%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT122^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 07:48:01 AM UTC 2026
% Result : Theorem 106.23s 52.50s
% Output : Refutation 107.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 327
% Syntax : Number of formulae : 884 ( 486 unt; 0 typ; 2 def)
% Number of atoms : 2637 ( 866 equ; 4 cnn)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 10807 ( 567 ~; 217 |; 163 &;9398 @)
% ( 0 <=>; 462 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 382 ( 382 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 12 con; 0-6 aty)
% Number of variables : 2452 ( 68 ^;2302 !; 80 ?;2452 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(code_natural_type,type,
code_natural: $tType ).
thf(code_term_type,type,
code_term: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(typerep_type,type,
typerep: $tType ).
thf(literal_type,type,
literal: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(enum_decl,type,
enum:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(typerep2_decl,type,
typerep2:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cl_HOL_Oequal_decl,type,
cl_HOL_Oequal:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(code_term_of_decl,type,
code_term_of:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(size_decl,type,
size:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(quickcheck_random_decl,type,
quickcheck_random:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_numeral_div_decl,type,
semiring_numeral_div:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(code_Suc_decl,type,
code_Suc: code_natural > code_natural ).
thf(code_case_natural_decl,type,
code_case_natural:
!>[TA: $tType] : ( TA > ( code_natural > TA ) > code_natural > TA ) ).
thf(code_rec_natural_decl,type,
code_rec_natural:
!>[TA: $tType] : ( TA > ( code_natural > TA > TA ) > code_natural > TA ) ).
thf(code_size_natural_decl,type,
code_size_natural: code_natural > nat ).
thf(coindu1529956631erates_decl,type,
coindu1529956631erates:
!>[TA: $tType] : ( ( TA > TA ) > TA > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu268472904append_decl,type,
coindu268472904append:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu300403952lexord_decl,type,
coindu300403952lexord:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1121789889_LCons_decl,type,
coindu1121789889_LCons:
!>[TA: $tType] : ( TA > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1598213697e_LNil_decl,type,
coindu1598213697e_LNil:
!>[TA: $tType] : ( coindu1593790203_llist @ TA ) ).
thf(coindu882539134_llist_decl,type,
coindu882539134_llist:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( coindu1593790203_llist @ TA ) > TB ) > ( coindu1593790203_llist @ TA ) > TB ) ).
thf(coindu1046438764le_lhd_decl,type,
coindu1046438764le_lhd:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > TA ) ).
thf(coindu987187967t_all2_decl,type,
coindu987187967t_all2:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > ( coindu1593790203_llist @ TB ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1062782156e_lmap_decl,type,
coindu1062782156e_lmap:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( coindu1593790203_llist @ TB ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu335574135_lnull_decl,type,
coindu335574135_lnull:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1047225960le_ltl_decl,type,
coindu1047225960le_ltl:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu567634248member_decl,type,
coindu567634248member:
!>[TA: $tType] : ( TA > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu749330388e_lnth_decl,type,
coindu749330388e_lnth:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > nat > TA ) ).
thf(coindu1696667936prefix_decl,type,
coindu1696667936prefix:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu574146665prefix_decl,type,
coindu574146665prefix:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1802687541_ltake_decl,type,
coindu1802687541_ltake:
!>[TA: $tType] : ( extended_enat > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu721411036eWhile_decl,type,
coindu721411036eWhile:
!>[TA: $tType] : ( ( TA > $o ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu847746867e_lzip_decl,type,
coindu847746867e_lzip:
!>[TA: $tType,TB: $tType] : ( ( coindu1593790203_llist @ TB ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ ( product_prod @ TB @ TA ) ) ) ).
thf(coindu1599971794_llist_decl,type,
coindu1599971794_llist:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > TA ) > ( TB > TB ) > TB > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu440805660e_enat_decl,type,
coindu440805660e_enat:
!>[TA: $tType] : ( TA > ( extended_enat > TA ) > extended_enat > TA ) ).
thf(coinductive_epred_decl,type,
coinductive_epred: extended_enat > extended_enat ).
thf(coindu1491768222unfold_decl,type,
coindu1491768222unfold:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > TA ) > TA > extended_enat ) ).
thf(semiri577515795es_aux_decl,type,
semiri577515795es_aux:
!>[TA: $tType] : ( ( product_prod @ TA @ TA ) > $o ) ).
thf(extended_case_enat_decl,type,
extended_case_enat:
!>[TA: $tType] : ( ( nat > TA ) > TA > extended_enat > TA ) ).
thf(extended_the_enat_decl,type,
extended_the_enat: extended_enat > nat ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(size_bool_decl,type,
size_bool: $o > nat ).
thf(default_default_decl,type,
default_default:
!>[TA: $tType] : TA ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(rec_nat_decl,type,
rec_nat:
!>[TA: $tType] : ( TA > ( nat > TA > TA ) > nat > TA ) ).
thf(semiri532925092at_aux_decl,type,
semiri532925092at_aux:
!>[TA: $tType] : ( ( TA > TA ) > nat > TA > TA ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_Unity_decl,type,
product_Unity: product_unit ).
thf(produc2004651681e_prod_decl,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_bool_decl,type,
product_rec_bool:
!>[TA: $tType] : ( TA > TA > $o > TA ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_unit_decl,type,
product_rec_unit:
!>[TA: $tType] : ( TA > product_unit > TA ) ).
thf(product_case_unit_decl,type,
product_case_unit:
!>[TA: $tType] : ( TA > product_unit > TA ) ).
thf(product_size_unit_decl,type,
product_size_unit: product_unit > nat ).
thf(type2_decl,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(xs_decl,type,
xs: coindu1593790203_llist @ a ).
thf(sk1_decl,type,
sk1:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > TA ) ).
thf(sk2_decl,type,
sk2:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [TA: $tType,A: coindu1593790203_llist @ TA] :
@+[B: TA] :
~ ! [C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [TA: $tType,A: coindu1593790203_llist @ TA] :
@+[B: coindu1593790203_llist @ TA] :
~ ( ( A
!= ( coindu1121789889_LCons @ TA @ ( sk1 @ TA @ A ) @ B ) ) ) ) ) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA] :
( ( ( coindu1062782156e_lmap @ TA @ TB @ A @ B )
= ( coindu1598213697e_LNil @ TB ) )
= ( B
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_lmap__eq__LNil) ).
thf(629,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA] :
( ( ( coindu1062782156e_lmap @ TA @ TB @ A @ B )
= ( coindu1598213697e_LNil @ TB ) )
= ( B
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( ( quickcheck_random @ TB @ ( type2 @ TB ) )
& ( quickcheck_random @ TA @ ( type2 @ TA ) ) )
=> ( quickcheck_random @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_64) ).
thf(365,plain,
! [TA: $tType,TB: $tType] :
( ( ( quickcheck_random @ TB @ ( type2 @ TB ) )
& ( quickcheck_random @ TA @ ( type2 @ TA ) ) )
=> ( quickcheck_random @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(283,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_lhd__lappend) ).
thf(1168,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_old_Oprod_Oinducts) ).
thf(479,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( ( code_term_of @ TB @ ( type2 @ TB ) )
& ( cl_HOL_Oequal @ TB @ ( type2 @ TB ) )
& ( quickcheck_random @ TA @ ( type2 @ TA ) ) )
=> ( quickcheck_random @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Quickcheck__Random_Orandom) ).
thf(347,plain,
! [TA: $tType,TB: $tType] :
( ( ( code_term_of @ TB @ ( type2 @ TB ) )
& ( cl_HOL_Oequal @ TB @ ( type2 @ TB ) )
& ( quickcheck_random @ TA @ ( type2 @ TA ) ) )
=> ( quickcheck_random @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(198,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_lappend_Odisc__iff_I2_J) ).
thf(846,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(5,axiom,
! [TA: $tType] :
( ( enum @ TA @ ( type2 @ TA ) )
=> ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Enum_Oenum_31) ).
thf(333,plain,
! [TA: $tType] :
( ( enum @ TA @ ( type2 @ TA ) )
=> ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(224,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_llist_Osplit__sel) ).
thf(962,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(266,axiom,
( ( extended_the_enat @ ( zero_zero @ extended_enat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_the__enat__0) ).
thf(1110,plain,
( ( extended_the_enat @ ( zero_zero @ extended_enat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: product_unit] :
( ( A @ ( product_case_unit @ TB @ B @ C ) )
= ( product_case_unit @ TA @ ( A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_unit_Ocase__distrib) ).
thf(339,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: product_unit] :
( ( A @ ( product_case_unit @ TB @ B @ C ) )
= ( product_case_unit @ TA @ ( A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(340,plain,
! [TA: $tType,TB: $tType,C: product_unit,B: TA,A: TA > TB] :
( ( A @ ( product_case_unit @ TA @ B @ C ) )
= ( product_case_unit @ TB @ ( A @ B ) @ C ) ),
inference(cnf,[status(esa)],[339]) ).
thf(341,plain,
! [TA: $tType,TB: $tType,C: product_unit,B: TA,A: TA > TB] :
( ( A @ ( product_case_unit @ TA @ B @ C ) )
= ( product_case_unit @ TB @ ( A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[340]) ).
thf(141,axiom,
( ( default_default @ product_unit )
= product_Unity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_default__unit__def) ).
thf(681,plain,
( ( default_default @ product_unit )
= product_Unity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(682,plain,
( product_Unity
= ( default_default @ product_unit ) ),
inference(lifteq,[status(thm)],[681]) ).
thf(1,conjecture,
( ( coindu1046438764le_lhd @ a @ xs )
= ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
( ( coindu1046438764le_lhd @ a @ xs )
!= ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(327,plain,
( ( coindu1046438764le_lhd @ a @ xs )
!= ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(328,plain,
( ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(lifteq,[status(thm)],[327]) ).
thf(1683,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > a] :
( ( ( product_case_unit @ a @ ( A @ B ) @ C )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,328]) ).
thf(1887,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ A )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[1683:[bind(A,$thf( ^ [D: TA] : ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(2106,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ A )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[1887]) ).
thf(2344,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > a] :
( ( ( product_case_unit @ a @ ( A @ B ) @ C )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[341,2106]) ).
thf(2351,plain,
! [TA: $tType,C: TA > product_unit,B: product_unit,A: TA] :
( ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( C @ A ) ) @ B )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[2344:[bind(A,$thf( ^ [F: TA] : ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( F @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ ( product_case_unit @ TA @ B @ C ) ))]]) ).
thf(2355,plain,
! [TA: $tType,C: TA > product_unit,B: product_unit,A: TA] :
( ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( C @ A ) ) @ B )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[2351]) ).
thf(3208,plain,
! [TA: $tType,C: TA > product_unit,B: product_unit,A: TA] :
( ( ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) ) @ B )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( product_Unity
!= ( C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[682,2355]) ).
thf(3224,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) ) @ A )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[3208:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [D: TA] : product_Unity ))]]) ).
thf(3234,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) ) @ A )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[3224]) ).
thf(3350,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > a] :
( ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( product_case_unit @ a @ ( A @ B ) @ C )
!= ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[341,3234]) ).
thf(3352,plain,
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[3350:[bind(A,$thf( ^ [E: TA] : ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) ) )),bind(B,$thf( B )),bind(C,$thf( D )),bind(D,$thf( D ))]]) ).
thf(3370,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > ( coindu1593790203_llist @ a )] :
( ( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( A @ B ) @ C ) @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= xs ) ),
inference(paramod_ordered,[status(thm)],[341,3352]) ).
thf(3373,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[3370:[bind(A,$thf( ^ [D: TA] : xs ))]]) ).
thf(3381,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[3373]) ).
thf(3914,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > a] :
( ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( product_case_unit @ a @ ( A @ B ) @ C )
!= ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ D ) @ ( zero_zero @ nat ) ) @ ( default_default @ product_unit ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,3381]) ).
thf(3918,plain,
! [TA: $tType,B: TA > product_unit,A: TA] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( B @ ( product_case_unit @ TA @ A @ ( default_default @ product_unit ) ) ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[3914:[bind(A,$thf( ^ [F: TA] : ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( H @ F ) ) @ ( zero_zero @ nat ) ) )),bind(B,$thf( B )),bind(C,$thf( default_default @ product_unit )),bind(D,$thf( H @ B ))]]) ).
thf(3928,plain,
! [TA: $tType,B: TA > product_unit,A: TA] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( B @ ( product_case_unit @ TA @ A @ ( default_default @ product_unit ) ) ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[3918]) ).
thf(4007,plain,
! [TA: $tType,B: TA > product_unit,A: TA] :
( ( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( product_Unity
!= ( B @ ( product_case_unit @ TA @ A @ ( default_default @ product_unit ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[682,3928]) ).
thf(4028,plain,
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[4007:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : product_Unity ))]]) ).
thf(4151,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > nat] :
( ( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ ( product_case_unit @ nat @ ( A @ B ) @ C ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( zero_zero @ nat ) ) ),
inference(paramod_ordered,[status(thm)],[341,4028]) ).
thf(4158,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[4151:[bind(A,$thf( ^ [D: TA] : ( zero_zero @ nat ) ))]]) ).
thf(4166,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[4158]) ).
thf(80,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_lappend__lnull1) ).
thf(518,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(320,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ( A
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_llist_Oexhaust__sel) ).
thf(1315,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ( A
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(113,axiom,
typerep2 @ typerep @ ( type2 @ typerep ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Typerep_Otyperep___Typerep_Otyperep_39) ).
thf(602,plain,
typerep2 @ typerep @ ( type2 @ typerep ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(9,axiom,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Typerep_Otyperep_48) ).
thf(342,plain,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(343,plain,
! [TA: $tType] :
( ~ ( typerep2 @ TA @ ( type2 @ TA ) )
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ) ),
inference(cnf,[status(esa)],[342]) ).
thf(2376,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ typerep @ ( type2 @ typerep ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[602,343]) ).
thf(2377,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ typerep @ ( type2 @ typerep ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2376]) ).
thf(2378,plain,
typerep2 @ ( coindu1593790203_llist @ typerep ) @ ( type2 @ ( coindu1593790203_llist @ typerep ) ),
inference(pattern_uni,[status(thm)],[2377:[bind_type(TA,$thf( typerep ))]]) ).
thf(3119,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ typerep ) @ ( type2 @ ( coindu1593790203_llist @ typerep ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2378,343]) ).
thf(3120,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ typerep ) @ ( type2 @ ( coindu1593790203_llist @ typerep ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3119]) ).
thf(3121,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ typerep ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ typerep ) ) ),
inference(pattern_uni,[status(thm)],[3120:[bind_type(TA,$thf( coindu1593790203_llist @ typerep ))]]) ).
thf(3861,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ typerep ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ typerep ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[3121,343]) ).
thf(3862,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ typerep ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ typerep ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3861]) ).
thf(3863,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ typerep ) ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ typerep ) ) ) ),
inference(pattern_uni,[status(thm)],[3862:[bind_type(TA,$thf( coindu1593790203_llist @ ( coindu1593790203_llist @ typerep ) ))]]) ).
thf(172,axiom,
quickcheck_random @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Quickcheck__Random_Orandom_51) ).
thf(777,plain,
quickcheck_random @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(96,axiom,
! [TA: $tType] :
( ( coindu1529956631erates @ TA )
= ( ^ [A: TA > TA,B: TA] : ( coindu1121789889_LCons @ TA @ B @ ( coindu1529956631erates @ TA @ A @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_iterates_Ocode) ).
thf(555,plain,
! [TA: $tType] :
( ( coindu1529956631erates @ TA )
= ( ^ [A: TA > TA,B: TA] : ( coindu1121789889_LCons @ TA @ B @ ( coindu1529956631erates @ TA @ A @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(134,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(666,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(315,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
= ( coindu335574135_lnull @ TA @ B ) )
=> ( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( ( coindu1047225960le_ltl @ TA @ A )
= ( coindu1047225960le_ltl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_llist_Oexpand) ).
thf(1295,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
= ( coindu335574135_lnull @ TA @ B ) )
=> ( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( ( coindu1047225960le_ltl @ TA @ A )
= ( coindu1047225960le_ltl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(34,axiom,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( typerep2 @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Typerep_Otyperep_30) ).
thf(408,plain,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( typerep2 @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA,E: TB,F: coindu1593790203_llist @ TB] :
( ( ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D )
= ( coindu1121789889_LCons @ TB @ E @ F ) )
= ( ~ ( A @ D )
& ( E
= ( B @ D ) )
& ( F
= ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_unfold__llist__eq__LCons) ).
thf(762,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA,E: TB,F: coindu1593790203_llist @ TB] :
( ( ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D )
= ( coindu1121789889_LCons @ TB @ E @ F ) )
= ( ~ ( A @ D )
& ( E
= ( B @ D ) )
& ( F
= ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(142,axiom,
! [TA: $tType] : ( coindu335574135_lnull @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_llist_Odisc_I1_J) ).
thf(683,plain,
! [TA: $tType] : ( coindu335574135_lnull @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(76,axiom,
typerep2 @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Typerep_Otyperep_32) ).
thf(507,plain,
typerep2 @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(2379,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ $o @ ( type2 @ $o ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[507,343]) ).
thf(2380,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ $o @ ( type2 @ $o ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2379]) ).
thf(2381,plain,
typerep2 @ ( coindu1593790203_llist @ $o ) @ ( type2 @ ( coindu1593790203_llist @ $o ) ),
inference(pattern_uni,[status(thm)],[2380:[bind_type(TA,$thf( $o ))]]) ).
thf(252,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
& ~ ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_llist_Osplit__sel__asm) ).
thf(1073,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
& ~ ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_old_Oprod_Oinject) ).
thf(449,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(77,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_llist_OdiscI_I1_J) ).
thf(508,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(509,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
| ( coindu335574135_lnull @ TA @ A ) ),
inference(cnf,[status(esa)],[508]) ).
thf(510,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
| ( coindu335574135_lnull @ TA @ A ) ),
inference(lifteq,[status(thm)],[509]) ).
thf(511,plain,
! [TA: $tType] : ( coindu335574135_lnull @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(simp,[status(thm)],[510]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coindu1593790203_llist @ TB] :
~ ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ C ) @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_llist_Orel__distinct_I2_J) ).
thf(597,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coindu1593790203_llist @ TB] :
~ ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ C ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_prod__cases6) ).
thf(614,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(139,axiom,
cl_HOL_Oequal @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___HOL_Oequal_22) ).
