%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP054^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 08:06:34 AM UTC 2026
% Result : Theorem 75.87s 14.88s
% Output : Refutation 77.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 263
% Syntax : Number of formulae : 575 ( 308 unt; 0 typ; 1 def)
% Number of atoms : 1231 ( 537 equ; 4 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 4104 ( 228 ~; 52 |; 91 &;3211 @)
% ( 0 <=>; 522 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 258 ( 258 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 42 usr; 14 con; 0-4 aty)
% Number of variables : 1124 ( 45 ^;1001 !; 77 ?;1124 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% 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(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(firstO1414030372_p_v_s_decl,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(minimalEnabled_p_v_s_decl,type,
minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $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(if_nat_decl,type,
if_nat: $o > nat > 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(tl_con485597044t_unit_decl,type,
tl_con485597044t_unit: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(tl_message_p_v_decl,type,
tl_message_p_v: list_message_p_v > list_message_p_v ).
thf(list_e1598815642t_unit_decl,type,
list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
thf(list_ex1_message_p_v_decl,type,
list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
thf(list_e581556831t_unit_decl,type,
list_e581556831t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
thf(list_ex_message_p_v_decl,type,
list_ex_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
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(remdup949903207t_unit_decl,type,
remdup949903207t_unit: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(remdup74979931ge_p_v_decl,type,
remdup74979931ge_p_v: list_message_p_v > list_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(collect_message_p_v_decl,type,
collect_message_p_v: ( message_p_v > $o ) > set_message_p_v ).
thf(member_message_p_v_decl,type,
member_message_p_v: message_p_v > set_message_p_v > $o ).
thf(consumedMsg_decl,type,
consumedMsg: message_p_v ).
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(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(sk1_decl,type,
sk1: ( message_p_v > $o ) > ( message_p_v > $o ) > message_p_v ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: message_p_v > $o,B: message_p_v > $o] :
@+[C: message_p_v] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(157,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_nat__neq__iff) ).
thf(892,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)],[157]) ).
thf(180,axiom,
ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_AssumptionFair_I2_J) ).
thf(993,plain,
ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1,conjecture,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(264,plain,
~ ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1311,plain,
( ~ $true
| ( ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= ( ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[993,264]) ).
thf(1312,plain,
( ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= ( ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ) ),
inference(simp,[status(thm)],[1311]) ).
thf(1316,plain,
( ( n1 != n0 )
| ( ( size_s1406904903t_unit @ ( fe @ n ) )
!= ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(simp,[status(thm)],[1312]) ).
thf(1319,plain,
( ( n1 != n0 )
| ( ( fe @ n )
!= ( fe @ index ) ) ),
inference(simp,[status(thm)],[1316]) ).
thf(1322,plain,
( ( n1 != n0 )
| ( n != index ) ),
inference(simp,[status(thm)],[1319]) ).
thf(192,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_nat__less__induct) ).
thf(1024,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)],[192]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',fact_211_diff__le__mono2) ).
thf(479,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)],[56]) ).
thf(243,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Suc__mono) ).
thf(1179,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)],[243]) ).
thf(126,axiom,
! [A: nat,B: list_message_p_v] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( tl_message_p_v @ B ) ) )
=> ( ( nth_message_p_v @ ( tl_message_p_v @ B ) @ A )
= ( nth_message_p_v @ B @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_nth__tl) ).
thf(777,plain,
! [A: nat,B: list_message_p_v] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( tl_message_p_v @ B ) ) )
=> ( ( nth_message_p_v @ ( tl_message_p_v @ B ) @ A )
= ( nth_message_p_v @ B @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(103,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_not0__implies__Suc) ).
thf(666,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',fact_36_Ex__less__Suc) ).
thf(1083,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)],[210]) ).
thf(169,axiom,
( ( fe @ index )
!= nil_co1338500125t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_NotEmpty_I2_J) ).
thf(962,plain,
( ( fe @ index )
!= nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',fact_33_All__less__Suc) ).
thf(977,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)],[174]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( if_nat @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Nat__Onat_T) ).
thf(523,plain,
! [A: nat,B: nat] :
( ( if_nat @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(204,axiom,
minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ConsumedMsg_I1_J) ).
thf(1068,plain,
minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(181,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_AssumptionCase1ImplThesis_H) ).
thf(994,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Suc__leD) ).
thf(308,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)],[18]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',fact_27_strict__inc__induct) ).
thf(741,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)],[120]) ).
thf(63,axiom,
! [A: list_message_p_v] :
( ( size_s1168481041ge_p_v @ ( tl_message_p_v @ A ) )
= ( minus_minus_nat @ ( size_s1168481041ge_p_v @ A ) @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_length__tl) ).
thf(511,plain,
! [A: list_message_p_v] :
( ( size_s1168481041ge_p_v @ ( tl_message_p_v @ A ) )
= ( minus_minus_nat @ ( size_s1168481041ge_p_v @ A ) @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(85,axiom,
! [A: list_message_p_v] :
( ( ( A = nil_message_p_v )
| ( ( tl_message_p_v @ A )
!= nil_message_p_v ) )
=> ( ( last_message_p_v @ ( tl_message_p_v @ A ) )
= ( last_message_p_v @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_last__tl) ).
thf(597,plain,
! [A: list_message_p_v] :
( ( ( A = nil_message_p_v )
| ( ( tl_message_p_v @ A )
!= nil_message_p_v ) )
=> ( ( last_message_p_v @ ( tl_message_p_v @ A ) )
= ( last_message_p_v @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(195,axiom,
! [A: nat,B: list_message_p_v] :
( ( ord_less_nat @ ( suc @ A ) @ ( size_s1168481041ge_p_v @ ( remdup74979931ge_p_v @ B ) ) )
=> ( ( nth_message_p_v @ ( remdup74979931ge_p_v @ B ) @ A )
!= ( nth_message_p_v @ ( remdup74979931ge_p_v @ B ) @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_remdups__adj__adjacent) ).
thf(1041,plain,
! [A: nat,B: list_message_p_v] :
( ( ord_less_nat @ ( suc @ A ) @ ( size_s1168481041ge_p_v @ ( remdup74979931ge_p_v @ B ) ) )
=> ( ( nth_message_p_v @ ( remdup74979931ge_p_v @ B ) @ A )
!= ( nth_message_p_v @ ( remdup74979931ge_p_v @ B ) @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(89,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_minus__nat_Odiff__0) ).
thf(614,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_diff__is__0__eq_H) ).
thf(269,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)],[5]) ).
thf(37,axiom,
! [A: set_message_p_v] :
( ( collect_message_p_v
@ ^ [B: message_p_v] : ( member_message_p_v @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Collect__mem__eq) ).
thf(385,plain,
! [A: set_message_p_v] :
( ( collect_message_p_v
@ ^ [B: message_p_v] : ( member_message_p_v @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(254,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( suc @ ( minus_minus_nat @ A @ one_one_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_Suc__diff__1) ).
thf(1233,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)],[254]) ).
