TSTP Solution File: COM156^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COM156^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:30:10 EDT 2024
% Result : Theorem 138.13s 102.93s
% Output : Refutation 138.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 148
% Syntax : Number of formulae : 257 ( 88 unt; 41 typ; 0 def)
% Number of atoms : 840 ( 168 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 4554 ( 50 ~; 4 |; 56 &;4150 @)
% ( 0 <=>; 294 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 266 ( 266 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 16 con; 0-5 aty)
% Number of variables : 1122 ( 52 ^ 970 !; 59 ?;1122 :)
% ( 41 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(state_type,type,
state: $tType ).
thf(rule_type,type,
rule: $tType ).
thf(abstra1326562878System_type,type,
abstra1326562878System:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > ( stream @ TB ) > ( set @ TA ) > $o ) ).
thf(abstra1332369113inWait_type,type,
abstra1332369113inWait:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > ( stream @ TB ) > TA > nat ) ).
thf(abstra1209608345urated_type,type,
abstra1209608345urated:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > ( stream @ TB ) > ( stream @ ( product_prod @ TA @ TB ) ) > $o ) ).
thf(abstra1874422341nabled_type,type,
abstra1874422341nabled:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > TB > TA > $o ) ).
thf(abstra523868654_epath_type,type,
abstra523868654_epath:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > ( stream @ TB ) > ( stream @ ( product_prod @ TA @ TB ) ) > $o ) ).
thf(abstra928354080m_fair_type,type,
abstra928354080m_fair:
!>[TA: $tType] : ( ( stream @ TA ) > ( stream @ TA ) > $o ) ).
thf(abstra1774373515_fenum_type,type,
abstra1774373515_fenum:
!>[TA: $tType] : ( ( stream @ TA ) > ( stream @ TA ) ) ).
thf(abstra1225283448mkTree_type,type,
abstra1225283448mkTree:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > ( stream @ TB ) > TA > ( abstra2103299360e_tree @ ( product_prod @ TA @ TB ) ) ) ).
thf(abstra1276541928ickEff_type,type,
abstra1276541928ickEff:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > TB > TA > ( fset @ TA ) ) ).
thf(abstra726722745urated_type,type,
abstra726722745urated:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > TB > ( stream @ ( product_prod @ TA @ TB ) ) > $o ) ).
thf(abstra1259602206m_trim_type,type,
abstra1259602206m_trim:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > ( stream @ TB ) > TA > ( stream @ TB ) ) ).
thf(abstra1874736267tem_wf_type,type,
abstra1874736267tem_wf:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > ( fset @ TA ) > $o ) > ( stream @ TB ) > ( abstra2103299360e_tree @ ( product_prod @ TA @ TB ) ) > $o ) ).
thf(abstra313004635_ipath_type,type,
abstra313004635_ipath:
!>[TA: $tType] : ( ( abstra2103299360e_tree @ TA ) > ( stream @ TA ) > $o ) ).
thf(abstra668420080finite_type,type,
abstra668420080finite:
!>[TA: $tType] : ( ( abstra2103299360e_tree @ TA ) > $o ) ).
thf(abstra1749095923e_cont_type,type,
abstra1749095923e_cont:
!>[TA: $tType] : ( ( abstra2103299360e_tree @ TA ) > ( fset @ ( abstra2103299360e_tree @ TA ) ) ) ).
thf(abstra573067619e_root_type,type,
abstra573067619e_root:
!>[TA: $tType] : ( ( abstra2103299360e_tree @ TA ) > TA ) ).
thf(fimage_type,type,
fimage:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( fset @ TB ) > ( fset @ TA ) ) ).
thf(fmember_type,type,
fmember:
!>[TA: $tType] : ( TA > ( fset @ TA ) > $o ) ).
thf(ord_Least_type,type,
ord_Least:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(sdrop_type,type,
sdrop:
!>[TA: $tType] : ( nat > ( stream @ TA ) > ( stream @ TA ) ) ).
thf(sdrop_while_type,type,
sdrop_while:
!>[TA: $tType] : ( ( TA > $o ) > ( stream @ TA ) > ( stream @ TA ) ) ).
thf(shd_type,type,
shd:
!>[TA: $tType] : ( ( stream @ TA ) > TA ) ).
thf(sset_type,type,
sset:
!>[TA: $tType] : ( ( stream @ TA ) > ( set @ TA ) ) ).
thf(stl_type,type,
stl:
!>[TA: $tType] : ( ( stream @ TA ) > ( stream @ TA ) ) ).
thf(szip_type,type,
szip:
!>[TA: $tType,TB: $tType] : ( ( stream @ TB ) > ( stream @ TA ) > ( stream @ ( product_prod @ TB @ TA ) ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(s_type,type,
s: set @ state ).
thf(eff_type,type,
eff: rule > state > ( fset @ state ) > $o ).
thf(ma_type,type,
ma: nat ).
thf(rs_type,type,
rs: stream @ rule ).
thf(rsa_type,type,
rsa: stream @ rule ).
thf(rules_type,type,
rules: stream @ rule ).
thf(s2_type,type,
s2: state ).
thf(steps_type,type,
steps: stream @ ( product_prod @ state @ rule ) ).
thf(stepsa_type,type,
stepsa: stream @ ( product_prod @ state @ rule ) ).
thf(thesis_type,type,
thesis: $o ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fset @ TA,C: TA > TB] :
( ( fmember @ TA @ A @ B )
=> ( fmember @ TB @ ( C @ A ) @ ( fimage @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_fimageI) ).
thf(138,plain,
! [TA: $tType,TB: $tType,A: TA,B: fset @ TA,C: TA > TB] :
( ( fmember @ TA @ A @ B )
=> ( fmember @ TB @ ( C @ A ) @ ( fimage @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(38,axiom,
abstra928354080m_fair @ rule @ rules @ ( abstra1774373515_fenum @ rule @ rules ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_fair__fenum) ).
thf(234,plain,
abstra928354080m_fair @ rule @ rules @ ( abstra1774373515_fenum @ rule @ rules ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType] :
( ( abstra1209608345urated @ TA @ TB )
= ( ^ [A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: stream @ ( product_prod @ TB @ TA )] :
! [D: TA] :
( ( member @ TA @ D @ ( sset @ TA @ B ) )
=> ( abstra726722745urated @ TA @ TB @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_RuleSystem__Defs_OSaturated__def) ).