thf(677,plain,
cl_HOL_Oequal @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(245,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( ( coindu1047225960le_ltl @ TA @ D )
= ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_llist_Ocoinduct__strong) ).
thf(1041,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( ( coindu1047225960le_ltl @ TA @ D )
= ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(203,axiom,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( typerep2 @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Option_Ooption___Typerep_Otyperep_36) ).
thf(861,plain,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( typerep2 @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(3366,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > nat] :
( ( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( A @ B ) @ C ) ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( zero_zero @ nat ) ) ),
inference(paramod_ordered,[status(thm)],[341,3352]) ).
thf(3375,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[3366:[bind(A,$thf( ^ [D: TA] : ( zero_zero @ nat ) ))]]) ).
thf(3382,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[3375]) ).
thf(72,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1598213697e_LNil @ TA ) ) ) @ C )
= ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_lappend__snocL1__conv__LCons2) ).
thf(500,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1598213697e_LNil @ TA ) ) ) @ C )
= ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,TC: $tType] : ( cl_HOL_Oequal @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Record_Otuple__isomorphism___HOL_Oequal_2) ).
thf(797,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( cl_HOL_Oequal @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(149,axiom,
! [A: product_unit] : ( A = product_Unity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_old_Ounit_Oexhaust) ).
thf(715,plain,
! [A: product_unit] : ( A = product_Unity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_unfold__llist_Osimps_I4_J) ).
thf(472,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(185,axiom,
! [TA: $tType] : ( size @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Option_Ooption___Nat_Osize_56) ).
thf(814,plain,
! [TA: $tType] : ( size @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(249,axiom,
code_term_of @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Code__Evaluation_Oterm__of_25) ).
thf(1063,plain,
code_term_of @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(88,axiom,
! [TA: $tType,A: TA] :
( ( product_case_unit @ TA @ A @ product_Unity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_old_Ounit_Ocase) ).
thf(538,plain,
! [TA: $tType,A: TA] :
( ( product_case_unit @ TA @ A @ product_Unity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___HOL_Oequal_20) ).
thf(929,plain,
! [TA: $tType,TB: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(930,plain,
! [TA: $tType,TB: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ TA @ TB ) @ ( type2 @ ( sum_sum @ TA @ TB ) ) ),
inference(cnf,[status(esa)],[929]) ).
thf(318,axiom,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ( size_size @ ( sum_sum @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_sum_Osize__neq) ).
thf(1310,plain,
! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
( ( size_size @ ( sum_sum @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(86,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_llist_Oleq__antisym) ).
thf(533,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(289,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ( A
= ( zero_zero @ extended_enat ) )
= ( B
= ( zero_zero @ extended_enat ) ) )
=> ( ( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ( B
!= ( zero_zero @ extended_enat ) )
=> ( ( coinductive_epred @ A )
= ( coinductive_epred @ B ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_co_Oenat_Oexpand) ).
thf(1196,plain,
! [A: extended_enat,B: extended_enat] :
( ( ( A
= ( zero_zero @ extended_enat ) )
= ( B
= ( zero_zero @ extended_enat ) ) )
=> ( ( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ( B
!= ( zero_zero @ extended_enat ) )
=> ( ( coinductive_epred @ A )
= ( coinductive_epred @ B ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ A @ B ) )
= ( coindu1062782156e_lmap @ TA @ TB @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_ltl__lmap) ).
thf(417,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ A @ B ) )
= ( coindu1062782156e_lmap @ TA @ TB @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(212,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ? [F: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ( E = F ) )
| ? [F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA,H: TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ H @ F ) )
& ( E
= ( coindu1121789889_LCons @ TA @ H @ G ) )
& ( ( A @ F @ G )
| ( coindu1696667936prefix @ TA @ F @ G ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_lprefix_Ocoinduct) ).
thf(885,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ? [F: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ( E = F ) )
| ? [F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA,H: TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ H @ F ) )
& ( E
= ( coindu1121789889_LCons @ TA @ H @ G ) )
& ( ( A @ F @ G )
| ( coindu1696667936prefix @ TA @ F @ G ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(163,axiom,
typerep2 @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Typerep_Otyperep_40) ).
thf(752,plain,
typerep2 @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(2391,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ extended_enat @ ( type2 @ extended_enat ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[752,343]) ).
thf(2392,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ extended_enat @ ( type2 @ extended_enat ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2391]) ).
thf(2393,plain,
typerep2 @ ( coindu1593790203_llist @ extended_enat ) @ ( type2 @ ( coindu1593790203_llist @ extended_enat ) ),
inference(pattern_uni,[status(thm)],[2392:[bind_type(TA,$thf( extended_enat ))]]) ).
thf(3279,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ extended_enat ) @ ( type2 @ ( coindu1593790203_llist @ extended_enat ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2393,343]) ).
thf(3280,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ extended_enat ) @ ( type2 @ ( coindu1593790203_llist @ extended_enat ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3279]) ).
thf(3281,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ extended_enat ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ extended_enat ) ) ),
inference(pattern_uni,[status(thm)],[3280:[bind_type(TA,$thf( coindu1593790203_llist @ extended_enat ))]]) ).
thf(3138,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ $o ) @ ( type2 @ ( coindu1593790203_llist @ $o ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2381,343]) ).
thf(3139,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ $o ) @ ( type2 @ ( coindu1593790203_llist @ $o ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3138]) ).
thf(3140,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ $o ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ $o ) ) ),
inference(pattern_uni,[status(thm)],[3139:[bind_type(TA,$thf( coindu1593790203_llist @ $o ))]]) ).
thf(101,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ C @ B )
=> ( ( coindu1696667936prefix @ TA @ A @ C )
| ( coindu1696667936prefix @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_lprefix__down__linear) ).
thf(565,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ C @ B )
=> ( ( coindu1696667936prefix @ TA @ A @ C )
| ( coindu1696667936prefix @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(307,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: tuple_isomorphism @ TC @ TB @ TA] :
( ( size_size @ ( tuple_isomorphism @ TC @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_tuple__isomorphism_Osize__neq) ).
thf(1265,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: tuple_isomorphism @ TC @ TB @ TA] :
( ( size_size @ ( tuple_isomorphism @ TC @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(306,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ E )
=> ( coindu335574135_lnull @ TA @ D ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_lprefix__coinduct) ).
thf(1254,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ E )
=> ( coindu335574135_lnull @ TA @ D ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_prod__cases4) ).
thf(651,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1685,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > nat] :
( ( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( A @ B ) @ C ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( zero_zero @ nat ) ) ),
inference(paramod_ordered,[status(thm)],[341,328]) ).
thf(1984,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[1685:[bind(A,$thf( ^ [D: TA] : ( zero_zero @ nat ) ))]]) ).
thf(2201,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[1984]) ).
thf(2483,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > ( coindu1593790203_llist @ a )] :
( ( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( A @ B ) @ C ) @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ D ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= xs ) ),
inference(paramod_ordered,[status(thm)],[341,2201]) ).
thf(2486,plain,
! [B: product_unit,A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ B ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[2483:[bind(A,$thf( ^ [E: TA] : xs ))]]) ).
thf(2491,plain,
! [B: product_unit,A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ B ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[2486]) ).
thf(273,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TB @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1046438764le_lhd @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) )
= ( product_Pair @ TB @ TA @ ( coindu1046438764le_lhd @ TB @ A ) @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_lzip_Osimps_I3_J) ).
thf(1127,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TB @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1046438764le_lhd @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) )
= ( product_Pair @ TB @ TA @ ( coindu1046438764le_lhd @ TB @ A ) @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] : ( cl_HOL_Oequal @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___HOL_Oequal_10) ).
thf(372,plain,
! [TA: $tType,TB: $tType] : ( cl_HOL_Oequal @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(74,axiom,
cl_HOL_Oequal @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___HOL_Oequal_12) ).
thf(504,plain,
cl_HOL_Oequal @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(162,axiom,
code_term_of @ code_term @ ( type2 @ code_term ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of_5) ).
thf(751,plain,
code_term_of @ code_term @ ( type2 @ code_term ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(319,axiom,
~ ( coindu335574135_lnull @ a @ xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1313,plain,
~ ( coindu335574135_lnull @ a @ xs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(274,axiom,
typerep2 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Typerep_Otyperep_29) ).
thf(1130,plain,
typerep2 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(2895,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ nat @ ( type2 @ nat ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[1130,343]) ).
thf(2896,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ nat @ ( type2 @ nat ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2895]) ).
thf(2897,plain,
typerep2 @ ( coindu1593790203_llist @ nat ) @ ( type2 @ ( coindu1593790203_llist @ nat ) ),
inference(pattern_uni,[status(thm)],[2896:[bind_type(TA,$thf( nat ))]]) ).
thf(106,axiom,
! [TA: $tType,A: TA] :
~ ( coindu567634248member @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_lmember__code_I1_J) ).
thf(586,plain,
! [TA: $tType,A: TA] :
~ ( coindu567634248member @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(587,plain,
! [TA: $tType,A: TA] :
~ ( coindu567634248member @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
inference(cnf,[status(esa)],[586]) ).
thf(323,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) )
= ( coindu721411036eWhile @ TA @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_ltakeWhile_Osimps_I4_J) ).
thf(1323,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) )
= ( coindu721411036eWhile @ TA @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1598213697e_LNil @ TB ) ) )
& ( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_ltl__unfold__llist) ).
thf(802,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1598213697e_LNil @ TB ) ) )
& ( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_llist_Odistinct_I1_J) ).
thf(344,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(90,axiom,
! [TA: $tType] :
( ( coindu335574135_lnull @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( A
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_lnull__def) ).
thf(542,plain,
! [TA: $tType] :
( ( coindu335574135_lnull @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( A
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( typerep2 @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Typerep_Otyperep_41) ).
thf(460,plain,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( typerep2 @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(98,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_lnull__lprefix) ).
thf(559,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(207,axiom,
! [A: product_unit > $o,B: product_unit] :
( ( A @ product_Unity )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_old_Ounit_Oinducts) ).
thf(870,plain,
! [A: product_unit > $o,B: product_unit] :
( ( A @ product_Unity )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(268,axiom,
cl_HOL_Oequal @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___HOL_Oequal_26) ).
thf(1115,plain,
cl_HOL_Oequal @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(299,axiom,
( ( size_size @ $o @ $false )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_bool_Osize_I4_J) ).
thf(1232,plain,
( ( size_size @ $o @ $false )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(62,axiom,
typerep2 @ code_term @ ( type2 @ code_term ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Evaluation_Oterm___Typerep_Otyperep_45) ).
thf(475,plain,
typerep2 @ code_term @ ( type2 @ code_term ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(2373,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ code_term @ ( type2 @ code_term ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[475,343]) ).
thf(2374,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ code_term @ ( type2 @ code_term ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2373]) ).
thf(2375,plain,
typerep2 @ ( coindu1593790203_llist @ code_term ) @ ( type2 @ ( coindu1593790203_llist @ code_term ) ),
inference(pattern_uni,[status(thm)],[2374:[bind_type(TA,$thf( code_term ))]]) ).
thf(3100,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ code_term ) @ ( type2 @ ( coindu1593790203_llist @ code_term ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2375,343]) ).
thf(3101,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ code_term ) @ ( type2 @ ( coindu1593790203_llist @ code_term ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3100]) ).
thf(3102,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_term ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_term ) ) ),
inference(pattern_uni,[status(thm)],[3101:[bind_type(TA,$thf( coindu1593790203_llist @ code_term ))]]) ).
thf(3838,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_term ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_term ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[3102,343]) ).
thf(3839,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_term ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_term ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3838]) ).
thf(3840,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_term ) ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_term ) ) ) ),
inference(pattern_uni,[status(thm)],[3839:[bind_type(TA,$thf( coindu1593790203_llist @ ( coindu1593790203_llist @ code_term ) ))]]) ).
thf(107,axiom,
enum @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Enum_Oenum_33) ).
thf(588,plain,
enum @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(334,plain,
! [TA: $tType] :
( ~ ( enum @ TA @ ( type2 @ TA ) )
| ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
inference(cnf,[status(esa)],[333]) ).
thf(1448,plain,
! [TA: $tType] :
( ~ $true
| ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ $o @ ( type2 @ $o ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[588,334]) ).
thf(1449,plain,
! [TA: $tType] :
( ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ $o @ ( type2 @ $o ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[1448]) ).
thf(1450,plain,
enum @ ( set @ $o ) @ ( type2 @ ( set @ $o ) ),
inference(pattern_uni,[status(thm)],[1449:[bind_type(TA,$thf( $o ))]]) ).
thf(2997,plain,
! [TA: $tType] :
( ~ $true
| ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ ( set @ $o ) @ ( type2 @ ( set @ $o ) ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[1450,334]) ).
thf(2998,plain,
! [TA: $tType] :
( ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ ( set @ $o ) @ ( type2 @ ( set @ $o ) ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2997]) ).
thf(2999,plain,
enum @ ( set @ ( set @ $o ) ) @ ( type2 @ ( set @ ( set @ $o ) ) ),
inference(pattern_uni,[status(thm)],[2998:[bind_type(TA,$thf( set @ $o ))]]) ).
thf(3383,plain,
! [TA: $tType] :
( ~ $true
| ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ ( set @ ( set @ $o ) ) @ ( type2 @ ( set @ ( set @ $o ) ) ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2999,334]) ).
thf(3384,plain,
! [TA: $tType] :
( ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ ( set @ ( set @ $o ) ) @ ( type2 @ ( set @ ( set @ $o ) ) ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3383]) ).
thf(3385,plain,
enum @ ( set @ ( set @ ( set @ $o ) ) ) @ ( type2 @ ( set @ ( set @ ( set @ $o ) ) ) ),
inference(pattern_uni,[status(thm)],[3384:[bind_type(TA,$thf( set @ ( set @ $o ) ))]]) ).
thf(238,axiom,
! [TA: $tType] :
( ( coindu440805660e_enat @ TA )
= ( ^ [A: TA,B: extended_enat > TA,C: extended_enat] :
( if @ TA
@ ( C
= ( zero_zero @ extended_enat ) )
@ A
@ ( B @ ( coinductive_epred @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_co_Oenat_Ocase__eq__if) ).
thf(1013,plain,
! [TA: $tType] :
( ( coindu440805660e_enat @ TA )
= ( ^ [A: TA,B: extended_enat > TA,C: extended_enat] :
( if @ TA
@ ( C
= ( zero_zero @ extended_enat ) )
@ A
@ ( B @ ( coinductive_epred @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_prod__induct4) ).
thf(770,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1625,plain,
! [TA: $tType,TC: $tType,D: TC,C: product_unit,B: TA,A: TA > ( coindu1593790203_llist @ TC )] :
( ~ ( coindu567634248member @ TC @ D @ ( product_case_unit @ ( coindu1593790203_llist @ TC ) @ ( A @ B ) @ C ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu1598213697e_LNil @ TC ) ) ),
inference(paramod_ordered,[status(thm)],[341,587]) ).
thf(2006,plain,
! [TC: $tType,B: TC,A: product_unit] :
~ ( coindu567634248member @ TC @ B @ ( product_case_unit @ ( coindu1593790203_llist @ TC ) @ ( coindu1598213697e_LNil @ TC ) @ A ) ),
inference(pre_uni,[status(thm)],[1625:[bind(A,$thf( ^ [E: TA] : ( coindu1598213697e_LNil @ TC ) ))]]) ).
thf(2222,plain,
! [TA: $tType,B: TA,A: product_unit] :
~ ( coindu567634248member @ TA @ B @ ( product_case_unit @ ( coindu1593790203_llist @ TA ) @ ( coindu1598213697e_LNil @ TA ) @ A ) ),
inference(simp,[status(thm)],[2006]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType] : ( size @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Nat_Osize_54) ).
thf(788,plain,
! [TA: $tType,TB: $tType] : ( size @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(789,plain,
! [TA: $tType,TB: $tType] : ( size @ ( sum_sum @ TA @ TB ) @ ( type2 @ ( sum_sum @ TA @ TB ) ) ),
inference(cnf,[status(esa)],[788]) ).
thf(109,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ B )
= ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_lappend__ltl) ).
thf(591,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ B )
= ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(244,axiom,
semiring_numeral_div @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Divides_Osemiring__numeral__div) ).
thf(1040,plain,
semiring_numeral_div @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(348,plain,
! [TA: $tType,TB: $tType] :
( ~ ( code_term_of @ TA @ ( type2 @ TA ) )
| ~ ( cl_HOL_Oequal @ TA @ ( type2 @ TA ) )
| ~ ( quickcheck_random @ TB @ ( type2 @ TB ) )
| ( quickcheck_random @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) ) ),
inference(cnf,[status(esa)],[347]) ).
thf(3298,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ nat ) @ ( type2 @ ( coindu1593790203_llist @ nat ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2897,343]) ).
thf(3299,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ nat ) @ ( type2 @ ( coindu1593790203_llist @ nat ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3298]) ).
thf(3300,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ nat ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ nat ) ) ),
inference(pattern_uni,[status(thm)],[3299:[bind_type(TA,$thf( coindu1593790203_llist @ nat ))]]) ).
thf(287,axiom,
! [A: extended_enat > extended_enat > $o,B: extended_enat,C: extended_enat] :
( ( A @ B @ C )
=> ( ! [D: extended_enat,E: extended_enat] :
( ( A @ D @ E )
=> ( ( ( D
= ( zero_zero @ extended_enat ) )
= ( E
= ( zero_zero @ extended_enat ) ) )
& ( ( D
!= ( zero_zero @ extended_enat ) )
=> ( ( E
!= ( zero_zero @ extended_enat ) )
=> ( ( A @ ( coinductive_epred @ D ) @ ( coinductive_epred @ E ) )
| ( ( coinductive_epred @ D )
= ( coinductive_epred @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_enat__coinduct) ).
thf(1183,plain,
! [A: extended_enat > extended_enat > $o,B: extended_enat,C: extended_enat] :
( ( A @ B @ C )
=> ( ! [D: extended_enat,E: extended_enat] :
( ( A @ D @ E )
=> ( ( ( D
= ( zero_zero @ extended_enat ) )
= ( E
= ( zero_zero @ extended_enat ) ) )
& ( ( D
!= ( zero_zero @ extended_enat ) )
=> ( ( E
!= ( zero_zero @ extended_enat ) )
=> ( ( A @ ( coinductive_epred @ D ) @ ( coinductive_epred @ E ) )
| ( ( coinductive_epred @ D )
= ( coinductive_epred @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_prod_Oinject) ).