thf(258,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_zero__less__iff__neq__zero) ).
thf(1260,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(27,axiom,
! [A: message_p_v > $o] :
~ ( list_ex_message_p_v @ A @ nil_message_p_v ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_list__ex__simps_I2_J) ).
thf(340,plain,
! [A: message_p_v > $o] :
~ ( list_ex_message_p_v @ A @ nil_message_p_v ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_le__SucI) ).
thf(538,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)],[69]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',fact_220_zero__induct__lemma) ).
thf(404,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)],[43]) ).
thf(159,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Suc__less__eq) ).
thf(898,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)],[159]) ).
thf(183,axiom,
( list_ex_message_p_v
= ( ^ [A: message_p_v > $o,B: list_message_p_v] :
? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ B ) )
& ( A @ ( nth_message_p_v @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_list__ex__length) ).
thf(1001,plain,
( list_ex_message_p_v
= ( ^ [A: message_p_v > $o,B: list_message_p_v] :
? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ B ) )
& ( A @ ( nth_message_p_v @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(257,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_infinite__descent0) ).
thf(1243,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)],[257]) ).
thf(128,axiom,
! [A: nat] :
? [B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Ex__list__of__length) ).
thf(782,plain,
! [A: nat] :
? [B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(11,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_One__nat__def) ).
thf(288,plain,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',fact_254_Suc__diff__eq__diff__pred) ).
thf(885,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)],[155]) ).
thf(197,axiom,
! [A: message_p_v] :
( ( minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ A )
=> ? [B: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ A @ B )
& ! [C: message_p_v,D: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ C @ D )
=> ( ord_less_eq_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_MinImplAllBigger) ).
thf(1046,plain,
! [A: message_p_v] :
( ( minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ A )
=> ? [B: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ A @ B )
& ! [C: message_p_v,D: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ C @ D )
=> ( ord_less_eq_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',fact_231_MinPredicate) ).
thf(570,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)],[79]) ).
thf(129,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_le__less__Suc__eq) ).
thf(785,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)],[129]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_le__SucE) ).
thf(504,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)],[61]) ).
thf(260,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_less__zeroE) ).
thf(1264,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(225,axiom,
( ord_less_nat
= ( ^ [A: nat] : ( ord_less_eq_nat @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_less__eq__Suc__le) ).
thf(1131,plain,
( ord_less_nat
= ( ^ [A: nat] : ( ord_less_eq_nat @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1132,plain,
( ( ^ [A: nat] : ( ord_less_eq_nat @ ( suc @ A ) ) )
= ord_less_nat ),
inference(lifteq,[status(thm)],[1131]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_227_Suc__diff__le) ).
thf(542,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)],[71]) ).
thf(76,axiom,
! [A: nat] :
? [B: list_message_p_v] :
( ( size_s1168481041ge_p_v @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Ex__list__of__length) ).
thf(559,plain,
! [A: nat] :
? [B: list_message_p_v] :
( ( size_s1168481041ge_p_v @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',fact_192_LastOfIndex) ).
thf(1147,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)],[231]) ).
thf(289,plain,
( ( suc @ zero_zero_nat )
= one_one_nat ),
inference(lifteq,[status(thm)],[288]) ).
thf(212,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_AssumptionFirstOccSetDecrOrConsumed_I1_J) ).
thf(1100,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(253,axiom,
ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_LengthStep) ).
thf(1232,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)],[253]) ).
thf(149,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_nat__less__le) ).
thf(869,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(870,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(lifteq,[status(thm)],[869]) ).
thf(9,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_le0) ).
thf(284,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',fact_243__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(770,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)],[124]) ).
thf(83,axiom,
! [A: list_message_p_v] :
( ( last_message_p_v @ ( remdup74979931ge_p_v @ A ) )
= ( last_message_p_v @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_last__remdups__adj) ).
thf(591,plain,
! [A: list_message_p_v] :
( ( last_message_p_v @ ( remdup74979931ge_p_v @ A ) )
= ( last_message_p_v @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(47,axiom,
( ( remdup74979931ge_p_v @ nil_message_p_v )
= nil_message_p_v ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_remdups__adj_Osimps_I1_J) ).
thf(442,plain,
( ( remdup74979931ge_p_v @ nil_message_p_v )
= nil_message_p_v ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(443,plain,
( ( remdup74979931ge_p_v @ nil_message_p_v )
= nil_message_p_v ),
inference(lifteq,[status(thm)],[442]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_219_diffs0__imp__equal) ).
thf(646,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)],[99]) ).
thf(64,axiom,
( ( tl_message_p_v @ nil_message_p_v )
= nil_message_p_v ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_list_Osel_I2_J) ).
thf(514,plain,
( ( tl_message_p_v @ nil_message_p_v )
= nil_message_p_v ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(233,axiom,
( list_e581556831t_unit
= ( ^ [A: config256849571t_unit > $o,B: list_c1059388851t_unit] :
? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ B ) )
& ( A @ ( nth_co1649820636t_unit @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_list__ex__length) ).
thf(1151,plain,
( list_e581556831t_unit
= ( ^ [A: config256849571t_unit > $o,B: list_c1059388851t_unit] :
? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ B ) )
& ( A @ ( nth_co1649820636t_unit @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',fact_117_less__Suc__eq__0__disj) ).
thf(1109,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)],[216]) ).
thf(23,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_zero__induct) ).
thf(321,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)],[23]) ).
thf(227,axiom,
( size_s1406904903t_unit
= ( ^ [A: list_c1059388851t_unit] : ( if_nat @ ( A = nil_co1338500125t_unit ) @ zero_zero_nat @ ( suc @ ( size_s1406904903t_unit @ ( tl_con485597044t_unit @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Nitpick_Osize__list__simp_I2_J) ).
thf(1136,plain,
( size_s1406904903t_unit
= ( ^ [A: list_c1059388851t_unit] : ( if_nat @ ( A = nil_co1338500125t_unit ) @ zero_zero_nat @ ( suc @ ( size_s1406904903t_unit @ ( tl_con485597044t_unit @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',fact_48_nth__equalityI) ).
thf(834,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)],[138]) ).
thf(29,axiom,
! [A: message_p_v > $o] :
~ ( list_ex1_message_p_v @ A @ nil_message_p_v ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_list__ex1__simps_I1_J) ).
thf(346,plain,
! [A: message_p_v > $o] :
~ ( list_ex1_message_p_v @ A @ nil_message_p_v ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(347,plain,
~ ? [A: message_p_v > $o] : ( list_ex1_message_p_v @ A @ nil_message_p_v ),
inference(miniscope,[status(thm)],[346]) ).
thf(348,plain,
! [A: message_p_v > $o] :
~ ( list_ex1_message_p_v @ A @ nil_message_p_v ),
inference(cnf,[status(esa)],[347]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( if_nat @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Nat__Onat_T) ).
thf(574,plain,
! [A: nat,B: nat] :
( ( if_nat @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(240,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_less__one) ).
thf(1169,plain,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',fact_217_eq__diff__iff) ).
