%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP060^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.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 08:06:36 AM UTC 2026
% Result : Theorem 74.42s 14.85s
% Output : Refutation 66.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 245
% Syntax : Number of formulae : 492 ( 270 unt; 0 typ; 0 def)
% Number of atoms : 1036 ( 419 equ; 4 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 3727 ( 172 ~; 22 |; 72 &;2947 @)
% ( 0 <=>; 514 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 260 ( 260 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 13 con; 0-4 aty)
% Number of variables : 1014 ( 18 ^; 934 !; 62 ?;1014 :)
% 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(message_p_v_type,type,
message_p_v: $tType ).
thf(nat_type,type,
nat: $tType ).
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(fLPThe1519354920_p_v_s_decl,type,
fLPThe1519354920_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_c1059388851t_unit ).
thf(fLPThe536531371_p_v_s_decl,type,
fLPThe536531371_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > nat > nat ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(prefix1615116500t_unit_decl,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(prefix47729710ge_p_v_decl,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(last_c571238084t_unit_decl,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(last_message_p_v_decl,type,
last_message_p_v: list_message_p_v > message_p_v ).
thf(nil_co1338500125t_unit_decl,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(nil_message_p_v_decl,type,
nil_message_p_v: list_message_p_v ).
thf(nth_co1649820636t_unit_decl,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(nth_message_p_v_decl,type,
nth_message_p_v: list_message_p_v > nat > message_p_v ).
thf(suc_decl,type,
suc: nat > nat ).
thf(size_s1406904903t_unit_decl,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(size_s1168481041ge_p_v_decl,type,
size_s1168481041ge_p_v: list_message_p_v > nat ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(fe_decl,type,
fe: nat > list_c1059388851t_unit ).
thf(ft_decl,type,
ft: nat > list_message_p_v ).
thf(index_decl,type,
index: nat ).
thf(msgInSet_decl,type,
msgInSet: message_p_v ).
thf(msg_decl,type,
msg: message_p_v ).
thf(n0_decl,type,
n0: nat ).
thf(n1_decl,type,
n1: nat ).
thf(nMsg_decl,type,
nMsg: nat ).
thf(n_decl,type,
n: nat ).
thf(103,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_diff__le__mono2) ).
thf(645,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)],[103]) ).
thf(32,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__imp__le__nat) ).
thf(365,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(57,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( prefix47729710ge_p_v @ A @ B )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ A ) )
=> ( ( nth_message_p_v @ A @ C )
= ( nth_message_p_v @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_PrefixSameOnLow) ).
thf(479,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)],[57]) ).
thf(3,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_not__gr0) ).
thf(249,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(178,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_less__Suc__eq__0__disj) ).
thf(941,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)],[178]) ).
thf(135,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat] :
( ( fLPThe1519354920_p_v_s @ A @ B @ C @ ( suc @ D ) )
= ( B @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ D ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_infiniteExecutionCfg_Osimps_I2_J) ).
thf(777,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat] :
( ( fLPThe1519354920_p_v_s @ A @ B @ C @ ( suc @ D ) )
= ( B @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ D ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(199,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_le__diff__iff_H) ).
thf(1005,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)],[199]) ).
thf(7,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_zero__reorient) ).
thf(276,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [A: list_c1059388851t_unit] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ A ) )
= ( A != nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_length__greater__0__conv) ).
thf(308,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)],[18]) ).
thf(209,axiom,
~ ? [A: nat] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
& ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ A )
& ( msg
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235__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(1073,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)],[209]) ).
thf(1,conjecture,
( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) )
= ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) )
!= ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(247,plain,
( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) )
!= ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_le0) ).
thf(379,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(204,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ n1 @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( msgInSet
!= ( nth_message_p_v @ ( ft @ index ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_Occ5_H) ).
thf(1041,plain,
! [A: nat] :
( ( ord_less_eq_nat @ n1 @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( msgInSet
!= ( nth_message_p_v @ ( ft @ index ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(243,axiom,
( msgInSet
!= ( nth_message_p_v @ ( ft @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_AssumpOcc6_H_I2_J) ).
thf(1173,plain,
( msgInSet
!= ( nth_message_p_v @ ( ft @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(71,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_le__0__eq) ).
thf(523,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_diff__diff__cancel) ).
thf(582,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)],[84]) ).
thf(74,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit,C: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ( prefix1615116500t_unit @ B @ C )
=> ( prefix1615116500t_unit @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_PrefixListTransitive) ).
thf(533,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)],[74]) ).
thf(180,axiom,
! [A: nat,B: nat > config256849571t_unit > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: config256849571t_unit] : ( B @ C @ D ) ) )
= ( ? [C: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_co1649820636t_unit @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_Skolem__list__nth) ).
thf(945,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)],[180]) ).
thf(76,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ ( suc @ D ) )
=> ( A @ D ) )
=> ( A @ ( minus_minus_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_zero__induct__lemma) ).
thf(538,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)],[76]) ).
thf(174,axiom,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_le__numeral__extra_I4_J) ).
thf(930,plain,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(111,axiom,
! [A: list_c1059388851t_unit] :
( ( A != nil_co1338500125t_unit )
=> ( ( last_c571238084t_unit @ A )
= ( nth_co1649820636t_unit @ A @ ( minus_minus_nat @ ( size_s1406904903t_unit @ A ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_last__conv__nth) ).
thf(670,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)],[111]) ).
thf(42,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_bot__nat__0_Onot__eq__extremum) ).
thf(404,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(230,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Suc__le__lessD) ).
thf(1127,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)],[230]) ).
thf(149,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( A
= ( suc @ ( minus_minus_nat @ A @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Suc__pred_H) ).
