%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP059^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:35 AM UTC 2026
% Result : Theorem 28.60s 8.50s
% Output : Refutation 30.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 271
% Syntax : Number of formulae : 593 ( 221 unt; 0 typ; 3 def)
% Number of atoms : 1636 ( 446 equ; 4 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 7552 ( 236 ~; 79 |; 89 &;6526 @)
% ( 0 <=>; 622 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 282 ( 282 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 47 usr; 16 con; 0-7 aty)
% Number of variables : 1286 ( 29 ^;1181 !; 73 ?;1286 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(v_type,type,
v: $tType ).
thf(s_type,type,
s: $tType ).
thf(p_type,type,
p: $tType ).
thf(size_decl,type,
size:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(neg_numeral_decl,type,
neg_numeral:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(wellorder_decl,type,
wellorder:
!>[TA: $tType] : $o ).
thf(comm_monoid_diff_decl,type,
comm_monoid_diff:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_decl,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(msgs_decl,type,
msgs:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( configuration_ext @ TD @ TC @ TB @ TA ) > ( message @ TD @ TC ) > nat ) ).
thf(enabled_decl,type,
enabled:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( message @ TC @ TB ) > $o ) ).
thf(isReceiverOf_decl,type,
isReceiverOf:
!>[TA: $tType,TB: $tType] : ( TB > ( message @ TB @ TA ) > $o ) ).
thf(firstOccurrence_decl,type,
firstOccurrence:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( message @ TC @ TB ) > nat > $o ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(prefixList_decl,type,
prefixList:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(last_decl,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(nth_decl,type,
nth:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(fe_decl,type,
fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
thf(firstOccSet_decl,type,
firstOccSet: nat > ( set @ ( message @ p @ v ) ) ).
thf(ft_decl,type,
ft: nat > ( list @ ( message @ p @ v ) ) ).
thf(index_decl,type,
index: nat ).
thf(msgInSet_decl,type,
msgInSet: message @ p @ v ).
thf(msg_decl,type,
msg: message @ p @ v ).
thf(n0_decl,type,
n0: nat ).
thf(n1_decl,type,
n1: nat ).
thf(nMsg_decl,type,
nMsg: nat ).
thf(n_decl,type,
n: nat ).
thf(p2_decl,type,
p2: p ).
thf(sk1_decl,type,
sk1: nat > ( nat > $o ) > nat ).
thf(sk2_decl,type,
sk2: ( nat > $o ) > nat ).
thf(sk19_decl,type,
sk19: p ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: nat,B: nat > $o] :
@+[C: nat] :
~ ( ( B @ C )
=> ( ord_less_eq @ nat @ C @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: nat > $o] :
@+[B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq @ nat @ C @ B ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: p] : ( isReceiverOf @ p @ v @ A @ msg ) ) ) ).
thf(200,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Suc__mono) ).
thf(1036,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)],[200]) ).
thf(86,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Suc__neq__Zero) ).
thf(629,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(248,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_infinite__descent) ).
thf(1190,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)],[248]) ).
thf(237,axiom,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225__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(1168,plain,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nat_Oinject) ).
thf(1105,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(50,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_not__less0) ).
thf(481,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Suc__less__eq) ).
thf(909,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)],[167]) ).
thf(85,axiom,
ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_AssumptionFair_I2_J) ).
thf(628,plain,
ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(253,axiom,
ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_ShorterTrace) ).
thf(1211,plain,
ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(62,axiom,
( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) @ ( one_one @ nat ) ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_EnabledOrConsumed) ).
thf(523,plain,
( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) @ ( one_one @ nat ) ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(104,axiom,
( ( fe @ index )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_NotEmpty_I2_J) ).
thf(683,plain,
( ( fe @ index )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(6,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_one__reorient) ).
thf(276,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(211,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_diff__Suc__Suc) ).
thf(1068,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)],[211]) ).
thf(191,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_zero__le) ).
thf(994,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(11,axiom,
( ( one_one @ nat )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_One__nat__def) ).
thf(307,plain,
( ( one_one @ nat )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(308,plain,
( ( suc @ ( zero_zero @ nat ) )
= ( one_one @ nat ) ),
inference(lifteq,[status(thm)],[307]) ).
thf(102,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_not__gr0) ).
thf(677,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(74,axiom,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_AssumptionSubset3_I4_J) ).
thf(597,plain,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(202,axiom,
wellorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(1041,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(251,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Suc__le__D) ).
thf(1205,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)],[251]) ).
thf(42,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(449,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(231,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_less__or__eq__imp__le) ).
thf(1142,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)],[231]) ).
thf(27,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( B @ ( zero_zero @ nat ) )
=> ( ~ ( B @ A )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C )
& ~ ( B @ ( suc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_NatPredicateTippingPoint) ).
thf(379,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)],[27]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_measure__induct__rule) ).
thf(550,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(58,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_diff__le__self) ).
thf(500,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(260,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_diff__left__mono) ).
thf(1233,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(144,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).
thf(836,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(59,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_less__numeral__extra_I3_J) ).
thf(502,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(503,plain,
! [TA: $tType] :
( ~ ( linord1659791738miring @ TA )
| ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(cnf,[status(esa)],[502]) ).
thf(1258,plain,
! [TA: $tType] :
( ~ $true
| ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) )
| ( ( linord1659791738miring @ nat )
!= ( linord1659791738miring @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[836,503]) ).
thf(1259,plain,
! [TA: $tType] :
( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) )
| ( ( linord1659791738miring @ nat )
!= ( linord1659791738miring @ TA ) ) ),
inference(simp,[status(thm)],[1258]) ).
thf(1260,plain,
~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ),
inference(pattern_uni,[status(thm)],[1259:[bind_type(TA,$thf( nat ))]]) ).
thf(119,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_diff__zero) ).
thf(747,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(100,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Ex__less__Suc2) ).
thf(670,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)],[100]) ).
thf(162,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_lift__Suc__mono__le) ).
thf(898,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(265,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_neq__if__length__neq) ).
thf(1243,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(109,axiom,
( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ nMsg )
= ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115__092_060open_062fe_Aindex_A_B_AnMsg_A_061_Afe_A_ISuc_Aindex_J_A_B_AnMsg_092_060close_062) ).
thf(709,plain,
( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ nMsg )
= ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(147,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_bot__nat__0_Onot__eq__extremum) ).
thf(841,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(37,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_diff__right__commute) ).
thf(436,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(93,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_less__Suc0) ).
thf(651,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(183,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_less__nat__zero__code) ).