thf(280,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)],[8]) ).
thf(148,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_less__Suc__eq) ).
thf(866,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)],[148]) ).
thf(220,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_AssumpGreaterOccurrence_I3_J) ).
thf(1119,plain,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(62,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_old_Onat_Odistinct_I1_J) ).
thf(507,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_232_PrefixListTransitive) ).
thf(312,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)],[20]) ).
thf(152,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_less__irrefl__nat) ).
thf(877,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(110,axiom,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Suc__n__not__le__n) ).
thf(692,plain,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',fact_237_PrefixListMonotonicity) ).
thf(1104,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)],[214]) ).
thf(3,axiom,
! [A: message_p_v > $o,B: message_p_v > $o] :
( ! [C: message_p_v] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_message_p_v @ A )
= ( collect_message_p_v @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Collect__cong) ).
thf(265,plain,
! [A: message_p_v > $o,B: message_p_v > $o] :
( ! [C: message_p_v] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_message_p_v @ A )
= ( collect_message_p_v @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: config256849571t_unit > $o] :
~ ( list_e1598815642t_unit @ A @ nil_co1338500125t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_list__ex1__simps_I1_J) ).
thf(305,plain,
! [A: config256849571t_unit > $o] :
~ ( list_e1598815642t_unit @ A @ nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(306,plain,
~ ? [A: config256849571t_unit > $o] : ( list_e1598815642t_unit @ A @ nil_co1338500125t_unit ),
inference(miniscope,[status(thm)],[305]) ).
thf(307,plain,
! [A: config256849571t_unit > $o] :
~ ( list_e1598815642t_unit @ A @ nil_co1338500125t_unit ),
inference(cnf,[status(esa)],[306]) ).
thf(207,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_less__antisym) ).
thf(1074,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)],[207]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',fact_250_MinPredicate2) ).
thf(292,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)],[13]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',fact_104_diff__induct) ).
thf(380,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)],[36]) ).
thf(165,axiom,
( ( fe @ ( suc @ index ) )
!= nil_co1338500125t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_NotEmpty_I1_J) ).
thf(940,plain,
( ( fe @ ( suc @ index ) )
!= nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(941,plain,
( ( fe @ ( suc @ index ) )
!= nil_co1338500125t_unit ),
inference(polarity_switch,[status(thm)],[940]) ).
thf(942,plain,
( ( fe @ ( suc @ index ) )
!= nil_co1338500125t_unit ),
inference(lifteq,[status(thm)],[941]) ).
thf(107,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_le__Suc__eq) ).
thf(678,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)],[107]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Suc__le__lessD) ).
thf(793,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)],[131]) ).
thf(247,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/sandbox/benchmark/theBenchmark.p',fact_173_dec__induct) ).
thf(1199,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)],[247]) ).
thf(200,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_neq0__conv) ).
thf(1057,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(234,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_le__neq__implies__less) ).
thf(1153,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)],[234]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_less__imp__diff__less) ).
thf(761,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)],[121]) ).
thf(135,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_not__less0) ).
thf(825,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',fact_223_diff__commute) ).
thf(302,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)],[16]) ).
thf(14,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(297,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(94,axiom,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_diff__Suc__1) ).
thf(630,plain,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(222,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_less__nat__zero__code) ).
thf(1123,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',fact_163_transitive__stepwise__le) ).
thf(349,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)],[30]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Suc__inject) ).
thf(275,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Suc__lessE) ).
thf(788,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)],[130]) ).
thf(92,axiom,
( ( remdup949903207t_unit @ nil_co1338500125t_unit )
= nil_co1338500125t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_remdups__adj_Osimps_I1_J) ).
thf(625,plain,
( ( remdup949903207t_unit @ nil_co1338500125t_unit )
= nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',fact_195_PrefixSameOnLow) ).
thf(889,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)],[156]) ).
thf(224,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( A
= ( suc @ ( minus_minus_nat @ A @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Suc__pred_H) ).
thf(1128,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)],[224]) ).
thf(1290,plain,
( ( ( fe @ one_one_nat )
!= nil_co1338500125t_unit )
| ( ( suc @ index )
!= ( suc @ zero_zero_nat ) ) ),
inference(paramod_ordered,[status(thm)],[289,942]) ).
thf(1291,plain,
( ( ( fe @ one_one_nat )
!= nil_co1338500125t_unit )
| ( index != zero_zero_nat ) ),
inference(simp,[status(thm)],[1290]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',fact_6_SameCfgOnLow) ).
thf(842,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)],[140]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',fact_255_last__conv__nth) ).
thf(1012,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)],[187]) ).
thf(142,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_zero__less__diff) ).
thf(847,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)],[142]) ).
thf(78,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_old_Onat_Odistinct_I2_J) ).
thf(566,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',fact_162_nat__induct__at__least) ).
thf(484,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)],[58]) ).
thf(236,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_less__not__refl) ).
thf(1159,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_73_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J) ).
thf(461,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)],[53]) ).
thf(285,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(cnf,[status(esa)],[284]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',fact_224_diff__less) ).
thf(1106,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)],[215]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',fact_234_KeepProperty) ).
thf(697,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)],[112]) ).
thf(151,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( suc @ ( minus_minus_nat @ A @ ( suc @ zero_zero_nat ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Suc__pred) ).
thf(874,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)],[151]) ).
thf(262,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_bot__nat__0_Onot__eq__extremum) ).
thf(1270,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(251,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_bot__nat__0_Oextremum__strict) ).
thf(1227,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_47_nth__equalityI) ).
thf(725,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)],[116]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',fact_29_less__trans__Suc) ).
thf(980,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)],[175]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_old_Onat_Oinject) ).
thf(388,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(228,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Suc__less__eq2) ).
thf(1138,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)],[228]) ).
thf(59,axiom,
! [A: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= zero_zero_nat )
= ( A = nil_message_p_v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_length__0__conv) ).
thf(499,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)],[59]) ).
thf(145,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_gr__zeroI) ).
thf(857,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(104,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_bot__nat__0_Oextremum__unique) ).
thf(669,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(68,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/sandbox/benchmark/theBenchmark.p',fact_72_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J) ).
thf(526,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)],[68]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',fact_119_All__less__Suc2) ).
thf(1016,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)],[189]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',fact_184_ex__least__nat__less) ).
thf(901,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)],[160]) ).
thf(55,axiom,
! [A: list_c1059388851t_unit] :
( ( last_c571238084t_unit @ ( remdup949903207t_unit @ A ) )
= ( last_c571238084t_unit @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_last__remdups__adj) ).
thf(476,plain,
! [A: list_c1059388851t_unit] :
( ( last_c571238084t_unit @ ( remdup949903207t_unit @ A ) )
= ( last_c571238084t_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(218,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_less__Suc__eq__le) ).
thf(1114,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)],[218]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',fact_241__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(1263,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)],[259]) ).
thf(515,plain,
( ( tl_message_p_v @ nil_message_p_v )
= nil_message_p_v ),
inference(lifteq,[status(thm)],[514]) ).
