%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP059^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 08:06:35 AM UTC 2026
% Result : Theorem 36.81s 7.47s
% Output : Refutation 32.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 245
% Syntax : Number of formulae : 492 ( 256 unt; 0 typ; 0 def)
% Number of atoms : 1058 ( 414 equ; 4 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 3792 ( 176 ~; 30 |; 84 &;2986 @)
% ( 0 <=>; 516 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 228 ( 228 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 14 con; 0-4 aty)
% Number of variables : 1002 ( 18 ^; 912 !; 72 ?;1002 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_c1059388851t_unit_type,type,
list_c1059388851t_unit: $tType ).
thf(config256849571t_unit_type,type,
config256849571t_unit: $tType ).
thf(list_message_p_v_type,type,
list_message_p_v: $tType ).
thf(set_message_p_v_type,type,
set_message_p_v: $tType ).
thf(message_p_v_type,type,
message_p_v: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(p_type,type,
p: $tType ).
thf(msgs_p1029620568t_unit_decl,type,
msgs_p1029620568t_unit: config256849571t_unit > message_p_v > nat ).
thf(enabled_p_v_s_decl,type,
enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
thf(isReceiverOf_p_v_decl,type,
isReceiverOf_p_v: p > message_p_v > $o ).
thf(firstO1414030372_p_v_s_decl,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > nat > nat ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(prefix1615116500t_unit_decl,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(prefix47729710ge_p_v_decl,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(last_c571238084t_unit_decl,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(last_message_p_v_decl,type,
last_message_p_v: list_message_p_v > message_p_v ).
thf(nil_co1338500125t_unit_decl,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(nil_message_p_v_decl,type,
nil_message_p_v: list_message_p_v ).
thf(nth_co1649820636t_unit_decl,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(nth_message_p_v_decl,type,
nth_message_p_v: list_message_p_v > nat > message_p_v ).
thf(suc_decl,type,
suc: nat > nat ).
thf(size_s1406904903t_unit_decl,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(size_s1168481041ge_p_v_decl,type,
size_s1168481041ge_p_v: list_message_p_v > nat ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(member_message_p_v_decl,type,
member_message_p_v: message_p_v > set_message_p_v > $o ).
thf(fe_decl,type,
fe: nat > list_c1059388851t_unit ).
thf(firstOccSet_decl,type,
firstOccSet: nat > set_message_p_v ).
thf(ft_decl,type,
ft: nat > list_message_p_v ).
thf(index_decl,type,
index: nat ).
thf(msgInSet_decl,type,
msgInSet: message_p_v ).
thf(msg_decl,type,
msg: message_p_v ).
thf(n0_decl,type,
n0: nat ).
thf(n1_decl,type,
n1: nat ).
thf(nMsg_decl,type,
nMsg: nat ).
thf(n_decl,type,
n: nat ).
thf(p2_decl,type,
p2: p ).
thf(105,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_bot__nat__0_Oextremum__uniqueI) ).
thf(645,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(238,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_n__not__Suc__n) ).
thf(1168,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(219,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_not__less__eq) ).
thf(1105,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_less__or__eq__imp__le) ).
thf(628,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)],[100]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ C )
=> ( ord_less_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_diff__less__mono2) ).
thf(777,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ C )
=> ( ord_less_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(20,axiom,
( ( nMsg != zero_zero_nat )
=> ( ~ ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) @ msg )
| ( msg
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_AssumptionSubset3_I6_J) ).
thf(308,plain,
( ( nMsg != zero_zero_nat )
=> ( ~ ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) @ msg )
| ( msg
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(135,axiom,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_AssumptionSubset3_I3_J) ).
thf(741,plain,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1,conjecture,
ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(247,plain,
~ ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,axiom,
( ( fe @ ( suc @ index ) )
!= nil_co1338500125t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_NotEmpty_I1_J) ).
thf(440,plain,
( ( fe @ ( suc @ index ) )
!= nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',fact_140_Nat_Oex__has__greatest__nat) ).
thf(269,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)],[10]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__Suc__eq) ).
thf(597,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(200,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( prefix47729710ge_p_v @ A @ B )
=> ( ord_less_nat @ ( size_s1168481041ge_p_v @ A ) @ ( size_s1168481041ge_p_v @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_PrefixListMonotonicity) ).
thf(1041,plain,
! [A: list_message_p_v,B: list_message_p_v] :
( ( prefix47729710ge_p_v @ A @ B )
=> ( ord_less_nat @ ( size_s1168481041ge_p_v @ A ) @ ( size_s1168481041ge_p_v @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(72,axiom,
( ? [A: nat] :
( ( ord_less_eq_nat @ n0 @ A )
& ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ A )
= msg ) )
=> ? [A: nat] :
( ( ord_less_eq_nat @ n @ A )
& ? [B: nat] :
( ( ord_less_eq_nat @ n0 @ B )
& ( ord_less_nat @ B @ ( size_s1168481041ge_p_v @ ( ft @ A ) ) )
& ( msg
= ( nth_message_p_v @ ( ft @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Case2ImplThesis) ).
thf(523,plain,
( ? [A: nat] :
( ( ord_less_eq_nat @ n0 @ A )
& ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ A )
= msg ) )
=> ? [A: nat] :
( ( ord_less_eq_nat @ n @ A )
& ? [B: nat] :
( ( ord_less_eq_nat @ n0 @ B )
& ( ord_less_nat @ B @ ( size_s1168481041ge_p_v @ ( ft @ A ) ) )
& ( msg
= ( nth_message_p_v @ ( ft @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(234,axiom,
! [A: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= zero_zero_nat )
= ( A = nil_message_p_v ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_length__0__conv) ).
thf(1158,plain,
! [A: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= zero_zero_nat )
= ( A = nil_message_p_v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(214,axiom,
! [A: nat,B: nat] : ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_diff__less__Suc) ).
