriction_Orestriction__stable2, fact_95_zero__less__iff__neq__zero, fact_243_add__strict__mono, fact_132_le0, fact_138_infinite__descent__measure, fact_27_local_Ohmlsl_Ovchop__disj__distr2, fact_195_add__eq__0__iff__both__eq__0, fact_97_not__less__zero, fact_58_local_Ohmlsl_Oclm__sing__not__interrupted, fact_86_view_Ohorizontal__chop__assoc2, fact_105_view_Osomewhere__leq, fact_40_hmlsl_Olen__stable__down, tcon_Real_Oreal___Groups_Omonoid__add_8, fact_70_local_Ohmlsl_Ofree__no__clm, fact_53_d__def, fact_108_hmlsl__regular_Obackwards__res__act, tcon_Product__Type_Ounit___Orderings_Owellorder_11, fact_226_nat__le__iff__add, fact_84_view_Ohorizontal__chop1, fact_26_local_Ohmlsl_Ohchop__assoc, fact_76_le__zero__eq, fact_11_local_Ohmlsl_Ores__decompose, fact_87_view_Ohorizontal__chop__empty__left, fact_247_less__add__eq__less, fact_25_local_Ohmlsl_Ohchop__disj__distr1, fact_167_le__trans, fact_39_hmlsl_Olen__stable__up, fact_18_local_Ohmlsl_Oclm__ge__zero, fact_81_zero__reorient, fact_112_hmlsl_Oext__eq__len__eq, fact_228_add__eq__self__zero, fact_201_nat__add__left__cancel__less, fact_107_restriction_Orestriction__card__somewhere__mon, fact_38_local_Ohmlsl_Olength__vchop__stable, fact_2_local_Ohmlsl_Olength__geq__zero, fact_141_nat__less__induct, fact_46_wd__clm_Ohyps_I2_J, fact_196_zero__eq__add__iff__both__eq__0, fact_144_less__not__refl2, fact_224_trans__le__add1, fact_66_local_Ohmlsl_Ofree__compose, fact_15_local_Ohmlsl_Otwo__lanes__no__car, tcon_Nat_Onat___Groups_Oone, fact_111_hmlsl__regular_Oreservation, tcon_Nat_Onat___Groups_Ocancel__semigroup__add, fact_162_less__imp__le__nat, fact_172_ex__least__nat__le, fact_251_not__add__less2, fact_48_local_Ohmlsl_Olength__meld, fact_30_local_Ohmlsl_Ov__chop__weaken1, tcon_Real_Oreal___Groups_Ozero_9, fact_42_hmlsl_Olen__view__hchop__right, fact_79_hmlsl_Olen__sub__int, fact_169_card__subset__less, fact_219_add__leD1, fact_220_add__leD2, fact_103_view_Ohorizontal__chop__width__stable, fact_57_local_Ohmlsl_Oclm__compose, fact_63__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_Ats_H_A_092_060_094bold_062_092_060midarrow_062wdc_I_Ad_A_J_A_092_060_094bold_062_092_060rightarrow_062_Ats_H_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, tcon_Nat_Onat___Groups_Omonoid__add, fact_119_restriction_Orestriction__stable1, fact_178_traffic_Ocreate__res__subseteq2, fact_131_less__one, fact_88_view_Ohorizontal__chop__empty__right, fact_69_local_Ohmlsl_Ofree__no__res, fact_80_view_Overtical__chop__width__mon, fact_125_restriction_Orestrict__eq__lan__subs, fact_113_view_Ohorizontal__chop__own__trans, fact_135_bot__nat__0_Onot__eq__extremum, fact_123_restriction_Orestriction__mon1, fact_248_trans__less__add2, fact_36_wd__clm_Ohyps_I1_J, fact_93_view_Overtical__chop__empty__down, fact_175_card__subset__le, fact_44_hmlsl_Olen__compose__hchop, fact_73_hmlsl__regular_Obackwards__wdc__res__stab, fact_200_Nat_Oadd__0__right, fact_223_add__le__mono1, fact_4__092_060open_062_092_060exists_062v_H_092_060le_062move_Ats_Ats_H_H_Av_O_A_I0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ac_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ac_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_J_A_092_060and_062_A0_A_060_A_092_060parallel_062ext_Av_H_092_060parallel_062_A_092_060and_062_Alen_Av_H_Ats_H_H_Ae_A_061_Aext_Av_H_A_092_060and_062_Arestrict_Av_H_A_Ires_Ats_H_H_J_Ae_A_061_Alan_Av_H_A_092_060and_062_A_124lan_Av_H_124_A_061_A1_092_060close_062, fact_139_linorder__neqE__nat, fact_149_infinite__descent0__measure, fact_14_local_Ohmlsl_Oempty__no__car, fact_75_not__gr__zero, fact_140_infinite__descent, tcon_Nat_Onat___Orderings_Owellorder, fact_221_le__Suc__ex, fact_10_local_Ohmlsl_Ores__compose, fact_3_hmlsl_Olen__empty__subview, fact_60_local_Ohmlsl_Ono__clm__before__res2, fact_9_move__stab, fact_92_view_Overtical__chop__empty__up, tcon_Nat_Onat___Groups_Ozero, fact_148_measure__induct, fact_8__