thf(177,axiom,
! [A: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= zero_zero_nat )
= ( A = nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_length__0__conv) ).
thf(984,plain,
! [A: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= zero_zero_nat )
= ( A = nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(60,axiom,
( ( size_s1168481041ge_p_v @ nil_message_p_v )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_list_Osize_I3_J) ).
thf(502,plain,
( ( size_s1168481041ge_p_v @ nil_message_p_v )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(503,plain,
( ( size_s1168481041ge_p_v @ nil_message_p_v )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[502]) ).
thf(201,axiom,
~ ( ord_less_nat @ nMsg @ n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_AssumpGreaterOccurrence_I1_J) ).
thf(1060,plain,
~ ( ord_less_nat @ nMsg @ n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(198,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_not__less__eq) ).
thf(1050,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',fact_212_le__diff__iff_H) ).
thf(457,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)],[52]) ).
thf(28,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_diff__zero) ).
thf(343,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(95,axiom,
! [A: config256849571t_unit > $o] :
~ ( list_e581556831t_unit @ A @ nil_co1338500125t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_list__ex__simps_I2_J) ).
thf(633,plain,
! [A: config256849571t_unit > $o] :
~ ( list_e581556831t_unit @ A @ nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(162,axiom,
! [A: nat,B: nat] : ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_diff__less__Suc) ).
thf(921,plain,
! [A: nat,B: nat] : ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(41,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_zero__diff) ).
thf(398,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',fact_90_AssumptionFairContr) ).
thf(1071,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)],[206]) ).
thf(239,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/sandbox/benchmark/theBenchmark.p',fact_194__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(1167,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)],[239]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',fact_4_length__induct) ).
thf(953,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)],[168]) ).
thf(211,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_ex__least__nat__le) ).
thf(1086,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)],[211]) ).
thf(164,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_lessI) ).
thf(938,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(170,axiom,
! [A: list_c1059388851t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ A ) )
= ( A != nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_length__greater__0__conv) ).
thf(965,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)],[170]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',fact_125_Case2ImplThesis) ).
thf(1273,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)],[263]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_nat_Oinject) ).
thf(444,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_Suc__lessD) ).
thf(733,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(185,axiom,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062) ).
thf(1007,plain,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(10,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_diff__le__self) ).
thf(286,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',fact_256_last__conv__nth) ).
thf(577,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)],[81]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',fact_12_size__neq__size__imp__neq) ).
thf(545,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)],[72]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_216_le__diff__iff) ).
thf(562,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)],[77]) ).
thf(173,axiom,
( enabled_p_v_s
= ( ^ [A: config256849571t_unit,B: message_p_v] : ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_enabled__def) ).
thf(975,plain,
( enabled_p_v_s
= ( ^ [A: config256849571t_unit,B: message_p_v] : ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(39,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Suc__neq__Zero) ).
thf(391,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(88,axiom,
! [A: list_c1059388851t_unit] :
( ( ( remdup949903207t_unit @ A )
= nil_co1338500125t_unit )
= ( A = nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_remdups__adj__Nil__iff) ).
thf(611,plain,
! [A: list_c1059388851t_unit] :
( ( ( remdup949903207t_unit @ A )
= nil_co1338500125t_unit )
= ( A = nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(25,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_le__zero__eq) ).
thf(335,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(250,axiom,
! [A: nat,B: list_c1059388851t_unit] :
( ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( tl_con485597044t_unit @ B ) ) )
=> ( ( nth_co1649820636t_unit @ ( tl_con485597044t_unit @ B ) @ A )
= ( nth_co1649820636t_unit @ B @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_nth__tl) ).
thf(1224,plain,
! [A: nat,B: list_c1059388851t_unit] :
( ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( tl_con485597044t_unit @ B ) ) )
=> ( ( nth_co1649820636t_unit @ ( tl_con485597044t_unit @ B ) @ A )
= ( nth_co1649820636t_unit @ B @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(70,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_bot__nat__0_Oextremum) ).
thf(540,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(105,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_diff__Suc__Suc) ).
thf(672,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)],[105]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',fact_161_full__nat__induct) ).
thf(681,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)],[108]) ).
thf(6,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_one__reorient) ).
thf(272,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(273,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(cnf,[status(esa)],[272]) ).
thf(274,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(lifteq,[status(thm)],[273]) ).
thf(219,axiom,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_zero__less__Suc) ).
thf(1117,plain,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',fact_196_PrefixSameOnLow) ).
thf(1144,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)],[230]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_diff__is__0__eq) ).
thf(318,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)],[22]) ).
thf(270,plain,
! [B: nat,A: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
| ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
inference(cnf,[status(esa)],[269]) ).
thf(271,plain,
! [B: nat,A: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
| ~ ( ord_less_eq_nat @ A @ B ) ),
inference(lifteq,[status(thm)],[270]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_230_diff__Suc__less) ).
thf(863,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)],[147]) ).
thf(122,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_gr0__implies__Suc) ).
thf(764,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(86,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_Zero__not__Suc) ).
thf(604,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(35,axiom,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_s1168481041ge_p_v @ ( remdup74979931ge_p_v @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_remdups__adj__length__ge1) ).
thf(377,plain,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_s1168481041ge_p_v @ ( remdup74979931ge_p_v @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',fact_45_Skolem__list__nth) ).
thf(990,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)],[179]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',fact_121_Ex__less__Suc2) ).
thf(880,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)],[153]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Suc__le__mono) ).
thf(649,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)],[100]) ).
thf(74,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Zero__neq__Suc) ).
thf(552,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',fact_214_diff__le__mono) ).
thf(594,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)],[84]) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',fact_46_Skolem__list__nth) ).
thf(1162,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)],[237]) ).
thf(66,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_zero__reorient) ).
thf(520,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(158,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_not__less__less__Suc__eq) ).
thf(895,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)],[158]) ).
thf(1061,plain,
~ ( ord_less_nat @ nMsg @ n1 ),
inference(polarity_switch,[status(thm)],[1060]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',fact_240_EnabledIntermediate) ).
thf(1112,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)],[217]) ).
thf(232,axiom,
! [A: list_c1059388851t_unit] : ( ord_less_eq_nat @ ( size_s1406904903t_unit @ ( remdup949903207t_unit @ A ) ) @ ( size_s1406904903t_unit @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_remdups__adj__length) ).
thf(1149,plain,
! [A: list_c1059388851t_unit] : ( ord_less_eq_nat @ ( size_s1406904903t_unit @ ( remdup949903207t_unit @ A ) ) @ ( size_s1406904903t_unit @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(963,plain,
( ( fe @ index )
!= nil_co1338500125t_unit ),
inference(polarity_switch,[status(thm)],[962]) ).
thf(964,plain,
( ( fe @ index )
!= nil_co1338500125t_unit ),
inference(lifteq,[status(thm)],[963]) ).