thf(1078,plain,
! [A: nat,B: nat] : ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(73,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ nMsg @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( ( nth_message_p_v @ ( ft @ index ) @ A )
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_OccSameMsg) ).
thf(533,plain,
! [A: nat] :
( ( ord_less_eq_nat @ nMsg @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( ( nth_message_p_v @ ( ft @ index ) @ A )
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(236,axiom,
( msg
!= ( nth_message_p_v @ ( ft @ index ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_AssumpOcc6_I2_J) ).
thf(1164,plain,
( msg
!= ( nth_message_p_v @ ( ft @ index ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(210,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Suc__less__SucD) ).
thf(1063,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(177,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_gr__implies__not__zero) ).
thf(930,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(113,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_not__less__less__Suc__eq) ).
thf(670,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(42,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_less__Suc0) ).
thf(404,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(167,axiom,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
=> ( ( last_message_p_v @ A )
= ( nth_message_p_v @ A @ ( minus_minus_nat @ ( size_s1168481041ge_p_v @ A ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_last__conv__nth) ).
thf(898,plain,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
=> ( ( last_message_p_v @ A )
= ( nth_message_p_v @ A @ ( minus_minus_nat @ ( size_s1168481041ge_p_v @ A ) @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(193,axiom,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_diff__Suc__1) ).
thf(1001,plain,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(17,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ( prefix1615116500t_unit @ B @ C )
=> ( prefix1615116500t_unit @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_PrefixListTransitive) ).
thf(301,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ( prefix1615116500t_unit @ B @ C )
=> ( prefix1615116500t_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(54,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_AssumptionSubset2_I4_J) ).
thf(436,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(189,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_strict__inc__induct) ).
thf(973,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(202,axiom,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_zero__less__Suc) ).
thf(1046,plain,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(206,axiom,
ord_less_nat @ zero_zero_nat @ nMsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_AssumpOcc6_I1_J) ).
thf(1055,plain,
ord_less_nat @ zero_zero_nat @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(84,axiom,
ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_AssumptionFair_I2_J) ).
thf(570,plain,
ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(68,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zero__reorient) ).
thf(504,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(124,axiom,
ord_less_nat @ zero_zero_nat @ one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_less__numeral__extra_I1_J) ).
thf(702,plain,
ord_less_nat @ zero_zero_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(208,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_diff__zero) ).
thf(1059,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(178,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_gr__implies__not0) ).
thf(934,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(34,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_nat__neq__iff) ).
thf(357,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)],[34]) ).
thf(245,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ nMsg @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( msg
!= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_AssumptionSubset3_I5_J) ).
thf(1191,plain,
! [A: nat] :
( ( ord_less_eq_nat @ nMsg @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( msg
!= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(163,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_le__SucI) ).
thf(870,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(187,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_diff__right__commute) ).
thf(969,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(46,axiom,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
=> ( ( last_c571238084t_unit @ A )
= ( nth_co1649820636t_unit @ A @ ( minus_minus_nat @ ( size_s1406904903t_unit @ A ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_last__conv__nth) ).
thf(416,plain,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
=> ( ( last_c571238084t_unit @ A )
= ( nth_co1649820636t_unit @ A @ ( minus_minus_nat @ ( size_s1406904903t_unit @ A ) @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(12,axiom,
? [A: p] : ( isReceiverOf_p_v @ A @ msgInSet ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_AssumptionSubset2_I1_J) ).
thf(289,plain,
? [A: p] : ( isReceiverOf_p_v @ A @ msgInSet ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(59,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Ex__less__Suc) ).
thf(448,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(149,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_transitive__stepwise__le) ).
thf(789,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(57,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_nat__less__le) ).
thf(443,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(23,axiom,
! [A: nat] :
? [B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_Ex__list__of__length) ).
thf(321,plain,
! [A: nat] :
? [B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(232,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( ( nth_co1649820636t_unit @ A @ C )
= ( nth_co1649820636t_unit @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_PrefixSameOnLow) ).
thf(1151,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( ( nth_co1649820636t_unit @ A @ C )
= ( nth_co1649820636t_unit @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(196,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_le__less__Suc__eq) ).
thf(1020,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(186,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_le__zero__eq) ).
thf(966,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(243,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= ( size_s1168481041ge_p_v @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ A ) )
=> ( ( nth_message_p_v @ A @ C )
= ( nth_message_p_v @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_nth__equalityI) ).
thf(1183,plain,
! [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= ( size_s1168481041ge_p_v @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ A ) )
=> ( ( nth_message_p_v @ A @ C )
= ( nth_message_p_v @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_old_Onat_Oinject) ).
thf(485,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(227,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_not__gr__zero) ).
thf(1136,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_linorder__neqE__nat) ).
thf(834,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)],[156]) ).
thf(204,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_lessI) ).
thf(1051,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(151,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_le0) ).
thf(821,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(96,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ zero_zero_nat )
=> ( ~ ( B @ A )
=> ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C )
& ~ ( B @ ( suc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_NatPredicateTippingPoint) ).
thf(602,plain,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ zero_zero_nat )
=> ( ~ ( B @ A )
=> ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C )
& ~ ( B @ ( suc @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(101,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062) ).
thf(634,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(132,axiom,
! [A: nat,B: nat > message_p_v > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: message_p_v] : ( B @ C @ D ) ) )
= ( ? [C: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_message_p_v @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Skolem__list__nth) ).
thf(734,plain,
! [A: nat,B: nat > message_p_v > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: message_p_v] : ( B @ C @ D ) ) )
= ( ? [C: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_message_p_v @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(110,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_less__not__refl) ).
thf(660,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(69,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_zero__le) ).
thf(507,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(14,axiom,
? [A: p] : ( isReceiverOf_p_v @ A @ msg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Occ1) ).
thf(293,plain,
? [A: p] : ( isReceiverOf_p_v @ A @ msg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(183,axiom,
~ ? [A: nat] :
( ( ord_less_nat @ A @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) )
& ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ A )
& ( msg
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062) ).