thf(821,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(215,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu300403952lexord @ TA @ A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ F @ D ) )
=> ( ( C
= ( coindu1121789889_LCons @ TA @ F @ E ) )
=> ~ ( coindu300403952lexord @ TA @ A @ D @ E ) ) )
=> ( ! [D: TA] :
( ? [E: coindu1593790203_llist @ TA] :
( B
= ( coindu1121789889_LCons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: coindu1593790203_llist @ TA] :
( C
= ( coindu1121789889_LCons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ( ( B
= ( coindu1598213697e_LNil @ TA ) )
=> ! [D: coindu1593790203_llist @ TA] : ( C != D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_llexord_Ocases) ).
thf(905,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu300403952lexord @ TA @ A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ F @ D ) )
=> ( ( C
= ( coindu1121789889_LCons @ TA @ F @ E ) )
=> ~ ( coindu300403952lexord @ TA @ A @ D @ E ) ) )
=> ( ! [D: TA] :
( ? [E: coindu1593790203_llist @ TA] :
( B
= ( coindu1121789889_LCons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: coindu1593790203_llist @ TA] :
( C
= ( coindu1121789889_LCons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ( ( B
= ( coindu1598213697e_LNil @ TA ) )
=> ! [D: coindu1593790203_llist @ TA] : ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(216,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu268472904append @ TA @ C @ A ) @ ( coindu268472904append @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_lprefix__lappend__sameI) ).
thf(924,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu268472904append @ TA @ C @ A ) @ ( coindu268472904append @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(66,axiom,
! [TA: $tType] :
( ( size @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_size__ne__size__imp__ne) ).
thf(485,plain,
! [TA: $tType] :
( ( size @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(192,axiom,
cl_HOL_Oequal @ product_unit @ ( type2 @ product_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___HOL_Oequal_8) ).
thf(834,plain,
cl_HOL_Oequal @ product_unit @ ( type2 @ product_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(280,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1802687541_ltake @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1802687541_ltake @ TA @ ( coinductive_epred @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_ltake_Octr_I2_J) ).
thf(1151,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1802687541_ltake @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1802687541_ltake @ TA @ ( coinductive_epred @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(221,axiom,
code_term_of @ product_unit @ ( type2 @ product_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Code__Evaluation_Oterm__of_7) ).
thf(937,plain,
code_term_of @ product_unit @ ( type2 @ product_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1684,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > ( coindu1593790203_llist @ a )] :
( ( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( A @ B ) @ C ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= xs ) ),
inference(paramod_ordered,[status(thm)],[341,328]) ).
thf(1954,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[1684:[bind(A,$thf( ^ [D: TA] : xs ))]]) ).
thf(2172,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[1954]) ).
thf(2359,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > ( coindu1593790203_llist @ a )] :
( ( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( A @ B ) @ C ) @ D ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= xs ) ),
inference(paramod_ordered,[status(thm)],[341,2172]) ).
thf(2363,plain,
! [B: product_unit,A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ B ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[2359:[bind(A,$thf( ^ [E: TA] : xs ))]]) ).
thf(2367,plain,
! [B: product_unit,A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ B ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[2363]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_prod__cases3) ).
thf(877,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(69,axiom,
enum @ product_unit @ ( type2 @ product_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Enum_Oenum_44) ).
thf(493,plain,
enum @ product_unit @ ( type2 @ product_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1445,plain,
! [TA: $tType] :
( ~ $true
| ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ product_unit @ ( type2 @ product_unit ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[493,334]) ).
thf(1446,plain,
! [TA: $tType] :
( ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ product_unit @ ( type2 @ product_unit ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[1445]) ).
thf(1447,plain,
enum @ ( set @ product_unit ) @ ( type2 @ ( set @ product_unit ) ),
inference(pattern_uni,[status(thm)],[1446:[bind_type(TA,$thf( product_unit ))]]) ).
thf(251,axiom,
( ( size_size @ $o )
= ( ^ [A: $o] : ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_size__bool) ).
thf(1071,plain,
( ( size_size @ $o )
= ( ^ [A: $o] : ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1072,plain,
( ( size_size @ $o )
= ( ^ [A: $o] : ( zero_zero @ nat ) ) ),
inference(lifteq,[status(thm)],[1071]) ).
thf(1314,plain,
~ ( coindu335574135_lnull @ a @ xs ),
inference(polarity_switch,[status(thm)],[1313]) ).
thf(1770,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > $o] :
( ~ ( product_case_unit @ $o @ ( A @ B ) @ C )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu335574135_lnull @ a @ xs ) ) ),
inference(paramod_ordered,[status(thm)],[341,1314]) ).
thf(1957,plain,
! [A: product_unit] :
~ ( product_case_unit @ $o @ ( coindu335574135_lnull @ a @ xs ) @ A ),
inference(pre_uni,[status(thm)],[1770:[bind(A,$thf( ^ [D: TA] : ( coindu335574135_lnull @ a @ xs ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(2175,plain,
! [A: product_unit] :
~ ( product_case_unit @ $o @ ( coindu335574135_lnull @ a @ xs ) @ A ),
inference(simp,[status(thm)],[1957]) ).
thf(2317,plain,
! [A: product_unit] :
~ ( product_case_unit @ $o @ $false @ A ),
inference(rewrite,[status(thm)],[2175,1314]) ).
thf(2319,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > $o] :
( ~ ( product_case_unit @ $o @ ( product_case_unit @ $o @ ( A @ B ) @ C ) @ D )
| ( A @ ( product_case_unit @ TA @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[341,2317]) ).
thf(2322,plain,
! [B: product_unit,A: product_unit] :
~ ( product_case_unit @ $o @ ( product_case_unit @ $o @ $false @ A ) @ B ),
inference(pre_uni,[status(thm)],[2319:[bind(A,$thf( ^ [E: TA] : $false ))]]) ).
thf(2325,plain,
! [B: product_unit,A: product_unit] :
~ ( product_case_unit @ $o @ ( product_case_unit @ $o @ $false @ A ) @ B ),
inference(simp,[status(thm)],[2322]) ).
thf(3157,plain,
! [A: product_unit] :
~ ( product_case_unit @ $o @ $false @ A ),
inference(rewrite,[status(thm)],[2325,2317]) ).
thf(131,axiom,
size @ product_unit @ ( type2 @ product_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Nat_Osize_67) ).
thf(660,plain,
size @ product_unit @ ( type2 @ product_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(67,axiom,
typerep2 @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Typerep_Otyperep_46) ).
thf(489,plain,
typerep2 @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(2382,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ code_natural @ ( type2 @ code_natural ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[489,343]) ).
thf(2383,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ code_natural @ ( type2 @ code_natural ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2382]) ).
thf(2384,plain,
typerep2 @ ( coindu1593790203_llist @ code_natural ) @ ( type2 @ ( coindu1593790203_llist @ code_natural ) ),
inference(pattern_uni,[status(thm)],[2383:[bind_type(TA,$thf( code_natural ))]]) ).
thf(3168,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ code_natural ) @ ( type2 @ ( coindu1593790203_llist @ code_natural ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2384,343]) ).
thf(3169,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ code_natural ) @ ( type2 @ ( coindu1593790203_llist @ code_natural ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3168]) ).
thf(3170,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_natural ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_natural ) ) ),
inference(pattern_uni,[status(thm)],[3169:[bind_type(TA,$thf( coindu1593790203_llist @ code_natural ))]]) ).
thf(3953,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_natural ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_natural ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[3170,343]) ).
thf(3954,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_natural ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_natural ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3953]) ).
thf(3955,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_natural ) ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ code_natural ) ) ) ),
inference(pattern_uni,[status(thm)],[3954:[bind_type(TA,$thf( coindu1593790203_llist @ ( coindu1593790203_llist @ code_natural ) ))]]) ).
thf(83,axiom,
! [TA: $tType,A: TA > TA,B: TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1529956631erates @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_iterates_Odisc__iff) ).
thf(527,plain,
! [TA: $tType,A: TA > TA,B: TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1529956631erates @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(3369,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > product_unit] :
( ( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( product_case_unit @ product_unit @ ( A @ B ) @ C ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( default_default @ product_unit ) ) ),
inference(paramod_ordered,[status(thm)],[341,3352]) ).
thf(3376,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( product_case_unit @ product_unit @ ( default_default @ product_unit ) @ A ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[3369:[bind(A,$thf( ^ [D: TA] : ( default_default @ product_unit ) ))]]) ).
thf(3378,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( product_case_unit @ product_unit @ ( default_default @ product_unit ) @ A ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[3376]) ).
thf(228,axiom,
( size_bool
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_size__bool__def) ).
thf(981,plain,
( size_bool
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(293,axiom,
! [A: typerep] :
( ( size_size @ typerep @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_typerep_Osize__neq) ).
thf(1215,plain,
! [A: typerep] :
( ( size_size @ typerep @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(126,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ! [C: coindu1593790203_llist @ TA] : ( B != C ) )
=> ~ ! [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
=> ( ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
=> ~ ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_lprefix_Ocases) ).
thf(634,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ! [C: coindu1593790203_llist @ TA] : ( B != C ) )
=> ~ ! [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
=> ( ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
=> ~ ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(270,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > TA] :
( ( A @ B )
=> ( ( coindu1491768222unfold @ TA @ A @ C @ B )
= ( zero_zero @ extended_enat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_enat__unfold__stop) ).
thf(1119,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > TA] :
( ( A @ B )
=> ( ( coindu1491768222unfold @ TA @ A @ C @ B )
= ( zero_zero @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(171,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu1598213697e_LNil @ TA )
= ( coindu268472904append @ TA @ A @ B ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_LNil__eq__lappend__iff) ).
thf(774,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu1598213697e_LNil @ TA )
= ( coindu268472904append @ TA @ A @ B ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(264,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ltakeWhile_Odisc_I1_J) ).
thf(1104,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(302,axiom,
! [TA: $tType,A: TA,B: extended_enat > TA] :
( ( coindu440805660e_enat @ TA @ A @ B @ ( zero_zero @ extended_enat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_enat__cocase__0) ).
thf(1242,plain,
! [TA: $tType,A: TA,B: extended_enat > TA] :
( ( coindu440805660e_enat @ TA @ A @ B @ ( zero_zero @ extended_enat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(199,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_llist_Octr__transfer_I1_J) ).
thf(849,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(24,axiom,
size @ literal @ ( type2 @ literal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_String_Oliteral___Nat_Osize_58) ).
thf(380,plain,
size @ literal @ ( type2 @ literal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ A @ B ) )
= ( coindu335574135_lnull @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_llist_Omap__disc__iff) ).
thf(512,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ A @ B ) )
= ( coindu335574135_lnull @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(140,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu268472904append @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_lappend__eq__LNil__iff) ).
thf(678,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu268472904append @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(84,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_llist_Oleq__trans) ).
thf(529,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(132,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ A )
& ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_lnull__lappend) ).
thf(661,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ A )
& ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(183,axiom,
! [TA: $tType] :
( ( coindu574146665prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_lstrict__prefix__def) ).
thf(810,plain,
! [TA: $tType] :
( ( coindu574146665prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( code_term_of @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Code__Evaluation_Oterm__of_9) ).
thf(381,plain,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( code_term_of @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(366,plain,
! [TA: $tType,TB: $tType] :
( ~ ( quickcheck_random @ TA @ ( type2 @ TA ) )
| ~ ( quickcheck_random @ TB @ ( type2 @ TB ) )
| ( quickcheck_random @ ( product_prod @ TA @ TB ) @ ( type2 @ ( product_prod @ TA @ TB ) ) ) ),
inference(cnf,[status(esa)],[365]) ).
thf(290,axiom,
( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_natural_Osize_I3_J) ).
thf(1206,plain,
( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( typerep2 @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Typerep_Otyperep_34) ).
thf(452,plain,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( typerep2 @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(798,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( cl_HOL_Oequal @ ( tuple_isomorphism @ TA @ TB @ TC ) @ ( type2 @ ( tuple_isomorphism @ TA @ TB @ TC ) ) ),
inference(cnf,[status(esa)],[797]) ).
thf(247,axiom,
! [TA: $tType,A: TA,B: code_natural > TA > TA] :
( ( code_rec_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_natural_Osimps_I6_J) ).
thf(1057,plain,
! [TA: $tType,A: TA,B: code_natural > TA > TA] :
( ( code_rec_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(309,axiom,
! [A: extended_enat,B: extended_enat] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ( B
!= ( zero_zero @ extended_enat ) )
=> ( ( ( coinductive_epred @ A )
= ( coinductive_epred @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_epred__inject) ).
thf(1274,plain,
! [A: extended_enat,B: extended_enat] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ( B
!= ( zero_zero @ extended_enat ) )
=> ( ( ( coinductive_epred @ A )
= ( coinductive_epred @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Nat_Osize_65) ).
thf(824,plain,
! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(825,plain,
! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TA @ TB ) @ ( type2 @ ( product_prod @ TA @ TB ) ) ),
inference(cnf,[status(esa)],[824]) ).
thf(173,axiom,
! [TA: $tType,A: TA] :
( ( product_rec_unit @ TA @ A @ product_Unity )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_old_Ounit_Orec) ).
thf(778,plain,
! [TA: $tType,A: TA] :
( ( product_rec_unit @ TA @ A @ product_Unity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( ( quickcheck_random @ TB @ ( type2 @ TB ) )
& ( quickcheck_random @ TA @ ( type2 @ TA ) ) )
=> ( quickcheck_random @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Quickcheck__Random_Orandom_53) ).
thf(349,plain,
! [TA: $tType,TB: $tType] :
( ( ( quickcheck_random @ TB @ ( type2 @ TB ) )
& ( quickcheck_random @ TA @ ( type2 @ TA ) ) )
=> ( quickcheck_random @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(284,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu987187967t_all2 @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TB] :
( ( ( coindu335574135_lnull @ TA @ B )
= ( coindu335574135_lnull @ TB @ C ) )
& ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ~ ( coindu335574135_lnull @ TB @ C )
=> ( ( A @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1046438764le_lhd @ TB @ C ) )
& ( coindu987187967t_all2 @ TA @ TB @ A @ ( coindu1047225960le_ltl @ TA @ B ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_llist_Orel__sel) ).
thf(1174,plain,
! [TA: $tType,TB: $tType] :
( ( coindu987187967t_all2 @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TB] :
( ( ( coindu335574135_lnull @ TA @ B )
= ( coindu335574135_lnull @ TB @ C ) )
& ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ~ ( coindu335574135_lnull @ TB @ C )
=> ( ( A @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1046438764le_lhd @ TB @ C ) )
& ( coindu987187967t_all2 @ TA @ TB @ A @ ( coindu1047225960le_ltl @ TA @ B ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(99,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ ( coindu268472904append @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_lprefix__lappend) ).
thf(561,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ ( coindu268472904append @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(146,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_not__lnull__conv) ).
thf(693,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_old_Oprod_Oexhaust) ).
thf(429,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(815,plain,
! [TA: $tType] : ( size @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ),
inference(cnf,[status(esa)],[814]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu1599971794_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > TA,D: TA] : ( if @ ( coindu1593790203_llist @ TB ) @ ( A @ D ) @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TB @ ( B @ D ) @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_unfold__llist_Ocode) ).
thf(729,plain,
! [TA: $tType,TB: $tType] :
( ( coindu1599971794_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > TA,D: TA] : ( if @ ( coindu1593790203_llist @ TB ) @ ( A @ D ) @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TB @ ( B @ D ) @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( A @ B )
=> ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_unfold__llist_Odisc_I1_J) ).
thf(361,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( A @ B )
=> ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(121,axiom,
cl_HOL_Oequal @ literal @ ( type2 @ literal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_String_Oliteral___HOL_Oequal_16) ).
thf(625,plain,
cl_HOL_Oequal @ literal @ ( type2 @ literal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(47,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_lprefix__LNil) ).
thf(435,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(3,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] : ( coindu300403952lexord @ TA @ A @ ( coindu1598213697e_LNil @ TA ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_llexord__LNil) ).
thf(329,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] : ( coindu300403952lexord @ TA @ A @ ( coindu1598213697e_LNil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(3937,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > a] :
( ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( product_case_unit @ a @ ( A @ B ) @ C )
!= ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ D ) ) @ ( default_default @ product_unit ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,3382]) ).
thf(3942,plain,
! [TA: $tType,B: TA > product_unit,A: TA] :
( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ ( B @ ( product_case_unit @ TA @ A @ ( default_default @ product_unit ) ) ) ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[3937:[bind(A,$thf( ^ [F: TA] : ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ ( H @ F ) ) ) )),bind(B,$thf( B )),bind(C,$thf( default_default @ product_unit )),bind(D,$thf( H @ B ))]]) ).
thf(3950,plain,
! [TA: $tType,B: TA > product_unit,A: TA] :
( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ ( B @ ( product_case_unit @ TA @ A @ ( default_default @ product_unit ) ) ) ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[3942]) ).
thf(4534,plain,
! [TA: $tType,B: TA > product_unit,A: TA] :
( ( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ ( default_default @ product_unit ) ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( product_Unity
!= ( B @ ( product_case_unit @ TA @ A @ ( default_default @ product_unit ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[682,3950]) ).
thf(4553,plain,
( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ ( default_default @ product_unit ) ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[4534:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : product_Unity ))]]) ).
thf(191,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ~ ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_llist_OdiscI_I2_J) ).
thf(830,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ~ ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(254,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TB @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu847746867e_lzip @ TB @ TA @ A @ B )
= ( coindu1121789889_LCons @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ ( coindu1046438764le_lhd @ TB @ A ) @ ( coindu1046438764le_lhd @ TA @ B ) ) @ ( coindu847746867e_lzip @ TB @ TA @ ( coindu1047225960le_ltl @ TB @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_lzip_Octr_I2_J) ).
thf(1079,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TB @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu847746867e_lzip @ TB @ TA @ A @ B )
= ( coindu1121789889_LCons @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ ( coindu1046438764le_lhd @ TB @ A ) @ ( coindu1046438764le_lhd @ TA @ B ) ) @ ( coindu847746867e_lzip @ TB @ TA @ ( coindu1047225960le_ltl @ TB @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(94,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_lprefix__ltlI) ).
thf(551,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(311,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ~ ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ( A
!= ( zero_zero @ extended_enat ) )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_ltake_Oexhaust) ).
thf(1281,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ~ ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ( A
!= ( zero_zero @ extended_enat ) )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(313,axiom,
( ( size_size @ literal )
= ( ^ [A: literal] : ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_size__literal__def) ).