thf(973,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(204,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_old_Onat_Oexhaust) ).
thf(1046,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(206,axiom,
( ( fe @ ( suc @ index ) )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_NotEmpty_I1_J) ).
thf(1053,plain,
( ( fe @ ( suc @ index ) )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(1054,plain,
( ( fe @ ( suc @ index ) )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
inference(polarity_switch,[status(thm)],[1053]) ).
thf(1055,plain,
( ( fe @ ( suc @ index ) )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
inference(lifteq,[status(thm)],[1054]) ).
thf(23,axiom,
size @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(372,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(60,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_nat__induct__at__least) ).
thf(504,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)],[60]) ).
thf(82,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( suc @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Suc__diff__1) ).
thf(619,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)],[82]) ).
thf(208,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_diff__gt__0__iff__gt) ).
thf(1059,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_less__SucI) ).
thf(460,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(140,axiom,
( ( nMsg
!= ( zero_zero @ nat ) )
=> ( ~ ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) @ msg )
| ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_AssumptionSubset3_I6_J) ).
thf(817,plain,
( ( nMsg
!= ( zero_zero @ nat ) )
=> ( ~ ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) @ msg )
| ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(266,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_diff__strict__right__mono) ).
thf(1247,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(182,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_eq__imp__le) ).
thf(969,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(125,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_less__diff__iff) ).
thf(770,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)],[125]) ).
thf(34,axiom,
( ( enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_EnabledOrConsumedAtLast) ).
thf(416,plain,
( ( enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15,axiom,
( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_AssumpOcc6_I2_J) ).
thf(325,plain,
( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(220,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( size_size @ ( list @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_PrefixListMonotonicity) ).
thf(1100,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( size_size @ ( list @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(55,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(492,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_not__less__less__Suc__eq) ).
thf(591,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)],[72]) ).
thf(233,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_not__less__eq) ).
thf(1151,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(135,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).
thf(806,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(51,axiom,
? [A: p] : ( isReceiverOf @ p @ v @ A @ msg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Occ1) ).
thf(484,plain,
? [A: p] : ( isReceiverOf @ p @ v @ A @ msg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(485,plain,
isReceiverOf @ p @ v @ sk19 @ msg,
inference(cnf,[status(esa)],[484]) ).
thf(143,axiom,
! [A: nat,B: message @ p @ v] :
( ( member @ ( message @ p @ v ) @ B @ ( firstOccSet @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062) ).
thf(834,plain,
! [A: nat,B: message @ p @ v] :
( ( member @ ( message @ p @ v ) @ B @ ( firstOccSet @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_less__imp__diff__less) ).
thf(602,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)],[76]) ).
thf(238,axiom,
ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_AssumptionSubset2_I3_J) ).
thf(1169,plain,
ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(7,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ( prefixList @ TA @ B @ C )
=> ( prefixList @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_PrefixListTransitive) ).
thf(279,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ( prefixList @ TA @ B @ C )
=> ( prefixList @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(280,plain,
! [TA: $tType,C: list @ TA,B: list @ TA,A: list @ TA] :
( ~ ( prefixList @ TA @ A @ B )
| ~ ( prefixList @ TA @ B @ C )
| ( prefixList @ TA @ A @ C ) ),
inference(cnf,[status(esa)],[279]) ).
thf(255,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_le__imp__less__Suc) ).
thf(1215,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)],[255]) ).
thf(107,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ nMsg @ A )
=> ( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
=> ( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Occ5) ).
thf(692,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ nMsg @ A )
=> ( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
=> ( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(179,axiom,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msgInSet,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_AssumptionSubset2_I2_J) ).
thf(956,plain,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_Suc__le__eq) ).
thf(866,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)],[156]) ).
thf(44,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_lift__Suc__antimono__le) ).
thf(453,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(29,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ ( suc @ D ) )
=> ( A @ D ) )
=> ( A @ ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_zero__induct__lemma) ).
thf(396,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)],[29]) ).
thf(193,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( minus_minus @ nat @ ( suc @ B ) @ A )
= ( minus_minus @ nat @ B @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_Suc__diff__eq__diff__pred) ).
thf(998,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)],[193]) ).
thf(188,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_diff__eq__diff__less__eq) ).
thf(988,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(264,axiom,
wellorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Owellorder_4) ).
thf(1242,plain,
wellorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(227,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
=> ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ A )
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_SameMsgOnLow) ).
thf(1119,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ 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)],[227]) ).
thf(126,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_old_Onat_Odistinct_I1_J) ).
thf(774,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(213,axiom,
! [A: nat,B: nat,C: nat,D: message @ p @ v] :
( ( ( ord_less_eq @ nat @ A @ B )
& ( ord_less @ nat @ B @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ C ) ) )
& ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) @ A ) @ D ) )
=> ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) @ B ) @ D )
| ? [E: nat] :
( ( ord_less_eq @ nat @ A @ E )
& ( ord_less @ nat @ E @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ C ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ C ) @ E )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_MessageStaysOrConsumed) ).
thf(1074,plain,
! [A: nat,B: nat,C: nat,D: message @ p @ v] :
( ( ( ord_less_eq @ nat @ A @ B )
& ( ord_less @ nat @ B @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ C ) ) )
& ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) @ A ) @ D ) )
=> ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) @ B ) @ D )
| ? [E: nat] :
( ( ord_less_eq @ nat @ A @ E )
& ( ord_less @ nat @ E @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ C ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ C ) @ E )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(158,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_1) ).
thf(871,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(281,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(282,plain,
! [TA: $tType,TB: $tType] :
( ~ ( order @ TB )
| ( order @ ( TA > TB ) ) ),
inference(cnf,[status(esa)],[281]) ).
thf(1284,plain,
! [TA: $tType,TB: $tType] :
( ~ $true
| ( order @ ( TA > TB ) )
| ( ( order @ nat )
!= ( order @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[871,282]) ).
thf(1285,plain,
! [TA: $tType,TB: $tType] :
( ( order @ ( TA > TB ) )
| ( ( order @ nat )
!= ( order @ TB ) ) ),
inference(simp,[status(thm)],[1284]) ).
thf(1286,plain,
! [TA: $tType] : ( order @ ( TA > nat ) ),
inference(pattern_uni,[status(thm)],[1285:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( nat ))]]) ).
thf(1304,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ~ $true
| ( order @ ( TB > TC ) )
| ( ( order @ ( TA > nat ) )
!= ( order @ TC ) ) ),
inference(paramod_ordered,[status(thm)],[1286,282]) ).