thf(956,plain,
~ ? [A: nat] :
( ( ord_less_nat @ A @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) )
& ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ A )
& ( msg
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(212,axiom,
! [A: nat,B: message_p_v] :
( ( member_message_p_v @ B @ ( firstOccSet @ A ) )
=> ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062) ).
thf(1074,plain,
! [A: nat,B: message_p_v] :
( ( member_message_p_v @ B @ ( firstOccSet @ A ) )
=> ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(61,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ one_one_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( B @ C )
=> ( B @ ( suc @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_nat__induct__non__zero) ).
thf(452,plain,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ one_one_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( B @ C )
=> ( B @ ( suc @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(3,axiom,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_MinPredicate) ).
thf(248,plain,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(71,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_old_Onat_Oinducts) ).
thf(512,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(175,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Suc__diff__diff) ).
thf(925,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_le__Suc__eq) ).
thf(761,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__SucE) ).
thf(366,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(128,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_le__neq__implies__less) ).
thf(714,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)],[128]) ).
thf(27,axiom,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Suc__n__not__le__n) ).
thf(334,plain,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(170,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_le__eq__less__or__eq) ).
thf(910,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(216,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Suc__less__eq2) ).
thf(1091,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(153,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_gr0I) ).
thf(825,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(223,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_gr__zeroI) ).
thf(1123,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(80,axiom,
! [A: nat] : ( prefix47729710ge_p_v @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_IPrefixList) ).
thf(561,plain,
! [A: nat] : ( prefix47729710ge_p_v @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(49,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_neq0__conv) ).
thf(424,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(148,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_EnabledInSuc) ).
thf(788,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(43,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_zero__less__iff__neq__zero) ).
thf(407,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat,D: message_p_v] :
( ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_nat @ B @ ( size_s1406904903t_unit @ ( fe @ C ) ) )
& ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ C ) @ A ) @ D ) )
=> ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ C ) @ B ) @ D )
| ? [E: nat] :
( ( ord_less_eq_nat @ A @ E )
& ( ord_less_nat @ E @ ( size_s1168481041ge_p_v @ ( ft @ C ) ) )
& ( ( nth_message_p_v @ ( ft @ C ) @ E )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_MessageStaysOrConsumed) ).
thf(693,plain,
! [A: nat,B: nat,C: nat,D: message_p_v] :
( ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_nat @ B @ ( size_s1406904903t_unit @ ( fe @ C ) ) )
& ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ C ) @ A ) @ D ) )
=> ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ C ) @ B ) @ D )
| ? [E: nat] :
( ( ord_less_eq_nat @ A @ E )
& ( ord_less_nat @ E @ ( size_s1168481041ge_p_v @ ( ft @ C ) ) )
& ( ( nth_message_p_v @ ( ft @ C ) @ E )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Suc__le__mono) ).
thf(467,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(4,axiom,
! [A: nat] :
? [B: list_message_p_v] :
( ( size_s1168481041ge_p_v @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_Ex__list__of__length) ).
thf(252,plain,
! [A: nat] :
? [B: list_message_p_v] :
( ( size_s1168481041ge_p_v @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(99,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_diff__less__mono) ).
thf(625,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(241,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ B @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_diffs0__imp__equal) ).
thf(1178,plain,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ B @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(89,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( suc @ ( minus_minus_nat @ B @ ( suc @ A ) ) )
= ( minus_minus_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Suc__diff__Suc) ).
thf(583,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( suc @ ( minus_minus_nat @ B @ ( suc @ A ) ) )
= ( minus_minus_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(138,axiom,
( ( nth_co1649820636t_unit @ ( fe @ index ) @ nMsg )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102__092_060open_062fe_Aindex_A_B_AnMsg_A_061_Afe_A_ISuc_Aindex_J_A_B_AnMsg_092_060close_062) ).
thf(757,plain,
( ( nth_co1649820636t_unit @ ( fe @ index ) @ nMsg )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_diff__diff__cancel) ).
thf(682,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Suc__lessE) ).
thf(551,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Suc__lessI) ).
thf(324,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(11,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
!= ( size_s1168481041ge_p_v @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_neq__if__length__neq) ).
thf(285,plain,
! [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
!= ( size_s1168481041ge_p_v @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(136,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ ( suc @ D ) )
=> ( A @ D ) )
=> ( A @ ( minus_minus_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zero__induct__lemma) ).
thf(742,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ ( suc @ D ) )
=> ( A @ D ) )
=> ( A @ ( minus_minus_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(107,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_lift__Suc__mono__less__iff) ).
thf(650,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(131,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq_nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_full__nat__induct) ).
thf(725,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq_nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(218,axiom,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ! [C: list_c1059388851t_unit] :
( ! [D: list_c1059388851t_unit] :
( ( ord_less_nat @ ( size_s1406904903t_unit @ D ) @ ( size_s1406904903t_unit @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_length__induct) ).
thf(1096,plain,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ! [C: list_c1059388851t_unit] :
( ! [D: list_c1059388851t_unit] :
( ( ord_less_nat @ ( size_s1406904903t_unit @ D ) @ ( size_s1406904903t_unit @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(92,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Suc__neq__Zero) ).
thf(593,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(146,axiom,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_AssumptionSubset2_I3_J) ).
thf(783,plain,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(65,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_less__nat__zero__code) ).
thf(488,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(29,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Suc__le__D) ).
thf(339,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(137,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Zero__neq__Suc) ).
thf(753,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(112,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msgInSet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_AssumptionSubset2_I2_J) ).
thf(669,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(168,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_diff__induct) ).
thf(901,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(104,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_bot__nat__0_Oextremum__unique) ).
thf(642,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(195,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__not__refl2) ).
thf(1016,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(116,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(679,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(123,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_AssumptionCase1ImplThesis_H) ).