thf(841,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)],[149]) ).
thf(11,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_less__zeroE) ).
thf(288,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__irrefl__nat) ).
thf(320,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(49,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_not__less__zero) ).
thf(436,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(105,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_diff__Suc__Suc) ).
thf(651,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(124,axiom,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zero__less__Suc) ).
thf(719,plain,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(86,axiom,
! [A: nat] : ( prefix47729710ge_p_v @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_IPrefixList) ).
thf(587,plain,
! [A: nat] : ( prefix47729710ge_p_v @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(167,axiom,
ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_ShorterTrace) ).
thf(917,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)],[167]) ).
thf(232,axiom,
! [A: nat] : ( prefix1615116500t_unit @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_IPrefixListEx) ).
thf(1132,plain,
! [A: nat] : ( prefix1615116500t_unit @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(94,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_diff__commute) ).
thf(606,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)],[94]) ).
thf(10,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_neq__if__length__neq) ).
thf(284,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)],[10]) ).
thf(88,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ n1 @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( msgInSet
!= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_AssumptionSubset2_I5_J) ).
thf(591,plain,
! [A: nat] :
( ( ord_less_eq_nat @ n1 @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( msgInSet
!= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(223,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( suc @ B ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_diff__Suc__eq__diff__pred) ).
thf(1109,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)],[223]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_le__SucE) ).
thf(623,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)],[97]) ).
thf(59,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( prefix47729710ge_p_v @ A @ B )
=> ( ord_less_nat @ ( size_s1168481041ge_p_v @ A ) @ ( size_s1168481041ge_p_v @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_PrefixListMonotonicity) ).
thf(485,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)],[59]) ).
thf(67,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_le__zero__eq) ).
thf(514,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(238,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_zero__induct) ).
thf(1151,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)],[238]) ).
thf(30,axiom,
( ? [A: nat] :
( ( ord_less_eq_nat @ n0 @ A )
& ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
& ( ( nth_message_p_v @ ( ft @ n ) @ A )
= msg ) )
=> ? [A: nat] :
( ( ord_less_eq_nat @ n @ A )
& ? [B: nat] :
( ( ord_less_eq_nat @ n0 @ B )
& ( ord_less_nat @ B @ ( size_s1168481041ge_p_v @ ( ft @ A ) ) )
& ( msg
= ( nth_message_p_v @ ( ft @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_Case2ImplThesis) ).
thf(353,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)],[30]) ).
thf(188,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_n__not__Suc__n) ).
thf(966,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(92,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Ex__less__Suc) ).
thf(602,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)],[92]) ).
thf(115,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_AssumptionSubset_I3_J) ).
thf(692,plain,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(226,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_diff__less) ).
thf(1119,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)],[226]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_gr__implies__not0) ).
thf(396,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(108,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_le__diff__iff) ).
thf(660,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)],[108]) ).
thf(45,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Nat_Oex__has__greatest__nat) ).
thf(411,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)],[45]) ).
thf(194,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_lift__Suc__mono__le) ).
thf(988,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)],[194]) ).
thf(50,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_bot__nat__0_Oextremum) ).
thf(439,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(6,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= ( size_s1168481041ge_p_v @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ A ) )
=> ( ( nth_message_p_v @ A @ C )
= ( nth_message_p_v @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_nth__equalityI) ).
thf(270,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)],[6]) ).
thf(141,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_diff__le__self) ).
thf(793,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_less__Suc__eq) ).
thf(810,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)],[143]) ).
thf(36,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_infinite__descent) ).
thf(381,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)],[36]) ).
thf(206,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_inc__induct) ).
thf(1047,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)],[206]) ).
thf(240,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ ( suc @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_diff__Suc__less) ).
thf(1163,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)],[240]) ).
thf(183,axiom,
( ( (=) @ list_c1059388851t_unit )
= ( ^ [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( ( nth_co1649820636t_unit @ A @ C )
= ( nth_co1649820636t_unit @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_list__eq__iff__nth__eq) ).
thf(952,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)],[183]) ).
thf(16,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_less__nat__zero__code) ).
thf(302,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(228,axiom,
ord_less_nat @ zero_zero_nat @ one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_less__numeral__extra_I1_J) ).
thf(1123,plain,
ord_less_nat @ zero_zero_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(147,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( ord_less_nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_dec__induct) ).
thf(820,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)],[147]) ).
thf(14,axiom,
! [A: nat,B: nat > message_p_v > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: message_p_v] : ( B @ C @ D ) ) )
= ( ? [C: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_message_p_v @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Skolem__list__nth) ).
thf(297,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)],[14]) ).
thf(185,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_le__Suc__eq) ).
thf(957,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)],[185]) ).
thf(163,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_diff__right__commute) ).
thf(894,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)],[163]) ).
thf(43,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_le__refl) ).
thf(407,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(116,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( suc @ ( minus_minus_nat @ A @ one_one_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Suc__diff__1) ).
thf(693,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)],[116]) ).
thf(100,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_AssumptionFair_I3_J) ).
thf(630,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(4,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
!= ( size_s1168481041ge_p_v @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_neq__if__length__neq) ).
thf(252,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)],[4]) ).
thf(157,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_diff__zero) ).
thf(879,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(25,axiom,
! [A: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= zero_zero_nat )
= ( A = nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_length__0__conv) ).
thf(329,plain,
! [A: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= zero_zero_nat )
= ( A = nil_co1338500125t_unit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(62,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
!= ( size_s1406904903t_unit @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_size__neq__size__imp__neq) ).
thf(493,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)],[62]) ).
thf(191,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( B @ D )
=> ( ( B @ ( suc @ D ) )
& ( C @ D ) ) ) )
=> ( ( B @ A )
=> ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_KeepProperty) ).