thf(1305,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( order @ ( TB > TC ) )
| ( ( order @ ( TA > nat ) )
!= ( order @ TC ) ) ),
inference(simp,[status(thm)],[1304]) ).
thf(1306,plain,
! [TA: $tType,TB: $tType] : ( order @ ( TB > TA > nat ) ),
inference(pattern_uni,[status(thm)],[1305:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > nat ))]]) ).
thf(249,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Suc__diff__diff) ).
thf(1199,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)],[249]) ).
thf(137,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( A
= ( suc @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Suc__pred_H) ).
thf(810,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)],[137]) ).
thf(111,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_eq__iff__diff__eq__0) ).
thf(714,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(133,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat] : ( A @ ( zero_zero @ nat ) @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_diff__induct) ).
thf(798,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)],[133]) ).
thf(174,axiom,
ord_less_eq @ nat @ n1 @ nMsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_AssumptionSubset_I1_J) ).
thf(942,plain,
ord_less_eq @ nat @ n1 @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(38,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_diff__self) ).
thf(439,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1,conjecture,
ord_less @ nat @ ( minus_minus @ nat @ nMsg @ ( suc @ ( zero_zero @ nat ) ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less @ nat @ ( minus_minus @ nat @ nMsg @ ( suc @ ( zero_zero @ nat ) ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(270,plain,
~ ( ord_less @ nat @ ( minus_minus @ nat @ nMsg @ ( suc @ ( zero_zero @ nat ) ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(63,axiom,
! [A: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,B: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,C: configuration_ext @ p @ v @ s @ product_unit,D: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),E: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),F: nat] :
( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( A @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_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: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( B @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J) ).
thf(529,plain,
! [A: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,B: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,C: configuration_ext @ p @ v @ s @ product_unit,D: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),E: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),F: nat] :
( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( A @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_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: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( B @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_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)],[63]) ).
thf(180,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_diff__strict__mono) ).
thf(957,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(118,axiom,
firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_AssumptionSubset_I2_J) ).
thf(746,plain,
firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(127,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not0__implies__Suc) ).
thf(778,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(203,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_gr__implies__not0) ).
thf(1042,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(269,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_nat__neq__iff) ).
thf(1255,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)],[269]) ).
thf(241,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(1174,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(141,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zero__induct) ).
thf(820,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)],[141]) ).
thf(30,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_bot__nat__0_Oextremum) ).
thf(407,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(139,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_le__refl) ).
thf(815,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(117,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_infinite__descent0) ).
thf(729,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)],[117]) ).
thf(262,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zero__less__iff__neq__zero) ).
thf(1238,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(256,axiom,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Occ2) ).
thf(1217,plain,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(75,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( minus_minus @ nat @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_eq__diff__iff) ).
thf(598,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)],[75]) ).
thf(5,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_2) ).
thf(275,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(130,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_PrefixSameOnLow) ).
thf(788,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(19,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ C )
=> ( ord_less @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_diff__less__mono2) ).
thf(361,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)],[19]) ).
thf(84,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_diff__eq__diff__eq) ).
thf(625,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(161,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_dec__induct) ).
thf(879,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)],[161]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Suc__inject) ).
thf(852,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(98,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_less__zeroE) ).
thf(665,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(236,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq @ nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_full__nat__induct) ).
thf(1159,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)],[236]) ).
thf(56,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ B @ C ) )
= ( ord_less_eq @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_le__diff__iff_H) ).
thf(493,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)],[56]) ).
thf(122,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_infinite__descent__measure) ).
thf(757,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(195,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_bot__nat__0_Oextremum__strict) ).
thf(1012,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(149,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_gr0I) ).
thf(847,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(61,axiom,
~ ? [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
& ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ A )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133__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(519,plain,
~ ? [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
& ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ A )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(217,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_diff__less) ).
thf(1089,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)],[217]) ).
thf(177,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_less__mono__imp__le__mono) ).
thf(948,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)],[177]) ).
thf(115,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_diff__0__right) ).
thf(725,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(157,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_nat__le__linear) ).
thf(869,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)],[157]) ).
thf(226,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_less__numeral__extra_I4_J) ).
thf(1117,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1118,plain,
! [TA: $tType] :
( ~ ( linord1659791738miring @ TA )
| ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(cnf,[status(esa)],[1117]) ).
thf(152,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ nMsg @ A )
=> ( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
=> ( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_AssumptionSubset3_I5_J) ).
thf(857,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ nMsg @ A )
=> ( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
=> ( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(224,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_less__trans__Suc) ).
thf(1111,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)],[224]) ).
thf(258,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_old_Onat_Oinject) ).
thf(1227,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(16,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_bot__nat__0_Oextremum__uniqueI) ).
thf(328,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Suc__lessD) ).
thf(642,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(164,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( minus_minus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_diff__numeral__special_I9_J) ).
thf(901,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( minus_minus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(105,axiom,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Suc__n__not__le__n) ).
thf(686,plain,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(225,axiom,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Skolem__list__nth) ).
thf(1114,plain,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(187,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_le__antisym) ).
thf(985,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)],[187]) ).
thf(267,axiom,
ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_AssumptionSubset3_I3_J) ).
thf(1249,plain,
ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(94,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_le__numeral__extra_I3_J) ).
thf(654,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(194,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_infinite__descent0__measure) ).
thf(1002,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_inc__induct) ).
thf(569,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)],[70]) ).
thf(83,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_less__iff__diff__less__0) ).
thf(622,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(145,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ A )
=> ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ A ) @ msg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_EnabledIntermediate) ).
thf(837,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ A )
=> ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ A ) @ msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(205,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_gr0__conv__Suc) ).
thf(1050,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(46,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_zero__reorient) ).
thf(457,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Nat_OlessE) ).
thf(605,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)],[77]) ).
thf(250,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Ex__less__Suc) ).
thf(1202,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)],[250]) ).
thf(216,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_All__less__Suc) ).
thf(1086,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)],[216]) ).
thf(263,axiom,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_AssumpOcc6_I3_J) ).
thf(1241,plain,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(87,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_less__Suc__eq__0__disj) ).
thf(633,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)],[87]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_less__not__refl2) ).
thf(541,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(239,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat] : ( ord_less_eq @ nat @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_less__eq__Suc__le) ).
thf(1170,plain,
( ( ord_less @ nat )
= ( ^ [A: nat] : ( ord_less_eq @ nat @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(132,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_less__not__refl3) ).
