%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP055^2 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:34 AM UTC 2026
% Result : Theorem 64.26s 44.35s
% Output : Refutation 65.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 237
% Syntax : Number of formulae : 476 ( 221 unt; 0 typ; 0 def)
% Number of atoms : 1123 ( 452 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 7953 ( 236 ~; 14 |; 56 &;7007 @)
% ( 0 <=>; 640 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 706 ( 706 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 45 usr; 10 con; 0-7 aty)
% Number of variables : 1544 ( 14 ^;1468 !; 62 ?;1544 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $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(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(wellorder_decl,type,
wellorder:
!>[TA: $tType] : $o ).
thf(boolean_algebra_decl,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_decl,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(bNF_Greatest_shift_decl,type,
bNF_Greatest_shift:
!>[TA: $tType,TB: $tType] : ( ( ( list @ TB ) > TA ) > TB > ( list @ TB ) > TA ) ).
thf(fLPThe1922692578sensus_decl,type,
fLPThe1922692578sensus:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( messageValue @ TA ) > TB ) > ( TC > TB > ( messageValue @ TA ) > ( message @ TC @ TA ) > nat ) > ( TC > TB ) > $o ) ).
thf(fLPThe137922386ionCfg_decl,type,
fLPThe137922386ionCfg:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) ).
thf(fLPThe221390223ionMsg_decl,type,
fLPThe221390223ionMsg:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > ( list @ ( message @ TC @ TB ) ) ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(nat2_decl,type,
nat2: int > nat ).
thf(prefixList_decl,type,
prefixList:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(gen_length_decl,type,
gen_length:
!>[TA: $tType] : ( nat > ( list @ TA ) > nat ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(n_lists_decl,type,
n_lists:
!>[TA: $tType] : ( nat > ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(nths_decl,type,
nths:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ nat ) > ( list @ TA ) ) ).
thf(product_lists_decl,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(subseqs_decl,type,
subseqs:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
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(cfg_decl,type,
cfg: configuration_ext @ p @ v @ s @ product_unit ).
thf(fe_decl,type,
fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
thf(m_decl,type,
m: nat ).
thf(n_decl,type,
n: nat ).
thf(na_decl,type,
na: nat ).
thf(201,axiom,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_list_Osize_I3_J) ).
thf(1036,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(50,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_19_length__0__conv) ).
thf(365,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)],[50]) ).
thf(110,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_n__not__Suc__n) ).
thf(628,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(142,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_242_lift__Suc__antimono__le) ).
thf(777,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)],[142]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_less__not__refl3) ).
thf(555,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(129,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_37_linorder__neqE__nat) ).
thf(730,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)],[129]) ).
thf(209,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_strict__sorted_Ocases) ).
thf(1068,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(28,axiom,
! [A: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ~ ! [B: nat] :
( ( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_neg__int__cases) ).
thf(308,plain,
! [A: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ~ ! [B: nat] :
( ( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Olinorder) ).
thf(247,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(165,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_remdups__adj_Oinduct) ).
thf(861,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(235,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_9_PrefixListMonotonicity) ).
thf(1173,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)],[235]) ).
thf(73,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_59_diff__induct) ).
thf(440,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)],[73]) ).
thf(84,axiom,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_list__ex1__simps_I1_J) ).
thf(511,plain,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(108,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_bot__nat__0_Onot__eq__extremum) ).
thf(614,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(17,axiom,
! [A: nat,B: int] :
( ( ord_less @ nat @ A @ ( nat2 @ B ) )
= ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_zless__nat__eq__int__zless) ).
thf(269,plain,
! [A: nat,B: int] :
( ( ord_less @ nat @ A @ ( nat2 @ B ) )
= ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(122,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_min__list_Ocases) ).
thf(677,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(213,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),D: nat] :
( ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ ( suc @ D ) )
= ( C @ ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ D ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_infiniteExecutionMsg_Osimps_I2_J) ).
thf(1078,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),D: nat] :
( ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ ( suc @ D ) )
= ( C @ ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ D ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(81,axiom,
! [TA: $tType,A: list @ TA] :
( ( n_lists @ TA @ ( zero_zero @ nat ) @ A )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_n__lists_Osimps_I1_J) ).
thf(500,plain,
! [TA: $tType,A: list @ TA] :
( ( n_lists @ TA @ ( zero_zero @ nat ) @ A )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(149,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_32_measure__induct) ).
thf(797,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)],[149]) ).
thf(177,axiom,
! [TA: $tType,A: set @ nat,B: TA] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( nths @ TA @ ( cons @ TA @ B @ ( nil @ TA ) ) @ A )
= ( cons @ TA @ B @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( nths @ TA @ ( cons @ TA @ B @ ( nil @ TA ) ) @ A )
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_nths__singleton) ).
thf(945,plain,
! [TA: $tType,A: set @ nat,B: TA] :
( ( ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( nths @ TA @ ( cons @ TA @ B @ ( nil @ TA ) ) @ A )
= ( cons @ TA @ B @ ( nil @ TA ) ) ) )
& ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( nths @ TA @ ( cons @ TA @ B @ ( nil @ TA ) ) @ A )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(538,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(207,axiom,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) )
= ( gen_length @ TA @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_length__code) ).
thf(1063,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) )
= ( gen_length @ TA @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(38,axiom,
ord @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oord_2) ).
thf(340,plain,
ord @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(194,axiom,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_lessI) ).
thf(1001,plain,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_old_Onat_Oinject) ).
thf(782,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > $o,E: ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > $o,F: configuration_ext @ TC @ TB @ TA @ product_unit,G: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),H: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),I: nat] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) )] : ( D @ J @ K @ L @ ( zero_zero @ nat ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),M: nat] :
( ( D @ J @ K @ L @ M )
=> ( ( E @ J @ K @ L @ M )
=> ( D @ J @ K @ L @ ( suc @ M ) ) ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) )] : ( E @ J @ K @ L @ ( zero_zero @ nat ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),M: nat] :
( ( D @ J @ K @ L @ M )
=> ( ( E @ J @ K @ L @ M )
=> ( E @ J @ K @ L @ ( suc @ M ) ) ) )
=> ( E @ F @ G @ H @ I ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J) ).
thf(885,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > $o,E: ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > $o,F: configuration_ext @ TC @ TB @ TA @ product_unit,G: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),H: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),I: nat] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) )] : ( D @ J @ K @ L @ ( zero_zero @ nat ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),M: nat] :
( ( D @ J @ K @ L @ M )
=> ( ( E @ J @ K @ L @ M )
=> ( D @ J @ K @ L @ ( suc @ M ) ) ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) )] : ( E @ J @ K @ L @ ( zero_zero @ nat ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),M: nat] :
( ( D @ J @ K @ L @ M )
=> ( ( E @ J @ K @ L @ M )
=> ( E @ J @ K @ L @ ( suc @ M ) ) ) )
=> ( E @ F @ G @ H @ I ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(25,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_of__nat__less__0__iff) ).