thf(626,plain,
( ( remdup949903207t_unit @ nil_co1338500125t_unit )
= nil_co1338500125t_unit ),
inference(lifteq,[status(thm)],[625]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',fact_238_EnabledOrConsumed) ).
thf(915,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)],[161]) ).
thf(166,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_AssumptionFair_I3_J) ).
thf(943,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(191,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_le__eq__less__or__eq) ).
thf(1022,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(176,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_EnabledInSuc) ).
thf(983,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',fact_43_list__eq__iff__nth__eq) ).
thf(780,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)],[127]) ).
thf(154,axiom,
! [A: nat] : ( prefix1615116500t_unit @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_IPrefixListEx) ).
thf(883,plain,
! [A: nat] : ( prefix1615116500t_unit @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(188,axiom,
member_message_p_v @ consumedMsg @ ( firstOccSet @ index ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ConsumedInSet) ).
thf(1015,plain,
member_message_p_v @ consumedMsg @ ( firstOccSet @ index ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(266,plain,
! [B: message_p_v > $o,A: message_p_v > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_message_p_v @ A )
= ( collect_message_p_v @ B ) ) ),
inference(cnf,[status(esa)],[265]) ).
thf(267,plain,
! [B: message_p_v > $o,A: message_p_v > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_message_p_v @ A )
= ( collect_message_p_v @ B ) ) ),
inference(lifteq,[status(thm)],[266]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_215_Nat_Odiff__diff__eq) ).
thf(438,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)],[46]) ).
thf(45,axiom,
! [A: list_c1059388851t_unit] :
( ( ( A = nil_co1338500125t_unit )
| ( ( tl_con485597044t_unit @ A )
!= nil_co1338500125t_unit ) )
=> ( ( last_c571238084t_unit @ ( tl_con485597044t_unit @ A ) )
= ( last_c571238084t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_last__tl) ).
thf(431,plain,
! [A: list_c1059388851t_unit] :
( ( ( A = nil_co1338500125t_unit )
| ( ( tl_con485597044t_unit @ A )
!= nil_co1338500125t_unit ) )
=> ( ( last_c571238084t_unit @ ( tl_con485597044t_unit @ A ) )
= ( last_c571238084t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(111,axiom,
! [A: list_message_p_v] : ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( remdup74979931ge_p_v @ A ) ) @ ( size_s1168481041ge_p_v @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_remdups__adj__length) ).
thf(695,plain,
! [A: list_message_p_v] : ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( remdup74979931ge_p_v @ A ) ) @ ( size_s1168481041ge_p_v @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(96,axiom,
! [A: message_p_v,B: message_p_v > $o] :
( ( member_message_p_v @ A @ ( collect_message_p_v @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_mem__Collect__eq) ).
thf(636,plain,
! [A: message_p_v,B: message_p_v > $o] :
( ( member_message_p_v @ A @ ( collect_message_p_v @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',fact_193__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(1044,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)],[196]) ).
thf(242,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_not__gr0) ).
thf(1176,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(87,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_le__antisym) ).
thf(608,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)],[87]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_251_diff__Suc__eq__diff__pred) ).
thf(473,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)],[54]) ).
thf(114,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ consumedMsg @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_AssumpGreaterOccurrence_I2_J) ).
thf(722,plain,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ consumedMsg @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(106,axiom,
! [A: list_message_p_v] :
( ( ( remdup74979931ge_p_v @ A )
= nil_message_p_v )
= ( A = nil_message_p_v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_remdups__adj__Nil__iff) ).
thf(675,plain,
! [A: list_message_p_v] :
( ( ( remdup74979931ge_p_v @ A )
= nil_message_p_v )
= ( A = nil_message_p_v ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',fact_5_length__induct) ).
thf(944,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)],[167]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',fact_28_less__Suc__induct) ).
thf(795,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)],[132]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_diff__diff__cancel) ).
thf(663,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)],[102]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',fact_203_Suc__diff__diff) ).
thf(374,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)],[34]) ).
thf(209,axiom,
! [A: message_p_v] :
( ( member_message_p_v @ A @ ( firstOccSet @ ( suc @ index ) ) )
=> ( member_message_p_v @ A @ ( firstOccSet @ index ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Subset) ).
thf(1081,plain,
! [A: message_p_v] :
( ( member_message_p_v @ A @ ( firstOccSet @ ( suc @ index ) ) )
=> ( member_message_p_v @ A @ ( firstOccSet @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(341,plain,
~ ? [A: message_p_v > $o] : ( list_ex_message_p_v @ A @ nil_message_p_v ),
inference(miniscope,[status(thm)],[340]) ).
thf(342,plain,
! [A: message_p_v > $o] :
~ ( list_ex_message_p_v @ A @ nil_message_p_v ),
inference(cnf,[status(esa)],[341]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fact_143_lift__Suc__mono__le) ).
thf(617,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)],[90]) ).
thf(65,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_old_Onat_Oexhaust) ).
thf(516,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',fact_71_length__greater__0__conv) ).
thf(968,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)],[171]) ).
thf(244,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/sandbox/benchmark/theBenchmark.p',fact_127_NotConsumedIntermediate) ).
thf(1181,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)],[244]) ).
thf(184,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_less__not__refl2) ).
thf(1003,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(82,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_old_Onat_Oinducts) ).
thf(580,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)],[82]) ).
thf(109,axiom,
! [A: nat] : ( prefix47729710ge_p_v @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_IPrefixList) ).
thf(690,plain,
! [A: nat] : ( prefix47729710ge_p_v @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(205,axiom,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_list_Osize_I3_J) ).
thf(1069,plain,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1070,plain,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[1069]) ).
thf(235,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Suc__le__eq) ).
thf(1156,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)],[235]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_235_NatPredicateTippingPoint) ).
thf(707,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)],[113]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_less__not__refl3) ).
thf(971,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(261,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/sandbox/benchmark/theBenchmark.p',fact_222_diff__less__mono2) ).
thf(1267,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)],[261]) ).
thf(252,axiom,
! [A: message_p_v] :
( ( minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ A )
=> ( member_message_p_v @ A @ ( firstOccSet @ index ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_MinImplFirstOcc) ).
thf(1230,plain,
! [A: message_p_v] :
( ( minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ A )
=> ( member_message_p_v @ A @ ( firstOccSet @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_nat__le__linear) ).
thf(310,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)],[19]) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',fact_128__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(1053,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)],[199]) ).
thf(139,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Suc__leI) ).
thf(840,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)],[139]) ).
thf(26,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_less__eq__nat_Osimps_I1_J) ).
thf(338,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(248,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Suc__less__SucD) ).
thf(1218,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)],[248]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',fact_228_less__diff__iff) ).
thf(1220,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)],[249]) ).
thf(194,axiom,
! [A: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ ( tl_con485597044t_unit @ A ) )
= ( minus_minus_nat @ ( size_s1406904903t_unit @ A ) @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_length__tl) ).
thf(1038,plain,
! [A: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ ( tl_con485597044t_unit @ A ) )
= ( minus_minus_nat @ ( size_s1406904903t_unit @ A ) @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(33,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_n__not__Suc__n) ).