thf(1291,plain,
( ( size_size @ literal )
= ( ^ [A: literal] : ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(196,axiom,
size @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Nat_Osize_52) ).
thf(842,plain,
size @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(237,axiom,
semiring_1 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1) ).
thf(1012,plain,
semiring_1 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(288,axiom,
quickcheck_random @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Quickcheck__Random_Orandom_49) ).
thf(1195,plain,
quickcheck_random @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(158,axiom,
semiring_1 @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Osemiring__1_69) ).
thf(742,plain,
semiring_1 @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(277,axiom,
( product_size_unit
= ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_size__unit__def) ).
thf(1143,plain,
( product_size_unit
= ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(297,axiom,
( ( code_size_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_natural_Osize_I1_J) ).
thf(1227,plain,
( ( code_size_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(39,axiom,
! [TA: $tType] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_ltl__simps_I1_J) ).
thf(420,plain,
! [TA: $tType] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(231,axiom,
! [TA: $tType,A: TA > TA,B: TA] :
( ( coindu1046438764le_lhd @ TA @ ( coindu1529956631erates @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I2_J) ).
thf(989,plain,
! [TA: $tType,A: TA > TA,B: TA] :
( ( coindu1046438764le_lhd @ TA @ ( coindu1529956631erates @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( ( B
= ( coindu1598213697e_LNil @ TB ) )
=> ( C
!= ( coindu1598213697e_LNil @ TA ) ) )
=> ~ ! [D: TB,E: coindu1593790203_llist @ TB] :
( ( B
= ( coindu1121789889_LCons @ TB @ D @ E ) )
=> ! [F: TA,G: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ F @ G ) )
=> ( ( A @ D @ F )
=> ~ ( coindu987187967t_all2 @ TB @ TA @ A @ E @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_llist_Orel__cases) ).
thf(697,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( ( B
= ( coindu1598213697e_LNil @ TB ) )
=> ( C
!= ( coindu1598213697e_LNil @ TA ) ) )
=> ~ ! [D: TB,E: coindu1593790203_llist @ TB] :
( ( B
= ( coindu1121789889_LCons @ TB @ D @ E ) )
=> ! [F: TA,G: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ F @ G ) )
=> ( ( A @ D @ F )
=> ~ ( coindu987187967t_all2 @ TB @ TA @ A @ E @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(258,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1046438764le_lhd @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_lhd__LCons) ).
thf(1089,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1046438764le_lhd @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(300,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
& ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_lprefix__expand) ).
thf(1234,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
& ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(250,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
=> ( ( coindu1802687541_ltake @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_ltake_Octr_I1_J) ).
thf(1064,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
=> ( ( coindu1802687541_ltake @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(255,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
( ( size_size @ ( product_prod @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_prod_Osize__neq) ).
thf(1082,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
( ( size_size @ ( product_prod @ TB @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(4155,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > ( coindu1593790203_llist @ a )] :
( ( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( A @ B ) @ C ) @ ( default_default @ product_unit ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= xs ) ),
inference(paramod_ordered,[status(thm)],[341,4028]) ).
thf(4159,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( default_default @ product_unit ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[4155:[bind(A,$thf( ^ [D: TA] : xs ))]]) ).
thf(4167,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( default_default @ product_unit ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[4159]) ).
thf(135,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ D ) )
& ( coindu1696667936prefix @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_lprefix__LCons__conv) ).
thf(669,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ D ) )
& ( coindu1696667936prefix @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( coindu1121789889_LCons @ TA @ A @ ( coindu268472904append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_lappend__code_I2_J) ).
thf(476,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( coindu1121789889_LCons @ TA @ A @ ( coindu268472904append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(239,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_ltakeWhile_Octr_I1_J) ).
thf(1016,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TB @ ( type2 @ TB ) )
& ( enum @ TA @ ( type2 @ TA ) ) )
=> ( enum @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Enum_Oenum_42) ).
thf(547,plain,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TB @ ( type2 @ TB ) )
& ( enum @ TA @ ( type2 @ TA ) ) )
=> ( enum @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(211,axiom,
! [TA: $tType,TB: $tType,TC: $tType] : ( size @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Record_Otuple__isomorphism___Nat_Osize_73) ).
thf(883,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( size @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(884,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( size @ ( tuple_isomorphism @ TA @ TB @ TC ) @ ( type2 @ ( tuple_isomorphism @ TA @ TB @ TC ) ) ),
inference(cnf,[status(esa)],[883]) ).
thf(325,axiom,
! [A: code_natural] :
( ( code_Suc @ A )
!= ( zero_zero @ code_natural ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_natural_Odistinct_I2_J) ).
thf(1329,plain,
! [A: code_natural] :
( ( code_Suc @ A )
!= ( zero_zero @ code_natural ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1292,plain,
( ( size_size @ literal )
= ( ^ [A: literal] : ( zero_zero @ nat ) ) ),
inference(lifteq,[status(thm)],[1291]) ).
thf(220,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_lappend_Odisc_I2_J) ).
thf(933,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(95,axiom,
! [TA: $tType] : ( cl_HOL_Oequal @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Option_Ooption___HOL_Oequal_18) ).
thf(553,plain,
! [TA: $tType] : ( cl_HOL_Oequal @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(554,plain,
! [TA: $tType] : ( cl_HOL_Oequal @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ),
inference(cnf,[status(esa)],[553]) ).
thf(164,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_lprefix__code_I2_J) ).
thf(753,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TB @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ~ ( coindu335574135_lnull @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_lzip_Odisc_I2_J) ).
thf(393,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TB @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ~ ( coindu335574135_lnull @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( product_rec_bool @ TA @ A @ B @ $false )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_old_Obool_Osimps_I6_J) ).
thf(515,plain,
! [TA: $tType,A: TA,B: TA] :
( ( product_rec_bool @ TA @ A @ B @ $false )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(248,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_ltake_Odisc__iff_I1_J) ).
thf(1060,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( ? [D: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ A @ D ) )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_LCons__lprefix__conv) ).
thf(569,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( ? [D: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ A @ D ) )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(275,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_llist_Ocoinduct) ).
thf(1131,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Pair__inject) ).
thf(654,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(73,axiom,
typerep2 @ product_unit @ ( type2 @ product_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Typerep_Otyperep_43) ).
thf(503,plain,
typerep2 @ product_unit @ ( type2 @ product_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(2370,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ product_unit @ ( type2 @ product_unit ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[503,343]) ).
thf(2371,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ product_unit @ ( type2 @ product_unit ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2370]) ).
thf(2372,plain,
typerep2 @ ( coindu1593790203_llist @ product_unit ) @ ( type2 @ ( coindu1593790203_llist @ product_unit ) ),
inference(pattern_uni,[status(thm)],[2371:[bind_type(TA,$thf( product_unit ))]]) ).
thf(3081,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ product_unit ) @ ( type2 @ ( coindu1593790203_llist @ product_unit ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2372,343]) ).
thf(3082,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ product_unit ) @ ( type2 @ ( coindu1593790203_llist @ product_unit ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3081]) ).
thf(3083,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ product_unit ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ product_unit ) ) ),
inference(pattern_uni,[status(thm)],[3082:[bind_type(TA,$thf( coindu1593790203_llist @ product_unit ))]]) ).
thf(115,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_ltake__is__lprefix) ).
thf(605,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(4152,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > ( coindu1593790203_llist @ a )] :
( ( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( A @ B ) @ C ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,4028]) ).
thf(4160,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ A ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[4152:[bind(A,$thf( ^ [D: TA] : ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4163,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ A ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[4160]) ).
thf(326,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA,B: TA] :
( ( semiri532925092at_aux @ TA @ A @ ( zero_zero @ nat ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_of__nat__aux_Osimps_I1_J) ).
thf(1333,plain,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA,B: TA] :
( ( semiri532925092at_aux @ TA @ A @ ( zero_zero @ nat ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(89,axiom,
quickcheck_random @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_68) ).
thf(541,plain,
quickcheck_random @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( typerep2 @ TC @ ( type2 @ TC ) )
& ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( code_term_of @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Record_Otuple__isomorphism___Code__Evaluation_Oterm__of_1) ).
thf(765,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( typerep2 @ TC @ ( type2 @ TC ) )
& ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( code_term_of @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_prod__induct6) ).
thf(398,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(137,axiom,
semiring_1 @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Osemiring__1_61) ).
thf(674,plain,
semiring_1 @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(242,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1802687541_ltake @ TA @ ( zero_zero @ extended_enat ) @ A )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_ltake__0) ).
thf(1026,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1802687541_ltake @ TA @ ( zero_zero @ extended_enat ) @ A )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(150,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ! [C: TA] : ( A @ C @ C )
=> ( coindu987187967t_all2 @ TA @ TA @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_llist_Orel__refl) ).
thf(718,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ! [C: TA] : ( A @ C @ C )
=> ( coindu987187967t_all2 @ TA @ TA @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(217,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TA,B: TA > TB] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ B @ A ) )
= ( coindu1062782156e_lmap @ TA @ TB @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_llist_Omap__sel_I2_J) ).
thf(926,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TA,B: TA > TB] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ B @ A ) )
= ( coindu1062782156e_lmap @ TA @ TB @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(321,axiom,
( ( size_bool @ $true )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_bool_Osize_I1_J) ).
thf(1318,plain,
( ( size_bool @ $true )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(257,axiom,
! [TA: $tType,A: option @ TA] :
( ( size_size @ ( option @ TA ) @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_option_Osize__neq) ).
thf(1086,plain,
! [TA: $tType,A: option @ TA] :
( ( size_size @ ( option @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(222,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_lappend_Odisc_I1_J) ).
thf(938,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(125,axiom,
quickcheck_random @ product_unit @ ( type2 @ product_unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_66) ).
thf(633,plain,
quickcheck_random @ product_unit @ ( type2 @ product_unit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TB] :
( ( ( coindu335574135_lnull @ TA @ A )
| ( coindu335574135_lnull @ TB @ B ) )
=> ( ( coindu847746867e_lzip @ TA @ TB @ A @ B )
= ( coindu1598213697e_LNil @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_lzip_Octr_I1_J) ).
thf(355,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TB] :
( ( ( coindu335574135_lnull @ TA @ A )
| ( coindu335574135_lnull @ TB @ B ) )
=> ( ( coindu847746867e_lzip @ TA @ TB @ A @ B )
= ( coindu1598213697e_LNil @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(356,plain,
! [TA: $tType,TB: $tType,B: coindu1593790203_llist @ TA,A: coindu1593790203_llist @ TB] :
( ( ~ ( coindu335574135_lnull @ TB @ A )
| ( ( coindu847746867e_lzip @ TB @ TA @ A @ B )
= ( coindu1598213697e_LNil @ ( product_prod @ TB @ TA ) ) ) )
& ( ~ ( coindu335574135_lnull @ TA @ B )
| ( ( coindu847746867e_lzip @ TB @ TA @ A @ B )
= ( coindu1598213697e_LNil @ ( product_prod @ TB @ TA ) ) ) ) ),
inference(cnf,[status(esa)],[355]) ).
thf(358,plain,
! [TA: $tType,TB: $tType,B: coindu1593790203_llist @ TA,A: coindu1593790203_llist @ TB] :
( ~ ( coindu335574135_lnull @ TA @ B )
| ( ( coindu847746867e_lzip @ TB @ TA @ A @ B )
= ( coindu1598213697e_LNil @ ( product_prod @ TB @ TA ) ) ) ),
inference(cnfConj,[status(thm)],[356]) ).
thf(360,plain,
! [TA: $tType,TB: $tType,B: coindu1593790203_llist @ TA,A: coindu1593790203_llist @ TB] :
( ( ( coindu847746867e_lzip @ TB @ TA @ A @ B )
= ( coindu1598213697e_LNil @ ( product_prod @ TB @ TA ) ) )
| ~ ( coindu335574135_lnull @ TA @ B ) ),
inference(lifteq,[status(thm)],[358]) ).
thf(97,axiom,
cl_HOL_Oequal @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___HOL_Oequal_4) ).
thf(558,plain,
cl_HOL_Oequal @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(178,axiom,
! [TA: $tType,A: TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu567634248member @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coindu567634248member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_lmember__code_I2_J) ).
thf(794,plain,
! [TA: $tType,A: TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu567634248member @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coindu567634248member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(310,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_lhd__ltake) ).
thf(1278,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1062782156e_lmap @ TA @ TB @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu1121789889_LCons @ TB @ ( A @ B ) @ ( coindu1062782156e_lmap @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_llist_Osimps_I13_J) ).
thf(412,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1062782156e_lmap @ TA @ TB @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( coindu1121789889_LCons @ TB @ ( A @ B ) @ ( coindu1062782156e_lmap @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(225,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
=> ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_ltake_Odisc_I1_J) ).
thf(965,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
=> ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(305,axiom,
! [TA: $tType,A: TA,B: nat > TA > TA] :
( ( rec_nat @ TA @ A @ B @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_old_Onat_Osimps_I6_J) ).
thf(1251,plain,
! [TA: $tType,A: TA,B: nat > TA > TA] :
( ( rec_nat @ TA @ A @ B @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(184,axiom,
typerep2 @ literal @ ( type2 @ literal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_String_Oliteral___Typerep_Otyperep_38) ).
thf(813,plain,
typerep2 @ literal @ ( type2 @ literal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(2388,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ literal @ ( type2 @ literal ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[813,343]) ).
thf(2389,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ literal @ ( type2 @ literal ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2388]) ).
thf(2390,plain,
typerep2 @ ( coindu1593790203_llist @ literal ) @ ( type2 @ ( coindu1593790203_llist @ literal ) ),
inference(pattern_uni,[status(thm)],[2389:[bind_type(TA,$thf( literal ))]]) ).
thf(3260,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ literal ) @ ( type2 @ ( coindu1593790203_llist @ literal ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2390,343]) ).
thf(3261,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ literal ) @ ( type2 @ ( coindu1593790203_llist @ literal ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3260]) ).
thf(3262,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ literal ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ literal ) ) ),
inference(pattern_uni,[status(thm)],[3261:[bind_type(TA,$thf( coindu1593790203_llist @ literal ))]]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_lzip_Odisc__iff_I1_J) ).
thf(745,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(105,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA,D: TA > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: coindu1593790203_llist @ TA,F: coindu1593790203_llist @ TA] :
( ( A @ E @ F )
=> ( ? [G: coindu1593790203_llist @ TA,H: coindu1593790203_llist @ TA,I: TA] :
( ( E
= ( coindu1121789889_LCons @ TA @ I @ G ) )
& ( F
= ( coindu1121789889_LCons @ TA @ I @ H ) )
& ( ( A @ G @ H )
| ( coindu300403952lexord @ TA @ D @ G @ H ) ) )
| ? [G: TA,H: TA,I: coindu1593790203_llist @ TA,J: coindu1593790203_llist @ TA] :
( ( E
= ( coindu1121789889_LCons @ TA @ G @ I ) )
& ( F
= ( coindu1121789889_LCons @ TA @ H @ J ) )
& ( D @ G @ H ) )
| ? [G: coindu1593790203_llist @ TA] :
( ( E
= ( coindu1598213697e_LNil @ TA ) )
& ( F = G ) ) ) )
=> ( coindu300403952lexord @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_llexord_Ocoinduct) ).
thf(573,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA,D: TA > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: coindu1593790203_llist @ TA,F: coindu1593790203_llist @ TA] :
( ( A @ E @ F )
=> ( ? [G: coindu1593790203_llist @ TA,H: coindu1593790203_llist @ TA,I: TA] :
( ( E
= ( coindu1121789889_LCons @ TA @ I @ G ) )
& ( F
= ( coindu1121789889_LCons @ TA @ I @ H ) )
& ( ( A @ G @ H )
| ( coindu300403952lexord @ TA @ D @ G @ H ) ) )
| ? [G: TA,H: TA,I: coindu1593790203_llist @ TA,J: coindu1593790203_llist @ TA] :
( ( E
= ( coindu1121789889_LCons @ TA @ G @ I ) )
& ( F
= ( coindu1121789889_LCons @ TA @ H @ J ) )
& ( D @ G @ H ) )
| ? [G: coindu1593790203_llist @ TA] :
( ( E
= ( coindu1598213697e_LNil @ TA ) )
& ( F = G ) ) ) )
=> ( coindu300403952lexord @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(294,axiom,
( ( size_size @ $o @ $true )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_bool_Osize_I3_J) ).
thf(1219,plain,
( ( size_size @ $o @ $true )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(281,axiom,
! [A: code_natural > $o,B: code_natural] :
( ( A @ ( zero_zero @ code_natural ) )
=> ( ! [C: code_natural] :
( ( A @ C )
=> ( A @ ( code_Suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_natural_Oinducts) ).
thf(1154,plain,
! [A: code_natural > $o,B: code_natural] :
( ( A @ ( zero_zero @ code_natural ) )
=> ( ! [C: code_natural] :
( ( A @ C )
=> ( A @ ( code_Suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(40,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
= ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_lprefix__lnull) ).
thf(423,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
= ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_surj__pair) ).
thf(402,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(154,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_lprefix__antisym) ).
thf(732,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(159,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_LNil__lprefix) ).
thf(743,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(190,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) ) )
= ( ~ ( A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_unfold__llist_Odisc__iff_I2_J) ).
thf(826,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) ) )
= ( ~ ( A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(91,axiom,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( code_term_of @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Code__Evaluation_Oterm__of) ).
thf(545,plain,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( code_term_of @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(235,axiom,
( ( product_size_unit @ product_Unity )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_unit_Osize_I1_J) ).
thf(1007,plain,
( ( product_size_unit @ product_Unity )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(2950,plain,
! [TA: $tType] :
( ~ $true
| ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ ( set @ product_unit ) @ ( type2 @ ( set @ product_unit ) ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[1447,334]) ).
thf(2951,plain,
! [TA: $tType] :
( ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ ( set @ product_unit ) @ ( type2 @ ( set @ product_unit ) ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[2950]) ).
thf(2952,plain,
enum @ ( set @ ( set @ product_unit ) ) @ ( type2 @ ( set @ ( set @ product_unit ) ) ),
inference(pattern_uni,[status(thm)],[2951:[bind_type(TA,$thf( set @ product_unit ))]]) ).
thf(3317,plain,
! [TA: $tType] :
( ~ $true
| ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ ( set @ ( set @ product_unit ) ) @ ( type2 @ ( set @ ( set @ product_unit ) ) ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[2952,334]) ).