thf(301,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(159,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_induct__list012) ).
thf(829,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(61,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_87_Suc__lessE) ).
thf(404,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)],[61]) ).
thf(145,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_less__Suc0) ).
thf(785,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(40,axiom,
! [A: nat,B: nat] : ( ord_less @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ A ) ) ) @ ( semiring_1_of_nat @ int @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_negative__zless) ).
thf(344,plain,
! [A: nat,B: nat] : ( ord_less @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ A ) ) ) @ ( semiring_1_of_nat @ int @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(206,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Zero__not__Suc) ).
thf(1059,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(155,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_73_not__less__less__Suc__eq) ).
thf(817,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)],[155]) ).
thf(97,axiom,
! [TA: $tType] :
( ( subseqs @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_subseqs_Osimps_I1_J) ).
thf(559,plain,
! [TA: $tType] :
( ( subseqs @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(161,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_16) ).
thf(853,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(228,axiom,
( ( fe @ ( zero_zero @ nat ) )
= ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ cfg @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_FE_I1_J) ).
thf(1147,plain,
( ( fe @ ( zero_zero @ nat ) )
= ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ cfg @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(66,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_243_lift__Suc__mono__le) ).
thf(421,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)],[66]) ).
thf(20,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_less__imp__of__nat__less) ).
thf(284,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(33,axiom,
! [A: nat] :
( ( nat2 @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_nat__zminus__int) ).
thf(325,plain,
! [A: nat] :
( ( nat2 @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(79,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_old_Onat_Oexhaust) ).
thf(492,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(31,axiom,
( ( nat2 @ ( one_one @ int ) )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_nat__1) ).
thf(321,plain,
( ( nat2 @ ( one_one @ int ) )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(115,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Zero__neq__Suc) ).
thf(646,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(78,axiom,
! [TA: $tType,A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( n_lists @ TA @ A @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( n_lists @ TA @ A @ ( nil @ TA ) )
= ( nil @ ( list @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_n__lists__Nil) ).
thf(485,plain,
! [TA: $tType,A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( n_lists @ TA @ A @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( n_lists @ TA @ A @ ( nil @ TA ) )
= ( nil @ ( list @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(230,axiom,
boolean_algebra @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Lattices_Oboolean__algebra_19) ).
thf(1151,plain,
boolean_algebra @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(42,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(348,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(151,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_111_length__induct) ).
thf(806,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)],[151]) ).
thf(204,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Suc__inject) ).
thf(1051,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(45,axiom,
linord1659791738miring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__nonzero__semiring) ).
thf(353,plain,
linord1659791738miring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(183,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_17) ).
thf(966,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(166,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_less__numeral__extra_I3_J) ).
thf(877,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(22,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_of__nat__mono) ).
thf(293,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(120,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_16_NatPredicateTippingPoint) ).
thf(660,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)],[120]) ).
thf(193,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_114_less__Suc__eq__0__disj) ).
thf(998,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)],[193]) ).
thf(190,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_23_Suc__mono) ).
thf(988,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)],[190]) ).
thf(69,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_49_size__neq__size__imp__neq) ).
thf(428,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)],[69]) ).
thf(107,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_11_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J) ).
thf(602,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)],[107]) ).
thf(187,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_nat_Oinject) ).
thf(981,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(138,axiom,
! [A: int] :
( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( nat2 @ A ) )
= ( ord_less @ int @ ( one_one @ int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_one__less__nat__eq) ).
thf(766,plain,
! [A: int] :
( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( nat2 @ A ) )
= ( ord_less @ int @ ( one_one @ int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(211,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone_10) ).
thf(1074,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_negative__eq__positive) ).
thf(248,plain,
! [A: nat,B: nat] :
( ( ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(176,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_129_not__gr__zero) ).
thf(942,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)],[176]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: list @ TA,D: ( list @ TB ) > ( list @ TC ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( ( size_size @ ( list @ TC ) @ B )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: list @ TB,G: TC,H: list @ TC,I: TA,J: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ F )
= ( size_size @ ( list @ TC ) @ H ) )
=> ( ( ( size_size @ ( list @ TC ) @ H )
= ( size_size @ ( list @ TA ) @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons @ TB @ E @ F ) @ ( cons @ TC @ G @ H ) @ ( cons @ TA @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_list__induct3) ).
thf(381,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: list @ TA,D: ( list @ TB ) > ( list @ TC ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( ( size_size @ ( list @ TC ) @ B )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: list @ TB,G: TC,H: list @ TC,I: TA,J: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ F )
= ( size_size @ ( list @ TC ) @ H ) )
=> ( ( ( size_size @ ( list @ TC ) @ H )
= ( size_size @ ( list @ TA ) @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons @ TB @ E @ F ) @ ( cons @ TC @ G @ H ) @ ( cons @ TA @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(89,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_133_gr__zeroI) ).
thf(534,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)],[89]) ).
thf(126,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_39_nat__less__induct) ).
thf(714,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)],[126]) ).
thf(232,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] :
( ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ ( zero_zero @ nat ) )
= ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_infiniteExecutionCfg_Osimps_I1_J) ).
thf(1153,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] :
( ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ ( zero_zero @ nat ) )
= ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(136,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_118_Ex__less__Suc2) ).
thf(761,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)],[136]) ).
thf(36,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_one__reorient) ).
thf(334,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(171,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_53_old_Onat_Oinducts) ).
thf(910,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)],[171]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_list__induct2_H) ).
thf(825,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(43,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1) ).
thf(349,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Suc__lessD) ).
thf(820,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(146,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_gr0__implies__Suc) ).
thf(788,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(153,axiom,
boolean_algebra @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_14) ).
thf(815,plain,
boolean_algebra @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_not__less__eq) ).
thf(879,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(71,axiom,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_zero__less__Suc) ).
thf(435,plain,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(238,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( prefixList @ TA @ A @ B )
=> ( prefixList @ TA @ ( cons @ TA @ C @ A ) @ ( cons @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_prefixList_Ointros_I2_J) ).