thf(352,plain,
! [TA: $tType,TB: $tType] :
( ( abstra1209608345urated @ TA @ TB )
= ( ^ [A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: stream @ ( product_prod @ TB @ TA )] :
! [D: TA] :
( ( member @ TA @ D @ ( sset @ TA @ B ) )
=> ( abstra726722745urated @ TA @ TB @ A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(95,axiom,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: stream @ TA] :
( ( abstra668420080finite @ TA @ A )
=> ~ ( abstra313004635_ipath @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_ftree__no__ipath) ).
thf(408,plain,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: stream @ TA] :
( ( abstra668420080finite @ TA @ A )
=> ~ ( abstra313004635_ipath @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',fact_231_prod__cases7) ).
thf(379,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)],[85]) ).
thf(87,axiom,
! [A: abstra2103299360e_tree @ ( product_prod @ state @ rule ),B: stream @ ( product_prod @ state @ rule )] :
( ( abstra1874736267tem_wf @ rule @ state @ eff @ rules @ A )
=> ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ A @ B )
=> ( abstra523868654_epath @ rule @ state @ eff @ rules @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_wf__ipath__epath) ).
thf(385,plain,
! [A: abstra2103299360e_tree @ ( product_prod @ state @ rule ),B: stream @ ( product_prod @ state @ rule )] :
( ( abstra1874736267tem_wf @ rule @ state @ eff @ rules @ A )
=> ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ A @ B )
=> ( abstra523868654_epath @ rule @ state @ eff @ rules @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: stream @ TB,B: stream @ TA] :
( ( stl @ ( product_prod @ TB @ TA ) @ ( szip @ TB @ TA @ A @ B ) )
= ( szip @ TB @ TA @ ( stl @ TB @ A ) @ ( stl @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_szip_Osimps_I2_J) ).
thf(142,plain,
! [TA: $tType,TB: $tType,A: stream @ TB,B: stream @ TA] :
( ( stl @ ( product_prod @ TB @ TA ) @ ( szip @ TB @ TA @ A @ B ) )
= ( szip @ TB @ TA @ ( stl @ TB @ A ) @ ( stl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(53,axiom,
! [A: stream @ rule,B: nat] :
( ( abstra928354080m_fair @ rule @ rules @ A )
=> ( abstra928354080m_fair @ rule @ rules @ ( sdrop @ rule @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_sdrop__fair) ).
thf(288,plain,
! [A: stream @ rule,B: nat] :
( ( abstra928354080m_fair @ rule @ rules @ A )
=> ( abstra928354080m_fair @ rule @ rules @ ( sdrop @ rule @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',fact_238_old_Oprod_Oinducts) ).
thf(301,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)],[58]) ).
thf(22,axiom,
! [TA: $tType,A: nat,B: stream @ TA] :
( ( sdrop @ TA @ A @ ( stl @ TA @ B ) )
= ( stl @ TA @ ( sdrop @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_sdrop__stl) ).
thf(174,plain,
! [TA: $tType,A: nat,B: stream @ TA] :
( ( sdrop @ TA @ A @ ( stl @ TA @ B ) )
= ( stl @ TA @ ( sdrop @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,axiom,
member @ state @ s2 @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_s) ).
thf(404,plain,
member @ state @ s2 @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(25,axiom,
! [TA: $tType,A: abstra2103299360e_tree @ TA] :
( ! [B: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ B @ ( abstra1749095923e_cont @ TA @ A ) )
=> ( abstra668420080finite @ TA @ B ) )
=> ( abstra668420080finite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_tfinite) ).
thf(184,plain,
! [TA: $tType,A: abstra2103299360e_tree @ TA] :
( ! [B: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ B @ ( abstra1749095923e_cont @ TA @ A ) )
=> ( abstra668420080finite @ TA @ B ) )
=> ( abstra668420080finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType] :
( ( abstra1326562878System @ TA @ TB )
= ( ^ [A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB] :
( ! [D: TB] :
( ( member @ TB @ D @ C )
=> ! [E: TA] :
( ( member @ TA @ E @ ( sset @ TA @ B ) )
=> ! [F: fset @ TB] :
( ( A @ E @ D @ F )
=> ! [G: TB] :
( ( fmember @ TB @ G @ F )
=> ( member @ TB @ G @ C ) ) ) ) )
& ! [D: TB] :
( ( member @ TB @ D @ C )
=> ? [E: TA] :
( ( member @ TA @ E @ ( sset @ TA @ B ) )
& ? [F: fset @ TB] : ( A @ E @ D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_RuleSystem__def) ).
thf(372,plain,
! [TA: $tType,TB: $tType] :
( ( abstra1326562878System @ TA @ TB )
= ( ^ [A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB] :
( ! [D: TB] :
( ( member @ TB @ D @ C )
=> ! [E: TA] :
( ( member @ TA @ E @ ( sset @ TA @ B ) )
=> ! [F: fset @ TB] :
( ( A @ E @ D @ F )
=> ! [G: TB] :
( ( fmember @ TB @ G @ F )
=> ( member @ TB @ G @ C ) ) ) ) )
& ! [D: TB] :
( ( member @ TB @ D @ C )
=> ? [E: TA] :
( ( member @ TA @ E @ ( sset @ TA @ B ) )
& ? [F: fset @ TB] : ( A @ E @ D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fset @ TA,C: TB,D: TA > TB] :
( ( fmember @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( fmember @ TB @ C @ ( fimage @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_rev__fimage__eqI) ).
thf(110,plain,
! [TA: $tType,TB: $tType,A: TA,B: fset @ TA,C: TB,D: TA > TB] :
( ( fmember @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( fmember @ TB @ C @ ( fimage @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: stream @ TB] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( abstra928354080m_fair @ TB @ B @ E )
=> ? [F: nat] : ( abstra1874422341nabled @ TB @ TA @ A @ ( shd @ TB @ ( sdrop @ TB @ F @ E ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_RuleSystem_OminWait__ex) ).
thf(344,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: stream @ TB] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( abstra928354080m_fair @ TB @ B @ E )
=> ? [F: nat] : ( abstra1874422341nabled @ TB @ TA @ A @ ( shd @ TB @ ( sdrop @ TB @ F @ E ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: stream @ TB] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( abstra928354080m_fair @ TB @ B @ E )
=> ( abstra928354080m_fair @ TB @ B @ ( abstra1259602206m_trim @ TB @ TA @ A @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_RuleSystem_Otrim__fair) ).