thf(3318,plain,
! [TA: $tType] :
( ( enum @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) )
| ( ( enum @ ( set @ ( set @ product_unit ) ) @ ( type2 @ ( set @ ( set @ product_unit ) ) ) )
!= ( enum @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3317]) ).
thf(3319,plain,
enum @ ( set @ ( set @ ( set @ product_unit ) ) ) @ ( type2 @ ( set @ ( set @ ( set @ product_unit ) ) ) ),
inference(pattern_uni,[status(thm)],[3318:[bind_type(TA,$thf( set @ ( set @ product_unit ) ))]]) ).
thf(197,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA] :
( ( ( coindu1598213697e_LNil @ TB )
= ( coindu1062782156e_lmap @ TA @ TB @ A @ B ) )
= ( B
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_LNil__eq__lmap) ).
thf(843,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA] :
( ( ( coindu1598213697e_LNil @ TB )
= ( coindu1062782156e_lmap @ TA @ TB @ A @ B ) )
= ( B
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(272,axiom,
( ( size_size @ $o )
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_size__bool__overloaded__def) ).
thf(1125,plain,
( ( size_size @ $o )
= ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_prod__cases) ).
thf(445,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(104,axiom,
code_term_of @ literal @ ( type2 @ literal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_String_Oliteral___Code__Evaluation_Oterm__of_15) ).
thf(572,plain,
code_term_of @ literal @ ( type2 @ literal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1311,plain,
! [TA: $tType,TB: $tType,A: sum_sum @ TA @ TB] :
( ( size_size @ ( sum_sum @ TA @ TB ) @ A )
!= ( zero_zero @ nat ) ),
inference(cnf,[status(esa)],[1310]) ).
thf(1312,plain,
! [TA: $tType,TB: $tType,A: sum_sum @ TA @ TB] :
( ( size_size @ ( sum_sum @ TA @ TB ) @ A )
!= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[1311]) ).
thf(118,axiom,
! [TA: $tType,A: TA > TA,B: TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1529956631erates @ TA @ A @ B ) )
= ( coindu1529956631erates @ TA @ A @ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I3_J) ).
thf(611,plain,
! [TA: $tType,A: TA > TA,B: TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1529956631erates @ TA @ A @ B ) )
= ( coindu1529956631erates @ TA @ A @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(301,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TA @ B )
& ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_ltakeWhile_Odisc__iff_I2_J) ).
thf(1239,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TA @ B )
& ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(6,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu300403952lexord @ TA @ A @ B @ C )
=> ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ D @ B ) @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_llexord__LCons__eq) ).
thf(335,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu300403952lexord @ TA @ A @ B @ C )
=> ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ D @ B ) @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(296,axiom,
! [TA: $tType,A: TA,B: extended_enat > TA] :
( ( coindu440805660e_enat @ TA @ A @ B @ ( zero_zero @ extended_enat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_co_Oenat_Ocase_I1_J) ).
thf(1224,plain,
! [TA: $tType,A: TA,B: extended_enat > TA] :
( ( coindu440805660e_enat @ TA @ A @ B @ ( zero_zero @ extended_enat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(136,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_llist_Oleq__refl) ).
thf(672,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_LCons__lprefix__LCons) ).
thf(466,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(259,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ltakeWhile_Odisc_I2_J) ).
thf(1092,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(350,plain,
! [TA: $tType,TB: $tType] :
( ~ ( quickcheck_random @ TA @ ( type2 @ TA ) )
| ~ ( quickcheck_random @ TB @ ( type2 @ TB ) )
| ( quickcheck_random @ ( sum_sum @ TA @ TB ) @ ( type2 @ ( sum_sum @ TA @ TB ) ) ) ),
inference(cnf,[status(esa)],[349]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_prod__induct5) ).
thf(784,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA] :
( ( coindu882539134_llist @ TA @ TB @ A @ B @ ( coindu1598213697e_LNil @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_llist_Osimps_I4_J) ).
thf(736,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA] :
( ( coindu882539134_llist @ TA @ TB @ A @ B @ ( coindu1598213697e_LNil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(22,axiom,
code_term_of @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Code__Evaluation_Oterm__of_11) ).
thf(377,plain,
code_term_of @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(271,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_lhd__LCons__ltl) ).
thf(1122,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(112,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_lappend__LNil2) ).
thf(599,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(317,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu882539134_llist @ TA @ TB )
= ( ^ [A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA,C: coindu1593790203_llist @ TB] : ( if @ TA @ ( coindu335574135_lnull @ TB @ C ) @ A @ ( B @ ( coindu1046438764le_lhd @ TB @ C ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_llist_Ocase__eq__if) ).
thf(1307,plain,
! [TA: $tType,TB: $tType] :
( ( coindu882539134_llist @ TA @ TB )
= ( ^ [A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA,C: coindu1593790203_llist @ TB] : ( if @ TA @ ( coindu335574135_lnull @ TB @ C ) @ A @ ( B @ ( coindu1046438764le_lhd @ TB @ C ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(204,axiom,
code_term_of @ typerep @ ( type2 @ typerep ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Typerep_Otyperep___Code__Evaluation_Oterm__of_13) ).
thf(863,plain,
code_term_of @ typerep @ ( type2 @ typerep ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(362,plain,
! [TA: $tType,TB: $tType,D: TB > TB,C: TB > TA,B: TB,A: TB > $o] :
( ~ ( A @ B )
| ( coindu335574135_lnull @ TA @ ( coindu1599971794_llist @ TB @ TA @ A @ C @ D @ B ) ) ),
inference(cnf,[status(esa)],[361]) ).
thf(102,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_lprefix__not__lnullD) ).
thf(567,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(210,axiom,
! [TA: $tType] :
( ( coindu987187967t_all2 @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( coindu1593790203_llist @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_llist_Orel__eq) ).
thf(880,plain,
! [TA: $tType] :
( ( coindu987187967t_all2 @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( coindu1593790203_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_unfold__llist_Odisc_I2_J) ).
thf(649,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(46,axiom,
quickcheck_random @ literal @ ( type2 @ literal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_String_Oliteral___Quickcheck__Random_Orandom_57) ).
thf(434,plain,
quickcheck_random @ literal @ ( type2 @ literal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( coindu1593790203_llist @ TA ) > TB,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu882539134_llist @ TB @ TA @ A @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_llist_Osimps_I5_J) ).
thf(494,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( coindu1593790203_llist @ TA ) > TB,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu882539134_llist @ TB @ TA @ A @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ~ ( coindu335574135_lnull @ TB @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_lzip_Oexhaust) ).
thf(758,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( ~ ( coindu335574135_lnull @ TB @ A )
=> ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( code_term_of @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Code__Evaluation_Oterm__of_19) ).
thf(816,plain,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( code_term_of @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(110,axiom,
! [TA: $tType] :
( ( coindu268472904append @ TA @ ( coindu1598213697e_LNil @ TA ) @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_lappend__LNil__LNil) ).
thf(594,plain,
! [TA: $tType] :
( ( coindu268472904append @ TA @ ( coindu1598213697e_LNil @ TA ) @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(65,axiom,
! [TA: $tType] :
( ( quickcheck_random @ TA @ ( type2 @ TA ) )
=> ( quickcheck_random @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Quickcheck__Random_Orandom_50) ).
thf(483,plain,
! [TA: $tType] :
( ( quickcheck_random @ TA @ ( type2 @ TA ) )
=> ( quickcheck_random @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_old_Oprod_Orec) ).
thf(626,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(240,axiom,
! [TA: $tType,A: code_natural > TA,B: code_natural > TA,C: code_natural] :
( ( ( A @ ( zero_zero @ code_natural ) )
= ( B @ ( zero_zero @ code_natural ) ) )
=> ( ! [D: code_natural] :
( ( A @ ( code_Suc @ D ) )
= ( B @ ( code_Suc @ D ) ) )
=> ( ( A @ C )
= ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_random__aux__rec) ).
thf(1022,plain,
! [TA: $tType,A: code_natural > TA,B: code_natural > TA,C: code_natural] :
( ( ( A @ ( zero_zero @ code_natural ) )
= ( B @ ( zero_zero @ code_natural ) ) )
=> ( ! [D: code_natural] :
( ( A @ ( code_Suc @ D ) )
= ( B @ ( code_Suc @ D ) ) )
=> ( ( A @ C )
= ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(314,axiom,
( ( size_size @ product_unit )
= ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_size__unit__overloaded__def) ).
thf(1293,plain,
( ( size_size @ product_unit )
= ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(285,axiom,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ B )
| ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_ltakeWhile_Odisc__iff_I1_J) ).
thf(1177,plain,
! [TA: $tType,A: TA > $o,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu721411036eWhile @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ B )
| ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(330,plain,
! [TA: $tType,B: coindu1593790203_llist @ TA,A: TA > TA > $o] : ( coindu300403952lexord @ TA @ A @ ( coindu1598213697e_LNil @ TA ) @ B ),
inference(cnf,[status(esa)],[329]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( typerep2 @ TC @ ( type2 @ TC ) )
& ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( typerep2 @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Record_Otuple__isomorphism___Typerep_Otyperep_47) ).
thf(462,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( typerep2 @ TC @ ( type2 @ TC ) )
& ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( typerep2 @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(267,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ltake_Osimps_I3_J) ).
thf(1112,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(202,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu268472904append @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_lappend_Octr_I1_J) ).
thf(858,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu268472904append @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(18,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_llist_Oexhaust) ).
thf(367,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_prod__cases5) ).
thf(799,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_prod__cases7) ).
thf(726,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(243,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
& ( ( coindu1046438764le_lhd @ TA @ A )
= B )
& ( ( coindu1047225960le_ltl @ TA @ A )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_eq__LConsD) ).
thf(1029,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
& ( ( coindu1046438764le_lhd @ TA @ A )
= B )
& ( ( coindu1047225960le_ltl @ TA @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(3368,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > a] :
( ( ( product_case_unit @ a @ ( product_case_unit @ a @ ( A @ B ) @ C ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,3352]) ).
thf(3377,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ A ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[3368:[bind(A,$thf( ^ [D: TA] : ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(3379,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ A ) @ ( default_default @ product_unit ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[3377]) ).
thf(3437,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > a] :
( ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( product_case_unit @ a @ ( A @ B ) @ C )
!= ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ D ) @ ( default_default @ product_unit ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,3379]) ).
thf(3445,plain,
! [TA: $tType,B: TA > product_unit,A: TA] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( B @ ( product_case_unit @ TA @ A @ ( default_default @ product_unit ) ) ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[3437:[bind(A,$thf( ^ [F: TA] : ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( F @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( default_default @ product_unit )),bind(D,$thf( F @ B ))]]) ).
thf(3451,plain,
! [TA: $tType,B: TA > product_unit,A: TA] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ ( B @ ( product_case_unit @ TA @ A @ ( default_default @ product_unit ) ) ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[3445]) ).
thf(229,axiom,
! [TA: $tType,A: TA,B: code_natural > TA] :
( ( code_case_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_natural_Osimps_I4_J) ).
thf(983,plain,
! [TA: $tType,A: TA,B: code_natural > TA] :
( ( code_case_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(303,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu749330388e_lnth @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_lnth__0) ).
thf(1245,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu749330388e_lnth @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(2357,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > nat] :
( ( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ D ) @ ( product_case_unit @ nat @ ( A @ B ) @ C ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( zero_zero @ nat ) ) ),
inference(paramod_ordered,[status(thm)],[341,2172]) ).
thf(2365,plain,
! [B: product_unit,A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ B ) @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[2357:[bind(A,$thf( ^ [E: TA] : ( zero_zero @ nat ) ))]]) ).
thf(2369,plain,
! [B: product_unit,A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ B ) @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[2365]) ).
thf(117,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu268472904append @ TA @ A @ B ) @ C )
= ( coindu268472904append @ TA @ A @ ( coindu268472904append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_lappend__assoc) ).
thf(608,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu268472904append @ TA @ A @ B ) @ C )
= ( coindu268472904append @ TA @ A @ ( coindu268472904append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(230,axiom,
! [TA: $tType] :
( ( zero @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_zero__reorient) ).
thf(986,plain,
! [TA: $tType] :
( ( zero @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_llist_Odisc_I2_J) ).
thf(563,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TB @ A )
& ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_lzip_Odisc__iff_I2_J) ).
thf(685,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TB @ A )
& ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(81,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_llist_Ocollapse_I1_J) ).
thf(521,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(54,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(455,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(200,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( coindu1062782156e_lmap @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_llist_Osimps_I12_J) ).
thf(851,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( coindu1062782156e_lmap @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(263,axiom,
( ( size_bool @ $false )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_bool_Osize_I2_J) ).
thf(1102,plain,
( ( size_bool @ $false )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(75,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_lprefix__code_I1_J) ).
thf(505,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1771,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > ( coindu1593790203_llist @ a )] :
( ~ ( coindu335574135_lnull @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( A @ B ) @ C ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= xs ) ),
inference(paramod_ordered,[status(thm)],[341,1314]) ).
thf(1937,plain,
! [A: product_unit] :
~ ( coindu335574135_lnull @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) ),
inference(pre_uni,[status(thm)],[1771:[bind(A,$thf( ^ [D: TA] : xs ))]]) ).
thf(2156,plain,
! [A: product_unit] :
~ ( coindu335574135_lnull @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) ),
inference(simp,[status(thm)],[1937]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: code_natural > TA > TA,C: code_natural] :
( ( code_rec_natural @ TA @ A @ B @ ( code_Suc @ C ) )
= ( B @ C @ ( code_rec_natural @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_natural_Osimps_I7_J) ).
thf(438,plain,
! [TA: $tType,A: TA,B: code_natural > TA > TA,C: code_natural] :
( ( code_rec_natural @ TA @ A @ B @ ( code_Suc @ C ) )
= ( B @ C @ ( code_rec_natural @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(253,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_ltake_Odisc_I2_J) ).
thf(1076,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(41,axiom,
size @ typerep @ ( type2 @ typerep ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Typerep_Otyperep___Nat_Osize_59) ).
thf(426,plain,
size @ typerep @ ( type2 @ typerep ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(85,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_lprefix__refl) ).
thf(531,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) )
= ( A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_unfold__llist_Odisc__iff_I1_J) ).
thf(374,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) )
= ( A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(127,axiom,
quickcheck_random @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Quickcheck__Random_Orandom_60) ).
thf(648,plain,
quickcheck_random @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(120,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: set @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) )] :
( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ A @ B ) @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ D @ E ) @ C )
=> ( ( coindu335574135_lnull @ TA @ D )
| ? [F: TA,G: coindu1593790203_llist @ TA,H: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ F @ G ) )
& ( E
= ( coindu1121789889_LCons @ TA @ F @ H ) )
& ( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ G @ H ) @ C )
| ( coindu1696667936prefix @ TA @ G @ H ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_lprefixI) ).
thf(617,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: set @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) )] :
( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ A @ B ) @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ D @ E ) @ C )
=> ( ( coindu335574135_lnull @ TA @ D )
| ? [F: TA,G: coindu1593790203_llist @ TA,H: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ F @ G ) )
& ( E
= ( coindu1121789889_LCons @ TA @ F @ H ) )
& ( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ G @ H ) @ C )
| ( coindu1696667936prefix @ TA @ G @ H ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(278,axiom,
! [TA: $tType] :
( ( semiring_numeral_div @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( semiri577515795es_aux @ TA @ ( product_Pair @ TA @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_divides__aux__eq) ).
thf(1145,plain,
! [TA: $tType] :
( ( semiring_numeral_div @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( semiri577515795es_aux @ TA @ ( product_Pair @ TA @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(754,plain,
! [TA: $tType,B: coindu1593790203_llist @ TA,A: TA] :
~ ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(cnf,[status(esa)],[753]) ).
thf(55,axiom,
! [TA: $tType] : ( cl_HOL_Oequal @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___HOL_Oequal) ).
thf(458,plain,
! [TA: $tType] : ( cl_HOL_Oequal @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(194,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu1598213697e_LNil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_lappend__code_I1_J) ).
thf(836,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu1598213697e_LNil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(68,axiom,
! [TA: $tType,A: extended_enat] :
( ( coindu1802687541_ltake @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_ltake__LNil) ).
thf(490,plain,
! [TA: $tType,A: extended_enat] :
( ( coindu1802687541_ltake @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( typerep2 @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Typerep_Otyperep) ).
thf(675,plain,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( typerep2 @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(291,axiom,
! [A: code_natural] :
( ( A
!= ( zero_zero @ code_natural ) )
=> ~ ! [B: code_natural] :
( A
!= ( code_Suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_natural_Oexhaust) ).
thf(1208,plain,
! [A: code_natural] :
( ( A
!= ( zero_zero @ code_natural ) )
=> ~ ! [B: code_natural] :
( A
!= ( code_Suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(108,axiom,
! [TA: $tType] :
( ( quickcheck_random @ TA @ ( type2 @ TA ) )
=> ( quickcheck_random @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Option_Ooption___Quickcheck__Random_Orandom_55) ).
thf(589,plain,
! [TA: $tType] :
( ( quickcheck_random @ TA @ ( type2 @ TA ) )
=> ( quickcheck_random @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coindu1593790203_llist @ TB,D: TA,E: coindu1593790203_llist @ TA] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ C ) @ ( coindu1121789889_LCons @ TA @ D @ E ) )
= ( ( A @ B @ D )
& ( coindu987187967t_all2 @ TB @ TA @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_llist_Orel__inject_I2_J) ).
thf(690,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coindu1593790203_llist @ TB,D: TA,E: coindu1593790203_llist @ TA] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ C ) @ ( coindu1121789889_LCons @ TA @ D @ E ) )
= ( ( A @ B @ D )
& ( coindu987187967t_all2 @ TB @ TA @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(241,axiom,
( ( zero_zero @ nat )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_zero__natural_Orsp) ).
thf(1025,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(226,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ~ ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_ltakeWhile_Oexhaust) ).
thf(971,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( ( coindu335574135_lnull @ TA @ A )
| ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) )
=> ~ ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(157,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_neq__LNil__conv) ).
thf(739,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1266,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: tuple_isomorphism @ TA @ TB @ TC] :
( ( size_size @ ( tuple_isomorphism @ TA @ TB @ TC ) @ A )
!= ( zero_zero @ nat ) ),
inference(cnf,[status(esa)],[1265]) ).