thf(794,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(97,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Ex__list__of__length) ).
thf(662,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Suc__lessI) ).
thf(926,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)],[169]) ).
thf(69,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_old_Onat_Oinducts) ).
thf(558,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)],[69]) ).
thf(212,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_le__zero__eq) ).
thf(1071,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(178,axiom,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_diff__0__eq__0) ).
thf(953,plain,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(245,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_lift__Suc__mono__less__iff) ).
thf(1185,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(166,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_less__one) ).
thf(906,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(32,axiom,
( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) )
= ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_LastOfIndex) ).
thf(412,plain,
( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) )
= ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(120,axiom,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ( ( B
= ( zero_zero @ nat ) )
| ~ ( A @ ( minus_minus @ nat @ B @ ( one_one @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_MinPredicate2) ).
thf(750,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)],[120]) ).
thf(1272,plain,
( ( ( fe @ ( one_one @ nat ) )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) )
| ( ( suc @ index )
!= ( suc @ ( zero_zero @ nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[308,1055]) ).
thf(1273,plain,
( ( ( fe @ ( one_one @ nat ) )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) )
| ( index
!= ( zero_zero @ nat ) ) ),
inference(simp,[status(thm)],[1272]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Suc__less__eq2) ).
thf(689,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)],[106]) ).
thf(25,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_diff__le__mono) ).
thf(375,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)],[25]) ).
thf(234,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_le0) ).
thf(1154,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(165,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_diff__right__mono) ).
thf(904,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(9,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Nat_Oex__has__greatest__nat) ).
thf(283,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)],[9]) ).
thf(284,plain,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ( ? [B: nat] :
! [C: nat] :
( ( A @ C )
=> ( ord_less_eq @ nat @ C @ B ) )
=> ? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq @ nat @ C @ B ) ) ) ) ),
inference(miniscope,[status(thm)],[283]) ).
thf(285,plain,
! [D: nat,C: nat,B: nat,A: nat > $o] :
( ( ~ ( A @ B )
| ( A @ ( sk1 @ C @ A ) )
| ( A @ ( sk2 @ A ) ) )
& ( ~ ( A @ B )
| ( A @ ( sk1 @ C @ A ) )
| ~ ( A @ D )
| ( ord_less_eq @ nat @ D @ ( sk2 @ A ) ) )
& ( ~ ( A @ B )
| ~ ( ord_less_eq @ nat @ ( sk1 @ C @ A ) @ C )
| ( A @ ( sk2 @ A ) ) )
& ( ~ ( A @ B )
| ~ ( ord_less_eq @ nat @ ( sk1 @ C @ A ) @ C )
| ~ ( A @ D )
| ( ord_less_eq @ nat @ D @ ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[284]) ).
thf(286,plain,
! [C: nat,B: nat,A: nat > $o] :
( ~ ( A @ B )
| ( A @ ( sk1 @ C @ A ) )
| ( A @ ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[285]) ).
thf(65,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ A )
= ( nth @ TA @ A @ ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_last__conv__nth) ).
thf(545,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ A )
= ( nth @ TA @ A @ ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(160,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( minus_minus @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_Nat_Odiff__diff__eq) ).
thf(875,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)],[160]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_le__neq__implies__less) ).
thf(711,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)],[110]) ).
thf(89,axiom,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_list_Osize_I3_J) ).
thf(639,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(640,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(cnf,[status(esa)],[639]) ).
thf(641,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[640]) ).
thf(13,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_length__induct) ).
thf(313,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1271,plain,
~ ( ord_less @ nat @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) ),
inference(rewrite,[status(thm)],[270,308]) ).
thf(1278,plain,
! [TA: $tType,TB: $tType] :
( ~ $true
| ( order @ ( TA > TB ) )
| ( ( order @ $o )
!= ( order @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[275,282]) ).
thf(1279,plain,
! [TA: $tType,TB: $tType] :
( ( order @ ( TA > TB ) )
| ( ( order @ $o )
!= ( order @ TB ) ) ),
inference(simp,[status(thm)],[1278]) ).
thf(1280,plain,
! [TA: $tType] : ( order @ ( TA > $o ) ),
inference(pattern_uni,[status(thm)],[1279:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( $o ))]]) ).
thf(1301,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ~ $true
| ( order @ ( TB > TC ) )
| ( ( order @ ( TA > $o ) )
!= ( order @ TC ) ) ),
inference(paramod_ordered,[status(thm)],[1280,282]) ).
thf(1302,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( order @ ( TB > TC ) )
| ( ( order @ ( TA > $o ) )
!= ( order @ TC ) ) ),
inference(simp,[status(thm)],[1301]) ).
thf(1303,plain,
! [TA: $tType,TB: $tType] : ( order @ ( TB > TA > $o ) ),
inference(pattern_uni,[status(thm)],[1302:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > $o ))]]) ).
thf(1310,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ~ $true
| ( order @ ( TC > TD ) )
| ( ( order @ ( TB > TA > $o ) )
!= ( order @ TD ) ) ),
inference(paramod_ordered,[status(thm)],[1303,282]) ).
thf(1311,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( order @ ( TC > TD ) )
| ( ( order @ ( TB > TA > $o ) )
!= ( order @ TD ) ) ),
inference(simp,[status(thm)],[1310]) ).
thf(1312,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( order @ ( TC > TB > TA > $o ) ),
inference(pattern_uni,[status(thm)],[1311:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > $o ))]]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Suc__le__lessD) ).
thf(611,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)],[78]) ).
thf(176,axiom,
! [TA: $tType] : ( size @ ( list @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_3) ).
thf(946,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(947,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(cnf,[status(esa)],[946]) ).
thf(40,axiom,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_AssumptionSubset2_I4_J) ).
thf(445,plain,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zero__less__diff) ).
thf(936,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)],[172]) ).
thf(49,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( B @ ( one_one @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( B @ C )
=> ( B @ ( suc @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_nat__induct__non__zero) ).
thf(466,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)],[49]) ).
thf(218,axiom,
! [A: message @ p @ v,B: nat,C: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ C ) @ ( ft @ C ) @ A @ B )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062) ).
thf(1092,plain,
! [A: message @ p @ v,B: nat,C: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ C ) @ ( ft @ C ) @ A @ B )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(185,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_gr__zeroI) ).
thf(979,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(163,axiom,
isReceiverOf @ p @ v @ p2 @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_AssumptionFair_I4_J) ).
thf(900,plain,
isReceiverOf @ p @ v @ p2 @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(142,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_diff__eq__diff__less) ).