thf(357,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: stream @ TB] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( abstra928354080m_fair @ TB @ B @ E )
=> ( abstra928354080m_fair @ TB @ B @ ( abstra1259602206m_trim @ TB @ TA @ A @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(17,axiom,
! [TA: $tType,A: stream @ TA] : ( abstra928354080m_fair @ TA @ A @ ( abstra1774373515_fenum @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_RuleSystem__Defs_Ofair__fenum) ).
thf(157,plain,
! [TA: $tType,A: stream @ TA] : ( abstra928354080m_fair @ TA @ A @ ( abstra1774373515_fenum @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(98,axiom,
! [A: rule,B: state] :
( ( abstra1874422341nabled @ rule @ state @ eff @ A @ B )
=> ( eff @ A @ B @ ( abstra1276541928ickEff @ rule @ state @ eff @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_pickEff) ).
thf(416,plain,
! [A: rule,B: state] :
( ( abstra1874422341nabled @ rule @ state @ eff @ A @ B )
=> ( eff @ A @ B @ ( abstra1276541928ickEff @ rule @ state @ eff @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(68,axiom,
! [A: state,B: stream @ rule,C: abstra2103299360e_tree @ ( product_prod @ state @ rule )] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( ( fmember @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ C @ ( abstra1749095923e_cont @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ B @ A ) ) )
=> ? [D: fset @ state,E: state] :
( ( member @ state @ E @ s )
& ( eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) @ A @ D )
& ( fmember @ state @ E @ D )
& ( C
= ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_in__cont__mkTree) ).
thf(325,plain,
! [A: state,B: stream @ rule,C: abstra2103299360e_tree @ ( product_prod @ state @ rule )] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( ( fmember @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ C @ ( abstra1749095923e_cont @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ B @ A ) ) )
=> ? [D: fset @ state,E: state] :
( ( member @ state @ E @ s )
& ( eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) @ A @ D )
& ( fmember @ state @ E @ D )
& ( C
= ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(64,axiom,
! [TA: $tType,A: fset @ TA,B: fset @ TA] :
( ! [C: TA] :
( ( fmember @ TA @ C @ A )
= ( fmember @ TA @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_fset__eqI) ).
thf(316,plain,
! [TA: $tType,A: fset @ TA,B: fset @ TA] :
( ! [C: TA] :
( ( fmember @ TA @ C @ A )
= ( fmember @ TA @ C @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',fact_233_prod__induct4) ).
thf(261,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)],[44]) ).
thf(34,axiom,
! [TA: $tType,A: ( stream @ TA ) > ( stream @ TA ) > $o,B: stream @ TA,C: stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: stream @ TA,E: stream @ TA] :
( ( A @ D @ E )
=> ( ( ( shd @ TA @ D )
= ( shd @ TA @ E ) )
& ( A @ ( stl @ TA @ D ) @ ( stl @ TA @ E ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_stream_Ocoinduct) ).
thf(216,plain,
! [TA: $tType,A: ( stream @ TA ) > ( stream @ TA ) > $o,B: stream @ TA,C: stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: stream @ TA,E: stream @ TA] :
( ( A @ D @ E )
=> ( ( ( shd @ TA @ D )
= ( shd @ TA @ E ) )
& ( A @ ( stl @ TA @ D ) @ ( stl @ TA @ E ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(66,axiom,
! [TA: $tType,A: stream @ TA,B: stream @ TA,C: nat] :
( ( abstra928354080m_fair @ TA @ A @ B )
=> ( abstra928354080m_fair @ TA @ A @ ( sdrop @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_RuleSystem__Defs_Osdrop__fair) ).
thf(321,plain,
! [TA: $tType,A: stream @ TA,B: stream @ TA,C: nat] :
( ( abstra928354080m_fair @ TA @ A @ B )
=> ( abstra928354080m_fair @ TA @ A @ ( sdrop @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: fset @ TA] :
( ( fimage @ TB @ TC @ A @ ( fimage @ TA @ TB @ B @ C ) )
= ( fimage @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_fimage__fimage) ).
thf(121,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: fset @ TA] :
( ( fimage @ TB @ TC @ A @ ( fimage @ TA @ TB @ B @ C ) )
= ( fimage @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,axiom,
! [TA: $tType,A: ( abstra2103299360e_tree @ TA ) > ( stream @ TA ) > $o,B: abstra2103299360e_tree @ TA,C: stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: abstra2103299360e_tree @ TA,E: stream @ TA] :
( ( A @ D @ E )
=> ? [F: abstra2103299360e_tree @ TA,G: stream @ TA,H: abstra2103299360e_tree @ TA] :
( ( D = F )
& ( E = G )
& ( ( abstra573067619e_root @ TA @ F )
= ( shd @ TA @ G ) )
& ( fmember @ ( abstra2103299360e_tree @ TA ) @ H @ ( abstra1749095923e_cont @ TA @ F ) )
& ( ( A @ H @ ( stl @ TA @ G ) )
| ( abstra313004635_ipath @ TA @ H @ ( stl @ TA @ G ) ) ) ) )
=> ( abstra313004635_ipath @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_ipath_Ocoinduct) ).
thf(221,plain,
! [TA: $tType,A: ( abstra2103299360e_tree @ TA ) > ( stream @ TA ) > $o,B: abstra2103299360e_tree @ TA,C: stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: abstra2103299360e_tree @ TA,E: stream @ TA] :
( ( A @ D @ E )
=> ? [F: abstra2103299360e_tree @ TA,G: stream @ TA,H: abstra2103299360e_tree @ TA] :
( ( D = F )
& ( E = G )
& ( ( abstra573067619e_root @ TA @ F )
= ( shd @ TA @ G ) )
& ( fmember @ ( abstra2103299360e_tree @ TA ) @ H @ ( abstra1749095923e_cont @ TA @ F ) )
& ( ( A @ H @ ( stl @ TA @ G ) )
| ( abstra313004635_ipath @ TA @ H @ ( stl @ TA @ G ) ) ) ) )
=> ( abstra313004635_ipath @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_227_prod__cases3) ).
thf(293,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)],[55]) ).