thf(370,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1329,plain,
( ~ $true
| ( ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= ( ord_less_nat @ nMsg @ n1 ) ) ),
inference(paramod_ordered,[status(thm)],[1007,1061]) ).
thf(1330,plain,
( ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= ( ord_less_nat @ nMsg @ n1 ) ),
inference(simp,[status(thm)],[1329]) ).
thf(1333,plain,
( ( nMsg != nMsg )
| ( ( size_s1406904903t_unit @ ( fe @ index ) )
!= n1 ) ),
inference(simp,[status(thm)],[1330]) ).
thf(1336,plain,
( ( size_s1406904903t_unit @ ( fe @ index ) )
!= n1 ),
inference(simp,[status(thm)],[1333]) ).
thf(98,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_diff__self__eq__0) ).
thf(643,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(229,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_linorder__neqE__nat) ).
thf(1141,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)],[229]) ).
thf(1023,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(lifteq,[status(thm)],[1022]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_gr__implies__not0) ).
thf(1008,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',fact_53_lift__Suc__mono__less) ).
thf(1240,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)],[256]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_less__SucI) ).
thf(845,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(93,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_bot__nat__0_Oextremum__uniqueI) ).
thf(627,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(75,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_le__0__eq) ).
thf(556,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(57,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_zero__le) ).
thf(482,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(1320,plain,
( ( n1 != n0 )
| ( ( size_s1406904903t_unit @ ( fe @ index ) )
!= zero_zero_nat )
| ( ( size_s1406904903t_unit @ ( fe @ n ) )
!= ( size_s1406904903t_unit @ nil_co1338500125t_unit ) ) ),
inference(paramod_ordered,[status(thm)],[1070,1316]) ).
thf(1321,plain,
( ( n1 != n0 )
| ( ( size_s1406904903t_unit @ ( fe @ index ) )
!= zero_zero_nat )
| ( ( fe @ n )
!= nil_co1338500125t_unit ) ),
inference(simp,[status(thm)],[1320]) ).
thf(976,plain,
( ( ^ [A: config256849571t_unit,B: message_p_v] : ( ord_less_nat @ zero_zero_nat @ ( msgs_p1029620568t_unit @ A @ B ) ) )
= enabled_p_v_s ),
inference(lifteq,[status(thm)],[975]) ).
thf(223,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_le__imp__less__Suc) ).
thf(1126,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)],[223]) ).
thf(32,axiom,
( ( tl_con485597044t_unit @ nil_co1338500125t_unit )
= nil_co1338500125t_unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_list_Osel_I2_J) ).
thf(368,plain,
( ( tl_con485597044t_unit @ nil_co1338500125t_unit )
= nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',fact_42_Nat_OlessE) ).
thf(771,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)],[125]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_eq__imp__le) ).
thf(450,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',fact_226_Suc__diff__Suc) ).
thf(1062,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)],[202]) ).
thf(213,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_less__Suc0) ).
thf(1101,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(101,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_nat__induct) ).
thf(652,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)],[101]) ).
thf(42,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_le__trans) ).
thf(401,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)],[42]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',fact_236_PrefixListMonotonicity) ).
thf(731,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)],[117]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',fact_126_MessageStaysOrConsumed) ).
thf(995,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)],[182]) ).
thf(12,axiom,
( size_s1168481041ge_p_v
= ( ^ [A: list_message_p_v] : ( if_nat @ ( A = nil_message_p_v ) @ zero_zero_nat @ ( suc @ ( size_s1168481041ge_p_v @ ( tl_message_p_v @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Nitpick_Osize__list__simp_I2_J) ).
thf(290,plain,
( size_s1168481041ge_p_v
= ( ^ [A: list_message_p_v] : ( if_nat @ ( A = nil_message_p_v ) @ zero_zero_nat @ ( suc @ ( size_s1168481041ge_p_v @ ( tl_message_p_v @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',fact_140_EnabledOrConsumedAtLast) ).
thf(1193,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)],[246]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',fact_49_lift__Suc__mono__less__iff) ).
thf(1077,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)],[208]) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',fact_44_list__eq__iff__nth__eq) ).
thf(832,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)],[137]) ).
thf(73,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_diff__0__eq__0) ).
thf(549,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(226,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_not__gr__zero) ).
thf(1133,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(15,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_le__refl) ).
thf(300,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_nat_OdiscI) ).
thf(620,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(49,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Suc__le__D) ).
thf(447,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)],[49]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',fact_233_PrefixListTransitive) ).
thf(315,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)],[21]) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',fact_229_diff__less__mono) ).
thf(854,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)],[144]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_less__or__eq__imp__le) ).
thf(735,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)],[119]) ).
thf(4,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Nat__Onat_T) ).
thf(268,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1327,plain,
( ~ $true
| ( ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1007,264]) ).
thf(1328,plain,
( ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(simp,[status(thm)],[1327]) ).
thf(1332,plain,
( ( nMsg != n1 )
| ( ( size_s1406904903t_unit @ ( fe @ index ) )
!= ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
inference(simp,[status(thm)],[1328]) ).
thf(1335,plain,
nMsg != n1,
inference(simp,[status(thm)],[1332]) ).
thf(193,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_less__mono__imp__le__mono) ).
thf(1033,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)],[193]) ).
thf(136,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_neq__if__length__neq) ).
thf(828,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)],[136]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',fact_76_SameMsgOnLow) ).
thf(1065,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)],[203]) ).
thf(238,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_less__imp__le__nat) ).
thf(1165,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(44,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Nat_Oex__has__greatest__nat) ).
thf(415,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)],[44]) ).
thf(241,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_size__neq__size__imp__neq) ).
thf(1172,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)],[241]) ).
thf(123,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__SucE) ).
thf(767,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)],[123]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_not__less__eq__eq) ).
thf(395,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)],[40]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',fact_142_lift__Suc__antimono__le) ).
thf(332,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)],[24]) ).
thf(146,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_not__less__zero) ).
thf(860,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(190,axiom,
! [A: nat,B: list_c1059388851t_unit] :
( ( ord_less_nat @ ( suc @ A ) @ ( size_s1406904903t_unit @ ( remdup949903207t_unit @ B ) ) )
=> ( ( nth_co1649820636t_unit @ ( remdup949903207t_unit @ B ) @ A )
!= ( nth_co1649820636t_unit @ ( remdup949903207t_unit @ B ) @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_remdups__adj__adjacent) ).
thf(1019,plain,
! [A: nat,B: list_c1059388851t_unit] :
( ( ord_less_nat @ ( suc @ A ) @ ( size_s1406904903t_unit @ ( remdup949903207t_unit @ B ) ) )
=> ( ( nth_co1649820636t_unit @ ( remdup949903207t_unit @ B ) @ A )
!= ( nth_co1649820636t_unit @ ( remdup949903207t_unit @ B ) @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',fact_85_SmallIndex) ).
thf(723,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)],[115]) ).