thf(1178,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( prefixList @ TA @ A @ B )
=> ( prefixList @ TA @ ( cons @ TA @ C @ A ) @ ( cons @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(234,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),D: nat,E: list @ ( configuration_ext @ p @ v @ s @ product_unit )] :
( ( ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ D )
= E )
=> ( ( ( D
= ( zero_zero @ nat ) )
=> ( E
!= ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( B @ ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ F ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_infiniteExecutionCfg_Oelims) ).
thf(1159,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),D: nat,E: list @ ( configuration_ext @ p @ v @ s @ product_unit )] :
( ( ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ D )
= E )
=> ( ( ( D
= ( zero_zero @ nat ) )
=> ( E
!= ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ A @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( B @ ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ F ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(116,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_not__less0) ).
thf(650,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(196,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_less__nat__zero__code) ).
thf(1006,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(47,axiom,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oboolean__algebra_11) ).
thf(356,plain,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(105,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_zero__reorient) ).
thf(593,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(215,axiom,
! [TA: $tType] :
( ( prefixList @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: TA,D: list @ TA] :
( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [C: list @ TA,D: list @ TA,E: TA] :
( ( A
= ( cons @ TA @ E @ C ) )
& ( B
= ( cons @ TA @ E @ D ) )
& ( prefixList @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_prefixList_Osimps) ).
thf(1082,plain,
! [TA: $tType] :
( ( prefixList @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: TA,D: list @ TA] :
( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [C: list @ TA,D: list @ TA,E: TA] :
( ( A
= ( cons @ TA @ E @ C ) )
& ( B
= ( cons @ TA @ E @ D ) )
& ( prefixList @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(90,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_8) ).
thf(537,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(212,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ( suc @ A )
= ( size_size @ ( list @ TA ) @ B ) )
= ( ? [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
& ( ( size_size @ ( list @ TA ) @ D )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Suc__length__conv) ).
thf(1075,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ( suc @ A )
= ( size_size @ ( list @ TA ) @ B ) )
= ( ? [C: TA,D: list @ TA] :
( ( B
= ( cons @ TA @ C @ D ) )
& ( ( size_size @ ( list @ TA ) @ D )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(114,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_list_OdiscI) ).
thf(642,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(94,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_pos__int__cases) ).
thf(547,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(34,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_zero__le) ).
thf(328,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(11,axiom,
! [A: int] :
( ( ( nat2 @ A )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_nat__0__iff) ).
thf(256,plain,
! [A: int] :
( ( ( nat2 @ A )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(202,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_38_infinite__descent) ).
thf(1039,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)],[202]) ).
thf(185,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( C @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ E )
= ( size_size @ ( list @ TA ) @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_list__induct2) ).
thf(970,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( C @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ E )
= ( size_size @ ( list @ TA ) @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(132,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_58_zero__induct) ).
thf(738,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)],[132]) ).
thf(188,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_verit__comp__simplify1_I3_J) ).
thf(984,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(143,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_less__not__refl) ).
thf(779,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(52,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_less__irrefl__nat) ).
thf(371,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(82,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_31_measure__induct__rule) ).
thf(503,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)],[82]) ).
thf(15,axiom,
! [A: nat] : ( ord_less @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ A ) ) ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_negative__zless__0) ).
thf(266,plain,
! [A: nat] : ( ord_less @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ A ) ) ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(172,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_75_less__Suc__induct) ).
thf(921,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)],[172]) ).
thf(58,axiom,
size @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(398,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(210,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_list_Oinject) ).
thf(1071,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(200,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_min__list_Oinduct) ).
thf(1026,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(148,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( cons @ TA @ A @ B ) )
= ( suc @ ( size_size @ ( list @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_length__Cons) ).
thf(794,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( cons @ TA @ A @ B ) )
= ( suc @ ( size_size @ ( list @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(24,axiom,
! [A: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ? [B: nat] :
( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_negD) ).
thf(298,plain,
! [A: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ? [B: nat] :
( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_of__nat__less__imp__less) ).
thf(264,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(130,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_sorted__wrt_Oinduct) ).
thf(733,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(85,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_10_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J) ).
thf(513,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)],[85]) ).
thf(227,axiom,
order @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_22) ).
thf(1146,plain,
order @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(98,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_strict__sorted_Oinduct) ).
thf(562,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(67,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_neq0__conv) ).
thf(423,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(60,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_12) ).
thf(402,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat_OdiscI) ).
thf(772,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(21,axiom,
! [A: int] :
( ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) )
=> ~ ! [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( A
!= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_int__cases4) ).
thf(286,plain,
! [A: int] :
( ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) )
=> ~ ! [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( A
!= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(125,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_76_less__trans__Suc) ).
thf(711,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)],[125]) ).
thf(101,axiom,
! [TA: $tType] : ( size @ ( list @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_18) ).
thf(579,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(180,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_78_less__antisym) ).
thf(958,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)],[180]) ).
thf(12,axiom,
! [A: nat > $o,B: int] :
( ( A @ ( nat2 @ B ) )
= ( ! [C: nat] :
( ( B
= ( semiring_1_of_nat @ int @ C ) )
=> ( A @ C ) )
& ( ( ord_less @ int @ B @ ( zero_zero @ int ) )
=> ( A @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_split__nat) ).
thf(259,plain,
! [A: nat > $o,B: int] :
( ( A @ ( nat2 @ B ) )
= ( ! [C: nat] :
( ( B
= ( semiring_1_of_nat @ int @ C ) )
=> ( A @ C ) )
& ( ( ord_less @ int @ B @ ( zero_zero @ int ) )
=> ( A @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(413,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(160,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_65_infinite__descent0__measure) ).
thf(843,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)],[160]) ).
thf(222,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: TA,D: list @ TA] :
( B
!= ( cons @ TA @ C @ D ) ) )
=> ~ ! [C: list @ TA,D: list @ TA,E: TA] :
( ( A
= ( cons @ TA @ E @ C ) )
=> ( ( B
= ( cons @ TA @ E @ D ) )
=> ~ ( prefixList @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_prefixList_Ocases) ).
thf(1125,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: TA,D: list @ TA] :
( B
!= ( cons @ TA @ C @ D ) ) )
=> ~ ! [C: list @ TA,D: list @ TA,E: TA] :
( ( A
= ( cons @ TA @ E @ C ) )
=> ( ( B
= ( cons @ TA @ E @ D ) )
=> ~ ( prefixList @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(74,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_89_Nat_OlessE) ).
thf(445,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)],[74]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_shift__def) ).
thf(572,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(29,axiom,
! [A: int > $o,B: int] :
( ! [C: nat] : ( A @ ( semiring_1_of_nat @ int @ C ) )
=> ( ! [C: nat] : ( A @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ C ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_int__of__nat__induct) ).