thf(104,axiom,
abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ rsa @ s2 ) @ stepsa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Suc_Oprems_I3_J) ).
thf(428,plain,
abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ rsa @ s2 ) @ stepsa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',fact_235_prod__induct6) ).
thf(312,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)],[62]) ).
thf(43,axiom,
! [TA: $tType,A: fset @ TA,B: fset @ TA,C: TA] :
( ( A = B )
=> ( ( ( fmember @ TA @ C @ A )
=> ~ ( fmember @ TA @ C @ B ) )
=> ~ ( ~ ( fmember @ TA @ C @ A )
=> ( fmember @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_fequalityCE) ).
thf(248,plain,
! [TA: $tType,A: fset @ TA,B: fset @ TA,C: TA] :
( ( A = B )
=> ( ( ( fmember @ TA @ C @ A )
=> ~ ( fmember @ TA @ C @ B ) )
=> ~ ( ~ ( fmember @ TA @ C @ A )
=> ( fmember @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( abstra1259602206m_trim @ TA @ TB )
= ( ^ [A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: TB] :
( sdrop_while @ TA
@ ^ [D: TA] :
~ ( abstra1874422341nabled @ TA @ TB @ A @ D @ C )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_RuleSystem__Defs_Otrim__def) ).
thf(201,plain,
! [TA: $tType,TB: $tType] :
( ( abstra1259602206m_trim @ TA @ TB )
= ( ^ [A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: TB] :
( sdrop_while @ TA
@ ^ [D: TA] :
~ ( abstra1874422341nabled @ TA @ TB @ A @ D @ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',fact_221_prod_Oinject) ).
thf(366,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)],[81]) ).
thf(75,axiom,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_trim__enabled) ).
thf(349,plain,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(105,axiom,
! [A: stream @ ( product_prod @ state @ rule )] :
( ( abstra1209608345urated @ rule @ state @ eff @ rules @ A )
= ( ! [B: rule] :
( ( member @ rule @ B @ ( sset @ rule @ rules ) )
=> ( abstra726722745urated @ rule @ state @ eff @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Saturated__def) ).
thf(429,plain,
! [A: stream @ ( product_prod @ state @ rule )] :
( ( abstra1209608345urated @ rule @ state @ eff @ rules @ A )
= ( ! [B: rule] :
( ( member @ rule @ B @ ( sset @ rule @ rules ) )
=> ( abstra726722745urated @ rule @ state @ eff @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB,D: nat,E: stream @ TA,F: TB] :
( ( abstra1326562878System @ TA @ TB @ A @ B @ C )
=> ( ( abstra1874422341nabled @ TA @ TB @ A @ ( shd @ TA @ ( sdrop @ TA @ D @ E ) ) @ F )
=> ( ord_less_eq @ nat @ ( abstra1332369113inWait @ TA @ TB @ A @ E @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_RuleSystem_OminWait__least) ).
thf(229,plain,
! [TA: $tType,TB: $tType,A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB,D: nat,E: stream @ TA,F: TB] :
( ( abstra1326562878System @ TA @ TB @ A @ B @ C )
=> ( ( abstra1874422341nabled @ TA @ TB @ A @ ( shd @ TA @ ( sdrop @ TA @ D @ E ) ) @ F )
=> ( ord_less_eq @ nat @ ( abstra1332369113inWait @ TA @ TB @ A @ E @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(107,axiom,
! [A: state] :
( ( member @ state @ A @ s )
=> ? [B: rule] :
( ( member @ rule @ B @ ( sset @ rule @ rules ) )
& ? [C: fset @ state] : ( eff @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_enabled__R) ).
thf(435,plain,
! [A: state] :
( ( member @ state @ A @ s )
=> ? [B: rule] :
( ( member @ rule @ B @ ( sset @ rule @ rules ) )
& ? [C: fset @ state] : ( eff @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(88,axiom,
! [A: stream @ rule,B: state] :
( ( abstra573067619e_root @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ A @ B ) )
= ( product_Pair @ state @ rule @ B @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_mkTree_Osimps_I1_J) ).
thf(388,plain,
! [A: stream @ rule,B: state] :
( ( abstra573067619e_root @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ A @ B ) )
= ( product_Pair @ state @ rule @ B @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(20,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_ex__has__least__nat) ).
thf(169,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(109,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: fset @ TA,B: fset @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( fmember @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( fimage @ TA @ TB @ C @ A )
= ( fimage @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_fimage__cong) ).
thf(124,plain,
! [TA: $tType,TB: $tType,A: fset @ TA,B: fset @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( fmember @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( fimage @ TA @ TB @ C @ A )
= ( fimage @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: ( abstra2103299360e_tree @ TA ) > $o] :
( ( abstra668420080finite @ TA @ A )
=> ( ! [C: abstra2103299360e_tree @ TA] :
( ! [D: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ D @ ( abstra1749095923e_cont @ TA @ C ) )
=> ( abstra668420080finite @ TA @ D ) )
=> ( ! [D: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ D @ ( abstra1749095923e_cont @ TA @ C ) )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_tfinite_Oinducts) ).
thf(193,plain,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: ( abstra2103299360e_tree @ TA ) > $o] :
( ( abstra668420080finite @ TA @ A )
=> ( ! [C: abstra2103299360e_tree @ TA] :
( ! [D: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ D @ ( abstra1749095923e_cont @ TA @ C ) )
=> ( abstra668420080finite @ TA @ D ) )
=> ( ! [D: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ D @ ( abstra1749095923e_cont @ TA @ C ) )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: fset @ TA] :
( ( A
= ( B @ C ) )
=> ( ( fmember @ TA @ C @ D )
=> ( fmember @ TB @ A @ ( fimage @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_fimage__eqI) ).
thf(134,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: fset @ TA] :
( ( A
= ( B @ C ) )
=> ( ( fmember @ TA @ C @ D )
=> ( fmember @ TB @ A @ ( fimage @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: TA] :
( ( abstra573067619e_root @ ( product_prod @ TA @ TB ) @ ( abstra1225283448mkTree @ TB @ TA @ A @ B @ C ) )
= ( product_Pair @ TA @ TB @ C @ ( shd @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_RuleSystem__Defs_OmkTree_Osimps_I1_J) ).