thf(974,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)],[191]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ B @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_diffs0__imp__equal) ).
thf(1106,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)],[222]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Suc__diff__diff) ).
thf(948,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)],[181]) ).
thf(41,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_le__numeral__extra_I3_J) ).
thf(403,plain,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(137,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( suc @ ( minus_minus_nat @ A @ ( suc @ zero_zero_nat ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Suc__pred) ).
thf(783,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)],[137]) ).
thf(154,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( ( nth_co1649820636t_unit @ A @ C )
= ( nth_co1649820636t_unit @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_PrefixSameOnLow) ).
thf(857,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)],[154]) ).
thf(69,axiom,
( ( size_s1168481041ge_p_v @ nil_message_p_v )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_list_Osize_I3_J) ).
thf(519,plain,
( ( size_s1168481041ge_p_v @ nil_message_p_v )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( minus_minus_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Nat_Odiff__diff__eq) ).
thf(578,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)],[83]) ).
thf(56,axiom,
! [A: list_message_p_v] :
( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ A ) )
= ( A != nil_message_p_v ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_length__greater__0__conv) ).
thf(476,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)],[56]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__not__refl3) ).
thf(526,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(121,axiom,
! [A: nat,B: nat] : ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_diff__less__Suc) ).
thf(706,plain,
! [A: nat,B: nat] : ( ord_less_nat @ ( minus_minus_nat @ A @ B ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(54,axiom,
( ( (=) @ list_message_p_v )
= ( ^ [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= ( size_s1168481041ge_p_v @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1168481041ge_p_v @ A ) )
=> ( ( nth_message_p_v @ A @ C )
= ( nth_message_p_v @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_list__eq__iff__nth__eq) ).
thf(471,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)],[54]) ).
thf(5,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_ex__least__nat__le) ).
thf(256,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)],[5]) ).
thf(203,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_less__SucI) ).
thf(1039,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(189,axiom,
ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__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(970,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)],[189]) ).
thf(38,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_bot__nat__0_Oextremum__uniqueI) ).
thf(393,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(196,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ A )
=> ( ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A )
!= msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_NotConsumedIntermediate) ).
thf(997,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)],[196]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Suc__mono) ).
thf(701,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)],[119]) ).
thf(128,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_old_Onat_Oinducts) ).
thf(738,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)],[128]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__less__Suc__eq) ).
thf(654,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)],[106]) ).
thf(246,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ nMsg @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( msg
!= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_AssumptionSubset3_I5_J) ).
thf(1192,plain,
! [A: nat] :
( ( ord_less_eq_nat @ nMsg @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
=> ( msg
!= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(192,axiom,
ord_less_eq_nat @ n1 @ nMsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_AssumptionSubset_I1_J) ).
thf(984,plain,
ord_less_eq_nat @ n1 @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(125,axiom,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_less__numeral__extra_I4_J) ).
thf(721,plain,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(198,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_not__less__eq__eq) ).
thf(1002,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)],[198]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_less__antisym) ).
thf(569,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)],[80]) ).
thf(219,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( suc @ ( minus_minus_nat @ B @ ( suc @ A ) ) )
= ( minus_minus_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Suc__diff__Suc) ).
thf(1099,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)],[219]) ).
thf(193,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat] :
( ( fLPThe536531371_p_v_s @ A @ B @ C @ ( suc @ D ) )
= ( C @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ D ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_infiniteExecutionMsg_Osimps_I2_J) ).
thf(985,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat] :
( ( fLPThe536531371_p_v_s @ A @ B @ C @ ( suc @ D ) )
= ( C @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ D ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(64,axiom,
! [A: nat] :
? [B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Ex__list__of__length) ).
thf(503,plain,
! [A: nat] :
? [B: list_c1059388851t_unit] :
( ( size_s1406904903t_unit @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(93,axiom,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Occ3_H) ).
thf(605,plain,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(19,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__not__refl) ).
thf(311,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(107,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_gr0__conv__Suc) ).
thf(657,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(242,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Suc__less__eq) ).
thf(1170,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)],[242]) ).
thf(202,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Suc__neq__Zero) ).
thf(1035,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(73,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ n @ A )
=> ! [B: nat] :
( ( ord_less_nat @ B @ ( size_s1168481041ge_p_v @ ( ft @ A ) ) )
=> ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ B )
=> ( msg
!= ( nth_message_p_v @ ( ft @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_AssumptionFairContr) ).
thf(530,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)],[73]) ).
thf(161,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Suc__less__eq2) ).
thf(888,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)],[161]) ).
thf(172,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_AssumptionSubset3_I4_J) ).
thf(926,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__antisym) ).
thf(430,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)],[47]) ).
thf(221,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ n1 @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( ( nth_message_p_v @ ( ft @ index ) @ A )
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_OccSameMsg_H) ).
thf(1103,plain,
! [A: nat] :
( ( ord_less_eq_nat @ n1 @ A )
=> ( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( ( nth_message_p_v @ ( ft @ index ) @ A )
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(8,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_less__eq__nat_Osimps_I1_J) ).
thf(279,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(114,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_diff__le__mono) ).
thf(689,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)],[114]) ).
thf(133,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_All__less__Suc2) ).
thf(772,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)],[133]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_less__Suc__induct) ).
thf(711,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)],[123]) ).
thf(12,axiom,
! [A: nat] :
? [B: list_message_p_v] :
( ( size_s1168481041ge_p_v @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Ex__list__of__length) ).
thf(291,plain,
! [A: nat] :
? [B: list_message_p_v] :
( ( size_s1168481041ge_p_v @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(229,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
=> ( ( nth_co1649820636t_unit @ ( fe @ index ) @ A )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_SameCfgOnLow) ).