thf(701,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(134,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ A )
=> ( ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A )
!= msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_NotConsumedIntermediate) ).
thf(738,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ A )
=> ( ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A )
!= msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_nat_Oinject) ).
thf(654,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_zero__less__diff) ).
thf(622,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(157,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__Suc__eq__0__disj) ).
thf(837,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(179,axiom,
ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_ShorterTrace) ).
thf(938,plain,
ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_le__antisym) ).
thf(266,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)],[9]) ).
thf(35,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ n @ A )
=> ! [B: nat] :
( ( ord_less_nat @ B @ ( size_s1168481041ge_p_v @ ( ft @ A ) ) )
=> ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ B )
=> ( msg
!= ( nth_message_p_v @ ( ft @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_AssumptionFairContr) ).
thf(360,plain,
! [A: nat] :
( ( ord_less_eq_nat @ n @ A )
=> ! [B: nat] :
( ( ord_less_nat @ B @ ( size_s1168481041ge_p_v @ ( ft @ A ) ) )
=> ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ B )
=> ( msg
!= ( nth_message_p_v @ ( ft @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(21,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ( minus_minus_nat @ B @ A )
= ( minus_minus_nat @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_eq__diff__iff) ).
thf(311,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ( minus_minus_nat @ B @ A )
= ( minus_minus_nat @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(174,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_old_Onat_Oexhaust) ).
thf(921,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(109,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_less__zeroE) ).
thf(657,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_less__Suc__eq__le) ).
thf(558,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(237,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_AssumptionSubset_I3_J) ).
thf(1167,plain,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(182,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_diff__self__eq__0) ).
thf(953,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(90,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_lift__Suc__mono__less) ).
thf(586,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(169,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( minus_minus_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Nat_Odiff__diff__eq) ).
thf(906,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( minus_minus_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_diff__le__mono) ).
thf(573,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(95,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_AssumptionFair_I3_J) ).
thf(601,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(233,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_size__neq__size__imp__neq) ).
thf(1154,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(142,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ n1 @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( msgInSet
!= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_AssumptionSubset2_I5_J) ).
thf(772,plain,
! [A: nat] :
( ( ord_less_eq_nat @ n1 @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( msgInSet
!= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(127,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_bot__nat__0_Onot__eq__extremum) ).
thf(711,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(75,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Suc__le__eq) ).
thf(545,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_le__diff__iff_H) ).
thf(579,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(13,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_le__refl) ).
thf(291,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(228,axiom,
( ( (=) @ list_c1059388851t_unit )
= ( ^ [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( ( nth_co1649820636t_unit @ A @ C )
= ( nth_co1649820636t_unit @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_list__eq__iff__nth__eq) ).
thf(1139,plain,
( ( (=) @ list_c1059388851t_unit )
= ( ^ [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( ( nth_co1649820636t_unit @ A @ C )
= ( nth_co1649820636t_unit @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(58,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_less__irrefl__nat) ).
thf(445,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',fact_79_infinite__descent0) ).
thf(804,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)],[150]) ).
thf(141,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__Suc__induct) ).
thf(764,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(246,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_All__less__Suc) ).
thf(1194,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(155,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
=> ( ( nth_co1649820636t_unit @ ( fe @ index ) @ A )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_SameCfgOnLow) ).
thf(831,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
=> ( ( nth_co1649820636t_unit @ ( fe @ index ) @ A )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(47,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( prefix47729710ge_p_v @ A @ B )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ A ) )
=> ( ( nth_message_p_v @ A @ C )
= ( nth_message_p_v @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_PrefixSameOnLow) ).
thf(419,plain,
! [A: list_message_p_v,B: list_message_p_v] :
( ( prefix47729710ge_p_v @ A @ B )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ A ) )
=> ( ( nth_message_p_v @ A @ C )
= ( nth_message_p_v @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(203,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_le__SucE) ).
thf(1048,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(191,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( suc @ ( minus_minus_nat @ A @ one_one_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Suc__diff__1) ).
thf(996,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( suc @ ( minus_minus_nat @ A @ one_one_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(230,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Zero__not__Suc) ).
thf(1144,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(133,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_AssumpOcc6_I3_J) ).
thf(737,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ nMsg @ one_one_nat ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(240,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_gr0__conv__Suc) ).
thf(1175,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( minus_minus_nat @ B @ ( minus_minus_nat @ A @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_Suc__diff__eq__diff__pred) ).
thf(784,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( minus_minus_nat @ B @ ( minus_minus_nat @ A @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(221,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( suc @ B ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_diff__Suc__eq__diff__pred) ).
thf(1117,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( suc @ B ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(60,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_AssumptionSubset_I2_J) ).
thf(451,plain,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Suc__less__eq) ).
thf(567,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(70,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ nMsg @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( msg
!= ( nth_message_p_v @ ( ft @ index ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Occ5) ).
thf(509,plain,
! [A: nat] :
( ( ord_less_eq_nat @ nMsg @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( msg
!= ( nth_message_p_v @ ( ft @ index ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(201,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( ( nth_message_p_v @ ( ft @ index ) @ A )
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_SameMsgOnLow) ).
thf(1043,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( ( nth_message_p_v @ ( ft @ index ) @ A )
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Suc__lessD) ).
thf(434,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(215,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nat__induct) ).
thf(1080,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(31,axiom,
( ( enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq_nat @ n0 @ A )
& ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ A )
= msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_EnabledOrConsumedAtLast) ).
thf(345,plain,
( ( enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq_nat @ n0 @ A )
& ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ A )
= msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(166,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Suc__diff__le) ).
thf(895,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(172,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_lift__Suc__mono__le) ).
thf(915,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(145,axiom,
! [A: list_message_p_v] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ A ) )
= ( A != nil_message_p_v ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_length__greater__0__conv) ).