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062, fact_168_le__refl, fact_24_local_Ohmlsl_Ohchop__disj__distr2, fact_153_less__zeroE, fact_154_not__less0, fact_115_restriction_Orestrict__subseteq, fact_150_bot__nat__0_Oextremum__strict, fact_173_le__0__eq, fact_164_nat__less__le, fact_47_local_Ohmlsl_Olength__split, fact_56_local_Ohmlsl_Oclm__decompose, fact_96_gr__implies__not__zero, fact_155_not__gr0, fact_128_restriction_Orestriction__clm__leq__one, fact_72_local_Ohmlsl_Oclm__not__free, fact_90_view_Overtical__chop__assoc1, fact_50_hmlsl_Olen__empty__on__subview2, fact_163_nat__le__linear, fact_136_less__nat__zero__code, fact_98_gr__zeroI, fact_176_card__empty__zero, fact_215_add__gr__0, fact_51_hmlsl_Olen__empty__on__subview1, fact_124_restriction_Orestriction__eq__view__card, fact_217_le__add1, fact_35_local_Ohmlsl_Oglobally__4, fact_202_nat__add__left__cancel__le, fact_49_local_Ohmlsl_Olength__dense, fact_147_measure__induct__rule, fact_20_local_Ohmlsl_Ohchop__weaken1, fact_171_bot__nat__0_Oextremum__unique, fact_133_bot__nat__0_Oextremum, fact_55_local_Ohmlsl_Oclm__dense, fact_67_local_Ohmlsl_Owidth__free, fact_225_trans__le__add2, fact_151_infinite__descent0, fact_74_view_Ohorizontal__chop__non__empty, fact_137_neq0__conv, fact_143_less__not__refl3, fact_21_local_Ohmlsl_Ohchop__weaken, fact_68_local_Ohmlsl_Ores__not__free, tcon_Real_Oreal___Groups_Ocancel__semigroup__add_7, fact_0_neg, fact_62_local_Ohmlsl_Otwo__res__no__car, fact_129_restriction_Orestriction__card__mon__trans, fact_158_le__neq__implies__less, fact_145_less__not__refl, fact_142_less__irrefl__nat, fact_116_restriction_Orestrict__view, fact_152_gr__implies__not0, fact_61_local_Ohmlsl_Ono__clm__before__res, fact_122_restriction_Orestriction__mon2, fact_13_local_Ohmlsl_Ocar__one__lane__non__empty, fact_183_add__left__cancel, fact_109_hmlsl__regular_Oreservation2, fact_12_local_Ohmlsl_Ores__dense, fact_161_le__eq__less__or__eq, fact_159_Nat_Oex__has__greatest__nat, fact_33_local_Ohmlsl_Oglobally__all__iff_H, fact_22_local_Ohmlsl_Ohchop__neg2, fact_184_add__right__cancel, fact_6_local_Ohmlsl_Owidth__res, fact_181_local_Ohmlsl_Owidth__add1, fact_31_local_Ohmlsl_Ov__chop__assoc, fact_249_trans__less__add1, fact_118_restriction_Orestriction__stable, fact_165_le__antisym, fact_231_le__iff__add, fact_166_eq__imp__le, fact_146_nat__neq__iff, fact_78_hmlsl__regular_Obackwards__wdr__res__stab, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, fact_100_view_Ohorizontal__chop__leq1, tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_2, fact_94_zero__le, fact_101_view_Overtical__chop__leq2, fact_121_restriction_Orestrict__clm, fact_102_view_Overtical__chop__leq1, fact_250_add__less__mono1, fact_130_hmlsl__regular_Obackwards__res__stab, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_126_restriction_Orestriction__card__mon1, fact_89_view_Overtical__chop1, fact_182_local_Ohmlsl_Owidth__add2, fact_104_view_Overtical__chop__length__stable, fact_17_local_Ohmlsl_Otwo__res__not__res, fact_110_hmlsl__regular_Oreservation1, fact_99_view_Ohorizontal__chop__leq2, fact_179_traffic_OatMostOneClm, conj_0, fact_37_local_Ohmlsl_Owidth__hchop__stable, fact_218_le__add2, fact_117_restriction_Orestrict__res, fact_188_add_Oright__neutral, fact_106_hmlsl_Oview__leq__len__leq, fact_54_local_Ohmlsl_Owidth__clm, fact_23_local_Ohmlsl_Ohchop__neg1, fact_91_view_Overtical__chop__assoc2, fact_1_local_Ohmlsl_Osensors__ge, fact_64_local_Ohmlsl_Ofree__dense, fact_114_view_Overtical__chop__own__trans, fact_28_local_Ohmlsl_Ovchop__disj__distr1, fact_29_local_Ohmlsl_Ov__chop__weaken2, fact_170_bot__nat__0_Oextremum__uniqueI, fact_156_gr0I
% 115.31/45.14 % No. of inferences in proof: 621
% 115.31/45.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 44817 ms resp. 43773 ms w/o parsing
% 116.66/45.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 116.66/45.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------