thf(1124,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)],[229]) ).
thf(9,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_not__less0) ).
thf(281,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(234,axiom,
( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) )
= ( last_c571238084t_unit @ ( fe @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_LastOfIndex) ).
thf(1139,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)],[234]) ).
thf(177,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_diff__induct) ).
thf(936,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)],[177]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Suc__le__eq) ).
thf(572,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)],[81]) ).
thf(139,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_not__less__less__Suc__eq) ).
thf(787,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)],[139]) ).
thf(216,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_AssumptionFirstOccSetDecrOrConsumed_I1_J) ).
thf(1092,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(169,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_lift__Suc__mono__less) ).
thf(919,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)],[169]) ).
thf(29,axiom,
! [A: list_message_p_v,B: list_message_p_v,C: list_message_p_v] :
( ( prefix47729710ge_p_v @ A @ B )
=> ( ( prefix47729710ge_p_v @ B @ C )
=> ( prefix47729710ge_p_v @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_PrefixListTransitive) ).
thf(350,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)],[29]) ).
thf(131,axiom,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ( ( B = zero_zero_nat )
| ~ ( A @ ( minus_minus_nat @ B @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_MinPredicate2) ).
thf(764,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)],[131]) ).
thf(165,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_less__SucE) ).
thf(900,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)],[165]) ).
thf(79,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_lessI) ).
thf(567,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_nat__le__linear) ).
thf(318,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)],[21]) ).
thf(227,axiom,
ord_less_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_060_Alength_A_Ife_Aindex_J_092_060close_062) ).
thf(1122,plain,
ord_less_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( size_s1406904903t_unit @ ( fe @ index ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(91,axiom,
( ( fe @ index )
!= nil_co1338500125t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_NotEmpty_I2_J) ).
thf(599,plain,
( ( fe @ index )
!= nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(211,axiom,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_AssumptionSubset2_I3_J) ).
thf(1080,plain,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(101,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq_nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_full__nat__induct) ).
thf(631,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)],[101]) ).
thf(145,axiom,
( ( nth_co1649820636t_unit @ ( fe @ index ) @ n1 )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062fe_Aindex_A_B_An1_A_061_Afe_A_ISuc_Aindex_J_A_B_An1_092_060close_062) ).
thf(816,plain,
( ( nth_co1649820636t_unit @ ( fe @ index ) @ n1 )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(95,axiom,
( ( fe @ ( suc @ index ) )
!= nil_co1338500125t_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_NotEmpty_I1_J) ).
thf(609,plain,
( ( fe @ ( suc @ index ) )
!= nil_co1338500125t_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(23,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_gr0I) ).
thf(323,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(89,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Suc__less__SucD) ).
thf(594,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)],[89]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_not__less__eq) ).
thf(848,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(237,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Suc__leD) ).
thf(1149,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)],[237]) ).
thf(98,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_EnabledInSuc) ).
thf(626,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(132,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_not0__implies__Suc) ).
thf(769,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(245,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ zero_zero_nat )
=> ( ~ ( B @ A )
=> ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C )
& ~ ( B @ ( suc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_NatPredicateTippingPoint) ).
thf(1177,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)],[245]) ).
thf(224,axiom,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_AssumptionSubset3_I3_J) ).
thf(1112,plain,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nat__neq__iff) ).
thf(367,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)],[33]) ).
thf(78,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_nat__induct__at__least) ).
thf(552,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)],[78]) ).
thf(239,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170__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(1162,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)],[239]) ).
thf(127,axiom,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J) ).
thf(726,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)],[127]) ).
thf(53,axiom,
! [A: list_c1059388851t_unit > $o,B: list_c1059388851t_unit] :
( ! [C: list_c1059388851t_unit] :
( ! [D: list_c1059388851t_unit] :
( ( ord_less_nat @ ( size_s1406904903t_unit @ D ) @ ( size_s1406904903t_unit @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_length__induct) ).
thf(462,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)],[53]) ).
thf(176,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_lift__Suc__mono__less__iff) ).
thf(932,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)],[176]) ).
thf(205,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_minus__nat_Odiff__0) ).
thf(1044,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(207,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_zero__diff) ).
thf(1066,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(136,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
=> ( ( nth_message_p_v @ ( ft @ index ) @ A )
= ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_SameMsgOnLow) ).
thf(780,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)],[136]) ).
thf(159,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( minus_minus_nat @ B @ ( minus_minus_nat @ A @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Suc__diff__eq__diff__pred) ).
thf(883,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)],[159]) ).
thf(201,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_strict__inc__induct) ).
thf(1015,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)],[201]) ).
thf(244,axiom,
ord_less_nat @ zero_zero_nat @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_AssumpOcc6_H_I1_J) ).
thf(1176,plain,
ord_less_nat @ zero_zero_nat @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(225,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Nat_OlessE) ).
thf(1113,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)],[225]) ).
thf(197,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_le__SucI) ).
thf(1000,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)],[197]) ).
thf(170,axiom,
ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__092_060open_062fe_Aindex_A_092_060in_062_D_Alength_092_060close_062) ).
thf(922,plain,
ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__diff__iff) ).
thf(685,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)],[113]) ).
thf(70,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_less__numeral__extra_I3_J) ).
thf(521,plain,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(152,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_one__reorient) ).
thf(851,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(220,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msgInSet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Occ2_H) ).
thf(1102,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(55,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_not__gr__zero) ).
thf(473,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_linorder__neqE__nat) ).
thf(490,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)],[61]) ).
thf(241,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Zero__not__Suc) ).
thf(1166,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(87,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_le__imp__less__Suc) ).
thf(589,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)],[87]) ).