thf(1267,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: tuple_isomorphism @ TA @ TB @ TC] :
( ( size_size @ ( tuple_isomorphism @ TA @ TB @ TC ) @ A )
!= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[1266]) ).
thf(262,axiom,
! [A: product_prod @ code_natural @ code_natural] :
( ! [B: code_natural] :
( A
!= ( product_Pair @ code_natural @ code_natural @ ( zero_zero @ code_natural ) @ B ) )
=> ~ ! [B: code_natural,C: code_natural] :
( A
!= ( product_Pair @ code_natural @ code_natural @ ( code_Suc @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_random__aux__set_Ocases) ).
thf(1098,plain,
! [A: product_prod @ code_natural @ code_natural] :
( ! [B: code_natural] :
( A
!= ( product_Pair @ code_natural @ code_natural @ ( zero_zero @ code_natural ) @ B ) )
=> ~ ! [B: code_natural,C: code_natural] :
( A
!= ( product_Pair @ code_natural @ code_natural @ ( code_Suc @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(246,axiom,
! [A: code_natural] :
( ( zero_zero @ code_natural )
!= ( code_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_natural_Odistinct_I1_J) ).
thf(1053,plain,
! [A: code_natural] :
( ( zero_zero @ code_natural )
!= ( code_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(4,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ D ) @ ( coindu1121789889_LCons @ TA @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_llexord__LCons__less) ).
thf(331,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ D ) @ ( coindu1121789889_LCons @ TA @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_prod__induct7) ).
thf(441,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(19,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_lnull__ltlI) ).
thf(370,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TB @ ( type2 @ TB ) )
& ( enum @ TA @ ( type2 @ TA ) ) )
=> ( enum @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Enum_Oenum) ).
thf(337,plain,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TB @ ( type2 @ TB ) )
& ( enum @ TA @ ( type2 @ TA ) ) )
=> ( enum @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(338,plain,
! [TA: $tType,TB: $tType] :
( ~ ( enum @ TA @ ( type2 @ TA ) )
| ~ ( enum @ TB @ ( type2 @ TB ) )
| ( enum @ ( TA > TB ) @ ( type2 @ ( TA > TB ) ) ) ),
inference(cnf,[status(esa)],[337]) ).
thf(256,axiom,
size @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(1085,plain,
size @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(182,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_lprefix__trans) ).
thf(808,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(357,plain,
! [TA: $tType,TB: $tType,B: coindu1593790203_llist @ TA,A: coindu1593790203_llist @ TB] :
( ~ ( coindu335574135_lnull @ TB @ A )
| ( ( coindu847746867e_lzip @ TB @ TA @ A @ B )
= ( coindu1598213697e_LNil @ ( product_prod @ TB @ TA ) ) ) ),
inference(cnfConj,[status(thm)],[356]) ).
thf(359,plain,
! [TA: $tType,TB: $tType,B: coindu1593790203_llist @ TA,A: coindu1593790203_llist @ TB] :
( ( ( coindu847746867e_lzip @ TB @ TA @ A @ B )
= ( coindu1598213697e_LNil @ ( product_prod @ TB @ TA ) ) )
| ~ ( coindu335574135_lnull @ TB @ A ) ),
inference(lifteq,[status(thm)],[357]) ).
thf(1216,plain,
~ ? [A: typerep] :
( ( size_size @ typerep @ A )
= ( zero_zero @ nat ) ),
inference(miniscope,[status(thm)],[1215]) ).
thf(1217,plain,
! [A: typerep] :
( ( size_size @ typerep @ A )
!= ( zero_zero @ nat ) ),
inference(cnf,[status(esa)],[1216]) ).
thf(1218,plain,
! [A: typerep] :
( ( size_size @ typerep @ A )
!= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[1217]) ).
thf(4154,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > a] :
( ( ( product_case_unit @ a @ ( A @ B ) @ C )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ ( zero_zero @ nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,4028]) ).
thf(4161,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ ( zero_zero @ nat ) ) @ A )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[4154:[bind(A,$thf( ^ [D: TA] : ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ ( zero_zero @ nat ) ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(4164,plain,
! [A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( default_default @ product_unit ) ) @ ( zero_zero @ nat ) ) @ A )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[4161]) ).
thf(2345,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > ( coindu1593790203_llist @ a )] :
( ( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ ( A @ B ) @ C ) @ ( zero_zero @ nat ) ) @ D )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= xs ) ),
inference(paramod_ordered,[status(thm)],[341,2106]) ).
thf(2350,plain,
! [B: product_unit,A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( zero_zero @ nat ) ) @ B )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[2345:[bind(A,$thf( ^ [E: TA] : xs ))]]) ).
thf(2354,plain,
! [B: product_unit,A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ A ) @ ( zero_zero @ nat ) ) @ B )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[2350]) ).
thf(336,plain,
! [TA: $tType,D: TA,C: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,A: TA > TA > $o] :
( ~ ( coindu300403952lexord @ TA @ A @ B @ C )
| ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ D @ B ) @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ),
inference(cnf,[status(esa)],[335]) ).
thf(276,axiom,
( ( size_size @ product_unit @ product_Unity )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_unit_Osize_I2_J) ).
thf(1141,plain,
( ( size_size @ product_unit @ product_Unity )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(295,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1599971794_llist @ ( coindu1593790203_llist @ TA ) @ TA @ ( coindu335574135_lnull @ TA ) @ ( coindu1046438764le_lhd @ TA ) @ ( coindu1047225960le_ltl @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_unfold__llist__id) ).
thf(1221,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1599971794_llist @ ( coindu1593790203_llist @ TA ) @ TA @ ( coindu335574135_lnull @ TA ) @ ( coindu1046438764le_lhd @ TA ) @ ( coindu1047225960le_ltl @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(205,axiom,
! [A: code_natural,B: code_natural] :
( ( ( code_Suc @ A )
= ( code_Suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_natural_Oinject) ).
thf(864,plain,
! [A: code_natural,B: code_natural] :
( ( ( code_Suc @ A )
= ( code_Suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) )
=> ( coindu335574135_lnull @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_lzip_Odisc_I1_J) ).
thf(386,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TB @ A )
| ( coindu335574135_lnull @ TA @ B ) )
=> ( coindu335574135_lnull @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(260,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) ) )
= ( ( A
!= ( zero_zero @ extended_enat ) )
& ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_ltake_Odisc__iff_I2_J) ).
thf(1094,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) ) )
= ( ( A
!= ( zero_zero @ extended_enat ) )
& ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(227,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_lprefix__lhdD) ).
thf(978,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(71,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_lappend__lnull2) ).
thf(497,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(208,axiom,
cl_HOL_Oequal @ code_term @ ( type2 @ code_term ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Evaluation_Oterm___HOL_Oequal_6) ).
thf(876,plain,
cl_HOL_Oequal @ code_term @ ( type2 @ code_term ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(286,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ( coindu1598213697e_LNil @ TA )
= ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( ( B
= ( coindu1598213697e_LNil @ TA ) )
| ( A
= ( zero_zero @ extended_enat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_LNil__eq__ltake__iff) ).
thf(1180,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ( coindu1598213697e_LNil @ TA )
= ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( ( B
= ( coindu1598213697e_LNil @ TA ) )
| ( A
= ( zero_zero @ extended_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(16,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_lprefix__lnullD) ).
thf(363,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TB @ ( type2 @ TB ) )
& ( enum @ TA @ ( type2 @ TA ) ) )
=> ( enum @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Enum_Oenum_35) ).
thf(931,plain,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TB @ ( type2 @ TB ) )
& ( enum @ TA @ ( type2 @ TA ) ) )
=> ( enum @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(4153,plain,
! [TA: $tType,C: product_unit,B: TA,A: TA > product_unit] :
( ( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( product_case_unit @ product_unit @ ( A @ B ) @ C ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( default_default @ product_unit ) ) ),
inference(paramod_ordered,[status(thm)],[341,4028]) ).
thf(4162,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( product_case_unit @ product_unit @ ( default_default @ product_unit ) @ A ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[4153:[bind(A,$thf( ^ [D: TA] : ( default_default @ product_unit ) ))]]) ).
thf(4165,plain,
! [A: product_unit] :
( ( coindu749330388e_lnth @ a @ ( product_case_unit @ ( coindu1593790203_llist @ a ) @ xs @ ( product_case_unit @ product_unit @ ( default_default @ product_unit ) @ A ) ) @ ( zero_zero @ nat ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[4162]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TB @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1047225960le_ltl @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) )
= ( coindu847746867e_lzip @ TB @ TA @ ( coindu1047225960le_ltl @ TB @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_lzip_Osimps_I4_J) ).
thf(524,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TB @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1047225960le_ltl @ ( product_prod @ TB @ TA ) @ ( coindu847746867e_lzip @ TB @ TA @ A @ B ) )
= ( coindu847746867e_lzip @ TB @ TA @ ( coindu1047225960le_ltl @ TB @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(2480,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > nat] :
( ( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( product_case_unit @ nat @ ( A @ B ) @ C ) @ D ) )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( zero_zero @ nat ) ) ),
inference(paramod_ordered,[status(thm)],[341,2201]) ).
thf(2485,plain,
! [B: product_unit,A: product_unit] :
( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) @ B ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[2480:[bind(A,$thf( ^ [E: TA] : ( zero_zero @ nat ) ))]]) ).
thf(2490,plain,
! [B: product_unit,A: product_unit] :
( ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) @ B ) )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[2485]) ).
thf(265,axiom,
( ( coinductive_epred @ ( zero_zero @ extended_enat ) )
= ( zero_zero @ extended_enat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_epred__0) ).
thf(1108,plain,
( ( coinductive_epred @ ( zero_zero @ extended_enat ) )
= ( zero_zero @ extended_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(2343,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > a] :
( ( ( product_case_unit @ a @ ( product_case_unit @ a @ ( A @ B ) @ C ) @ D )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[341,2106]) ).
thf(2348,plain,
! [B: product_unit,A: product_unit] :
( ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ A ) @ B )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[2343:[bind(A,$thf( ^ [E: TA] : ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2352,plain,
! [B: product_unit,A: product_unit] :
( ( product_case_unit @ a @ ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) @ A ) @ B )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[2348]) ).
thf(1083,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( size_size @ ( product_prod @ TA @ TB ) @ A )
!= ( zero_zero @ nat ) ),
inference(cnf,[status(esa)],[1082]) ).
thf(1084,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( size_size @ ( product_prod @ TA @ TB ) @ A )
!= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[1083]) ).
thf(144,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ C @ A ) @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Le__LCons) ).
thf(688,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ C @ A ) @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(214,axiom,
! [TA: $tType] :
( ( quickcheck_random @ TA @ ( type2 @ TA ) )
=> ( quickcheck_random @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Quickcheck__Random_Orandom_74) ).
thf(903,plain,
! [TA: $tType] :
( ( quickcheck_random @ TA @ ( type2 @ TA ) )
=> ( quickcheck_random @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(324,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) )
= ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ltakeWhile_Osimps_I3_J) ).
thf(1326,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu721411036eWhile @ TA @ B @ A ) )
= ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(161,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_ltl__simps_I2_J) ).
thf(748,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(13,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_lappend_Oexhaust) ).
thf(351,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: code_natural > TA,C: code_natural] :
( ( code_case_natural @ TA @ A @ B @ ( code_Suc @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_natural_Osimps_I5_J) ).
thf(390,plain,
! [TA: $tType,A: TA,B: code_natural > TA,C: code_natural] :
( ( code_case_natural @ TA @ A @ B @ ( code_Suc @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(124,axiom,
code_term_of @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Code__Evaluation_Oterm__of_21) ).
thf(632,plain,
code_term_of @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(174,axiom,
! [TA: $tType] :
( ( coindu1696667936prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ? [C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B = C ) )
| ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
& ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
& ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_lprefix_Osimps) ).
thf(781,plain,
! [TA: $tType] :
( ( coindu1696667936prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ? [C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B = C ) )
| ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
& ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
& ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(233,axiom,
! [TA: $tType,TB: $tType,A: ( coindu1593790203_llist @ TB ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: coindu1593790203_llist @ TB,F: coindu1593790203_llist @ TA] :
( ( A @ E @ F )
=> ( ( ( coindu335574135_lnull @ TB @ E )
= ( coindu335574135_lnull @ TA @ F ) )
& ( ~ ( coindu335574135_lnull @ TB @ E )
=> ( ~ ( coindu335574135_lnull @ TA @ F )
=> ( ( D @ ( coindu1046438764le_lhd @ TB @ E ) @ ( coindu1046438764le_lhd @ TA @ F ) )
& ( A @ ( coindu1047225960le_ltl @ TB @ E ) @ ( coindu1047225960le_ltl @ TA @ F ) ) ) ) ) ) )
=> ( coindu987187967t_all2 @ TB @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_llist_Orel__coinduct) ).
thf(995,plain,
! [TA: $tType,TB: $tType,A: ( coindu1593790203_llist @ TB ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: coindu1593790203_llist @ TB,F: coindu1593790203_llist @ TA] :
( ( A @ E @ F )
=> ( ( ( coindu335574135_lnull @ TB @ E )
= ( coindu335574135_lnull @ TA @ F ) )
& ( ~ ( coindu335574135_lnull @ TB @ E )
=> ( ~ ( coindu335574135_lnull @ TA @ F )
=> ( ( D @ ( coindu1046438764le_lhd @ TB @ E ) @ ( coindu1046438764le_lhd @ TA @ F ) )
& ( A @ ( coindu1047225960le_ltl @ TB @ E ) @ ( coindu1047225960le_ltl @ TA @ F ) ) ) ) ) ) )
=> ( coindu987187967t_all2 @ TB @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TA,C: coindu1593790203_llist @ TA] :
~ ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_llist_Orel__distinct_I1_J) ).
thf(378,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TA,C: coindu1593790203_llist @ TA] :
~ ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(45,axiom,
code_term_of @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Code__Evaluation_Oterm__of_3) ).
thf(433,plain,
code_term_of @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(292,axiom,
! [TA: $tType] :
( ( coindu721411036eWhile @ TA )
= ( ^ [A: TA > $o,B: coindu1593790203_llist @ TA] :
( if @ ( coindu1593790203_llist @ TA )
@ ( ( coindu335574135_lnull @ TA @ B )
| ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) )
@ ( coindu1598213697e_LNil @ TA )
@ ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu721411036eWhile @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_ltakeWhile_Ocode) ).
thf(1212,plain,
! [TA: $tType] :
( ( coindu721411036eWhile @ TA )
= ( ^ [A: TA > $o,B: coindu1593790203_llist @ TA] :
( if @ ( coindu1593790203_llist @ TA )
@ ( ( coindu335574135_lnull @ TA @ B )
| ~ ( A @ ( coindu1046438764le_lhd @ TA @ B ) ) )
@ ( coindu1598213697e_LNil @ TA )
@ ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu721411036eWhile @ TA @ A @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(26,axiom,
! [TA: $tType] :
( ( coindu300403952lexord @ TA )
= ( ^ [A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ? [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ F @ D ) )
& ( C
= ( coindu1121789889_LCons @ TA @ F @ E ) )
& ( coindu300403952lexord @ TA @ A @ D @ E ) )
| ? [D: TA,E: TA,F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ D @ F ) )
& ( C
= ( coindu1121789889_LCons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1598213697e_LNil @ TA ) )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_llexord_Osimps) ).
thf(383,plain,
! [TA: $tType] :
( ( coindu300403952lexord @ TA )
= ( ^ [A: TA > TA > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ? [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ F @ D ) )
& ( C
= ( coindu1121789889_LCons @ TA @ F @ E ) )
& ( coindu300403952lexord @ TA @ A @ D @ E ) )
| ? [D: TA,E: TA,F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ D @ F ) )
& ( C
= ( coindu1121789889_LCons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1598213697e_LNil @ TA ) )
& ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(345,plain,
! [TA: $tType,B: coindu1593790203_llist @ TA,A: TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(cnf,[status(esa)],[344]) ).
thf(346,plain,
! [TA: $tType,B: coindu1593790203_llist @ TA,A: TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( code_term_of @ TC @ ( type2 @ TC ) )
& ( cl_HOL_Oequal @ TC @ ( type2 @ TC ) )
& ( quickcheck_random @ TC @ ( type2 @ TC ) )
& ( quickcheck_random @ TB @ ( type2 @ TB ) )
& ( quickcheck_random @ TA @ ( type2 @ TA ) ) )
=> ( quickcheck_random @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Record_Otuple__isomorphism___Quickcheck__Random_Orandom_72) ).
thf(549,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( code_term_of @ TC @ ( type2 @ TC ) )
& ( cl_HOL_Oequal @ TC @ ( type2 @ TC ) )
& ( quickcheck_random @ TC @ ( type2 @ TC ) )
& ( quickcheck_random @ TB @ ( type2 @ TB ) )
& ( quickcheck_random @ TA @ ( type2 @ TA ) ) )
=> ( quickcheck_random @ ( tuple_isomorphism @ TC @ TB @ TA ) @ ( type2 @ ( tuple_isomorphism @ TC @ TB @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TB @ ( type2 @ TB ) )
& ( cl_HOL_Oequal @ TA @ ( type2 @ TA ) ) )
=> ( cl_HOL_Oequal @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___HOL_Oequal_28) ).
thf(536,plain,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TB @ ( type2 @ TB ) )
& ( cl_HOL_Oequal @ TA @ ( type2 @ TA ) ) )
=> ( cl_HOL_Oequal @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(44,axiom,
cl_HOL_Oequal @ typerep @ ( type2 @ typerep ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Typerep_Otyperep___HOL_Oequal_14) ).
thf(432,plain,
cl_HOL_Oequal @ typerep @ ( type2 @ typerep ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(35,axiom,
! [TA: $tType] :
( ( enum @ TA @ ( type2 @ TA ) )
=> ( enum @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Option_Ooption___Enum_Oenum_37) ).
thf(410,plain,
! [TA: $tType] :
( ( enum @ TA @ ( type2 @ TA ) )
=> ( enum @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(298,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_unfold__llist_Osimps_I3_J) ).
thf(1229,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(187,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_llist_Oinject) ).
thf(818,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: extended_enat,B: TA > TB,C: coindu1593790203_llist @ TA] :
( ( coindu1802687541_ltake @ TB @ A @ ( coindu1062782156e_lmap @ TA @ TB @ B @ C ) )
= ( coindu1062782156e_lmap @ TA @ TB @ B @ ( coindu1802687541_ltake @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_ltake__lmap) ).