thf(831,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(4,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_le__numeral__extra_I4_J) ).
thf(273,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(274,plain,
! [TA: $tType] :
( ~ ( linord1659791738miring @ TA )
| ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(cnf,[status(esa)],[273]) ).
thf(192,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ A @ B ) @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_diff__less__Suc) ).
thf(996,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ A @ B ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] : ( size @ ( message @ TB @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_AsynchronousSystem_Omessage___Nat_Osize_6) ).
thf(271,plain,
! [TA: $tType,TB: $tType] : ( size @ ( message @ TB @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(154,axiom,
! [A: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ A )
=> ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_SmallIndex) ).
thf(863,plain,
! [A: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ A )
=> ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(129,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Zero__not__Suc) ).
thf(784,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(80,axiom,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_AssumptionCase1ImplThesis_H) ).
thf(616,plain,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(228,axiom,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_MinPredicate) ).
thf(1122,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)],[228]) ).
thf(214,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Suc__lessE) ).
thf(1080,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)],[214]) ).
thf(21,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_not__less__zero) ).
thf(367,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(73,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_diff__self__eq__0) ).
thf(594,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(175,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq @ nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_le__Suc__eq) ).
thf(943,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)],[175]) ).
thf(99,axiom,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_lessI) ).
thf(668,plain,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(242,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq @ nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_le__SucE) ).
thf(1177,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)],[242]) ).
thf(48,axiom,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_size__neq__size__imp__neq) ).
thf(462,plain,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(171,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_old_Onat_Odistinct_I2_J) ).
thf(932,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(181,axiom,
( ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ 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_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ A ) ) )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_Case2ImplThesis) ).
thf(959,plain,
( ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ 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_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ A ) ) )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(277,plain,
! [TA: $tType,A: TA] :
( ~ ( one @ TA )
| ( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(cnf,[status(esa)],[276]) ).
thf(278,plain,
! [TA: $tType,A: TA] :
( ( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) )
| ~ ( one @ TA ) ),
inference(lifteq,[status(thm)],[277]) ).
thf(45,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_diff__strict__left__mono) ).
thf(455,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(196,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Suc__le__mono) ).
thf(1015,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)],[196]) ).
thf(28,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_less__eq__nat_Osimps_I1_J) ).
thf(394,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ( ord_less @ nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__Suc__induct) ).
thf(299,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)],[10]) ).
thf(268,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_nat_OdiscI) ).
thf(1250,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(221,axiom,
! [TA: $tType,A: list @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ TA ) @ A ) )
= ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_length__greater__0__conv) ).
thf(1102,plain,
! [TA: $tType,A: list @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ TA ) @ A ) )
= ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(96,axiom,
~ ? [A: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
& ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ A )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062) ).
thf(658,plain,
~ ? [A: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
& ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ A )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(168,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_ex__least__nat__le) ).
thf(912,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)],[168]) ).
thf(684,plain,
( ( fe @ index )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
inference(polarity_switch,[status(thm)],[683]) ).
thf(685,plain,
( ( fe @ index )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
inference(lifteq,[status(thm)],[684]) ).
thf(88,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_le__0__eq) ).
thf(636,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(108,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_ex__least__nat__less) ).
thf(695,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)],[108]) ).
thf(114,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_less__irrefl__nat) ).
thf(722,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(54,axiom,
! [A: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_IPrefixListEx) ).
thf(490,plain,
! [A: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(252,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ n1 @ A )
=> ( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
=> ( msgInSet
!= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_AssumptionSubset2_I5_J) ).
thf(1208,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ n1 @ A )
=> ( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
=> ( msgInSet
!= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(103,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_list__eq__iff__nth__eq) ).
thf(680,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(66,axiom,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_zero__less__Suc) ).
thf(548,plain,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_le__SucI) ).
thf(617,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)],[81]) ).
thf(173,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
=> ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ A )
= ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_SameCfgOnLow) ).
thf(939,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
=> ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ A )
= ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(197,axiom,
! [A: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,B: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,C: configuration_ext @ p @ v @ s @ product_unit,D: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),E: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),F: nat] :
( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( A @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_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: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( B @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J) ).
thf(1018,plain,
! [A: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,B: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,C: configuration_ext @ p @ v @ s @ product_unit,D: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),E: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),F: nat] :
( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( A @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_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: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( B @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_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)],[197]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ B @ ( minus_minus @ nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_diff__diff__cancel) ).
thf(648,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)],[92]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_less__Suc__eq__le) ).
thf(487,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)],[53]) ).
thf(159,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_not__gr__zero) ).
thf(872,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(33,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_diff__mono) ).
thf(414,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(326,plain,
( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ),
inference(polarity_switch,[status(thm)],[325]) ).
thf(327,plain,
( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ),
inference(lifteq,[status(thm)],[326]) ).
thf(190,axiom,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_EnabledInSuc) ).
thf(993,plain,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(235,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_diff__commute) ).
thf(1156,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)],[235]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq @ nat @ A @ B ) )
= ( ord_less_eq @ nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_not__less__eq__eq) ).
thf(409,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)],[31]) ).
thf(259,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( suc @ ( minus_minus @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Suc__pred) ).
thf(1230,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)],[259]) ).
thf(101,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_gr__implies__not__zero) ).
thf(673,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ ( suc @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_diff__Suc__less) ).
thf(791,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)],[131]) ).
thf(201,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__SucE) ).
thf(1038,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)],[201]) ).
thf(112,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ nMsg @ A )
=> ( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
=> ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ A )
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_OccSameMsg) ).
thf(717,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ nMsg @ A )
=> ( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ 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)],[112]) ).
thf(261,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_diff__ge__0__iff__ge) ).
thf(1235,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(215,axiom,
comm_monoid_diff @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(1085,plain,
comm_monoid_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(257,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_nat__less__induct) ).
thf(1218,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)],[257]) ).
thf(17,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_strict__inc__induct) ).
thf(331,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)],[17]) ).
thf(246,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(1188,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(230,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ nMsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_AssumpOcc6_I1_J) ).
thf(1141,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(95,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_le__eq__less__or__eq) ).
thf(656,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_Suc__diff__le) ).
thf(613,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)],[79]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_measure__induct) ).
thf(1094,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(41,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_neq0__conv) ).
thf(446,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_diff__is__0__eq) ).
thf(497,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)],[57]) ).
thf(189,axiom,
? [A: p] : ( isReceiverOf @ p @ v @ A @ msgInSet ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_AssumptionSubset2_I1_J) ).