thf(179,axiom,
ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_AssumptionFair_I2_J) ).
thf(944,plain,
ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(142,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ one_one_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( B @ C )
=> ( B @ ( suc @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_nat__induct__non__zero) ).
thf(795,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)],[142]) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_less__trans__Suc) ).
thf(927,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)],[173]) ).
thf(236,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_nat_Odistinct_I1_J) ).
thf(1145,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_less__not__refl2) ).
thf(458,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(233,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Suc__lessE) ).
thf(1134,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)],[233]) ).
thf(104,axiom,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Suc__n__not__le__n) ).
thf(648,plain,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(60,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__trans) ).
thf(487,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)],[60]) ).
thf(212,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_diff__is__0__eq_H) ).
thf(1081,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)],[212]) ).
thf(129,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat,E: list_message_p_v] :
( ( ( fLPThe536531371_p_v_s @ A @ B @ C @ D )
= E )
=> ( ( ( D = zero_zero_nat )
=> ( E != nil_message_p_v ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( C @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ F ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_infiniteExecutionMsg_Oelims) ).
thf(749,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v,D: nat,E: list_message_p_v] :
( ( ( fLPThe536531371_p_v_s @ A @ B @ C @ D )
= E )
=> ( ( ( D = zero_zero_nat )
=> ( E != nil_message_p_v ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( C @ ( fLPThe1519354920_p_v_s @ A @ B @ C @ F ) @ ( fLPThe536531371_p_v_s @ A @ B @ C @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_nat_OdiscI) ).
thf(640,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(160,axiom,
ord_less_nat @ ( minus_minus_nat @ n1 @ one_one_nat ) @ ( size_s1168481041ge_p_v @ ( ft @ index ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_SmallIndexTrace_H) ).
thf(887,plain,
ord_less_nat @ ( minus_minus_nat @ n1 @ one_one_nat ) @ ( size_s1168481041ge_p_v @ ( ft @ index ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(190,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_diff__is__0__eq) ).
thf(971,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)],[190]) ).
thf(184,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Suc__lessI) ).
thf(954,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)],[184]) ).
thf(44,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__eq__less__or__eq) ).
thf(409,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(218,axiom,
ord_less_nat @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__092_060open_062n1_A_N_ASuc_A0_A_060_Alength_A_Ife_Aindex_J_A_N_ASuc_A0_092_060close_062) ).
thf(1098,plain,
ord_less_nat @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(112,axiom,
! [A: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,B: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,C: config256849571t_unit,D: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,E: list_c1059388851t_unit > list_message_p_v > list_message_p_v,F: nat] :
( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( A @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( B @ G @ H @ I @ zero_zero_nat )
=> ( ! [G: config256849571t_unit,H: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,I: list_c1059388851t_unit > list_message_p_v > list_message_p_v,J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J) ).
thf(673,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)],[112]) ).
thf(51,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_infinite__descent0) ).
thf(441,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)],[51]) ).
thf(214,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_nat_Oinject) ).
thf(1085,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(182,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ n1 ) @ msgInSet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Occ4_H) ).
thf(951,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ n1 ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_Suc__leI) ).
thf(585,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)],[85]) ).
thf(34,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_nat__less__induct) ).
thf(370,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)],[34]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_less__imp__diff__less) ).
thf(703,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)],[120]) ).
thf(235,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_old_Onat_Odistinct_I2_J) ).
thf(1141,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(156,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_transitive__stepwise__le) ).
thf(864,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)],[156]) ).
thf(20,axiom,
! [A: list_message_p_v,B: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
!= ( size_s1168481041ge_p_v @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_size__neq__size__imp__neq) ).
thf(314,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)],[20]) ).
thf(96,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_nat__induct) ).
thf(612,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)],[96]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__or__eq__imp__le) ).
thf(497,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)],[63]) ).
thf(195,axiom,
! [A: nat,B: nat,C: nat,D: message_p_v] :
( ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_nat @ B @ ( size_s1406904903t_unit @ ( fe @ C ) ) )
& ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ C ) @ A ) @ D ) )
=> ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ C ) @ B ) @ D )
| ? [E: nat] :
( ( ord_less_eq_nat @ A @ E )
& ( ord_less_nat @ E @ ( size_s1168481041ge_p_v @ ( ft @ C ) ) )
& ( ( nth_message_p_v @ ( ft @ C ) @ E )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_MessageStaysOrConsumed) ).
thf(991,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)],[195]) ).
thf(99,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_gr0__implies__Suc) ).
thf(627,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(213,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_AssumptionCase1ImplThesis_H) ).
thf(1084,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(31,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( prefix1615116500t_unit @ A @ B )
=> ( ord_less_nat @ ( size_s1406904903t_unit @ A ) @ ( size_s1406904903t_unit @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_PrefixListMonotonicity) ).
thf(363,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)],[31]) ).
thf(175,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) @ msgInSet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_AssumpOcc6_H_I3_J) ).
thf(931,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(58,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_le__neq__implies__less) ).
thf(482,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)],[58]) ).
thf(166,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_ex__least__nat__less) ).
thf(903,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)],[166]) ).
thf(162,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(891,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(150,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Zero__neq__Suc) ).
thf(844,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Suc__lessD) ).
thf(699,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(144,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq_nat @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ C ) @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_lift__Suc__antimono__le) ).
thf(813,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)],[144]) ).
thf(37,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_zero__less__iff__neq__zero) ).
thf(390,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(138,axiom,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msgInSet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_AssumptionSubset2_I2_J) ).
thf(786,plain,
enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(187,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_All__less__Suc) ).
thf(963,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)],[187]) ).
thf(68,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_zero__le) ).
thf(517,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_diff__less__mono) ).