thf(237,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: TA] :
( ( abstra573067619e_root @ ( product_prod @ TA @ TB ) @ ( abstra1225283448mkTree @ TB @ TA @ A @ B @ C ) )
= ( product_Pair @ TA @ TB @ C @ ( shd @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(14,axiom,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: stream @ TA,C: abstra2103299360e_tree @ TA] :
( ( ( abstra573067619e_root @ TA @ A )
= ( shd @ TA @ B ) )
=> ( ( fmember @ ( abstra2103299360e_tree @ TA ) @ C @ ( abstra1749095923e_cont @ TA @ A ) )
=> ( ( abstra313004635_ipath @ TA @ C @ ( stl @ TA @ B ) )
=> ( abstra313004635_ipath @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ipath_Ointros) ).
thf(148,plain,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: stream @ TA,C: abstra2103299360e_tree @ TA] :
( ( ( abstra573067619e_root @ TA @ A )
= ( shd @ TA @ B ) )
=> ( ( fmember @ ( abstra2103299360e_tree @ TA ) @ C @ ( abstra1749095923e_cont @ TA @ A ) )
=> ( ( abstra313004635_ipath @ TA @ C @ ( stl @ TA @ B ) )
=> ( abstra313004635_ipath @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(50,axiom,
! [TA: $tType,A: fset @ TA,B: fset @ TA,C: TA] :
( ( A = B )
=> ( ( fmember @ TA @ C @ A )
= ( fmember @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_eqfset__imp__iff) ).
thf(279,plain,
! [TA: $tType,A: fset @ TA,B: fset @ TA,C: TA] :
( ( A = B )
=> ( ( fmember @ TA @ C @ A )
= ( fmember @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',fact_220_old_Oprod_Oinject) ).
thf(296,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)],[56]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: fset @ TA,B: TA > TB > $o] :
( ! [C: TA] :
( ( fmember @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( fmember @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_fset__choice) ).
thf(375,plain,
! [TA: $tType,TB: $tType,A: fset @ TA,B: TA > TB > $o] :
( ! [C: TA] :
( ( fmember @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( fmember @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(102,axiom,
! [A: stream @ rule,B: stream @ ( product_prod @ state @ rule )] :
( ( member @ state @ s2 @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ A )
=> ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ A @ s2 ) @ B )
=> ? [C: nat,D: state] :
( ( member @ state @ D @ s )
& ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( sdrop @ rule @ C @ A ) @ D ) @ ( sdrop @ ( product_prod @ state @ rule ) @ ma @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Suc_Ohyps) ).
thf(423,plain,
! [A: stream @ rule,B: stream @ ( product_prod @ state @ rule )] :
( ( member @ state @ s2 @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ A )
=> ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ A @ s2 ) @ B )
=> ? [C: nat,D: state] :
( ( member @ state @ D @ s )
& ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( sdrop @ rule @ C @ A ) @ D ) @ ( sdrop @ ( product_prod @ state @ rule ) @ ma @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: stream @ TB] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( abstra928354080m_fair @ TB @ B @ E )
=> ( abstra1874422341nabled @ TB @ TA @ A @ ( shd @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ E @ D ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_RuleSystem_Otrim__enabled) ).
thf(286,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: stream @ TB] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( abstra928354080m_fair @ TB @ B @ E )
=> ( abstra1874422341nabled @ TB @ TA @ A @ ( shd @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ E @ D ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: TB,C: TA] :
( ( abstra1874422341nabled @ TB @ TA @ A @ B @ C )
=> ( A @ B @ C @ ( abstra1276541928ickEff @ TB @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_RuleSystem__Defs_OpickEff) ).
thf(291,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: TB,C: TA] :
( ( abstra1874422341nabled @ TB @ TA @ A @ B @ C )
=> ( A @ B @ C @ ( abstra1276541928ickEff @ TB @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(5,axiom,
! [TA: $tType,A: fset @ TA] :
( ( fimage @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_fimage__ident) ).
thf(118,plain,
! [TA: $tType,A: fset @ TA] :
( ( fimage @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: TA] :
( ( abstra1749095923e_cont @ ( product_prod @ TA @ TB ) @ ( abstra1225283448mkTree @ TB @ TA @ A @ B @ C ) )
= ( fimage @ TA @ ( abstra2103299360e_tree @ ( product_prod @ TA @ TB ) ) @ ( abstra1225283448mkTree @ TB @ TA @ A @ ( stl @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ B @ C ) ) ) @ ( abstra1276541928ickEff @ TB @ TA @ A @ ( shd @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ B @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_RuleSystem__Defs_OmkTree_Osimps_I2_J) ).
thf(204,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: TA] :
( ( abstra1749095923e_cont @ ( product_prod @ TA @ TB ) @ ( abstra1225283448mkTree @ TB @ TA @ A @ B @ C ) )
= ( fimage @ TA @ ( abstra2103299360e_tree @ ( product_prod @ TA @ TB ) ) @ ( abstra1225283448mkTree @ TB @ TA @ A @ ( stl @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ B @ C ) ) ) @ ( abstra1276541928ickEff @ TB @ TA @ A @ ( shd @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ B @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(97,axiom,
! [A: rule,B: state] :
( ( abstra1874422341nabled @ rule @ state @ eff @ A @ B )
= ( '?' @ ( fset @ state ) @ ( eff @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_enabled__def) ).
thf(413,plain,
! [A: rule,B: state] :
( ( abstra1874422341nabled @ rule @ state @ eff @ A @ B )
= ( ? [C: fset @ state] : ( eff @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: stream @ TA] :
( ( member @ TA @ A @ ( sset @ TA @ ( stl @ TA @ B ) ) )
=> ( member @ TA @ A @ ( sset @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_stl__sset) ).
thf(191,plain,
! [TA: $tType,A: TA,B: stream @ TA] :
( ( member @ TA @ A @ ( sset @ TA @ ( stl @ TA @ B ) ) )
=> ( member @ TA @ A @ ( sset @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: abstra2103299360e_tree @ ( product_prod @ TA @ TB ),D: stream @ ( product_prod @ TA @ TB )] :
( ( abstra1874736267tem_wf @ TB @ TA @ A @ B @ C )
=> ( ( abstra313004635_ipath @ ( product_prod @ TA @ TB ) @ C @ D )
=> ( abstra523868654_epath @ TB @ TA @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_RuleSystem__Defs_Owf__ipath__epath) ).