thf(991,plain,
? [A: p] : ( isReceiverOf @ p @ v @ A @ msgInSet ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(43,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ A )
=> ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A )
!= msg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_NotConsumedIntermediate) ).
thf(450,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ A )
=> ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A )
!= msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(243,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Zero__neq__Suc) ).
thf(1180,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(68,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_less__imp__le__nat) ).
thf(556,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(184,axiom,
! [A: nat] :
( ( minus_minus @ nat @ ( suc @ A ) @ ( one_one @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_diff__Suc__1) ).
thf(976,plain,
! [A: nat] :
( ( minus_minus @ nat @ ( suc @ A ) @ ( one_one @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(229,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_transitive__stepwise__le) ).
thf(1126,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)],[229]) ).
thf(247,axiom,
firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_AssumptionSubset_I3_J) ).
thf(1189,plain,
firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(223,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_diff__le__mono2) ).
thf(1108,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)],[223]) ).
thf(26,axiom,
order @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_5) ).
thf(378,plain,
order @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1287,plain,
! [TA: $tType,TB: $tType] :
( ~ $true
| ( order @ ( TA > TB ) )
| ( ( order @ product_unit )
!= ( order @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[378,282]) ).
thf(1288,plain,
! [TA: $tType,TB: $tType] :
( ( order @ ( TA > TB ) )
| ( ( order @ product_unit )
!= ( order @ TB ) ) ),
inference(simp,[status(thm)],[1287]) ).
thf(1289,plain,
! [TA: $tType] : ( order @ ( TA > product_unit ) ),
inference(pattern_uni,[status(thm)],[1288:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( product_unit ))]]) ).
thf(148,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_minus__nat_Odiff__0) ).
thf(844,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1274,plain,
! [TA: $tType] :
( ~ $true
| ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
| ( ( linord1659791738miring @ nat )
!= ( linord1659791738miring @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[836,1118]) ).
thf(1275,plain,
! [TA: $tType] :
( ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
| ( ( linord1659791738miring @ nat )
!= ( linord1659791738miring @ TA ) ) ),
inference(simp,[status(thm)],[1274]) ).
thf(1276,plain,
~ ( ord_less @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) ),
inference(pattern_uni,[status(thm)],[1275:[bind_type(TA,$thf( nat ))]]) ).
thf(71,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ n @ A )
=> ! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ A ) ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ B )
=> ( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_AssumptionFairContr) ).
thf(588,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ n @ A )
=> ! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ A ) ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ B )
=> ( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(138,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_lift__Suc__mono__less) ).
thf(813,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(14,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_nth__equalityI) ).
thf(319,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(209,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ A @ ( suc @ B ) )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_diff__Suc__eq__diff__pred) ).
thf(1062,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)],[209]) ).
thf(18,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( B @ D )
=> ( ( B @ ( suc @ D ) )
& ( C @ D ) ) ) )
=> ( ( B @ A )
=> ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_KeepProperty) ).
thf(351,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)],[18]) ).
thf(128,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_diff__less__mono) ).
thf(781,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)],[128]) ).
thf(198,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_less__antisym) ).
thf(1030,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)],[198]) ).
thf(36,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_bot__nat__0_Oextremum__unique) ).
thf(433,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(170,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_less__Suc__eq) ).
thf(929,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)],[170]) ).
thf(254,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_less__not__refl) ).
thf(1212,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1307,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ~ $true
| ( order @ ( TB > TC ) )
| ( ( order @ ( TA > product_unit ) )
!= ( order @ TC ) ) ),
inference(paramod_ordered,[status(thm)],[1289,282]) ).
thf(1308,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( order @ ( TB > TC ) )
| ( ( order @ ( TA > product_unit ) )
!= ( order @ TC ) ) ),
inference(simp,[status(thm)],[1307]) ).
thf(1309,plain,
! [TA: $tType,TB: $tType] : ( order @ ( TB > TA > product_unit ) ),
inference(pattern_uni,[status(thm)],[1308:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > product_unit ))]]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_le__diff__iff) ).
thf(763,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)],[123]) ).
thf(272,plain,
! [TA: $tType,TB: $tType] : ( size @ ( message @ TA @ TB ) ),
inference(cnf,[status(esa)],[271]) ).
thf(232,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_le__trans) ).
thf(1148,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)],[232]) ).
thf(35,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_nat__induct) ).
thf(422,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)],[35]) ).
thf(155,axiom,
ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132__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(865,plain,
ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_less__numeral__extra_I1_J) ).
thf(373,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(136,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_le__less__Suc__eq) ).
thf(807,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)],[136]) ).
thf(207,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zero__diff) ).
thf(1056,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(199,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_le__iff__diff__le__0) ).
thf(1033,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(210,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_All__less__Suc2) ).
thf(1065,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)],[210]) ).
thf(113,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_Suc__leD) ).
thf(720,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)],[113]) ).
thf(240,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Suc__leI) ).
thf(1172,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)],[240]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_linorder__neqE__nat) ).
thf(767,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)],[124]) ).
thf(146,axiom,
! [A: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_IPrefixList) ).
thf(839,plain,
! [A: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(116,axiom,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ nMsg ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_Occ4) ).
thf(728,plain,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ nMsg ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_diffs0__imp__equal) ).
thf(860,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)],[153]) ).
thf(91,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_nat_Odistinct_I1_J) ).
thf(644,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(150,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_nat__less__le) ).
thf(850,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(186,axiom,
( ( n1
!= ( zero_zero @ nat ) )
=> ( ~ ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) @ msgInSet )
| ( msgInSet
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_AssumptionSubset2_I6_J) ).
thf(982,plain,
( ( n1
!= ( zero_zero @ nat ) )
=> ( ~ ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) @ msgInSet )
| ( msgInSet
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(39,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_gr0__implies__Suc) ).
thf(442,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( suc @ ( minus_minus @ nat @ B @ ( suc @ A ) ) )
= ( minus_minus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Suc__diff__Suc) ).
thf(369,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)],[22]) ).
thf(52,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(486,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(134,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_diff__is__0__eq_H) ).
thf(803,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)],[134]) ).
thf(244,axiom,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_AssumptionFair_I3_J) ).
thf(1184,plain,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(12,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_n__not__Suc__n) ).
thf(309,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(121,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Suc__less__SucD) ).
thf(755,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)],[121]) ).
thf(20,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_length__0__conv) ).