thf(780,plain,
! [A: list_message_p_v] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ A ) )
= ( A != nil_message_p_v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(81,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_AssumptionSubset3_I4_J) ).
thf(563,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_nat__le__linear) ).
thf(299,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)],[16]) ).
thf(51,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_bot__nat__0_Oextremum) ).
thf(431,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(171,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_diff__0__eq__0) ).
thf(912,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(118,axiom,
( ( fe @ index )
!= nil_co1338500125t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_NotEmpty_I2_J) ).
thf(685,plain,
( ( fe @ index )
!= nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Suc__leI) ).
thf(1076,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(91,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_neq__if__length__neq) ).
thf(589,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(5,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_one__reorient) ).
thf(255,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Suc__mono) ).
thf(648,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat_OdiscI) ).
thf(617,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(180,axiom,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J) ).
thf(939,plain,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(30,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_diff__commute) ).
thf(342,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(111,axiom,
( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq_nat @ n0 @ A )
& ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ A )
= msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_EnabledOrConsumed) ).
thf(663,plain,
( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq_nat @ n0 @ A )
& ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ A )
= msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__trans__Suc) ).
thf(548,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(242,axiom,
( ( size_s1168481041ge_p_v @ nil_message_p_v )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_list_Osize_I3_J) ).
thf(1181,plain,
( ( size_s1168481041ge_p_v @ nil_message_p_v )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__SucI) ).
thf(823,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(120,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_not0__implies__Suc) ).
thf(690,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(164,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_dec__induct) ).
thf(872,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(45,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_less__eq__nat_Osimps_I1_J) ).
thf(414,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',fact_169_less__mono__imp__le__mono) ).
thf(327,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)],[25]) ).
thf(8,axiom,
! [A: list_message_p_v,B: list_message_p_v,C: list_message_p_v] :
( ( prefix47729710ge_p_v @ A @ B )
=> ( ( prefix47729710ge_p_v @ B @ C )
=> ( prefix47729710ge_p_v @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_PrefixListTransitive) ).
thf(263,plain,
! [A: list_message_p_v,B: list_message_p_v,C: list_message_p_v] :
( ( prefix47729710ge_p_v @ A @ B )
=> ( ( prefix47729710ge_p_v @ B @ C )
=> ( prefix47729710ge_p_v @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(190,axiom,
! [A: nat,B: nat > config256849571t_unit > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: config256849571t_unit] : ( B @ C @ D ) ) )
= ( ? [C: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_co1649820636t_unit @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Skolem__list__nth) ).
thf(993,plain,
! [A: nat,B: nat > config256849571t_unit > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: config256849571t_unit] : ( B @ C @ D ) ) )
= ( ? [C: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_co1649820636t_unit @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(198,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Suc__inject) ).
thf(1025,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(15,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
!= ( size_s1168481041ge_p_v @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_size__neq__size__imp__neq) ).
thf(295,plain,
! [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
!= ( size_s1168481041ge_p_v @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(205,axiom,
! [A: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ A )
=> ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_SmallIndex) ).
thf(1053,plain,
! [A: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ A )
=> ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(114,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_not__less__zero) ).
thf(673,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(129,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( ( nth_co1649820636t_unit @ A @ C )
= ( nth_co1649820636t_unit @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_nth__equalityI) ).
thf(717,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( ( nth_co1649820636t_unit @ A @ C )
= ( nth_co1649820636t_unit @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_le__diff__iff) ).
thf(840,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Suc__leD) ).
thf(951,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(63,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_nat__induct__at__least) ).
thf(470,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(87,axiom,
! [A: list_c1059388851t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ A ) )
= ( A != nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_length__greater__0__conv) ).
thf(576,plain,
! [A: list_c1059388851t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ A ) )
= ( A != nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(125,axiom,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ( ( B = zero_zero_nat )
| ~ ( A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_MinPredicate2) ).
thf(703,plain,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ( ( B = zero_zero_nat )
| ~ ( A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(229,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_le__0__eq) ).
thf(1141,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(197,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_less__numeral__extra_I3_J) ).
thf(1023,plain,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(94,axiom,
ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062) ).
thf(600,plain,
ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(161,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_diff__is__0__eq_H) ).
thf(864,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(85,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ord_less_nat @ ( size_s1406904903t_unit @ A ) @ ( size_s1406904903t_unit @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_PrefixListMonotonicity) ).
thf(571,plain,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ord_less_nat @ ( size_s1406904903t_unit @ A ) @ ( size_s1406904903t_unit @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(217,axiom,
( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) )
= ( last_c571238084t_unit @ ( fe @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_LastOfIndex) ).
thf(1094,plain,
( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) )
= ( last_c571238084t_unit @ ( fe @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(40,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_old_Onat_Odistinct_I2_J) ).
thf(386,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(160,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_inc__induct) ).
thf(845,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(119,axiom,
( ord_less_nat
= ( ^ [A: nat] : ( ord_less_eq_nat @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_less__eq__Suc__le) ).
thf(688,plain,
( ord_less_nat
= ( ^ [A: nat] : ( ord_less_eq_nat @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(139,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_diff__le__self) ).
thf(759,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(165,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_old_Onat_Odistinct_I1_J) ).
thf(891,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(224,axiom,
( ( n1 != zero_zero_nat )
=> ( ~ ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) @ msgInSet )
| ( msgInSet
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_AssumptionSubset2_I6_J) ).
thf(1126,plain,
( ( n1 != zero_zero_nat )
=> ( ~ ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) @ msgInSet )
| ( msgInSet
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(244,axiom,
! [A: message_p_v,B: nat,C: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ C ) @ ( ft @ C ) @ A @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062) ).
thf(1189,plain,
! [A: message_p_v,B: nat,C: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ C ) @ ( ft @ C ) @ A @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ ( last_c571238084t_unit @ ( fe @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(159,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_le__numeral__extra_I3_J) ).
thf(844,plain,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(220,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_infinite__descent) ).