thf(402,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: abstra2103299360e_tree @ ( product_prod @ TA @ TB ),D: stream @ ( product_prod @ TA @ TB )] :
( ( abstra1874736267tem_wf @ TB @ TA @ A @ B @ C )
=> ( ( abstra313004635_ipath @ ( product_prod @ TA @ TB ) @ C @ D )
=> ( abstra523868654_epath @ TB @ TA @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(89,axiom,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A )
= ( sdrop @ rule @ ( abstra1332369113inWait @ rule @ state @ eff @ B @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_trim__alt) ).
thf(391,plain,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A )
= ( sdrop @ rule @ ( abstra1332369113inWait @ rule @ state @ eff @ B @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',fact_229_prod__cases5) ).
thf(382,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)],[86]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_surj__pair) ).
thf(335,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)],[70]) ).
thf(18,axiom,
! [TA: $tType,A: stream @ TA] :
( ( sset @ TA @ ( abstra1774373515_fenum @ TA @ A ) )
= ( sset @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_RuleSystem__Defs_Osset__fenum) ).
thf(159,plain,
! [TA: $tType,A: stream @ TA] :
( ( sset @ TA @ ( abstra1774373515_fenum @ TA @ A ) )
= ( sset @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
! [TA: $tType,A: TA,B: stream @ TA,C: TA > ( stream @ TA ) > $o] :
( ( member @ TA @ A @ ( sset @ TA @ B ) )
=> ( ! [D: stream @ TA] : ( C @ ( shd @ TA @ D ) @ D )
=> ( ! [D: stream @ TA,E: TA] :
( ( member @ TA @ E @ ( sset @ TA @ ( stl @ TA @ D ) ) )
=> ( ( C @ E @ ( stl @ TA @ D ) )
=> ( C @ E @ D ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_sset__induct) ).
thf(187,plain,
! [TA: $tType,A: TA,B: stream @ TA,C: TA > ( stream @ TA ) > $o] :
( ( member @ TA @ A @ ( sset @ TA @ B ) )
=> ( ! [D: stream @ TA] : ( C @ ( shd @ TA @ D ) @ D )
=> ( ! [D: stream @ TA,E: TA] :
( ( member @ TA @ E @ ( sset @ TA @ ( stl @ TA @ D ) ) )
=> ( ( C @ E @ ( stl @ TA @ D ) )
=> ( C @ E @ D ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
! [TA: $tType,A: abstra2103299360e_tree @ TA] :
( ( abstra668420080finite @ TA @ A )
=> ! [B: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ B @ ( abstra1749095923e_cont @ TA @ A ) )
=> ( abstra668420080finite @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_tfinite_Ocases) ).
thf(172,plain,
! [TA: $tType,A: abstra2103299360e_tree @ TA] :
( ( abstra668420080finite @ TA @ A )
=> ! [B: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ B @ ( abstra1749095923e_cont @ TA @ A ) )
=> ( abstra668420080finite @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: stream @ TB,B: stream @ TA] :
( ( shd @ ( product_prod @ TB @ TA ) @ ( szip @ TB @ TA @ A @ B ) )
= ( product_Pair @ TB @ TA @ ( shd @ TB @ A ) @ ( shd @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_szip_Osimps_I1_J) ).
thf(274,plain,
! [TA: $tType,TB: $tType,A: stream @ TB,B: stream @ TA] :
( ( shd @ ( product_prod @ TB @ TA ) @ ( szip @ TB @ TA @ A @ B ) )
= ( product_Pair @ TB @ TA @ ( shd @ TB @ A ) @ ( shd @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(100,axiom,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( abstra928354080m_fair @ rule @ rules @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_trim__fair) ).
thf(419,plain,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( abstra928354080m_fair @ rule @ rules @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType] :
( ( abstra1874422341nabled @ TA @ TB )
= ( ^ [A: TA > TB > ( fset @ TB ) > $o,B: TA,C: TB] :
? [D: fset @ TB] : ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_RuleSystem__Defs_Oenabled__def) ).
thf(245,plain,
! [TA: $tType,TB: $tType] :
( ( abstra1874422341nabled @ TA @ TB )
= ( ^ [A: TA > TB > ( fset @ TB ) > $o,B: TA,C: TB] :
? [D: fset @ TB] : ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',fact_230_prod__cases6) ).
thf(303,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)],[59]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_236_prod__induct7) ).
thf(271,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)],[46]) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',fact_232_prod__induct3) ).
thf(323,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)],[67]) ).
thf(11,axiom,
! [A: stream @ rule] :
( ( abstra928354080m_fair @ rule @ rules @ A )
=> ( abstra928354080m_fair @ rule @ rules @ ( stl @ rule @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_fair__stl) ).
thf(140,plain,
! [A: stream @ rule] :
( ( abstra928354080m_fair @ rule @ rules @ A )
=> ( abstra928354080m_fair @ rule @ rules @ ( stl @ rule @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',fact_226_Pair__inject) ).
thf(240,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)],[41]) ).
thf(29,axiom,
! [A: stream @ rule,B: state] :
( ( abstra1749095923e_cont @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ A @ B ) )
= ( fimage @ state @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ A @ B ) ) ) @ ( abstra1276541928ickEff @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_mkTree_Osimps_I2_J) ).
thf(198,plain,
! [A: stream @ rule,B: state] :
( ( abstra1749095923e_cont @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ A @ B ) )
= ( fimage @ state @ ( abstra2103299360e_tree @ ( product_prod @ state @ rule ) ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( stl @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ A @ B ) ) ) @ ( abstra1276541928ickEff @ rule @ state @ eff @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(91,axiom,
! [A: state,B: rule,C: fset @ state,D: state] :
( ( member @ state @ A @ s )
=> ( ( member @ rule @ B @ ( sset @ rule @ rules ) )
=> ( ( eff @ B @ A @ C )
=> ( ( fmember @ state @ D @ C )
=> ( member @ state @ D @ s ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_eff__S) ).
thf(399,plain,
! [A: state,B: rule,C: fset @ state,D: state] :
( ( member @ state @ A @ s )
=> ( ( member @ rule @ B @ ( sset @ rule @ rules ) )
=> ( ( eff @ B @ A @ C )
=> ( ( fmember @ state @ D @ C )
=> ( member @ state @ D @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA,C: fset @ TA] :
( ( A = B )
=> ( ( fmember @ TA @ A @ C )
= ( fmember @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_eqfelem__imp__iff) ).