thf(364,plain,
! [TA: $tType,A: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2524,plain,
$false,
inference(e,[status(thm)],[1036,629,1190,1168,1105,481,909,628,1211,523,683,276,1068,994,308,677,597,1041,1205,449,1142,379,550,500,1233,1260,747,670,898,1243,709,841,436,651,973,1046,1055,372,504,619,1059,460,817,1247,969,770,416,325,1100,492,591,1151,806,485,834,602,1169,280,1215,692,956,866,453,396,998,988,1242,1119,774,307,1074,1306,1199,810,714,798,942,439,270,529,957,746,778,1042,1255,1174,820,407,815,729,1238,1217,598,275,788,361,625,879,852,665,1159,493,757,1012,847,484,519,1089,948,725,869,1118,857,1111,1227,328,642,901,686,1114,985,1249,654,1002,569,622,837,1050,457,503,605,1202,1086,1241,633,541,1170,1286,794,662,926,558,1071,953,1185,906,412,750,1273,279,689,375,1154,904,286,281,545,875,711,641,313,1271,1312,611,947,445,936,466,1092,979,900,831,274,996,271,863,784,1117,616,1122,1080,367,594,943,668,1177,462,932,959,278,455,1015,394,299,1250,1102,658,912,685,636,695,722,490,1208,680,548,617,939,1018,836,648,487,872,414,327,993,282,1156,409,1230,1053,673,791,1038,717,502,1235,1085,1218,331,1188,1141,656,613,1094,446,497,991,450,1180,556,976,1126,1189,1108,1289,844,1276,588,813,319,1062,946,351,781,1030,378,433,929,1212,1309,763,272,1280,1303,1148,422,273,865,373,807,1056,1033,1065,720,283,1172,767,839,728,860,644,850,982,442,871,369,486,803,1184,309,639,755,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP059^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n017.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:40:07 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.98/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.91/1.17 % [INFO] Parsing done (365ms).
% 1.91/1.18 % [INFO] Running in sequential loop mode.
% 3.15/1.57 % [INFO] eprover registered as external prover.
% 3.15/1.58 % [INFO] Scanning for conjecture ...
% 3.55/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 267 axioms. Running axiom selection ...
% 3.88/1.88 % [INFO] Axiom selection finished. Selected 267 axioms (removed 0 axioms).
% 4.96/2.14 % [INFO] Problem is higher-order (TPTP THF).
% 4.96/2.16 % [INFO] Type checking passed.
% 4.96/2.17 % [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 ...
% 28.60/8.49 % External prover 'e' found a proof!
% 28.60/8.49 % [INFO] Killing All external provers ...
% 28.60/8.49 % Time passed: 8130ms (effective reasoning time: 7302ms)
% 28.60/8.49 % 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)>
% 28.60/8.49 % Axioms used in derivation (267): fact_190_diff__le__self, fact_8_zero__less__diff, fact_120_NatPredicateTippingPoint, fact_20_not__gr__zero, fact_108_gr0__conv__Suc, fact_217_EnabledIntermediate, fact_68_nat_OdiscI, fact_248_less__numeral__extra_I4_J, fact_42_nat__less__induct, fact_10_zero__less__Suc, fact_61_old_Onat_Oexhaust, fact_125_AssumptionSubset2_I1_J, fact_73_strict__inc__induct, fact_167_le__SucE, fact_135_OccSameMsg, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, fact_37_n__not__Suc__n, fact_88_Nat_OlessE, tcon_Nat_Onat___Nat_Osize, fact_243_diff__numeral__special_I9_J, fact_58_diff__strict__mono, fact_156_MinPredicate, fact_22_diff__zero, fact_96_gr0I, fact_27_Suc__mono, fact_32_zero__reorient, fact_141_diff__Suc__1, fact_39_infinite__descent__measure, fact_236_EnabledOrConsumed, fact_34_measure__induct, fact_1_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, fact_140_less__one, fact_94_not__less0, fact_177_le__0__eq, fact_246_less__numeral__extra_I3_J, fact_212_nat__induct__non__zero, fact_13_diff__self__eq__0, fact_163_diff__left__mono, fact_49_diff__commute, fact_227_Occ2, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, fact_162_diff__mono, fact_224_MessageStaysOrConsumed, fact_102_less__iff__diff__less__0, fact_221_AssumptionFair_I3_J, fact_4_SmallIndex, fact_208_diff__less__mono, fact_5_AssumptionSubset3_I3_J, fact_161_zero__le, fact_218_length__greater__0__conv, fact_60_old_Onat_Oinducts, fact_51_gr__implies__not__zero, fact_31_AssumptionSubset_I1_J, fact_90_bot__nat__0_Oextremum__strict, fact_77_less__antisym, fact_103_lift__Suc__mono__less__iff, fact_171_Suc__n__not__le__n, fact_53_gr__zeroI, fact_196_Suc__leI, fact_189_diff__le__mono, fact_214_Suc__diff__eq__diff__pred, fact_206_Suc__diff__le, fact_123_AssumpOcc6_I2_J, fact_250__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062, fact_85_Suc__lessI, fact_75_less__trans__Suc, fact_183_less__or__eq__imp__le, fact_84_less__SucE, fact_24_diff__0__right, fact_222_AssumptionSubset3_I4_J, fact_231_length__induct, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, fact_101_diff__less__mono2, fact_48_size__neq__size__imp__neq, fact_59_not0__implies__Suc, fact_176_less__eq__nat_Osimps_I1_J, fact_247_le__numeral__extra_I4_J, fact_204_le__imp__less__Suc, fact_6_AssumptionSubset2_I3_J, fact_199_inc__induct, fact_166_Suc__leD, fact_87_Suc__lessD, fact_202_less__Suc__eq__le, fact_187_le__diff__iff, fact_99_diffs0__imp__equal, tcon_Product__Type_Ounit___Orderings_Owellorder_4, fact_38_Suc__inject, fact_216_AssumptionSubset3_I6_J, fact_115__092_060open_062fe_Aindex_A_B_AnMsg_A_061_Afe_A_ISuc_Aindex_J_A_B_AnMsg_092_060close_062, tcon_Nat_Onat___Groups_Oone, fact_239_AssumptionSubset2_I2_J, fact_131_diff__diff__cancel, fact_66_diff__induct, fact_225__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