thf(405,plain,
! [TA: $tType,TB: $tType,A: extended_enat,B: TA > TB,C: coindu1593790203_llist @ TA] :
( ( coindu1802687541_ltake @ TB @ A @ ( coindu1062782156e_lmap @ TA @ TB @ B @ C ) )
= ( coindu1062782156e_lmap @ TA @ TB @ B @ ( coindu1802687541_ltake @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(279,axiom,
! [TA: $tType] :
( ( coindu1802687541_ltake @ TA )
= ( ^ [A: extended_enat,B: coindu1593790203_llist @ TA] :
( if @ ( coindu1593790203_llist @ TA )
@ ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
@ ( coindu1598213697e_LNil @ TA )
@ ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1802687541_ltake @ TA @ ( coinductive_epred @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_ltake_Ocode) ).
thf(1148,plain,
! [TA: $tType] :
( ( coindu1802687541_ltake @ TA )
= ( ^ [A: extended_enat,B: coindu1593790203_llist @ TA] :
( if @ ( coindu1593790203_llist @ TA )
@ ( ( A
= ( zero_zero @ extended_enat ) )
| ( coindu335574135_lnull @ TA @ B ) )
@ ( coindu1598213697e_LNil @ TA )
@ ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1802687541_ltake @ TA @ ( coinductive_epred @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(206,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1062782156e_lmap @ TA @ TB @ A @ ( coindu268472904append @ TA @ B @ C ) )
= ( coindu268472904append @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ A @ B ) @ ( coindu1062782156e_lmap @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_lmap__lappend__distrib) ).
thf(867,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1062782156e_lmap @ TA @ TB @ A @ ( coindu268472904append @ TA @ B @ C ) )
= ( coindu268472904append @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ A @ B ) @ ( coindu1062782156e_lmap @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(155,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(735,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(269,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu847746867e_lzip @ TA @ TB )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TB] :
( if @ ( coindu1593790203_llist @ ( product_prod @ TA @ TB ) )
@ ( ( coindu335574135_lnull @ TA @ A )
| ( coindu335574135_lnull @ TB @ B ) )
@ ( coindu1598213697e_LNil @ ( product_prod @ TA @ TB ) )
@ ( coindu1121789889_LCons @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1046438764le_lhd @ TB @ B ) ) @ ( coindu847746867e_lzip @ TA @ TB @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TB @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_lzip_Ocode) ).
thf(1116,plain,
! [TA: $tType,TB: $tType] :
( ( coindu847746867e_lzip @ TA @ TB )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TB] :
( if @ ( coindu1593790203_llist @ ( product_prod @ TA @ TB ) )
@ ( ( coindu335574135_lnull @ TA @ A )
| ( coindu335574135_lnull @ TB @ B ) )
@ ( coindu1598213697e_LNil @ ( product_prod @ TA @ TB ) )
@ ( coindu1121789889_LCons @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1046438764le_lhd @ TB @ B ) ) @ ( coindu847746867e_lzip @ TA @ TB @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TB @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(261,axiom,
zero @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(1097,plain,
zero @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(193,axiom,
zero @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_62) ).
thf(835,plain,
zero @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(201,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_prod__induct3) ).
thf(854,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(316,axiom,
! [TA: $tType] :
( ( quickcheck_random @ TA @ ( type2 @ TA ) )
=> ! [A: code_natural > code_natural > $o,B: code_natural,C: code_natural] :
( ! [D: code_natural] : ( A @ ( zero_zero @ code_natural ) @ D )
=> ( ! [D: code_natural,E: code_natural] :
( ! [F: product_prod @ TA @ ( product_unit > code_term )] : ( A @ D @ E )
=> ( A @ ( code_Suc @ D ) @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_random__aux__set_Oinduct) ).
thf(1303,plain,
! [TA: $tType] :
( ( quickcheck_random @ TA @ ( type2 @ TA ) )
=> ! [A: code_natural > code_natural > $o,B: code_natural,C: code_natural] :
( ! [D: code_natural] : ( A @ ( zero_zero @ code_natural ) @ D )
=> ( ! [D: code_natural,E: code_natural] :
( ( A @ D @ E )
=> ( A @ ( code_Suc @ D ) @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(304,axiom,
! [TA: $tType,A: nat > TA,B: TA] :
( ( extended_case_enat @ TA @ A @ B @ ( zero_zero @ extended_enat ) )
= ( A @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_case__enat__0) ).
thf(1248,plain,
! [TA: $tType,A: nat > TA,B: TA] :
( ( extended_case_enat @ TA @ A @ B @ ( zero_zero @ extended_enat ) )
= ( A @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_ssubst__Pair__rhs) ).
thf(790,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(373,plain,
! [TA: $tType,TB: $tType] : ( cl_HOL_Oequal @ ( product_prod @ TA @ TB ) @ ( type2 @ ( product_prod @ TA @ TB ) ) ),
inference(cnf,[status(esa)],[372]) ).
thf(114,axiom,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( code_term_of @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Option_Ooption___Code__Evaluation_Oterm__of_17) ).
thf(603,plain,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( code_term_of @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(564,plain,
! [TA: $tType,B: coindu1593790203_llist @ TA,A: TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(cnf,[status(esa)],[563]) ).
thf(312,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ( coindu1802687541_ltake @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) )
= ( ( B
= ( coindu1598213697e_LNil @ TA ) )
| ( A
= ( zero_zero @ extended_enat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_ltake__eq__LNil__iff) ).
thf(1288,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( ( coindu1802687541_ltake @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) )
= ( ( B
= ( coindu1598213697e_LNil @ TA ) )
| ( A
= ( zero_zero @ extended_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(147,axiom,
zero @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ozero_70) ).
thf(696,plain,
zero @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(282,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ B )
| ( A
= ( zero_zero @ extended_enat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_lnull__ltake) ).
thf(1165,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ B )
| ( A
= ( zero_zero @ extended_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( code_term_of @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Code__Evaluation_Oterm__of_27) ).
thf(415,plain,
! [TA: $tType,TB: $tType] :
( ( ( typerep2 @ TB @ ( type2 @ TB ) )
& ( typerep2 @ TA @ ( type2 @ TA ) ) )
=> ( code_term_of @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(213,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1047225960le_ltl @ TA @ B ) ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu268472904append @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_ltl__lappend) ).
thf(897,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1047225960le_ltl @ TA @ B ) ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu268472904append @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA,C: TB,D: coindu1593790203_llist @ TB] :
( ( ( coindu1062782156e_lmap @ TA @ TB @ A @ B )
= ( coindu1121789889_LCons @ TB @ C @ D ) )
= ( ? [E: TA,F: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ E @ F ) )
& ( C
= ( A @ E ) )
& ( D
= ( coindu1062782156e_lmap @ TA @ TB @ A @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_lmap__eq__LCons__conv) ).
thf(767,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: coindu1593790203_llist @ TA,C: TB,D: coindu1593790203_llist @ TB] :
( ( ( coindu1062782156e_lmap @ TA @ TB @ A @ B )
= ( coindu1121789889_LCons @ TB @ C @ D ) )
= ( ? [E: TA,F: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ E @ F ) )
& ( C
= ( A @ E ) )
& ( D
= ( coindu1062782156e_lmap @ TA @ TB @ A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1054,plain,
~ ? [A: code_natural] :
( ( zero_zero @ code_natural )
= ( code_Suc @ A ) ),
inference(miniscope,[status(thm)],[1053]) ).
thf(1055,plain,
! [A: code_natural] :
( ( zero_zero @ code_natural )
!= ( code_Suc @ A ) ),
inference(cnf,[status(esa)],[1054]) ).
thf(1056,plain,
! [A: code_natural] :
( ( code_Suc @ A )
!= ( zero_zero @ code_natural ) ),
inference(lifteq,[status(thm)],[1055]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: coindu1593790203_llist @ TB,E: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ( coindu987187967t_all2 @ TB @ TA @ A @ D @ E )
=> ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ D ) @ ( coindu1121789889_LCons @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_llist_Orel__intros_I2_J) ).
thf(664,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: coindu1593790203_llist @ TB,E: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ( coindu987187967t_all2 @ TB @ TA @ A @ D @ E )
=> ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ D ) @ ( coindu1121789889_LCons @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(58,axiom,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA @ ( type2 @ TA ) )
=> ( cl_HOL_Oequal @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___HOL_Oequal_24) ).
thf(464,plain,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA @ ( type2 @ TA ) )
=> ( cl_HOL_Oequal @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(332,plain,
! [TA: $tType,E: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,C: TA,B: TA,A: TA > TA > $o] :
( ~ ( A @ B @ C )
| ( coindu300403952lexord @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ D ) @ ( coindu1121789889_LCons @ TA @ C @ E ) ) ),
inference(cnf,[status(esa)],[331]) ).
thf(308,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > TA] :
( ( ( A @ B )
=> ( ( coinductive_epred @ ( coindu1491768222unfold @ TA @ A @ C @ B ) )
= ( zero_zero @ extended_enat ) ) )
& ( ~ ( A @ B )
=> ( ( coinductive_epred @ ( coindu1491768222unfold @ TA @ A @ C @ B ) )
= ( coindu1491768222unfold @ TA @ A @ C @ ( C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_epred__enat__unfold) ).
thf(1268,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > TA] :
( ( ( A @ B )
=> ( ( coinductive_epred @ ( coindu1491768222unfold @ TA @ A @ C @ B ) )
= ( zero_zero @ extended_enat ) ) )
& ( ~ ( A @ B )
=> ( ( coinductive_epred @ ( coindu1491768222unfold @ TA @ A @ C @ B ) )
= ( coindu1491768222unfold @ TA @ A @ C @ ( C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(42,axiom,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( code_term_of @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Code__Evaluation_Oterm__of_23) ).
thf(427,plain,
! [TA: $tType] :
( ( typerep2 @ TA @ ( type2 @ TA ) )
=> ( code_term_of @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(528,plain,
! [TA: $tType,B: TA,A: TA > TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1529956631erates @ TA @ A @ B ) ),
inference(cnf,[status(esa)],[527]) ).
thf(459,plain,
! [TA: $tType] : ( cl_HOL_Oequal @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) ),
inference(cnf,[status(esa)],[458]) ).
thf(232,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu721411036eWhile @ TA @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ltakeWhile_Octr_I2_J) ).
thf(992,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > $o] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( B @ ( coindu1046438764le_lhd @ TA @ A ) )
=> ( ( coindu721411036eWhile @ TA @ B @ A )
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu721411036eWhile @ TA @ B @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(3884,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ $o ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ $o ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[3140,343]) ).
thf(3885,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ $o ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ $o ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3884]) ).
thf(3886,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ $o ) ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ $o ) ) ) ),
inference(pattern_uni,[status(thm)],[3885:[bind_type(TA,$thf( coindu1593790203_llist @ ( coindu1593790203_llist @ $o ) ))]]) ).
thf(234,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( coindu1802687541_ltake @ TA @ ( coinductive_epred @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_ltake_Osimps_I4_J) ).
thf(1004,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( A
!= ( zero_zero @ extended_enat ) )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) )
= ( coindu1802687541_ltake @ TA @ ( coinductive_epred @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > TB] :
( ( A @ B )
=> ( ( coindu1599971794_llist @ TB @ TA @ A @ C @ D @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_unfold__llist_Octr_I1_J) ).
thf(395,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > TB] :
( ( A @ B )
=> ( ( coindu1599971794_llist @ TB @ TA @ A @ C @ D @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(2342,plain,
! [TA: $tType,D: product_unit,C: product_unit,B: TA,A: TA > nat] :
( ( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( A @ B ) @ C ) ) @ D )
!= ( coindu1046438764le_lhd @ a @ xs ) )
| ( ( A @ ( product_case_unit @ TA @ B @ C ) )
!= ( zero_zero @ nat ) ) ),
inference(paramod_ordered,[status(thm)],[341,2106]) ).
thf(2349,plain,
! [B: product_unit,A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) ) @ B )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(pre_uni,[status(thm)],[2342:[bind(A,$thf( ^ [E: TA] : ( zero_zero @ nat ) ))]]) ).
thf(2353,plain,
! [B: product_unit,A: product_unit] :
( ( product_case_unit @ a @ ( coindu749330388e_lnth @ a @ xs @ ( product_case_unit @ nat @ ( zero_zero @ nat ) @ A ) ) @ B )
!= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(simp,[status(thm)],[2349]) ).
thf(195,axiom,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu1802687541_ltake @ TA @ ( coinductive_epred @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) )
= ( coindu1047225960le_ltl @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_ltake__epred__ltl) ).
thf(839,plain,
! [TA: $tType,A: extended_enat,B: coindu1593790203_llist @ TA] :
( ( coindu1802687541_ltake @ TA @ ( coinductive_epred @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) )
= ( coindu1047225960le_ltl @ TA @ ( coindu1802687541_ltake @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(3815,plain,
! [TA: $tType] :
( ~ $true
| ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ product_unit ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ product_unit ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(paramod_ordered,[status(thm)],[3083,343]) ).
thf(3816,plain,
! [TA: $tType] :
( ( typerep2 @ ( coindu1593790203_llist @ TA ) @ ( type2 @ ( coindu1593790203_llist @ TA ) ) )
| ( ( typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ product_unit ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ product_unit ) ) ) )
!= ( typerep2 @ TA @ ( type2 @ TA ) ) ) ),
inference(simp,[status(thm)],[3815]) ).
thf(3817,plain,
typerep2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ product_unit ) ) ) @ ( type2 @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ ( coindu1593790203_llist @ product_unit ) ) ) ),
inference(pattern_uni,[status(thm)],[3816:[bind_type(TA,$thf( coindu1593790203_llist @ ( coindu1593790203_llist @ product_unit ) ))]]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B )
= ( coindu1121789889_LCons @ TB @ ( C @ B ) @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_unfold__llist_Octr_I2_J) ).
thf(723,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B )
= ( coindu1121789889_LCons @ TB @ ( C @ B ) @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(368,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ( A
= ( coindu1121789889_LCons @ TA @ ( sk1 @ TA @ A ) @ ( sk2 @ TA @ A ) ) ) ),
inference(cnf,[status(esa)],[367]) ).
thf(369,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ( ( coindu1121789889_LCons @ TA @ ( sk1 @ TA @ A ) @ ( sk2 @ TA @ A ) )
= A ) ),
inference(lifteq,[status(thm)],[368]) ).
thf(116,axiom,
size @ extended_enat @ ( type2 @ extended_enat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Nat_Osize_63) ).
thf(607,plain,
size @ extended_enat @ ( type2 @ extended_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(322,axiom,
! [TA: $tType,A: TA > $o,B: TA > TA,C: TA] :
( ( ( coindu1491768222unfold @ TA @ A @ B @ C )
= ( zero_zero @ extended_enat ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_enat__unfold__eq__0) ).
thf(1320,plain,
! [TA: $tType,A: TA > $o,B: TA > TA,C: TA] :
( ( ( coindu1491768222unfold @ TA @ A @ B @ C )
= ( zero_zero @ extended_enat ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TA,B: TA > TB] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ B @ A ) )
= ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_llist_Omap__sel_I1_J) ).
thf(1009,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TA,B: TA > TB] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1062782156e_lmap @ TA @ TB @ B @ A ) )
= ( B @ ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(165,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( product_rec_bool @ TA @ A @ B @ $true )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_old_Obool_Osimps_I5_J) ).
thf(755,plain,
! [TA: $tType,A: TA,B: TA] :
( ( product_rec_bool @ TA @ A @ B @ $true )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1087,plain,
! [TA: $tType,A: option @ TA] :
( ( size_size @ ( option @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(cnf,[status(esa)],[1086]) ).
thf(1088,plain,
! [TA: $tType,A: option @ TA] :
( ( size_size @ ( option @ TA ) @ A )
!= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[1087]) ).
thf(53,axiom,
size @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Nat_Osize_71) ).
thf(454,plain,
size @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(364,plain,
! [TA: $tType,B: coindu1593790203_llist @ TA,A: coindu1593790203_llist @ TA] :
( ~ ( coindu1696667936prefix @ TA @ A @ B )
| ~ ( coindu335574135_lnull @ TA @ B )
| ( coindu335574135_lnull @ TA @ A ) ),
inference(cnf,[status(esa)],[363]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_internal__case__prod__conv) ).
thf(469,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(223,axiom,
! [A: extended_enat > extended_enat > $o,B: extended_enat,C: extended_enat] :
( ( A @ B @ C )
=> ( ! [D: extended_enat,E: extended_enat] :
( ( A @ D @ E )
=> ( ( D
= ( zero_zero @ extended_enat ) )
= ( E
= ( zero_zero @ extended_enat ) ) ) )
=> ( ! [D: extended_enat,E: extended_enat] :
( ( A @ D @ E )
=> ( ( D
!= ( zero_zero @ extended_enat ) )
=> ( ( E
!= ( zero_zero @ extended_enat ) )
=> ( ( A @ ( coinductive_epred @ D ) @ ( coinductive_epred @ E ) )
| ( ( coinductive_epred @ D )
= ( coinductive_epred @ E ) ) ) ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_enat__coinduct2) ).
thf(940,plain,
! [A: extended_enat > extended_enat > $o,B: extended_enat,C: extended_enat] :
( ( A @ B @ C )
=> ( ! [D: extended_enat,E: extended_enat] :
( ( A @ D @ E )
=> ( ( D
= ( zero_zero @ extended_enat ) )
= ( E
= ( zero_zero @ extended_enat ) ) ) )
=> ( ! [D: extended_enat,E: extended_enat] :
( ( A @ D @ E )
=> ( ( D
!= ( zero_zero @ extended_enat ) )
=> ( ( E
!= ( zero_zero @ extended_enat ) )
=> ( ( A @ ( coinductive_epred @ D ) @ ( coinductive_epred @ E ) )
| ( ( coinductive_epred @ D )
= ( coinductive_epred @ E ) ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(6067,plain,
$false,
inference(e,[status(thm)],[629,365,1168,479,347,846,333,962,1110,4166,518,1315,3863,777,555,666,1295,408,762,683,2381,1073,449,511,597,614,677,1041,861,3382,500,797,715,472,814,3121,1063,538,930,1310,533,1196,417,885,3281,3140,565,1265,1254,651,2491,1127,372,504,751,1313,2897,587,1323,802,344,542,460,559,870,1115,1232,3840,3385,1013,770,2222,789,1450,591,1040,348,3300,1183,821,905,475,924,485,834,1151,937,2367,877,1447,1072,3157,660,3955,507,527,3378,602,981,1215,634,1119,774,1104,1242,849,380,512,678,529,661,810,381,366,1206,452,798,1057,1274,334,825,778,349,1174,561,693,429,788,815,729,361,625,435,329,4553,830,493,1079,551,1281,1291,842,1012,682,1195,742,1143,1227,3102,420,989,697,1089,1234,3381,1064,328,1082,339,4167,669,476,489,2172,1016,547,884,1329,1292,933,554,753,393,515,2355,1060,569,1131,654,3083,503,605,4163,1333,508,541,765,398,674,1026,718,926,343,1318,1086,938,633,360,558,1071,794,586,1278,412,965,1251,3262,745,573,1219,824,1154,423,402,3234,732,2393,743,826,545,1007,3319,843,1125,445,572,1312,611,1239,335,1224,672,466,1092,350,3170,3352,681,784,736,377,1122,2378,599,1307,863,362,567,880,649,434,494,758,816,4028,594,483,626,1022,1293,1177,330,462,1112,858,367,799,726,1029,3451,983,1245,2369,608,986,563,2390,685,521,455,883,851,1102,505,2999,2156,438,1076,2952,426,531,374,648,617,342,1145,355,754,553,458,836,490,675,1208,589,690,1025,2375,971,327,739,1267,1098,1053,331,441,370,338,1085,808,359,1130,1218,4164,2354,336,1141,1221,864,386,1094,978,497,876,1180,363,931,4165,524,3928,2490,1108,2352,1084,688,903,1326,588,813,748,351,390,632,781,995,2384,378,433,929,1212,383,346,549,536,752,432,410,1229,818,405,1148,867,735,1116,3379,1097,835,854,1303,1248,790,373,603,564,2201,1314,341,1288,696,1165,415,897,767,1056,664,464,332,1268,427,528,459,992,3886,1004,2372,395,2353,839,3817,723,369,607,3950,1320,337,1009,755,1088,2106,454,364,469,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT122^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n006.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:58:09 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.08/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.13/1.43 % [INFO] Parsing done (610ms).