thf(306,plain,
! [TA: $tType,A: TA,B: TA,C: fset @ TA] :
( ( A = B )
=> ( ( fmember @ TA @ A @ C )
= ( fmember @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_234_prod__induct5) ).
thf(299,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)],[57]) ).
thf(108,axiom,
! [A: state,B: nat] :
( ( member @ state @ A @ s )
=> ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( sdrop @ rule @ B @ rsa ) @ A ) @ ( sdrop @ ( product_prod @ state @ rule ) @ ma @ stepsa ) )
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(438,plain,
! [A: state,B: nat] :
( ( member @ state @ A @ s )
=> ( ( abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ ( sdrop @ rule @ B @ rsa ) @ A ) @ ( sdrop @ ( product_prod @ state @ rule ) @ ma @ stepsa ) )
=> thesis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(19,axiom,
! [TA: $tType,A: ( stream @ TA ) > ( stream @ TA ) > $o,B: stream @ TA,C: stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: stream @ TA,E: stream @ TA] :
( ( A @ D @ E )
=> ( ( ( shd @ TA @ D )
= ( shd @ TA @ E ) )
& ( ( A @ ( stl @ TA @ D ) @ ( stl @ TA @ E ) )
| ( ( stl @ TA @ D )
= ( stl @ TA @ E ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_stream_Ocoinduct__strong) ).
thf(162,plain,
! [TA: $tType,A: ( stream @ TA ) > ( stream @ TA ) > $o,B: stream @ TA,C: stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: stream @ TA,E: stream @ TA] :
( ( A @ D @ E )
=> ( ( ( shd @ TA @ D )
= ( shd @ TA @ E ) )
& ( ( A @ ( stl @ TA @ D ) @ ( stl @ TA @ E ) )
| ( ( stl @ TA @ D )
= ( stl @ TA @ E ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(77,axiom,
! [A: nat,B: stream @ rule,C: state] :
( ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ A @ B ) ) @ C )
=> ( ord_less_eq @ nat @ ( abstra1332369113inWait @ rule @ state @ eff @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_minWait__least) ).
thf(355,plain,
! [A: nat,B: stream @ rule,C: state] :
( ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ A @ B ) ) @ C )
=> ( ord_less_eq @ nat @ ( abstra1332369113inWait @ rule @ state @ eff @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(13,axiom,
! [TA: $tType,A: stream @ TA,B: stream @ TA] :
( ( ( ( shd @ TA @ A )
= ( shd @ TA @ B ) )
& ( ( stl @ TA @ A )
= ( stl @ TA @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_stream_Oexpand) ).
thf(145,plain,
! [TA: $tType,A: stream @ TA,B: stream @ TA] :
( ( ( ( shd @ TA @ A )
= ( shd @ TA @ B ) )
& ( ( stl @ TA @ A )
= ( stl @ TA @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: stream @ TB,C: TB > TA > ( fset @ TA ) > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TB] :
( ( member @ TB @ E @ ( sset @ TB @ B ) )
=> ! [F: fset @ TA] :
( ( C @ E @ D @ F )
=> ! [G: TA] :
( ( fmember @ TA @ G @ F )
=> ( member @ TA @ G @ A ) ) ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ ( sset @ TB @ B ) )
& ? [F: fset @ TA] : ( C @ E @ D @ F ) ) )
=> ( abstra1326562878System @ TB @ TA @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_RuleSystem_Ointro) ).
thf(263,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: stream @ TB,C: TB > TA > ( fset @ TA ) > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TB] :
( ( member @ TB @ E @ ( sset @ TB @ B ) )
=> ! [F: fset @ TA] :
( ( C @ E @ D @ F )
=> ! [G: TA] :
( ( fmember @ TA @ G @ F )
=> ( member @ TA @ G @ A ) ) ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ ( sset @ TB @ B ) )
& ? [F: fset @ TA] : ( C @ E @ D @ F ) ) )
=> ( abstra1326562878System @ TB @ TA @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(61,axiom,
! [TA: $tType,A: stream @ TA] : ( member @ TA @ ( shd @ TA @ A ) @ ( sset @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_shd__sset) ).
thf(310,plain,
! [TA: $tType,A: stream @ TA] : ( member @ TA @ ( shd @ TA @ A ) @ ( sset @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_228_prod__cases4) ).
thf(338,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)],[71]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: TA,C: fset @ TA] :
( ( A = B )
=> ( ( fmember @ TA @ B @ C )
=> ( fmember @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_eq__fmem__trans) ).
thf(359,plain,
! [TA: $tType,A: TA,B: TA,C: fset @ TA] :
( ( A = B )
=> ( ( fmember @ TA @ B @ C )
=> ( fmember @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(23,axiom,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: stream @ TA] :
( ( abstra313004635_ipath @ TA @ A @ B )
=> ~ ( ( ( abstra573067619e_root @ TA @ A )
= ( shd @ TA @ B ) )
=> ! [C: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ C @ ( abstra1749095923e_cont @ TA @ A ) )
=> ~ ( abstra313004635_ipath @ TA @ C @ ( stl @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_ipath_Ocases) ).
thf(177,plain,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: stream @ TA] :
( ( abstra313004635_ipath @ TA @ A @ B )
=> ~ ( ( ( abstra573067619e_root @ TA @ A )
= ( shd @ TA @ B ) )
=> ! [C: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ C @ ( abstra1749095923e_cont @ TA @ A ) )
=> ~ ( abstra313004635_ipath @ TA @ C @ ( stl @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(24,axiom,
! [TA: $tType,A: stream @ TA,B: stream @ TA] :
( ( abstra928354080m_fair @ TA @ A @ B )
=> ( abstra928354080m_fair @ TA @ A @ ( stl @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_RuleSystem__Defs_Ofair__stl) ).