thf(134,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_gr0__conv__Suc) ).
thf(822,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',fact_239__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(850,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)],[143]) ).
thf(276,plain,
! [B: nat,A: nat] :
( ( ( suc @ A )
!= ( suc @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[275]) ).
thf(277,plain,
! [B: nat,A: nat] :
( ( ( suc @ A )
!= ( suc @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[276]) ).
thf(150,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Suc__lessI) ).
thf(871,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)],[150]) ).
thf(221,axiom,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_s1406904903t_unit @ ( remdup949903207t_unit @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_remdups__adj__length__ge1) ).
thf(1120,plain,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_s1406904903t_unit @ ( remdup949903207t_unit @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(369,plain,
( ( tl_con485597044t_unit @ nil_co1338500125t_unit )
= nil_co1338500125t_unit ),
inference(lifteq,[status(thm)],[368]) ).
thf(255,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_gr__implies__not__zero) ).
thf(1236,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(178,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_gr0I) ).
thf(987,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',fact_174_inc__induct) ).
thf(803,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)],[133]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',fact_252_nat__induct__non__zero) ).
thf(923,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)],[163]) ).
thf(245,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_infinite__descent) ).
thf(1184,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)],[245]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',fact_10_neq__if__length__neq) ).
thf(639,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)],[97]) ).
thf(31,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_nat_Odistinct_I1_J) ).
thf(364,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',fact_210_diff__right__commute) ).
thf(454,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)],[51]) ).
thf(9667,plain,
$false,
inference(e,[status(thm)],[892,1322,1024,479,1179,777,666,1083,962,977,523,1068,994,308,741,511,597,1041,614,269,385,1233,1260,340,538,404,898,1001,1243,782,288,885,1046,570,785,504,1264,1132,542,559,1147,289,1100,1232,1319,870,284,770,591,443,646,514,1151,1109,321,1136,834,348,574,1169,280,866,1119,507,312,877,692,1104,265,307,1074,292,380,942,678,793,1199,1057,1153,761,825,302,297,630,1123,349,275,788,625,889,1128,1291,842,1012,847,566,484,1159,461,285,1106,697,874,1270,1227,725,980,388,1138,869,499,857,669,526,1016,901,476,1114,1263,515,1131,984,503,1060,1050,457,343,633,921,398,1071,1167,953,1086,938,965,1273,264,444,733,1007,286,577,545,562,975,391,611,335,1224,540,672,681,274,1117,1144,318,271,863,764,604,377,990,880,649,552,594,1162,520,895,1061,1112,1149,964,626,915,943,1022,983,780,883,1015,267,438,431,695,636,1044,1176,608,473,722,675,944,795,663,374,1081,342,617,516,968,1181,1003,580,690,1070,1156,707,971,1267,1230,310,993,1053,502,840,338,1218,1220,1038,370,1336,643,1141,1023,1008,1240,845,627,556,482,1321,976,1126,368,771,1316,450,1062,1101,652,401,731,995,290,1193,1077,272,832,346,549,1133,300,620,447,315,854,735,305,268,1335,1033,828,1065,1165,415,1172,767,395,332,860,1019,723,822,850,277,442,871,1120,369,1236,987,803,940,923,1184,639,364,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP054^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.08/0.23 % Computer : n017.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 19:39:22 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.06/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.04/1.19 % [INFO] Parsing done (375ms).
% 2.34/1.21 % [INFO] Running in sequential loop mode.
% 2.95/1.46 % [INFO] eprover registered as external prover.
% 2.95/1.46 % [INFO] Scanning for conjecture ...
% 3.36/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 261 axioms. Running axiom selection ...
% 3.69/1.68 % [INFO] Axiom selection finished. Selected 261 axioms (removed 0 axioms).
% 4.53/1.86 % [INFO] Problem is higher-order (TPTP THF).
% 4.53/1.88 % [INFO] Type checking passed.
% 4.53/1.88 % [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 ...
% 75.87/14.87 % External prover 'e' found a proof!
% 75.87/14.87 % [INFO] Killing All external provers ...
% 75.87/14.87 % Time passed: 14503ms (effective reasoning time: 13655ms)
% 75.87/14.87 % 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)>
% 75.87/14.88 % Axioms used in derivation (261): fact_131_not__gr__zero, fact_203_Suc__diff__diff, fact_145_nat__le__linear, fact_19_old_Onat_Oinject, fact_84_list__ex__simps_I2_J, fact_6_SameCfgOnLow, fact_256_last__conv__nth, fact_39_Suc__lessI, fact_92_AssumptionCase1ImplThesis_H, fact_99_old_Onat_Oexhaust, fact_225_diff__less__Suc, fact_191_gr__zeroI, fact_250_MinPredicate2, fact_220_zero__induct__lemma, fact_186_remdups__adj__length__ge1, fact_41_Suc__lessD, fact_185_zero__reorient, fact_175_Suc__le__lessD, fact_115_infinite__descent0, fact_235_NatPredicateTippingPoint, fact_3_AssumptionFair_I2_J, fact_70_length__greater__0__conv, fact_78_less__nat__zero__code, help_If_2_1_If_001t__Nat__Onat_T, fact_162_nat__induct__at__least, fact_42_Nat_OlessE, fact_56_nat__less__induct, fact_184_ex__least__nat__less, fact_126_MessageStaysOrConsumed, fact_28_less__Suc__induct, fact_112_not__less0, fact_22_Suc__mono, fact_53_lift__Suc__mono__less, fact_113_less__zeroE, fact_231_MinPredicate, fact_79_bot__nat__0_Onot__eq__extremum, fact_173_dec__induct, fact_136_EnabledInSuc, fact_76_SameMsgOnLow, fact_164_less__mono__imp__le__mono, fact_194__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_9_neq__if__length__neq, fact_45_Skolem__list__nth, fact_66_remdups__adj__adjacent, fact_152_le__0__eq, fact_244_diff__Suc__1, fact_95_list_Osel_I2_J, fact_97_not0__implies__Suc, fact_124_MinImplFirstOcc, fact_116_bot__nat__0_Oextremum__strict, fact_107_old_Onat_Odistinct_I1_J, fact