thf(313,plain,
! [A: int > $o,B: int] :
( ! [C: nat] : ( A @ ( semiring_1_of_nat @ int @ C ) )
=> ( ! [C: nat] : ( A @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ C ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(219,axiom,
ord_less @ nat @ m @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_MLessN) ).
thf(1107,plain,
ord_less @ nat @ m @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(44,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_220_le__zero__eq) ).
thf(350,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)],[44]) ).
thf(92,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_not__Cons__self2) ).
thf(540,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(56,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_18_length__greater__0__conv) ).
thf(391,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)],[56]) ).
thf(223,axiom,
linorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Olinorder_21) ).
thf(1139,plain,
linorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(137,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_77_Suc__less__SucD) ).
thf(764,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)],[137]) ).
thf(19,axiom,
! [A: int] :
( ( A
!= ( zero_zero @ int ) )
=> ( ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) )
=> ~ ! [B: nat] :
( ( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_int__cases3) ).
thf(274,plain,
! [A: int] :
( ( A
!= ( zero_zero @ int ) )
=> ( ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) )
=> ~ ! [B: nat] :
( ( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(203,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_remdups__adj_Ocases) ).
thf(1048,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(226,axiom,
! [TA: $tType,A: TA,B: list @ TA] : ( prefixList @ TA @ ( nil @ TA ) @ ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prefixList_Ointros_I1_J) ).
thf(1144,plain,
! [TA: $tType,A: TA,B: list @ TA] : ( prefixList @ TA @ ( nil @ TA ) @ ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(6,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] : ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_nat__int__comparison_I2_J) ).
thf(245,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] : ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(83,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_verit__comp__simplify1_I1_J) ).
thf(509,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(236,axiom,
ord_less @ nat @ m @ ( suc @ na ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_IA_I2_J) ).
thf(1175,plain,
ord_less @ nat @ m @ ( suc @ na ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(54,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ nat @ ( nat2 @ B ) @ ( nat2 @ A ) )
= ( ord_less @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_nat__mono__iff) ).
thf(377,plain,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ nat @ ( nat2 @ B ) @ ( nat2 @ A ) )
= ( ord_less @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: configuration_ext @ TC @ TB @ TA @ product_unit,E: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),F: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),G: nat] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ ( suc @ G ) )
= ( E @ ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ G ) @ ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J) ).
thf(990,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: configuration_ext @ TC @ TB @ TA @ product_unit,E: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),F: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),G: nat] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ ( suc @ G ) )
= ( E @ ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ G ) @ ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: configuration_ext @ TC @ TB @ TA @ product_unit,E: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),F: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),G: nat] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ ( suc @ G ) )
= ( F @ ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ G ) @ ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J) ).
thf(362,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: configuration_ext @ TC @ TB @ TA @ product_unit,E: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),F: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),G: nat] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ ( suc @ G ) )
= ( F @ ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ G ) @ ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(75,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_list__nonempty__induct) ).
thf(451,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(131,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_9) ).
thf(737,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(30,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_of__nat__le__iff) ).
thf(318,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(26,axiom,
! [A: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( nat2 @ A )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_nat__le__0) ).
thf(303,plain,
! [A: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( nat2 @ A )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) > ( list @ ( message @ TA @ TB ) ) > ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ),F: ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) > ( list @ ( message @ TA @ TB ) ) > ( list @ ( message @ TA @ TB ) )] :
( ( fLPThe1922692578sensus @ TA @ TC @ TB @ A @ B @ C )
=> ( ( fLPThe137922386ionCfg @ TA @ TB @ TC @ D @ E @ F @ ( zero_zero @ nat ) )
= ( cons @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ D @ ( nil @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J) ).
thf(1122,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) > ( list @ ( message @ TA @ TB ) ) > ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ),F: ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) > ( list @ ( message @ TA @ TB ) ) > ( list @ ( message @ TA @ TB ) )] :
( ( fLPThe1922692578sensus @ TA @ TC @ TB @ A @ B @ C )
=> ( ( fLPThe137922386ionCfg @ TA @ TB @ TC @ D @ E @ F @ ( zero_zero @ nat ) )
= ( cons @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) @ D @ ( nil @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(135,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_79_Suc__less__eq2) ).
thf(758,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)],[135]) ).
thf(154,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder_5) ).
thf(816,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(32,axiom,
( ( zero_zero @ nat )
= ( nat2 @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_nat__zero__as__int) ).
thf(323,plain,
( ( zero_zero @ nat )
= ( nat2 @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(128,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_old_Onat_Odistinct_I2_J) ).
thf(726,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(124,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_nat__induct) ).
thf(700,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)],[124]) ).
thf(229,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_5_PrefixListTransitive) ).
thf(1149,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)],[229]) ).
thf(139,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_113_lift__Suc__mono__less) ).
thf(769,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)],[139]) ).
thf(35,axiom,
! [A: int] :
( ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) )
=> ~ ! [B: nat] :
( A
!= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_int__cases) ).
thf(330,plain,
! [A: int] :
( ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) )
=> ~ ! [B: nat] :
( A
!= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(163,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_13) ).
thf(858,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(95,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_not0__implies__Suc) ).
thf(552,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(3,axiom,
one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oone) ).
thf(240,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: int,B: nat] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ nat @ ( nat2 @ A ) @ B )
= ( ord_less @ int @ A @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_nat__less__iff) ).
thf(251,plain,
! [A: int,B: nat] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ nat @ ( nat2 @ A ) @ B )
= ( ord_less @ int @ A @ ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_list_Oexhaust) ).
thf(399,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(1066,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(237,axiom,
( ( ord_less @ nat @ m @ na )
=> ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ m ) @ ( fe @ na ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_IA_I1_J) ).
thf(1176,plain,
( ( ord_less @ nat @ m @ na )
=> ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ m ) @ ( fe @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(57,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Suc__neq__Zero) ).
thf(394,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(27,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_int__ops_I1_J) ).
thf(306,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,axiom,
order @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oorder_1) ).
thf(241,plain,
order @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(117,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_gr0__conv__Suc) ).
thf(653,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType] : ( size @ ( message @ TB @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_AsynchronousSystem_Omessage___Nat_Osize_24) ).
thf(675,plain,
! [TA: $tType,TB: $tType] : ( size @ ( message @ TB @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(68,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_compl__less__swap1) ).
thf(426,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(88,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_of__nat__0__less__iff) ).
thf(531,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(123,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_74_strict__inc__induct) ).
thf(680,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)],[123]) ).
thf(53,axiom,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( gen_length @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( gen_length @ TA @ ( suc @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_gen__length__code_I2_J) ).