thf(1108,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)],[220]) ).
thf(36,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_diff__le__mono2) ).
thf(363,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(78,axiom,
! [A: nat] : ( prefix1615116500t_unit @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_IPrefixListEx) ).
thf(556,plain,
! [A: nat] : ( prefix1615116500t_unit @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(122,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_One__nat__def) ).
thf(699,plain,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(185,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_gr0__implies__Suc) ).
thf(963,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(18,axiom,
isReceiverOf_p_v @ p2 @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_AssumptionFair_I4_J) ).
thf(304,plain,
isReceiverOf_p_v @ p2 @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(209,axiom,
ord_less_eq_nat @ n1 @ nMsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_AssumptionSubset_I1_J) ).
thf(1062,plain,
ord_less_eq_nat @ n1 @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_eq__imp__le) ).
thf(258,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_less__one) ).
thf(351,plain,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(41,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_ex__least__nat__less) ).
thf(390,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(199,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_zero__induct) ).
thf(1030,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(52,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_Occ2) ).
thf(433,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(39,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zero__diff) ).
thf(383,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(74,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_nat__less__induct) ).
thf(536,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)],[74]) ).
thf(235,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_not__less__eq__eq) ).
thf(1161,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(226,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_less__imp__diff__less) ).
thf(1133,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(192,axiom,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_list_Osize_I3_J) ).
thf(999,plain,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Nat_OlessE) ).
thf(315,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__not__refl3) ).
thf(410,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7,axiom,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_le__numeral__extra_I4_J) ).
thf(262,plain,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(231,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Ex__less__Suc2) ).
thf(1148,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_Suc__le__lessD) ).
thf(422,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(162,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( suc @ ( minus_minus_nat @ A @ ( suc @ zero_zero_nat ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Suc__pred) ).
thf(867,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( suc @ ( minus_minus_nat @ A @ ( suc @ zero_zero_nat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(82,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_lift__Suc__antimono__le) ).
thf(564,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ C ) @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',fact_135_le__trans) ).
thf(305,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)],[19]) ).
thf(173,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__antisym) ).
thf(918,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(55,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_minus__nat_Odiff__0) ).
thf(437,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(239,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_bot__nat__0_Oextremum__strict) ).
thf(1172,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(207,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_not__gr0) ).
thf(1056,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(154,axiom,
! [A: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= zero_zero_nat )
= ( A = nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_length__0__conv) ).
thf(828,plain,
! [A: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= zero_zero_nat )
= ( A = nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(211,axiom,
! [A: list_message_p_v > $o,B: list_message_p_v] :
( ! [C: list_message_p_v] :
( ! [D: list_message_p_v] :
( ( ord_less_nat @ ( size_s1168481041ge_p_v @ D ) @ ( size_s1168481041ge_p_v @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_length__induct) ).
thf(1065,plain,
! [A: list_message_p_v > $o,B: list_message_p_v] :
( ! [C: list_message_p_v] :
( ! [D: list_message_p_v] :
( ( ord_less_nat @ ( size_s1168481041ge_p_v @ D ) @ ( size_s1168481041ge_p_v @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(176,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_less__imp__le__nat) ).
thf(928,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(184,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ ( suc @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_diff__Suc__less) ).
thf(960,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ ( suc @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(102,axiom,
~ ? [A: nat] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
& ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ A )
& ( msg
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062) ).
thf(635,plain,
~ ? [A: nat] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
& ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ A )
& ( msg
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(50,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nat_Odistinct_I1_J) ).
thf(427,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(130,axiom,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_less__numeral__extra_I4_J) ).
thf(723,plain,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(194,axiom,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J) ).
thf(1004,plain,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( B @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_diff__less) ).
thf(1120,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_diff__Suc__Suc) ).
thf(501,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',fact_189_ex__least__nat__le) ).
thf(369,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)],[38]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_le__imp__less__Suc) ).
thf(332,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(225,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_less__diff__iff) ).
thf(1129,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(28,axiom,
( ( (=) @ list_message_p_v )
= ( ^ [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= ( size_s1168481041ge_p_v @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ A ) )
=> ( ( nth_message_p_v @ A @ C )
= ( nth_message_p_v @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_list__eq__iff__nth__eq) ).
thf(337,plain,
( ( (=) @ list_message_p_v )
= ( ^ [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= ( size_s1168481041ge_p_v @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ A ) )
=> ( ( nth_message_p_v @ A @ C )
= ( nth_message_p_v @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( A
= ( suc @ ( minus_minus_nat @ A @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Suc__pred_H) ).
thf(354,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( A
= ( suc @ ( minus_minus_nat @ A @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(143,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ A )
=> ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ A ) @ msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_EnabledIntermediate) ).
thf(775,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ A )
=> ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ A ) @ msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(103,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_not__less0) ).
thf(639,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(115,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_All__less__Suc2) ).
thf(676,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(66,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( B @ D )
=> ( ( B @ ( suc @ D ) )
& ( C @ D ) ) ) )
=> ( ( B @ A )
=> ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_KeepProperty) ).
thf(491,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( B @ D )
=> ( ( B @ ( suc @ D ) )
& ( C @ D ) ) ) )
=> ( ( B @ A )
=> ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_diff__is__0__eq) ).
thf(708,plain,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(188,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ nMsg ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_Occ4) ).