thf(667,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)],[110]) ).
thf(210,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Suc__le__D) ).
thf(1077,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)],[210]) ).
thf(130,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_AssumptionSubset2_I4_J) ).
thf(763,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_gr__implies__not__zero) ).
thf(346,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(77,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_diff__self__eq__0) ).
thf(549,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(75,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nat__less__le) ).
thf(536,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(48,axiom,
! [A: list_message_p_v] :
( ( ( size_s1168481041ge_p_v @ A )
= zero_zero_nat )
= ( A = nil_message_p_v ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_length__0__conv) ).
thf(433,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)],[48]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_eq__imp__le) ).
thf(510,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(15,axiom,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_list_Osize_I3_J) ).
thf(300,plain,
( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(146,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ A )
=> ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ A ) @ msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_EnabledIntermediate) ).
thf(818,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)],[146]) ).
thf(153,axiom,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_diff__Suc__1) ).
thf(854,plain,
! [A: nat] :
( ( minus_minus_nat @ ( suc @ A ) @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zero__less__diff) ).
thf(790,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)],[140]) ).
thf(17,axiom,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe536531371_p_v_s @ A @ B @ C @ zero_zero_nat )
= nil_message_p_v ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_infiniteExecutionMsg_Osimps_I1_J) ).
thf(305,plain,
! [A: config256849571t_unit,B: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,C: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe536531371_p_v_s @ A @ B @ C @ zero_zero_nat )
= nil_message_p_v ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_gr__zeroI) ).
thf(326,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(27,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_less__mono__imp__le__mono) ).
thf(341,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)],[27]) ).
thf(65,axiom,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_MinPredicate) ).
thf(506,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)],[65]) ).
thf(164,axiom,
! [A: list_message_p_v] :
( ( A != nil_message_p_v )
=> ( ( last_message_p_v @ A )
= ( nth_message_p_v @ A @ ( minus_minus_nat @ ( size_s1168481041ge_p_v @ A ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_last__conv__nth) ).
thf(897,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)],[164]) ).
thf(109,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_diff__0__eq__0) ).
thf(664,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(40,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_neq0__conv) ).
thf(400,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_less__Suc__eq__le) ).
thf(960,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)],[186]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Suc__le__mono) ).
thf(696,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)],[117]) ).
thf(13,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_bot__nat__0_Oextremum__unique) ).
thf(294,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(168,axiom,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ) @ msgInSet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36__092_060open_062enabled_A_Ife_Aindex_A_B_A_Ilength_A_Ife_Aindex_J_A_N_A1_J_J_AmsgInSet_092_060close_062) ).
thf(918,plain,
enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_Suc__diff__le) ).
thf(575,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)],[82]) ).
thf(46,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_bot__nat__0_Oextremum__strict) ).
thf(427,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(155,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ( minus_minus_nat @ B @ A )
= ( minus_minus_nat @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_eq__diff__iff) ).
thf(860,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)],[155]) ).
thf(90,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__Suc0) ).
thf(596,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(126,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ C )
=> ( ord_less_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_diff__less__mono2) ).
thf(723,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)],[126]) ).
thf(217,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Suc__inject) ).
thf(1093,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(148,axiom,
( ord_less_nat
= ( ^ [A: nat] : ( ord_less_eq_nat @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_less__eq__Suc__le) ).
thf(839,plain,
( ord_less_nat
= ( ^ [A: nat] : ( ord_less_eq_nat @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(26,axiom,
! [A: list_message_p_v > $o,B: list_message_p_v] :
( ! [C: list_message_p_v] :
( ! [D: list_message_p_v] :
( ( ord_less_nat @ ( size_s1168481041ge_p_v @ D ) @ ( size_s1168481041ge_p_v @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_length__induct) ).
thf(332,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)],[26]) ).
thf(231,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_old_Onat_Oinject) ).
thf(1129,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(200,axiom,
! [A: list_c1059388851t_unit,B: list_c1059388851t_unit] :
( ( ( size_s1406904903t_unit @ A )
= ( size_s1406904903t_unit @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1406904903t_unit @ A ) )
=> ( ( nth_co1649820636t_unit @ A @ C )
= ( nth_co1649820636t_unit @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_nth__equalityI) ).
thf(1009,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)],[200]) ).
thf(171,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_less__one) ).
thf(923,plain,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(134,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_One__nat__def) ).
thf(775,plain,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(215,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_old_Onat_Odistinct_I1_J) ).
thf(1088,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(208,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_old_Onat_Oexhaust) ).
thf(1069,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(122,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Ex__less__Suc2) ).
thf(708,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)],[122]) ).
thf(158,axiom,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_AssumptionSubset_I2_J) ).
thf(882,plain,
firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(28113,plain,
$false,
inference(e,[status(thm)],[645,365,479,249,941,777,1005,276,308,1073,247,379,1041,1173,523,582,533,945,538,930,670,404,1127,841,288,320,436,651,719,587,917,1132,606,284,591,1109,623,485,514,1151,353,966,602,692,1119,396,660,411,988,439,270,793,810,381,1047,1163,952,302,1123,820,297,957,894,407,693,630,252,879,329,493,974,1106,948,403,783,857,519,578,476,526,706,471,256,1039,970,393,997,701,738,654,1192,984,721,1002,569,1099,985,503,605,311,657,1170,1035,530,888,926,430,1103,279,689,772,711,291,1124,281,1139,936,572,787,1092,919,350,764,900,567,318,1122,599,1080,631,816,609,323,594,848,1149,626,769,1177,1112,367,552,1162,726,462,932,1044,1066,780,883,1015,1176,1113,1000,922,685,521,851,1102,473,490,1166,589,944,795,927,1145,458,1134,648,487,1081,749,640,887,971,954,409,1098,673,441,1085,951,585,370,703,1141,864,314,612,497,991,627,1084,363,931,482,903,891,844,699,813,390,786,963,517,667,1077,763,346,549,536,433,510,300,818,854,790,305,326,341,506,897,664,400,960,696,294,918,575,427,860,596,723,1093,839,332,1129,1009,923,775,1088,1069,708,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP060^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.22 % Computer : n008.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 19:45:24 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.23/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.60/1.30 % [INFO] Parsing done (396ms).