thf(374,plain,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( gen_length @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( gen_length @ TA @ ( suc @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(10,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(255,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(152,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_neq__Nil__conv) ).
thf(812,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > $o,E: ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > $o,F: configuration_ext @ TC @ TB @ TA @ product_unit,G: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),H: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),I: nat] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) )] : ( D @ J @ K @ L @ ( zero_zero @ nat ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),M: nat] :
( ( D @ J @ K @ L @ M )
=> ( ( E @ J @ K @ L @ M )
=> ( D @ J @ K @ L @ ( suc @ M ) ) ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) )] : ( E @ J @ K @ L @ ( zero_zero @ nat ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),M: nat] :
( ( D @ J @ K @ L @ M )
=> ( ( E @ J @ K @ L @ M )
=> ( E @ J @ K @ L @ ( suc @ M ) ) ) )
=> ( D @ F @ G @ H @ I ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J) ).
thf(617,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > $o,E: ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ) ) > nat > $o,F: configuration_ext @ TC @ TB @ TA @ product_unit,G: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),H: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),I: nat] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) )] : ( D @ J @ K @ L @ ( zero_zero @ nat ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),M: nat] :
( ( D @ J @ K @ L @ M )
=> ( ( E @ J @ K @ L @ M )
=> ( D @ J @ K @ L @ ( suc @ M ) ) ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) )] : ( E @ J @ K @ L @ ( zero_zero @ nat ) )
=> ( ! [J: configuration_ext @ TC @ TB @ TA @ product_unit,K: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),L: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),M: nat] :
( ( D @ J @ K @ L @ M )
=> ( ( E @ J @ K @ L @ M )
=> ( E @ J @ K @ L @ ( suc @ M ) ) ) )
=> ( D @ F @ G @ H @ I ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(175,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_116_All__less__Suc2) ).
thf(939,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)],[175]) ).
thf(214,axiom,
ord_less @ nat @ m @ na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062m_A_060_An_092_060close_062) ).
thf(1081,plain,
ord_less @ nat @ m @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(133,axiom,
! [TA: $tType,A: list @ TA,B: set @ nat] :
( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( member @ nat @ C @ B ) )
=> ( ( nths @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_nths__all) ).
thf(749,plain,
! [TA: $tType,A: list @ TA,B: set @ nat] :
( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( member @ nat @ C @ B ) )
=> ( ( nths @ TA @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) > ( list @ ( message @ TA @ TB ) ) > ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ),F: ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) > ( list @ ( message @ TA @ TB ) ) > ( list @ ( message @ TA @ TB ) )] :
( ( fLPThe1922692578sensus @ TA @ TC @ TB @ A @ B @ C )
=> ( ( fLPThe221390223ionMsg @ TA @ TB @ TC @ D @ E @ F @ ( zero_zero @ nat ) )
= ( nil @ ( message @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J) ).
thf(525,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC > ( messageValue @ TB ) > TC,B: TA > TC > ( messageValue @ TB ) > ( message @ TA @ TB ) > nat,C: TA > TC,D: configuration_ext @ TA @ TB @ TC @ product_unit,E: ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) > ( list @ ( message @ TA @ TB ) ) > ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ),F: ( list @ ( configuration_ext @ TA @ TB @ TC @ product_unit ) ) > ( list @ ( message @ TA @ TB ) ) > ( list @ ( message @ TA @ TB ) )] :
( ( fLPThe1922692578sensus @ TA @ TC @ TB @ A @ B @ C )
=> ( ( fLPThe221390223ionMsg @ TA @ TB @ TC @ D @ E @ F @ ( zero_zero @ nat ) )
= ( nil @ ( message @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(195,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_transpose_Ocases) ).
thf(1003,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(23,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_of__nat__less__iff) ).
thf(295,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(233,axiom,
( ( m = na )
| ( ord_less @ nat @ m @ na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062) ).
thf(1156,plain,
( ( m = na )
| ( ord_less @ nat @ m @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(179,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_splice_Oinduct) ).
thf(954,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_less__not__refl2) ).
thf(409,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(192,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_shuffles_Oinduct) ).
thf(993,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(147,axiom,
! [TA: $tType,A: set @ nat] :
( ( nths @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_nths__nil) ).
thf(791,plain,
! [TA: $tType,A: set @ nat] :
( ( nths @ TA @ ( nil @ TA ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(103,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_gr0I) ).
thf(585,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(216,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] :
( ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ ( zero_zero @ nat ) )
= ( nil @ ( message @ p @ v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_infiniteExecutionMsg_Osimps_I1_J) ).
thf(1085,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] :
( ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ ( zero_zero @ nat ) )
= ( nil @ ( message @ p @ v ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(178,axiom,
! [A: int,B: int] :
( ( ord_less @ nat @ ( nat2 @ A ) @ ( nat2 @ B ) )
= ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
& ( ord_less @ int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_zless__nat__conj) ).
thf(951,plain,
! [A: int,B: int] :
( ( ord_less @ nat @ ( nat2 @ A ) @ ( nat2 @ B ) )
= ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
& ( ord_less @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(225,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),D: nat] :
( ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ ( suc @ D ) )
= ( B @ ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ D ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_infiniteExecutionCfg_Osimps_I2_J) ).
thf(1141,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),D: nat] :
( ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ ( suc @ D ) )
= ( B @ ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ D ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(118,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Ex__list__of__length) ).
thf(656,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(199,axiom,
! [TA: $tType,A: nat] :
( ( gen_length @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_gen__length__code_I1_J) ).
thf(1023,plain,
! [TA: $tType,A: nat] :
( ( gen_length @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(186,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_85_less__SucE) ).
thf(978,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)],[186]) ).
thf(224,axiom,
ord @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oord_23) ).
thf(1140,plain,
ord @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(76,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_67_infinite__descent0) ).
thf(465,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)],[76]) ).
thf(174,axiom,
! [TA: $tType,A: nat > TA > $o,B: nat > TA > TA > $o] :
( ? [C: TA] : ( A @ ( zero_zero @ nat ) @ C )
=> ( ! [C: TA,D: nat] :
( ( A @ D @ C )
=> ? [E: TA] :
( ( A @ ( suc @ D ) @ E )
& ( B @ D @ C @ E ) ) )
=> ? [C: nat > TA] :
! [D: nat] :
( ( A @ D @ ( C @ D ) )
& ( B @ D @ ( C @ D ) @ ( C @ ( suc @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_dependent__nat__choice) ).