thf(972,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ nMsg ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(17711,plain,
$false,
inference(e,[status(thm)],[645,1168,1105,628,777,308,741,247,440,269,597,1041,523,1158,1078,533,1164,1063,930,670,404,898,1001,301,436,973,1046,1055,570,504,702,1059,934,357,1191,870,969,416,289,448,789,443,321,1151,1020,966,1183,485,1136,834,1051,821,602,634,734,660,507,293,956,1074,452,248,512,925,761,366,714,334,910,1091,825,1123,561,424,788,407,693,467,252,625,1178,583,757,682,551,324,285,742,650,725,1096,593,783,488,339,753,669,901,642,1016,679,701,738,654,622,837,938,266,360,311,921,657,558,1167,953,586,906,573,601,1154,772,711,545,579,291,1139,445,804,764,1194,831,419,1048,996,1144,737,1175,784,1117,451,567,509,1043,434,1080,345,895,915,780,563,299,431,912,685,1076,589,255,648,617,939,342,663,548,1181,823,690,872,414,327,263,993,1025,295,1053,673,717,840,951,470,576,703,1141,1023,600,864,571,1094,386,845,688,759,891,1126,1189,844,1108,363,556,699,963,304,1062,258,351,390,1030,433,383,536,1161,1133,999,315,410,262,1148,422,867,564,305,918,437,1172,1056,828,1065,928,960,635,427,723,1004,1120,501,369,332,1129,337,354,775,639,676,491,708,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP059^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.06/0.12 % Computer : n012.cluster.edu
% 0.06/0.12 % Model : x86_64 x86_64
% 0.06/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.12 % Memory : 8046.5625MB
% 0.06/0.12 % OS : Linux 6.8.0-71-generic
% 0.06/0.12 % CPULimit : 300
% 0.06/0.12 % WCLimit : 300
% 0.06/0.12 % DateTime : Tue Sep 29 19:44:18 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.41/0.43 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.62 % [INFO] Parsing done (189ms).
% 1.19/0.63 % [INFO] Running in sequential loop mode.
% 1.70/0.81 % [INFO] eprover registered as external prover.
% 1.70/0.82 % [INFO] Scanning for conjecture ...
% 1.70/0.88 % [INFO] Found a conjecture (or negated_conjecture) and 244 axioms. Running axiom selection ...
% 1.91/0.95 % [INFO] Axiom selection finished. Selected 244 axioms (removed 0 axioms).
% 2.26/1.06 % [INFO] Problem is higher-order (TPTP THF).
% 2.26/1.08 % [INFO] Type checking passed.
% 2.26/1.08 % [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 ...
% 36.81/7.47 % External prover 'e' found a proof!
% 36.81/7.47 % [INFO] Killing All external provers ...
% 36.81/7.47 % Time passed: 7249ms (effective reasoning time: 6842ms)
% 36.81/7.47 % 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)>
% 36.81/7.47 % Axioms used in derivation (244): fact_99_diff__less, fact_226_Skolem__list__nth, fact_8_zero__less__diff, fact_233_LastOfIndex, fact_73_less__SucE, fact_106_IPrefixListEx, fact_207_AssumptionSubset3_I4_J, fact_103_ShorterTrace, fact_123_Occ5, fact_38_less__not__refl2, fact_203_length__greater__0__conv, fact_10_zero__less__Suc, fact_45_gr__implies__not__zero, fact_216_neq__if__length__neq, fact_175_le__diff__iff_H, fact_16_less__nat__zero__code, fact_44_zero__less__iff__neq__zero, fact_14_Suc__diff__diff, fact_149_zero__le, fact_78_bot__nat__0_Oextremum__strict, fact_182_dec__induct, fact_50_old_Onat_Oexhaust, fact_113_SameMsgOnLow, fact_104_NotEmpty_I1_J, fact_30_diff__right__commute, fact_125_diff__is__0__eq_H, fact_222_list_Osize_I3_J, fact_168_le__neq__implies__less, fact_201_EnabledIntermediate, fact_25_lessI, fact_183_inc__induct, fact_101_SameCfgOnLow, fact_218_Ex__list__of__length, fact_146_KeepProperty, fact_40_nat__neq__iff, fact_1_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, fact_234_EnabledOrConsumedAtLast, fact_13_diff__Suc__Suc, fact_114_le__zero__eq, fact_118_diff__diff__cancel, fact_187_less__eq__Suc__le, fact_176_diff__le__mono2, fact_108_NotEmpty_I2_J, fact_215_neq__if__length__neq, fact_231_EnabledInSuc, fact_192_diff__less__mono, fact_111_Occ1, fact_5_AssumptionSubset3_I3_J, fact_4_SmallIndex, fact_166_le__eq__less__or__eq, fact_138_nat__le__linear, fact_160_less__eq__nat_Osimps_I1_J, fact_46_not__less__zero, fact_77_Nat_OlessE, fact_56_nat__induct, fact_184_Suc__le__lessD, fact_217_Ex__list__of__length, fact_230_Case2ImplThesis, fact_159_transitive__stepwise__le, fact_235_last__conv__nth, fact_189_ex__least__nat__le, fact_136_eq__imp__le, fact_169_less__mono__imp__le__mono, fact_49_old_Onat_Oinducts, fact_6_AssumptionSubset2_I3_J, fact_200_AssumptionSubset3_I6_J, fact_191_less__diff__iff, fact_227_nth__equalityI, fact_86_minus__nat_Odiff__0, fact_51_Zero__not__Suc, fact_28_AssumptionSubset_I1_J, fact_132_AssumptionFairContr, fact_170_eq__diff__iff, fact_199_AssumptionSubset2_I6_J, fact_65_Suc__less__SucD, fact_186_less__Suc__eq__le, fact_54_zero__induct, fact_66_less__antisym, fact_232_AssumptionSubset2_I2_J, fact_53_Suc__neq__Zero, fact_7_Suc__pred, fact_210__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062, fact_2_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