_16_less__not__refl3, fact_7_Ex__list__of__length, fact_82_remdups__adj__Nil__iff, fact_17_less__irrefl__nat, fact_86_zero__less__Suc, fact_90_AssumptionFairContr, fact_21_Suc__less__eq, fact_183_last__tl, fact_81_remdups__adj__Nil__iff, fact_212_le__diff__iff_H, fact_55_infinite__descent, fact_237_PrefixListMonotonicity, fact_85_SmallIndex, fact_100_Zero__not__Suc, fact_252_nat__induct__non__zero, fact_209_Suc__pred, fact_52_Collect__cong, fact_89_length__0__conv, fact_132_le__zero__eq, fact_75_ConsumedInSet, fact_40_Suc__lessE, fact_130_Nitpick_Osize__list__simp_I2_J, fact_248_one__reorient, fact_36_Ex__less__Suc, fact_110_gr0I, fact_176_le__less__Suc__eq, fact_59_AssumptionFair_I3_J, fact_122_list_Osize_I3_J, fact_238_EnabledOrConsumed, fact_157_Suc__le__D, fact_38_less__SucE, fact_174_inc__induct, fact_61_list__ex__length, fact_205_diff__diff__cancel, fact_34_not__less__eq, fact_150_bot__nat__0_Oextremum__uniqueI, fact_242_less__one, fact_148_le__trans, fact_114_gr__implies__not0, fact_201_diff__0__eq__0, fact_245_length__tl, fact_227_Suc__diff__le, fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062, fact_44_list__eq__iff__nth__eq, fact_208_diff__is__0__eq, fact_24_Suc__inject, fact_192_LastOfIndex, fact_18_nat_Oinject, fact_216_le__diff__iff, fact_215_Nat_Odiff__diff__eq, help_If_3_1_If_001t__Nat__Onat_T, fact_213_diff__le__self, fact_94_remdups__adj_Osimps_I1_J, fact_199_diff__zero, fact_229_diff__less__mono, fact_20_NotEmpty_I1_J, fact_188_zero__less__iff__neq__zero, fact_138_last__remdups__adj, fact_153_less__eq__nat_Osimps_I1_J, fact_210_diff__right__commute, fact_106_nat_OdiscI, fact_2_NotEmpty_I2_J, fact_65_LengthStep, fact_221_less__imp__diff__less, fact_243__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_93_remdups__adj_Osimps_I1_J, fact_23_lessI, help_If_1_1_If_001t__Nat__Onat_T, fact_54_linorder__neqE__nat, fact_4_length__induct, fact_198_cancel__comm__monoid__add__class_Odiff__cancel, fact_163_transitive__stepwise__le, fact_135_Suc__le__mono, fact_167_le__eq__less__or__eq, fact_214_diff__le__mono, fact_236_PrefixListMonotonicity, fact_246_length__tl, fact_14_less__not__refl, fact_64_list__ex1__simps_I1_J, fact_171_Suc__leI, fact_74_AssumpGreaterOccurrence_I3_J, fact_26_not__less__less__Suc__eq, fact_234_KeepProperty, fact_73_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, fact_98_old_Onat_Oinducts, fact_96_list_Osel_I2_J, fact_88_length__0__conv, fact_72_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, fact_143_lift__Suc__mono__le, fact_247_Suc__diff__1, fact_219_diffs0__imp__equal, fact_134_le0, fact_109_nat_Odistinct_I1_J, fact_187_remdups__adj__length__ge1, fact_125_Case2ImplThesis, fact_30_Suc__less__SucD, fact_228_less__diff__iff, fact_161_full__nat__induct, fact_207_diff__is__0__eq_H, fact_47_nth__equalityI, fact_222_diff__less__mono2, fact_141_zero__le, fact_15_less__not__refl2, fact_101_Zero__neq__Suc, fact_133_bot__nat__0_Oextremum, fact_103_zero__induct, fact_154_Suc__leD, fact_119_All__less__Suc2, fact_25_n__not__Suc__n, fact_118_gr0__implies__Suc, fact_29_less__trans__Suc, fact_195_PrefixSameOnLow, fact_127_NotConsumedIntermediate, fact_165_le__neq__implies__less, fact_190_not__less__zero, fact_178_less__eq__Suc__le, fact_32_Suc__less__eq2, fact_232_PrefixListTransitive, fact_12_size__neq__size__imp__neq, fact_35_less__Suc__eq, fact_123_list_Osize_I3_J, fact_60_list__ex__length, fact_105_nat__induct, fact_111_not__gr0, fact_108_old_Onat_Odistinct_I2_J, fact_182_last__tl, fact_144_Nat_Oex__has__greatest__nat, fact_37_less__SucI, fact_177_less__Suc__eq__le, fact_83_list__ex__simps_I2_J, fact_254_Suc__diff__eq__diff__pred, fact_211_diff__le__mono2, fact_31_less__antisym, fact_169_nat__less__le, fact_87_less__Suc0, fact_239__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_223_diff__commute, fact_120_gr0__conv__Suc, fact_8_Ex__list__of__length, fact_57_Subset, fact_233_PrefixListTransitive, fact_91_AssumptionFirstOccSetDecrOrConsumed_I1_J, fact_147_eq__imp__le, fact_146_le__antisym, fact_46_Skolem__list__nth, fact_27_strict__inc__induct, fact_241__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_257_enabled__def, fact_58_IPrefixListEx, fact_69_nth__tl, fact_189_gr__implies__not__zero, fact_168_less__imp__le__nat, fact_48_nth__equalityI, fact_142_lift__Suc__antimono__le, fact_200_zero__diff, fact_230_diff__Suc__less, fact_172_Suc__le__eq, fact_128__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_13_nat__neq__iff, fact_129_Nitpick_Osize__list__simp_I2_J, fact_5_length__induct, fact_67_remdups__adj__adjacent, fact_181_remdups__adj__length, fact_253_Suc__pred_H, fact_202_diff__self__eq__0, fact_170_ex__least__nat__le, fact_43_list__eq__iff__nth__eq, fact_0_AssumpGreaterOccurrence_I1_J, fact_155_le__SucE, fact_33_All__less__Suc, fact_196_PrefixSameOnLow, fact_117_less__Suc__eq__0__disj, fact_140_EnabledOrConsumedAtLast, fact_218_minus__nat_Odiff__0, fact_180_remdups__adj__length, fact_255_last__conv__nth, fact_62_AssumpGreaterOccurrence_I2_J, fact_68_nth__tl, fact_104_diff__induct, fact_160_not__less__eq__eq, fact_224_diff__less, fact_149_le__refl, fact_206_zero__less__diff, fact_251_diff__Suc__eq__diff__pred, fact_249_One__nat__def, fact_197_IPrefixList, fact_240_EnabledIntermediate, fact_166_less__or__eq__imp__le, fact_10_neq__if__length__neq, fact_11_size__neq__size__imp__neq, fact_139_last__remdups__adj, fact_50_mem__Collect__eq, fact_159_Suc__n__not__le__n, fact_151_bot__nat__0_Oextremum__unique, fact_77_neq0__conv, fact_193__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_158_le__Suc__eq, fact_63_list__ex1__simps_I1_J, fact_49_lift__Suc__mono__less__iff, fact_226_Suc__diff__Suc, fact_51_Collect__mem__eq, fact_179_le__imp__less__Suc, fact_204_diff__Suc__Suc, fact_102_Suc__neq__Zero, fact_217_eq__diff__iff, fact_71_length__greater__0__conv, fact_156_le__SucI, fact_80_ConsumedMsg_I1_J, fact_137_MinImplAllBigger, fact_121_Ex__less__Suc2
% 75.87/14.88 % No. of inferences in proof: 574
% 75.87/14.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14503 ms resp. 13655 ms w/o parsing
% 77.44/15.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.44/15.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------