thf(931,plain,
! [TA: $tType,A: nat > TA > $o,B: nat > TA > TA > $o] :
( ? [C: TA] : ( A @ ( zero_zero @ nat ) @ C )
=> ( ! [C: TA,D: nat] :
( ( A @ D @ C )
=> ? [E: TA] :
( ( A @ ( suc @ D ) @ E )
& ( B @ D @ C @ E ) ) )
=> ? [C: nat > TA] :
! [D: nat] :
( ( A @ D @ ( C @ D ) )
& ( B @ D @ ( C @ D ) @ ( C @ ( suc @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(77,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_product__lists_Osimps_I1_J) ).
thf(482,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(102,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_nat_Odistinct_I1_J) ).
thf(581,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(51,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_83_Ex__less__Suc) ).
thf(368,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)],[51]) ).
thf(140,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_15) ).
thf(771,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(220,axiom,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),D: nat,E: list @ ( message @ p @ v )] :
( ( ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ D )
= E )
=> ( ( ( D
= ( zero_zero @ nat ) )
=> ( E
!= ( nil @ ( message @ p @ v ) ) ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( C @ ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ F ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_infiniteExecutionMsg_Oelims) ).
thf(1108,plain,
! [A: configuration_ext @ p @ v @ s @ product_unit,B: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),C: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),D: nat,E: list @ ( message @ p @ v )] :
( ( ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ D )
= E )
=> ( ( ( D
= ( zero_zero @ nat ) )
=> ( E
!= ( nil @ ( message @ p @ v ) ) ) )
=> ~ ! [F: nat] :
( ( D
= ( suc @ F ) )
=> ( E
!= ( C @ ( fLPThe137922386ionCfg @ p @ v @ s @ A @ B @ C @ F ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ A @ B @ C @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(104,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_zero__less__imp__eq__int) ).
thf(588,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__SucI) ).
thf(961,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(182,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_86_Suc__lessI) ).
thf(963,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)],[182]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: configuration_ext @ TC @ TB @ TA @ product_unit,E: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),F: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),G: nat,H: list @ ( message @ TC @ TB )] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ( ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ G )
= H )
=> ( ( ( G
= ( zero_zero @ nat ) )
=> ( H
!= ( nil @ ( message @ TC @ TB ) ) ) )
=> ~ ! [I: nat] :
( ( G
= ( suc @ I ) )
=> ( H
!= ( F @ ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ I ) @ ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims) ).
thf(896,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: configuration_ext @ TC @ TB @ TA @ product_unit,E: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),F: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),G: nat,H: list @ ( message @ TC @ TB )] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ( ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ G )
= H )
=> ( ( ( G
= ( zero_zero @ nat ) )
=> ( H
!= ( nil @ ( message @ TC @ TB ) ) ) )
=> ~ ! [I: nat] :
( ( G
= ( suc @ I ) )
=> ( H
!= ( F @ ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ I ) @ ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(111,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_136_zero__less__iff__neq__zero) ).
thf(632,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)],[111]) ).
thf(65,axiom,
! [TA: $tType,A: list @ TA,B: nat] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( suc @ B ) )
= ( ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( ( size_size @ ( list @ TA ) @ D )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_length__Suc__conv) ).
thf(418,plain,
! [TA: $tType,A: list @ TA,B: nat] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( suc @ B ) )
= ( ? [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
& ( ( size_size @ ( list @ TA ) @ D )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(173,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_compl__less__swap2) ).
thf(929,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(18,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(272,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(41,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_le__numeral__extra_I4_J) ).
thf(346,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(70,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_24_Suc__less__eq) ).
thf(432,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)],[70]) ).
thf(184,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_80_All__less__Suc) ).
thf(967,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)],[184]) ).
thf(13,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_less__numeral__extra_I4_J) ).
thf(262,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_map__tailrec__rev_Oinduct) ).
thf(854,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(39,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_of__nat__0) ).
thf(341,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(16,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_3) ).
thf(268,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(48,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_successively_Oinduct) ).
thf(358,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(72,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_82_less__Suc__eq) ).
thf(437,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)],[72]) ).
thf(205,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_not__gr0) ).
thf(1056,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(112,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_old_Onat_Odistinct_I1_J) ).
thf(635,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_list_Odistinct_I1_J) ).
thf(415,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1,conjecture,
prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ m ) @ ( fe @ na ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ m ) @ ( fe @ na ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(239,plain,
~ ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ m ) @ ( fe @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_of__nat__1) ).
thf(242,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: configuration_ext @ TC @ TB @ TA @ product_unit,E: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),F: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),G: nat,H: list @ ( configuration_ext @ TC @ TB @ TA @ product_unit )] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ( ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ G )
= H )
=> ( ( ( G
= ( zero_zero @ nat ) )
=> ( H
!= ( cons @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) @ D @ ( nil @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) ) )
=> ~ ! [I: nat] :
( ( G
= ( suc @ I ) )
=> ( H
!= ( E @ ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ I ) @ ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ I ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims) ).
thf(1093,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > ( messageValue @ TB ) > TA,B: TC > TA > ( messageValue @ TB ) > ( message @ TC @ TB ) > nat,C: TC > TA,D: configuration_ext @ TC @ TB @ TA @ product_unit,E: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ),F: ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( list @ ( message @ TC @ TB ) ),G: nat,H: list @ ( configuration_ext @ TC @ TB @ TA @ product_unit )] :
( ( fLPThe1922692578sensus @ TC @ TA @ TB @ A @ B @ C )
=> ( ( ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ G )
= H )
=> ( ( ( G
= ( zero_zero @ nat ) )
=> ( H
!= ( cons @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) @ D @ ( nil @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) ) ) )
=> ~ ! [I: nat] :
( ( G
= ( suc @ I ) )
=> ( H
!= ( E @ ( fLPThe137922386ionCfg @ TC @ TB @ TA @ D @ E @ F @ I ) @ ( fLPThe221390223ionMsg @ TC @ TB @ TA @ D @ E @ F @ I ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(189,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_7) ).
thf(987,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(100,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_135_gr__implies__not__zero) ).
thf(575,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)],[100]) ).
thf(231,axiom,
wellorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Owellorder_20) ).
thf(1152,plain,
wellorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(164,axiom,
wellorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(860,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(106,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_36_infinite__descent__measure) ).
thf(596,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)],[106]) ).
thf(198,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_arg__min__list_Oinduct) ).
thf(1019,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(87,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__zeroE) ).
thf(528,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(127,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_insert__Nil) ).
thf(723,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(157,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_112_lift__Suc__mono__less__iff) ).
thf(822,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)],[157]) ).
thf(150,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_bot__nat__0_Oextremum__strict) ).
thf(803,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(37,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_of__nat__le__0__iff) ).