_229_neq__if__length__neq, fact_138_diff__is__0__eq, fact_181_less__imp__le__nat, fact_89_infinite__descent0__measure, fact_7_Suc__pred, fact_143_AssumptionSubset2_I5_J, fact_97_zero__induct__lemma, fact_2_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, fact_55_diff__strict__right__mono, fact_36_diff__eq__diff__eq, fact_244__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062, fact_129_le0, fact_193_MinPredicate2, fact_203_less__eq__Suc__le, tcon_Product__Type_Ounit___Orderings_Oorder_5, fact_172_not__less__eq__eq, fact_44_less__not__refl3, fact_211_ex__least__nat__less, fact_223_AssumptionSubset2_I4_J, fact_105_less__Suc__eq__0__disj, fact_150_eq__imp__le, fact_127_le__zero__eq, fact_191_le__diff__iff_H, fact_245_le__numeral__extra_I3_J, fact_46_less__not__refl, fact_117_NotEmpty_I1_J, fact_122_AssumptionFair_I4_J, fact_65_zero__induct, fact_83_less__SucI, fact_215_AssumptionSubset2_I6_J, fact_64_Suc__neq__Zero, fact_25_diff__self, fact_57_diff__eq__diff__less, fact_50_zero__less__iff__neq__zero, fact_165_diff__eq__diff__less__eq, fact_121_NotEmpty_I2_J, fact_111_Suc__diff__Suc, fact_30_AssumptionSubset_I2_J, tcon_Nat_Onat___Orderings_Owellorder, fact_232_list_Osize_I3_J, fact_63_Zero__neq__Suc, fact_16_neq0__conv, tcon_Nat_Onat___Groups_Ozero, tcon_HOL_Obool___Orderings_Oorder_2, fact_160_PrefixSameOnLow, fact_182_le__eq__less__or__eq, fact_15_Suc__diff__diff, fact_106_gr0__implies__Suc, fact_146_AssumptionFairContr, fact_52_not__less__zero, fact_80_not__less__eq, fact_144__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062, fact_35_diff__right__commute, fact_19_nat_Oinject, fact_126_SameMsgOnLow, fact_230_Ex__list__of__length, fact_62_Zero__not__Suc, fact_130_bot__nat__0_Oextremum, fact_184_le__neq__implies__less, fact_109_Ex__less__Suc2, fact_142_AssumptionSubset3_I5_J, fact_201_le__less__Suc__eq, fact_76_Suc__less__SucD, fact_242_last__conv__nth, fact_79_All__less__Suc, fact_17_less__nat__zero__code, fact_210_diff__Suc__eq__diff__pred, fact_9_less__Suc0, fact_148_le__refl, fact_145_Suc__diff__1, fact_237_Case2ImplThesis, tcon_AsynchronousSystem_Omessage___Nat_Osize_6, fact_158_lift__Suc__mono__le, fact_155_PrefixListTransitive, fact_173_full__nat__induct, fact_164_diff__right__mono, fact_200_Suc__le__lessD, fact_159_KeepProperty, fact_74_less__Suc__induct, fact_213_Suc__pred_H, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_26_Suc__less__eq, fact_28_lessI, fact_134_NotConsumedIntermediate, fact_41_infinite__descent, fact_33_measure__induct__rule, fact_209_One__nat__def, fact_186_eq__diff__iff, fact_235_nth__equalityI, fact_174_nat__induct__at__least, fact_43_less__irrefl__nat, fact_21_cancel__comm__monoid__add__class_Odiff__cancel, fact_139_diff__is__0__eq_H, fact_151_le__antisym, fact_180_nat__less__le, fact_82_Ex__less__Suc, fact_56_diff__strict__left__mono, fact_23_zero__diff, fact_71_nat_Odistinct_I1_J, fact_220_Occ4, fact_192_diff__le__mono2, fact_233_list__eq__iff__nth__eq, fact_133__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_226_length__0__conv, fact_110_diff__less__Suc, fact_149_le__trans, fact_157_lift__Suc__antimono__le, fact_178_bot__nat__0_Oextremum__unique, fact_104_lift__Suc__mono__less, fact_137_Occ5, fact_170_le__Suc__eq, fact_70_old_Onat_Odistinct_I2_J, fact_45_less__not__refl2, fact_234_Skolem__list__nth, fact_128_Suc__le__mono, fact_205_ex__least__nat__le, fact_169_Suc__le__D, fact_219_AssumptionFair_I2_J, fact_179_bot__nat__0_Oextremum__uniqueI, fact_124_Occ1, fact_3_AssumptionSubset_I3_J, fact_95_not__gr0, fact_249_less__numeral__extra_I1_J, fact_0_AssumpOcc6_I1_J, fact_12_diff__0__eq__0, fact_107_All__less__Suc2, fact_78_Suc__less__eq2, fact_29_bot__nat__0_Onot__eq__extremum, fact_175_transitive__stepwise__le, fact_152_nat__le__linear, tcon_fun___Orderings_Oorder, fact_154_Nat_Oex__has__greatest__nat, fact_81_less__Suc__eq, fact_195_le__iff__diff__le__0, fact_112_diff__less, fact_11_diff__gt__0__iff__gt, fact_91_infinite__descent0, fact_188_Nat_Odiff__diff__eq, fact_147_AssumpOcc6_I3_J, fact_100_less__imp__diff__less, fact_119_IPrefixListEx, tcon_List_Olist___Nat_Osize_3, fact_207_less__diff__iff, tcon_Nat_Onat___Orderings_Oorder_1, fact_114_SameCfgOnLow, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_67_nat__induct, fact_116_ShorterTrace, fact_241_EnabledOrConsumedAtLast, fact_18_old_Onat_Oinject, fact_136_diff__ge__0__iff__ge, fact_69_old_Onat_Odistinct_I1_J, fact_185_less__mono__imp__le__mono, fact_14_diff__Suc__Suc, fact_197_Suc__le__eq, fact_86_Suc__lessE, fact_168_le__SucI, fact_72_not__less__less__Suc__eq, fact_92_gr__implies__not0, fact_118_IPrefixList, fact_93_less__zeroE, fact_194_PrefixListMonotonicity, fact_238_EnabledInSuc, fact_113_diff__Suc__less, fact_198_dec__induct, fact_153_one__reorient, fact_228_AssumptionCase1ImplThesis_H, fact_98_minus__nat_Odiff__0, fact_132__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_54_eq__iff__diff__eq__0, fact_47_nat__neq__iff, fact_240_LastOfIndex, fact_40_linorder__neqE__nat
% 28.60/8.50 % No. of inferences in proof: 590
% 28.60/8.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8130 ms resp. 7302 ms w/o parsing
% 30.45/8.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.45/8.72 % [INFO] Killing All external provers ...
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