% 2.60/1.31 % [INFO] Running in sequential loop mode.
% 3.78/1.70 % [INFO] eprover registered as external prover.
% 3.78/1.71 % [INFO] Scanning for conjecture ...
% 3.97/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 244 axioms. Running axiom selection ...
% 4.16/1.99 % [INFO] Axiom selection finished. Selected 244 axioms (removed 0 axioms).
% 5.06/2.22 % [INFO] Problem is higher-order (TPTP THF).
% 5.06/2.25 % [INFO] Type checking passed.
% 5.06/2.25 % [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 ...
% 74.42/14.84 % External prover 'e' found a proof!
% 74.42/14.84 % [INFO] Killing All external provers ...
% 74.42/14.84 % Time passed: 14460ms (effective reasoning time: 13524ms)
% 74.42/14.84 % 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)>
% 74.42/14.85 % Axioms used in derivation (244): fact_95_All__less__Suc2, fact_44_Suc__diff__1, fact_228_AssumpOcc6_H_I2_J, fact_226_infiniteExecutionCfg_Osimps_I2_J, fact_204_list_Osize_I3_J, fact_198_less__numeral__extra_I3_J, fact_203_less__numeral__extra_I1_J, fact_9_NotEmpty_I1_J, fact_69_infinite__descent0, fact_39_zero__less__diff, fact_63_less__imp__le__nat, fact_150_Suc__lessI, fact_170__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_128_nat_Odistinct_I1_J, fact_206_nth__equalityI, fact_87_inc__induct, fact_189_Ex__list__of__length, fact_100_nat__induct__at__least, fact_106_le__SucI, fact_14_NotEmpty_I2_J, fact_107_le__SucE, fact_126_old_Onat_Odistinct_I1_J, fact_67_le__eq__less__or__eq, fact_104_le__Suc__eq, fact_175_le__zero__eq, fact_72_Nat_Oex__has__greatest__nat, fact_223_PrefixListMonotonicity, fact_157_Suc__pred_H, fact_54_less__zeroE, fact_234_NotConsumedIntermediate, fact_149_less__SucE, fact_80_lift__Suc__mono__le, fact_98_diff__less, fact_222_MinPredicate2, fact_26_less__nat__zero__code, fact_75_size__neq__size__imp__neq, fact_217_MinPredicate, fact_229_AssumptionFairContr, fact_2__092_060open_062fe_Aindex_A_B_An1_A_061_Afe_A_ISuc_Aindex_J_A_B_An1_092_060close_062, fact_242_AssumptionSubset2_I5_J, fact_4_AssumptionSubset2_I3_J, fact_129_minus__nat_Odiff__0, fact_179_EnabledInSuc, fact_30_bot__nat__0_Oextremum, fact_36__092_060open_062enabled_A_Ife_Aindex_A_B_A_Ilength_A_Ife_Aindex_J_A_N_A1_J_J_AmsgInSet_092_060close_062, fact_42_less__one, fact_109_diff__le__mono2, fact_60_less__not__refl3, fact_82_le__imp__less__Suc, fact_49_not__gr0, fact_152_Suc__lessD, fact_64_less__irrefl__nat, fact_193_le__numeral__extra_I3_J, fact_124_nat__induct, fact_240_Occ5_H, fact_89_Suc__le__eq, fact_243_AssumptionSubset3_I5_J, fact_97_Ex__less__Suc2, fact_21__092_060open_062fe_Aindex_A_092_060in_062_D_Alength_092_060close_062, fact_73_le__neq__implies__less, fact_210_list__eq__iff__nth__eq, fact_74_less__mono__imp__le__mono, fact_125_nat_OdiscI, fact_15__092_060open_062n1_A_N_ASuc_A0_A_060_Alength_A_Ife_Aindex_J_A_N_ASuc_A0_092_060close_062, fact_215_AssumptionFair_I3_J, fact_147_Ex__less__Suc, fact_68_ex__least__nat__less, fact_153_Nat_OlessE, fact_202_length__induct, fact_78_bot__nat__0_Oextremum__unique, fact_166_length__greater__0__conv, fact_220_KeepProperty, fact_221_NatPredicateTippingPoint, fact_205_list_Osize_I3_J, fact_85_le__less__Suc__eq, fact_211_list__eq__iff__nth__eq, fact_224_PrefixListMonotonicity, fact_31_diff__self__eq__0, fact_12_AssumpOcc6_H_I3_J, fact_171_LastOfIndex, fact_24_lessI, fact_90_Suc__leI, fact_216_AssumptionFair_I2_J, fact_187_neq__if__length__neq, fact_118_old_Onat_Oexhaust, fact_114_le__diff__iff, fact_92_less__diff__iff, fact_71_linorder__neqE__nat, fact_163_zero__induct__lemma, fact_195_gr__implies__not__zero, fact_123_diff__induct, fact_32_diff__0__eq__0, fact_43_Suc__pred, fact_55_nat__less__le, fact_144_All__less__Suc, fact_159_Suc__inject, fact_27_bot__nat__0_Onot__eq__extremum, fact_176_not__gr__zero, fact_17_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, fact_79_bot__nat__0_Oextremum__uniqueI, fact_120_Zero__neq__Suc, fact_84_less__Suc__eq__le, fact_174_Occ2_H, fact_151_Suc__lessE, fact_20_AssumptionSubset_I1_J, fact_191_last__conv__nth, fact_177_zero__diff, fact_113_Nat_Odiff__diff__eq, fact_197_gr__zeroI, fact_232_SameMsgOnLow, fact_35_AssumptionSubset2_I4_J, fact_178_diff__zero, fact_168_length__0__conv, fact_130_diffs0__imp__equal, fact_19_nat_Oinject, fact_238_MessageStaysOrConsumed, fact_1_SameCfgOnLow, fact_58_nat__le__linear, fact_169_EnabledIntermediate, fact_148_less__SucI, fact_102_not__less__eq__eq, fact_108_Suc__leD, fact_239_AssumptionSubset_I3_J, fact_158_n__not__Suc__n, fact_57_less__not__refl, fact_208_Skolem__list__nth, fact_122_zero__induct, fact_37_zero__less__Suc, fact_13__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_213_PrefixSameOnLow, fact_0_Occ3_H, fact_77_bot__nat__0_Oextremum__strict, fact_66_infinite__descent, fact_181_AssumptionSubset3_I4_J, fact_112_diff__le__mono, fact_5_AssumpOcc6_H_I1_J, fact_162_Suc__diff__Suc, fact_65_nat__less__induct, fact_61_ex__least__nat__le, fact_48_le__refl, fact_40_diff__is__0__eq, fact_154_less__imp__diff__less, fact_116_not0__implies__Suc, fact_117_old_Onat_Oinducts, fact_115_eq__diff__iff, fact_70_less__or__eq__imp__le, fact_236_OccSameMsg_H, fact_33_diff__diff__cancel, fact_99_transitive__stepwise__le, fact_142_less__antisym, fact_86_Suc__le__lessD, fact_194_zero__less__iff__neq__zero, fact_81_lift__Suc__antimono__le, fact_137_not__less__less__Suc__eq, fact_139_less__Suc__induct, fact_46_gr0I, fact_76_size__neq__size__imp__neq, fact_50_le__trans, fact_233_SmallIndexTrace_H, fact_214_infiniteExecutionMsg_Osimps_I1_J, fact_134_nat__induct__non__zero, fact_196_not__less__zero, fact_235__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_131_lift__Suc__mono__less__iff, fact_155_diff__less__mono2, fact_83_less__eq__Suc__le, fact_22_Suc__less__eq, fact_93_less__Suc__eq__0__disj, fact_172_cancel__comm__monoid__add__class_Odiff__cancel, fact_111_diff__le__self, fact_227_infiniteExecutionMsg_Osimps_I2_J, fact_51_eq__imp__le, fact_62_gr__implies__not0, fact_207_nth__equalityI, fact_186_neq__if__length__neq, fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_060_Alength_A_Ife_Aindex_J_092_060close_062, fact_6_diff__Suc__1, fact_188_Ex__list__of__length, fact_225_infiniteExecutionMsg_Oelims, fact_212_PrefixSameOnLow, fact_28_Suc__le__mono, fact_180_AssumptionSubset2_I2_J, fact_8_Suc__diff__diff, fact_143_Suc__less__eq2, fact_136_One__nat__def, fact_88_dec__induct, fact_237_AssumptionSubset_I2_J, fact_230_IPrefixList, fact_146_less__Suc__eq, fact_167_length__0__conv, fact_182_AssumptionCase1ImplThesis_H, fact_38_less__Suc0, fact_127_old_Onat_Odistinct_I2_J, fact_199_le__numeral__extra_I4_J, fact_192_zero__le, fact_91_diff__less__mono, fact_141_Suc__less__SucD, fact_161_diff__less__Suc, fact_10_IPrefixListEx, fact_218_PrefixListTransitive, fact_59_less__not__refl2, fact_11_diff__Suc__eq__diff__pred, fact_119_Zero__not__Suc, fact_200_less__numeral__extra_I4_J, fact_184_one__reorient, fact_164_AssumptionSubset3_I3_J, fact_140_less__trans__Suc, fact_52_not__less0, fact_132_lift__Suc__mono__less, fact_47_le__0__eq, fact_173_AssumptionFirstOccSetDecrOrConsumed_I1_J, fact_145_not__less__eq, fact_16_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, fact_190_last__conv__nth, fact_135_Suc__diff__le, fact_18_old_Onat_Oinject, fact_110_le__diff__iff_H, fact_41_diff__is__0__eq_H, fact_53_le__antisym, fact_156_Suc__diff__eq__diff__pred, fact_23_Suc__mono, fact_45_less__eq__nat_Osimps_I1_J, fact_56_nat__neq__iff, fact_121_Suc__neq__Zero, fact_96_gr0__conv__Suc, fact_165_length__greater__0__conv, fact_231_ShorterTrace, fact_94_gr0__implies__Suc, fact_138_strict__inc__induct, fact_103_Suc__n__not__le__n, fact_185_diff__right__commute, fact_7_diff__Suc__Suc, fact_105_Suc__le__D, fact_133_diff__Suc__less, fact_241_Case2ImplThesis, fact_209_Skolem__list__nth, fact_29_le0, fact_201_length__induct, fact_219_PrefixListTransitive, fact_160_diff__commute, fact_101_full__nat__induct, fact_34_Occ4_H, fact_25_neq0__conv, fact_183_zero__reorient
% 74.42/14.85 % No. of inferences in proof: 492
% 74.42/14.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14460 ms resp. 13524 ms w/o parsing
% 66.73/14.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 66.73/14.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------