thf(337,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(46,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_not__less__zero) ).
thf(354,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(197,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_list_Oinducts) ).
thf(1009,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(119,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_6) ).
thf(659,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_gr__implies__not0) ).
thf(543,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(113,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_compl__less__compl__iff) ).
thf(639,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(134,axiom,
! [A: int] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat2 @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_zero__less__nat__eq) ).
thf(755,plain,
! [A: int] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat2 @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(217,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( prefixList @ TA @ A @ B )
=> ( ! [D: TA,E: list @ TA] : ( C @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: list @ TA,E: list @ TA,F: TA] :
( ( prefixList @ TA @ D @ E )
=> ( ( C @ D @ E )
=> ( C @ ( cons @ TA @ F @ D ) @ ( cons @ TA @ F @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_prefixList_Oinducts) ).
thf(1088,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( prefixList @ TA @ A @ B )
=> ( ! [D: TA,E: list @ TA] : ( C @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: list @ TA,E: list @ TA,F: TA] :
( ( prefixList @ TA @ D @ E )
=> ( ( C @ D @ E )
=> ( C @ ( cons @ TA @ F @ D ) @ ( cons @ TA @ F @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(80,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_50_neq__if__length__neq) ).
thf(496,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)],[80]) ).
thf(168,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_48_nat__neq__iff) ).
thf(882,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)],[168]) ).
thf(1180,plain,
$false,
inference(e,[status(thm)],[1036,365,628,777,555,730,1068,308,247,861,1173,440,511,614,269,677,1078,500,797,945,538,1063,340,1001,782,885,301,829,404,785,344,1059,817,559,853,1147,421,284,325,492,321,646,485,1151,348,806,1051,353,966,877,293,660,998,988,428,602,981,766,1074,248,942,381,534,714,1153,761,334,910,825,349,820,788,815,879,435,1178,1159,650,1006,356,593,1082,537,1075,642,547,328,256,1039,970,738,984,779,371,503,266,921,398,1071,1026,794,298,264,733,513,1146,562,423,402,772,286,711,579,958,259,413,843,1125,445,572,313,1107,350,540,391,1139,764,274,1048,1144,245,509,1175,377,990,362,451,737,318,303,1122,758,816,323,726,700,1149,769,330,858,552,240,251,399,1066,1176,394,306,241,653,675,426,531,680,374,255,812,617,939,1081,749,525,1003,295,1156,954,409,993,791,585,1085,951,1141,656,1023,978,1140,465,931,482,581,368,771,1108,588,961,963,896,632,418,929,272,346,432,967,262,854,341,268,358,437,1056,635,415,239,242,1093,987,575,1152,860,596,1019,528,723,822,803,337,354,1009,659,543,639,755,1088,496,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP055^2 : 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
% 0.08/0.20 % Computer : n018.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 19:46:26 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.21 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
% 0.87/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.48/1.20 % [INFO] Parsing done (421ms).
% 2.48/1.21 % [INFO] Running in sequential loop mode.
% 3.69/1.60 % [INFO] eprover registered as external prover.
% 3.69/1.61 % [INFO] Scanning for conjecture ...
% 3.88/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 293 axioms. Running axiom selection ...
% 4.46/1.93 % [INFO] Axiom selection finished. Selected 236 axioms (removed 57 axioms).
% 5.33/2.29 % [INFO] Problem is higher-order (TPTP THF).
% 5.71/2.33 % [INFO] Type checking passed.
% 5.71/2.34 % [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 ...
% 64.26/44.34 % External prover 'e' found a proof!
% 64.26/44.34 % [INFO] Killing All external provers ...
% 64.26/44.34 % Time passed: 43996ms (effective reasoning time: 43123ms)
% 64.26/44.34 % 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)>
% 64.26/44.35 % Axioms used in derivation (236): fact_135_gr__implies__not__zero, fact_93_list__nonempty__induct, fact_70_not__less0, tcon_Nat_Onat___Orderings_Oord_8, fact_230_of__nat__le__0__iff, fact_58_zero__induct, fact_110_list_Odistinct_I1_J, fact_17_infiniteExecutionCfg_Osimps_I1_J, fact_233_nat__0__iff, tcon_Set_Oset___Orderings_Oorder_12, fact_89_Nat_OlessE, fact_194_int__of__nat__induct, fact_203_zero__less__nat__eq, fact_241_one__reorient, fact_109_list_OdiscI, fact_19_length__0__conv, fact_77_Suc__less__SucD, tcon_Nat_Onat___Groups_Ozero_9, fact_52_not0__implies__Suc, fact_217_split__nat, fact_212_nat__zero__as__int, fact_140_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims, fact_68_gr__implies__not0, tcon_AsynchronousSystem_Omessage___Nat_Osize_24, fact_152_gen__length__code_I2_J, fact_222_of__nat__le__iff, fact_243_lift__Suc__mono__le, fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062, tcon_Nat_Onat___Nat_Osize, fact_22_lessI, tcon_Int_Oint___Groups_Ozero, fact_1_MLessN, fact_172_int__ops_I1_J, fact_200_compl__less__compl__iff, fact_105_list__induct2_H, fact_37_linorder__neqE__nat, fact_88_Suc__lessD, tcon_Int_Oint___Orderings_Oord_2, fact_166_of__nat__less__imp__less, fact_39_nat__less__induct, fact_149_product__lists_Osimps_I1_J, fact_213_nat__mono__iff, fact_100_shuffles_Oinduct, fact_108_list_Oexhaust, tcon_fun___Orderings_Oord, fact_35_Suc__inject, fact_119_length__Suc__conv, fact_26_less__nat__zero__code, fact_151_length__code, fact_53_old_Onat_Oinducts, fact_128_infiniteExecutionMsg_Osimps_I1_J, tcon_Product__Type_Ounit___Orderings_Olinorder_21, fact_122_list__induct3, fact