, fact_196_nat__induct__non__zero, fact_67_Suc__less__eq2, fact_165_less__imp__le__nat, fact_150_Suc__leD, fact_21_diff__zero, fact_185_le__less__Suc__eq, fact_243__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062, fact_229_EnabledOrConsumed, fact_180_Suc__leI, fact_107_NatPredicateTippingPoint, fact_48_not0__implies__Suc, fact_18_nat_Oinject, fact_26_bot__nat__0_Onot__eq__extremum, fact_141_PrefixListTransitive, fact_126_less__one, fact_75_Suc__lessE, fact_238_le__numeral__extra_I3_J, fact_209_MessageStaysOrConsumed, fact_115_Suc__le__mono, fact_239_less__numeral__extra_I3_J, fact_211_length__0__conv, fact_220_length__induct, fact_167_less__or__eq__imp__le, fact_163_bot__nat__0_Oextremum__uniqueI, fact_155_Suc__n__not__le__n, fact_36_less__irrefl__nat, fact_178_PrefixListMonotonicity, fact_161_le__0__eq, fact_93_gr0__implies__Suc, fact_79_infinite__descent0, fact_47_gr__zeroI, fact_80_gr__implies__not0, fact_219_length__induct, fact_35_nat__less__induct, fact_17_old_Onat_Oinject, fact_100_diff__Suc__less, fact_213_Occ2, fact_42_size__neq__size__imp__neq, fact_15_neq0__conv, fact_179_PrefixListMonotonicity, fact_143_MinPredicate, fact_76_Suc__lessD, fact_164_nat__less__le, fact_96_Ex__less__Suc2, fact_12_diff__self__eq__0, fact_112_AssumptionSubset2_I1_J, fact_148_PrefixSameOnLow, fact_43_diff__commute, fact_59_old_Onat_Odistinct_I2_J, fact_19_not__gr__zero, fact_102__092_060open_062fe_Aindex_A_B_AnMsg_A_061_Afe_A_ISuc_Aindex_J_A_B_AnMsg_092_060close_062, fact_151_le__SucE, fact_110_AssumpOcc6_I2_J, fact_24_Suc__mono, fact_109_AssumptionFair_I4_J, fact_9_less__Suc0, fact_63_less__Suc__induct, fact_173_diff__le__mono, fact_58_old_Onat_Odistinct_I1_J, fact_32_Suc__inject, fact_124_diff__is__0__eq, fact_116_le0, fact_152_le__SucI, fact_119__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062, fact_212_length__0__conv, fact_22_zero__diff, fact_81_less__zeroE, fact_198_Suc__diff__eq__diff__pred, fact_153_Suc__le__D, fact_87_diffs0__imp__equal, fact_74_Suc__lessI, fact_208_AssumptionSubset2_I4_J, fact_90_lift__Suc__mono__less__iff, fact_144_lift__Suc__antimono__le, fact_37_less__not__refl3, fact_133_AssumpOcc6_I3_J, fact_41_size__neq__size__imp__neq, fact_62_strict__inc__induct, fact_224_list__eq__iff__nth__eq, fact_34_infinite__descent, fact_134_le__refl, fact_72_less__SucI, fact_237__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062, fact_105_IPrefixList, fact_84_gr0I, fact_23_Suc__less__eq, fact_135_le__trans, fact_82_not__less0, fact_98_Suc__diff__Suc, fact_95_gr0__conv__Suc, fact_92_less__Suc__eq__0__disj, fact_68_All__less__Suc, fact_172_Nat_Odiff__diff__eq, fact_0_AssumpOcc6_I1_J, fact_69_not__less__eq, fact_20_cancel__comm__monoid__add__class_Odiff__cancel, fact_236_last__conv__nth, fact_3_AssumptionSubset_I3_J, fact_145_lift__Suc__mono__le, fact_142_PrefixListTransitive, fact_197_Suc__pred_H, fact_55_diff__induct, fact_29_zero__reorient, fact_194_diff__Suc__eq__diff__pred, fact_188_le__imp__less__Suc, fact_139_one__reorient, fact_137_le__antisym, fact_128_AssumptionSubset3_I5_J, fact_240_le__numeral__extra_I4_J, fact_120__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062, fact_154_le__Suc__eq, fact_11_diff__0__eq__0, fact_177_MinPredicate2, fact_129_AssumptionSubset2_I5_J, fact_241_less__numeral__extra_I4_J, fact_204_AssumptionFair_I2_J, fact_39_less__not__refl, fact_88_less__imp__diff__less, fact_85_zero__induct__lemma, fact_122_OccSameMsg, fact_242_less__numeral__extra_I1_J, fact_157_full__nat__induct, fact_83_not__gr0, fact_158_nat__induct__at__least, fact_33_linorder__neqE__nat, fact_71_Ex__less__Suc, fact_117_bot__nat__0_Oextremum, fact_174_diff__le__self, fact_147_PrefixSameOnLow, fact_31_n__not__Suc__n, fact_228_nth__equalityI, fact_205_Occ4, fact_214_AssumptionCase1ImplThesis_H, fact_89_diff__less__mono2, fact_127_diff__Suc__1, fact_195_ex__least__nat__less, fact_190_Suc__diff__le, fact_156_not__less__eq__eq, fact_131_Suc__diff__1, fact_193_One__nat__def, fact_70_less__Suc__eq, fact_130__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062, fact_61_not__less__less__Suc__eq, fact_171_le__diff__iff, fact_57_nat_OdiscI, fact_60_nat_Odistinct_I1_J, fact_91_lift__Suc__mono__less, fact_206_AssumptionFair_I3_J, fact_52_Zero__neq__Suc, fact_181_Suc__le__eq, fact_225_Skolem__list__nth, fact_121_NotConsumedIntermediate, fact_202_length__greater__0__conv, fact_94_All__less__Suc2, fact_162_bot__nat__0_Oextremum__unique, fact_27_AssumptionSubset_I2_J, fact_140_Nat_Oex__has__greatest__nat, fact_223_list__eq__iff__nth__eq, fact_64_less__trans__Suc, fact_221_list_Osize_I3_J, fact_97_diff__less__Suc
% 36.81/7.47 % No. of inferences in proof: 492
% 36.81/7.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7249 ms resp. 6842 ms w/o parsing
% 32.93/7.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.93/7.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------