% 3.13/1.45 % [INFO] Running in sequential loop mode.
% 4.39/1.98 % [INFO] eprover registered as external prover.
% 4.39/1.99 % [INFO] Scanning for conjecture ...
% 4.89/2.19 % [INFO] Found a conjecture (or negated_conjecture) and 328 axioms. Running axiom selection ...
% 5.30/2.38 % [INFO] Axiom selection finished. Selected 324 axioms (removed 4 axioms).
% 7.05/2.88 % [INFO] Problem is higher-order (TPTP THF).
% 7.43/2.93 % [INFO] Type checking passed.
% 7.43/2.94 % [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 ...
% 21.28/6.57 % [INFO] [Domain constraints] Detected constraint on product_unit
% 21.28/6.57 % [INFO] [Domain constraints] dom(product_unit) ⊆ {product_Unity}
% 22.26/6.89 % [INFO] [Domain constraints] Detected constraint on product_unit
% 22.26/6.89 % [INFO] [Domain constraints] dom(product_unit) ⊆ {product_Unity}
% 106.03/52.49 % External prover 'e' found a proof!
% 106.03/52.49 % [INFO] Killing All external provers ...
% 106.03/52.49 % Time passed: 52157ms (effective reasoning time: 51037ms)
% 106.03/52.49 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 106.23/52.50 % Axioms used in derivation (324): fact_112_prod__cases4, fact_129_llexord__LCons__eq, fact_72_lappend__lnull1, fact_106_unfold__llist_Ocode, fact_226_ltake_Ocode, fact_130_llexord__LNil, fact_213_lhd__ltake, fact_4_ltakeWhile_Odisc__iff_I1_J, fact_137_natural_Oexhaust, tcon_Product__Type_Oprod___Nat_Osize_65, tcon_Product__Type_Oprod___Enum_Oenum_42, fact_191_size__unit__overloaded__def, tcon_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of_5, fact_143_case__enat__0, fact_168_lprefix__code_I2_J, fact_193_size__unit__def, fact_10_lzip_Odisc__iff_I2_J, tcon_Nat_Onat___Rings_Osemiring__1, tcon_fun___Typerep_Otyperep, fact_203_llist_Orel__sel, fact_0_lzip_Oexhaust, fact_183_size__bool__overloaded__def, tcon_String_Oliteral___Typerep_Otyperep_38, fact_142_random__aux__set_Oinduct, fact_194_unit_Osize_I2_J, fact_150_lprefix__code_I1_J, tcon_Typerep_Otyperep___HOL_Oequal_14, tcon_String_Oliteral___Nat_Osize_58, fact_93_llist_Ocase__eq__if, fact_136_natural_Oinducts, fact_214_llist_Orel__cases, tcon_fun___HOL_Oequal_28, fact_131_natural_Osimps_I5_J, fact_145_size__ne__size__imp__ne, fact_147_lprefix__refl, tcon_Nat_Onat___Nat_Osize, tcon_HOL_Obool___Enum_Oenum_33, tcon_Product__Type_Ounit___Enum_Oenum_44, fact_236_co_Oenat_Ocase__eq__if, fact_56_llist_Odistinct_I1_J, fact_234_ltake_Osimps_I4_J, fact_201_unit_Ocase__distrib, fact_223_llist_Orel__refl, fact_153_lprefix__lnull, fact_146_lprefix__expand, fact_63_ltakeWhile_Ocode, fact_89_llist_Osplit__sel, tcon_Set_Oset___Quickcheck__Random_Orandom_50, tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_64, fact_170_lprefix_Osimps, fact_48_LNil__eq__lappend__iff, fact_167_lprefixI, fact_58_llist_Osimps_I13_J, fact_60_ltl__simps_I2_J, fact_192_ssubst__Pair__rhs, tcon_Record_Otuple__isomorphism___Code__Evaluation_Oterm__of_1, tcon_HOL_Obool___HOL_Oequal_22, fact_25_lhd__lappend, fact_186_size__bool__def, fact_211_LNil__eq__ltake__iff, tcon_Product__Type_Oprod___Code__Evaluation_Oterm__of_9, fact_97_unfold__llist__eq__LCons, fact_232_co_Oenat_Oexpand, fact_184_old_Obool_Osimps_I5_J, fact_116_prod__induct3, fact_188_size__literal__def, fact_127_llexord_Ocoinduct, fact_225_llist_Orel__coinduct, fact_53_lappend__assoc, fact_164_lprefix__antisym, fact_189_typerep_Osize__neq, fact_36_lhd__LCons__ltl, tcon_Extended__Nat_Oenat___Quickcheck__Random_Orandom_60, fact_230_epred__inject, fact_163_llist_Oleq__trans, fact_81_ltakeWhile_Octr_I2_J, fact_209_ltake_Odisc__iff_I1_J, fact_13_ltake_Oexhaust, fact_144_the__enat__0, fact_159_lprefix__ltlI, tcon_Nat_Onat___Quickcheck__Random_Orandom_49, fact_148_llist_Oleq__refl, fact_6_ltakeWhile_Odisc_I1_J, fact_100_unfold__llist_Octr_I2_J, fact_64_lzip_Octr_I2_J, fact_219_ltake__eq__LNil__iff, fact_160_lprefix__lappend__sameI, fact_107_ltl__unfold__llist, fact_198_old_Ounit_Oexhaust, fact_224_ltake_Octr_I1_J, fact_169_lprefix_Ocases, tcon_Code__Numeral_Onatural___Rings_Osemiring__1_69, fact_18_natural_Osize_I3_J, fact_206_llist_Orel__inject_I2_J, fact_77_llist_Ocollapse_I1_J, fact_122_old_Oprod_Oinducts, fact_217_ltake_Odisc_I2_J, fact_85_lzip_Octr_I1_J, fact_120_prod__induct7, fact_98_unfold__llist_Odisc_I1_J, tcon_Record_Otuple__isomorphism___Typerep_Otyperep_47, tcon_fun___Enum_Oenum, fact_237_enat__unfold__stop, fact_113_prod__cases5, fact_114_prod__cases6, fact_140_random__aux__set_Ocases, fact_154_lprefix__lnullD, tcon_Sum__Type_Osum___HOL_Oequal_20, fact_86_old_Oprod_Oinject, fact_47_lappend__eq__LNil__iff, fact_197_old_Ounit_Oinducts, fact_71_lappend_Odisc_I1_J, tcon_Record_Otuple__isomorphism___Quickcheck__Random_Orandom_72, fact_2_ltakeWhile_Oexhaust, fact_158_LNil__lprefix, fact_17_natural_Osize_I1_J, fact_195_old_Ounit_Orec, tcon_fun___Quickcheck__Random_Orandom, help_If_1_1_T, tcon_Typerep_Otyperep___Code__Evaluation_Oterm__of_13, fact_178_size__bool, fact_57_llist_Osimps_I12_J, tcon_Product__Type_Ounit___Code__Evaluation_Oterm__of_7, fact_52_llist_Oexhaust, fact_65_lzip_Osimps_I4_J, fact_227_ltake_Octr_I2_J, tcon_Product__Type_Ounit___HOL_Oequal_8, fact_104_llist_Osimps_I5_J, tcon_Option_Ooption___Code__Evaluation_Oterm__of_17, fact_139_natural_Odistinct_I2_J, fact_125_llexord_Ocases, tcon_Extended__Nat_Oenat___Code__Evaluation_Oterm__of_11, fact_175_bool_Osize_I4_J, fact_34_ltl__lmap, tcon_Product__Type_Ounit___Typerep_Otyperep_43, fact_95_unfold__llist_Odisc__iff_I1_J, tcon_Typerep_Otyperep___Nat_Osize_59, fact_24_llist_Omap__sel_I1_J, tcon_Option_Ooption___HOL_Oequal_18, fact_149_LCons__lprefix__LCons, tcon_Extended__Nat_Oenat___Typerep_Otyperep_40, tcon_Nat_Onat___Code__Evaluation_Oterm__of_25, tcon_Option_Ooption___Quickcheck__Random_Orandom_55, fact_138_natural_Odistinct_I1_J, fact_205_ltake__LNil, fact_88_natural_Osimps_I4_J, fact_79_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I3_J, tcon_HOL_Obool___Code__Evaluation_Oterm__of_21, fact_12_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I2_J, tcon_Code__Evaluation_Oterm___Typerep_Otyperep_45, tcon_Nat_Onat___Groups_Ozero, fact_135_natural_Osimps_I7_J, tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Typerep_Otyperep_48, fact_141_random__aux__rec, fact_94_divides__aux__eq, fact_228_ltake__epred__ltl, fact_199_default__unit__def, tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Code__Evaluation_Oterm__of, fact_5_ltakeWhile_Odisc_I2_J, fact_99_unfold__llist_Odisc_I2_J, fact_171_lprefix_Ocoinduct, fact_11_lzip_Odisc__iff_I1_J, tcon_HOL_Obool___Typerep_Otyperep_32, fact_68_llist_OdiscI_I2_J, tcon_Nat_Onat___HOL_Oequal_26, fact_14_lzip_Odisc_I1_J, fact_179_sum_Osize__neq, tcon_Nat_Onat___Divides_Osemiring__numeral__div, tcon_fun___Code__Evaluation_Oterm__of_27, fact_174_lprefix__coinduct, fact_8_zero__natural_Orsp, fact_103_unfold__llist_Osimps_I3_J, fact_156_LCons__lprefix__conv, fact_66_lnull__ltlI, fact_19_lzip_Osimps_I3_J, fact_9_zero__reorient, fact_212_ltake__0, fact_1_lappend_Oexhaust, tcon_Extended__Nat_Oenat___Groups_Ozero_62, fact_62_lzip_Ocode, fact_59_ltl__simps_I1_J, fact_37_eq__LConsD, fact_133_lmember__code_I2_J, fact_35_ltl__lappend, fact_91_unfold__llist__id, tcon_String_Oliteral___HOL_Oequal_16, fact_78_lnull__def, fact_155_lprefix__not__lnullD, fact_46_lmap__lappend__distrib, fact_161_lprefix__lappend, fact_221_llist_Octr__transfer_I1_J, fact_32_lappend__LNil2, fact_27_llist_Oinject, tcon_Code__Evaluation_Oterm___HOL_Oequal_6, fact_126_llexord_Osimps, fact_152_lnull__lprefix, fact_54_lmap__eq__LNil, fact_123_old_Oprod_Orec, tcon_String_Oliteral___Quickcheck__Random_Orandom_57, tcon_Product__Type_Ounit___Nat_Osize_67, fact_39_lappend__ltl, fact_101_unfold__llist_Octr_I1_J, fact_55_LNil__eq__lmap, tcon_Sum__Type_Osum___Enum_Oenum_35, fact_67_llist_Odisc_I2_J, tcon_Option_Ooption___Nat_Osize_56, fact_181_bool_Osize_I2_J, tcon_Set_Oset___Code__Evaluation_Oterm__of_23, fact_20_ltakeWhile_Octr_I1_J, fact_26_old_Onat_Osimps_I6_J, fact_75_llist_Odisc_I1_J, tcon_Code__Numeral_Onatural___Groups_Ozero_70, fact_50_lappend__LNil__LNil, fact_16_iterates_Odisc__iff, help_If_3_1_T, tcon_Typerep_Otyperep___Typerep_Otyperep_39, help_If_2_1_T, fact_162_lprefix__trans, fact_235_epred__enat__unfold, fact_121_old_Oprod_Oexhaust, fact_61_lappend_Octr_I1_J, fact_134_natural_Oinject, fact_51_neq__LNil__conv, fact_23_lnth__0, fact_229_epred__0, tcon_Code__Numeral_Onatural___Code__Evaluation_Oterm__of_3, fact_96_unfold__llist_Odisc__iff_I2_J, fact_222_llist_Orel__eq, fact_173_lprefix__lhdD, fact_119_prod__induct6, fact_166_lprefix__down__linear, fact_70_lappend_Odisc_I2_J, fact_190_option_Osize__neq, tcon_Extended__Nat_Oenat___HOL_Oequal_12, fact_22_of__nat__aux_Osimps_I1_J, fact_187_tuple__isomorphism_Osize__neq, tcon_Sum__Type_Osum___Code__Evaluation_Oterm__of_19, tcon_Code__Numeral_Onatural___Nat_Osize_71, fact_82_llist_Oexpand, fact_165_llist_Oleq__antisym, tcon_Sum__Type_Osum___Quickcheck__Random_Orandom_53, fact_132_lmember__code_I1_J, tcon_Product__Type_Oprod___Typerep_Otyperep_41, fact_49_lmap__eq__LCons__conv, fact_204_ltake__is__lprefix, fact_28_lappend_Odisc__iff_I2_J, fact_117_prod__induct4, fact_218_ltake_Odisc_I1_J, fact_40_llist_Omap__sel_I2_J, tcon_String_Oliteral___Code__Evaluation_Oterm__of_15, fact_124_internal__case__prod__conv, fact_185_old_Obool_Osimps_I6_J, tcon_HOL_Obool___Quickcheck__Random_Orandom_51, fact_151_lprefix__LNil, fact_109_prod__cases, fact_215_llist_Orel__distinct_I1_J, fact_83_llist_Ocoinduct, fact_80_iterates_Ocode, fact_202_ltake_Osimps_I3_J, tcon_Extended__Nat_Oenat___Nat_Osize_63, fact_21_ltakeWhile_Osimps_I4_J, tcon_Option_Ooption___Enum_Oenum_37, fact_216_llist_Orel__distinct_I2_J, fact_87_prod_Oinject, tcon_Set_Oset___Typerep_Otyperep_30, fact_30_lappend__code_I2_J, fact_3_ltakeWhile_Odisc__iff_I2_J, fact_196_unit_Osize_I1_J, fact_172_lprefix__LCons__conv, tcon_Nat_Onat___Typerep_Otyperep_29, tcon_HOL_Obool___Nat_Osize_52, fact_240_co_Oenat_Ocase_I1_J, fact_74_lhd__LCons, fact_92_natural_Osimps_I6_J, fact_128_llexord__LCons__less, tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Quickcheck__Random_Orandom_74, fact_111_prod__cases3, tcon_Sum__Type_Osum___Typerep_Otyperep_34, fact_176_bool_Osize_I3_J, fact_177_lstrict__prefix__def, fact_7_ltakeWhile_Osimps_I3_J, fact_102_unfold__llist_Osimps_I4_J, tcon_Product__Type_Oprod___HOL_Oequal_10, fact_118_prod__induct5, fact_157_Le__LCons, fact_238_enat__unfold__eq__0, tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___HOL_Oequal, fact_29_lnull__lappend, fact_207_ltake__lmap, fact_231_enat__coinduct, fact_115_prod__cases7, tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_66, fact_73_lappend__lnull2, tcon_Set_Oset___HOL_Oequal_24, fact_69_not__lnull__conv, fact_210_ltake_Odisc__iff_I2_J, fact_84_llist_Ocoinduct__strong, fact_76_llist_OdiscI_I1_J, fact_220_llist_Orel__intros_I2_J, tcon_Record_Otuple__isomorphism___HOL_Oequal_2, conj_0, fact_31_llist_Omap__disc__iff, tcon_Option_Ooption___Typerep_Otyperep_36, tcon_Extended__Nat_Oenat___Rings_Osemiring__1_61, fact_90_llist_Osplit__sel__asm, fact_108_surj__pair, tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_68, fact_38_llist_Oexhaust__sel, fact_208_lnull__ltake, tcon_Code__Numeral_Onatural___Typerep_Otyperep_46, tcon_Record_Otuple__isomorphism___Nat_Osize_73, fact_233_enat__coinduct2, fact_15_lzip_Odisc_I2_J, fact_45_lappend__snocL1__conv__LCons2, fact_180_prod_Osize__neq, fact_182_bool_Osize_I1_J, fact_239_enat__cocase__0, fact_110_Pair__inject, fact_200_old_Ounit_Ocase, fact_105_llist_Osimps_I4_J, tcon_Sum__Type_Osum___Nat_Osize_54, tcon_Set_Oset___Enum_Oenum_31, tcon_Code__Numeral_Onatural___HOL_Oequal_4, fact_33_lappend__code_I1_J
% 106.23/52.50 % No. of inferences in proof: 882
% 106.23/52.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 52157 ms resp. 51037 ms w/o parsing
% 107.72/52.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 107.72/52.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------