_31_measure__induct__rule, fact_121_list_Osize_I3_J, fact_102_min__list_Ocases, fact_132_zero__reorient, fact_107_list_Oinducts, tcon_HOL_Obool___Orderings_Olinorder_15, tcon_Product__Type_Ounit___Orderings_Oorder_22, fact_59_diff__induct, fact_0__092_060open_062m_A_060_An_092_060close_062, fact_115_gr0__implies__Suc, tcon_HOL_Obool___Orderings_Oord_17, fact_50_neq__if__length__neq, fact_124_infiniteExecutionCfg_Oelims, fact_199_negD, fact_28_list_Oinject, fact_73_not__less__less__Suc__eq, tcon_Nat_Onat___Groups_Oone_10, fact_150_subseqs_Osimps_I1_J, tcon_Int_Oint___Orderings_Oorder_1, fact_173_neg__int__cases, fact_94_successively_Oinduct, fact_198_negative__zless__0, fact_99_transpose_Ocases, fact_130_length__Cons, fact_75_less__Suc__induct, fact_76_less__trans__Suc, fact_40_less__irrefl__nat, fact_20_less__Suc0, tcon_Product__Type_Ounit___Lattices_Oboolean__algebra_19, fact_101_min__list_Oinduct, fact_30_nat_Oinject, fact_36_infinite__descent__measure, fact_165_less__imp__of__nat__less, fact_244_zero__le, fact_117_gr0__conv__Suc, fact_245_le__numeral__extra_I3_J, fact_134_not__less__zero, fact_223_of__nat__1, fact_129_not__gr__zero, fact_63_old_Onat_Odistinct_I2_J, fact_162_of__nat__less__iff, fact_27_bot__nat__0_Onot__eq__extremum, fact_246_less__numeral__extra_I4_J, tcon_Int_Oint___Orderings_Olinorder, fact_158_nths__nil, fact_125_infiniteExecutionMsg_Oelims, fact_81_not__less__eq, fact_41_less__not__refl3, fact_112_lift__Suc__mono__less__iff, fact_114_less__Suc__eq__0__disj, fact_231_nat__1, fact_201_compl__less__swap2, fact_64_nat_Odistinct_I1_J, fact_197_int__cases3, fact_55_Zero__not__Suc, fact_147_shift__def, fact_103_induct__list012, fact_123_list__induct2, tcon_Nat_Onat___Orderings_Owellorder, fact_48_nat__neq__iff, fact_155_nths__singleton, tcon_HOL_Obool___Orderings_Oorder_16, fact_242_lift__Suc__antimono__le, fact_232_nat__le__0, tcon_Nat_Onat___Rings_Osemiring__1_6, tcon_Nat_Onat___Orderings_Oorder_7, fact_193_int__cases, fact_91_strict__sorted_Ocases, fact_7_FE_I1_J, fact_146_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J, fact_11_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, fact_56_Zero__neq__Suc, fact_32_measure__induct, fact_61_nat_OdiscI, fact_42_less__not__refl2, tcon_Nat_Onat___Orderings_Olinorder_5, fact_87_Suc__lessE, fact_118_Ex__less__Suc2, tcon_Int_Oint___Rings_Osemiring__1, fact_66_bot__nat__0_Oextremum__strict, fact_47_less__not__refl, fact_170_list__ex1__simps_I1_J, fact_239_verit__comp__simplify1_I3_J, fact_78_less__antisym, fact_168_pos__int__cases, fact_2_IA_I1_J, fact_54_old_Onat_Oexhaust, fact_10_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, fact_138_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_3, fact_159_of__nat__0, fact_16_NatPredicateTippingPoint, tcon_Set_Oset___Orderings_Oord_13, fact_131_dependent__nat__choice, fact_104_splice_Oinduct, fact_5_PrefixListTransitive, fact_38_infinite__descent, tcon_Set_Oset___Lattices_Oboolean__algebra_11, tcon_fun___Lattices_Oboolean__algebra, fact_33_not__Cons__self2, fact_195_int__cases4, fact_142_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, fact_8_prefixList_Ointros_I2_J, fact_18_length__greater__0__conv, fact_186_negative__eq__positive, fact_218_one__less__nat__eq, fact_145_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J, fact_133_gr__zeroI, fact_49_size__neq__size__imp__neq, fact_4_IA_I2_J, fact_82_less__Suc__eq, fact_12_prefixList_Ointros_I1_J, fact_90_strict__sorted_Oinduct, fact_95_arg__min__list_Oinduct, fact_71_not__gr0, fact_113_lift__Suc__mono__less, fact_120_Suc__length__conv, fact_51_Ex__list__of__length, fact_148_less__numeral__extra_I3_J, fact_15_prefixList_Oinducts, tcon_Product__Type_Ounit___Orderings_Owellorder_20, fact_24_Suc__less__eq, fact_74_strict__inc__induct, fact_9_PrefixListMonotonicity, fact_143_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J, fact_67_infinite__descent0, fact_79_Suc__less__eq2, fact_144_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J, fact_84_less__SucI, fact_111_length__induct, fact_171_nat__int__comparison_I2_J, fact_21_zero__less__Suc, fact_167_nths__all, fact_210_nat__zminus__int, fact_163_of__nat__less__0__iff, tcon_HOL_Obool___Lattices_Oboolean__algebra_14, fact_139_n__lists_Osimps_I1_J, fact_209_zless__nat__conj, fact_240_le__numeral__extra_I4_J, fact_156_of__nat__0__less__iff, tcon_fun___Orderings_Oorder, fact_69_less__zeroE, fact_214_zless__nat__eq__int__zless, fact_65_infinite__descent0__measure, fact_116_All__less__Suc2, fact_187_negative__zless, fact_85_less__SucE, fact_60_nat__induct, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_136_zero__less__iff__neq__zero, fact_83_Ex__less__Suc, fact_106_neq__Nil__conv, fact_80_All__less__Suc, fact_220_le__zero__eq, tcon_Product__Type_Ounit___Orderings_Oord_23, fact_141_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, fact_196_verit__comp__simplify1_I1_J, fact_62_old_Onat_Odistinct_I1_J, fact_219_nat__less__iff, fact_126_infiniteExecutionMsg_Osimps_I2_J, fact_96_remdups__adj_Oinduct, fact_13_prefixList_Ocases, fact_23_Suc__mono, fact_247_of__nat__mono, fact_137_n__lists__Nil, fact_154_insert__Nil, tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, fact_14_prefixList_Osimps, tcon_Int_Oint___Groups_Oone, fact_153_gen__length__code_I1_J, fact_202_compl__less__swap1, fact_29_old_Onat_Oinject, fact_72_gr0I, tcon_List_Olist___Nat_Osize_18, fact_57_Suc__neq__Zero, fact_127_infiniteExecutionCfg_Osimps_I2_J, fact_34_n__not__Suc__n, fact_92_map__tailrec__rev_Oinduct, fact_86_Suc__lessI, fact_97_sorted__wrt_Oinduct, fact_25_neq0__conv, fact_169_zero__less__imp__eq__int, fact_98_remdups__adj_Ocases
% 64.26/44.35 % No. of inferences in proof: 476
% 64.26/44.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 43996 ms resp. 43123 ms w/o parsing
% 65.28/44.61 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 65.28/44.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------