thf(182,plain,
! [TA: $tType,A: stream @ TA,B: stream @ TA] :
( ( abstra928354080m_fair @ TA @ A @ B )
=> ( abstra928354080m_fair @ TA @ A @ ( stl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(16,axiom,
! [TA: $tType] :
( ( abstra313004635_ipath @ TA )
= ( ^ [A: abstra2103299360e_tree @ TA,B: stream @ TA] :
? [C: abstra2103299360e_tree @ TA,D: stream @ TA,E: abstra2103299360e_tree @ TA] :
( ( A = C )
& ( B = D )
& ( ( abstra573067619e_root @ TA @ C )
= ( shd @ TA @ D ) )
& ( fmember @ ( abstra2103299360e_tree @ TA ) @ E @ ( abstra1749095923e_cont @ TA @ C ) )
& ( abstra313004635_ipath @ TA @ E @ ( stl @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ipath_Osimps) ).
thf(154,plain,
! [TA: $tType] :
( ( abstra313004635_ipath @ TA )
= ( ^ [A: abstra2103299360e_tree @ TA,B: stream @ TA] :
? [C: abstra2103299360e_tree @ TA,D: stream @ TA,E: abstra2103299360e_tree @ TA] :
( ( A = C )
& ( B = D )
& ( ( abstra573067619e_root @ TA @ C )
= ( shd @ TA @ D ) )
& ( fmember @ ( abstra2103299360e_tree @ TA ) @ E @ ( abstra1749095923e_cont @ TA @ C ) )
& ( abstra313004635_ipath @ TA @ E @ ( stl @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(63,axiom,
( ( sset @ rule @ ( abstra1774373515_fenum @ rule @ rules ) )
= ( sset @ rule @ rules ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_sset__fenum) ).
thf(314,plain,
( ( sset @ rule @ ( abstra1774373515_fenum @ rule @ rules ) )
= ( sset @ rule @ rules ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(37,axiom,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: abstra2103299360e_tree @ TA] :
( ( ( ( abstra573067619e_root @ TA @ A )
= ( abstra573067619e_root @ TA @ B ) )
& ( ( abstra1749095923e_cont @ TA @ A )
= ( abstra1749095923e_cont @ TA @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_tree_Oexpand) ).
thf(231,plain,
! [TA: $tType,A: abstra2103299360e_tree @ TA,B: abstra2103299360e_tree @ TA] :
( ( ( ( abstra573067619e_root @ TA @ A )
= ( abstra573067619e_root @ TA @ B ) )
& ( ( abstra1749095923e_cont @ TA @ A )
= ( abstra1749095923e_cont @ TA @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB,D: TB,E: stream @ TA] :
( ( abstra1326562878System @ TA @ TB @ A @ B @ C )
=> ( ( member @ TB @ D @ C )
=> ( ( abstra928354080m_fair @ TA @ B @ E )
=> ( ( abstra1259602206m_trim @ TA @ TB @ A @ E @ D )
= ( sdrop @ TA @ ( abstra1332369113inWait @ TA @ TB @ A @ E @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_RuleSystem_Otrim__alt) ).
thf(363,plain,
! [TA: $tType,TB: $tType,A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB,D: TB,E: stream @ TA] :
( ( abstra1326562878System @ TA @ TB @ A @ B @ C )
=> ( ( member @ TB @ D @ C )
=> ( ( abstra928354080m_fair @ TA @ B @ E )
=> ( ( abstra1259602206m_trim @ TA @ TB @ A @ E @ D )
= ( sdrop @ TA @ ( abstra1332369113inWait @ TA @ TB @ A @ E @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB,D: TB,E: stream @ TA] :
( ( abstra1326562878System @ TA @ TB @ A @ B @ C )
=> ( ( member @ TB @ D @ C )
=> ( ( abstra928354080m_fair @ TA @ B @ E )
=> ( member @ TA @ ( shd @ TA @ ( abstra1259602206m_trim @ TA @ TB @ A @ E @ D ) ) @ ( sset @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_RuleSystem_Otrim__in__R) ).
thf(319,plain,
! [TA: $tType,TB: $tType,A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB,D: TB,E: stream @ TA] :
( ( abstra1326562878System @ TA @ TB @ A @ B @ C )
=> ( ( member @ TB @ D @ C )
=> ( ( abstra928354080m_fair @ TA @ B @ E )
=> ( member @ TA @ ( shd @ TA @ ( abstra1259602206m_trim @ TA @ TB @ A @ E @ D ) ) @ ( sset @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: fset @ TA] :
( ( fmember @ TB @ A @ ( fimage @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( fmember @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_fimageE) ).
thf(114,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: fset @ TA] :
( ( fmember @ TB @ A @ ( fimage @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( fmember @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(99,axiom,
abstra928354080m_fair @ rule @ rules @ rsa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Suc_Oprems_I2_J) ).
thf(418,plain,
abstra928354080m_fair @ rule @ rules @ rsa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: TB,F: fset @ TA,G: TA] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( member @ TB @ E @ ( sset @ TB @ B ) )
=> ( ( A @ E @ D @ F )
=> ( ( fmember @ TA @ G @ F )
=> ( member @ TA @ G @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_RuleSystem_Oeff__S) ).
thf(235,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: TB,F: fset @ TA,G: TA] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( member @ TB @ E @ ( sset @ TB @ B ) )
=> ( ( A @ E @ D @ F )
=> ( ( fmember @ TA @ G @ F )
=> ( member @ TA @ G @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB,D: stream @ TA,E: TB] :
( ( abstra1326562878System @ TA @ TB @ A @ B @ C )
=> ( ( abstra1332369113inWait @ TA @ TB @ A @ D @ E )
= ( ord_Least @ nat
@ ^ [F: nat] : ( abstra1874422341nabled @ TA @ TB @ A @ ( shd @ TA @ ( sdrop @ TA @ F @ D ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_RuleSystem_OminWait__def) ).
thf(207,plain,
! [TA: $tType,TB: $tType,A: TA > TB > ( fset @ TB ) > $o,B: stream @ TA,C: set @ TB,D: stream @ TA,E: TB] :
( ( abstra1326562878System @ TA @ TB @ A @ B @ C )
=> ( ( abstra1332369113inWait @ TA @ TB @ A @ D @ E )
= ( ord_Least @ nat
@ ^ [F: nat] : ( abstra1874422341nabled @ TA @ TB @ A @ ( shd @ TA @ ( sdrop @ TA @ F @ D ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_old_Oprod_Oexhaust) ).
thf(346,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)],[74]) ).
thf(15,axiom,
! [TA: $tType] :
( ( abstra668420080finite @ TA )
= ( ^ [A: abstra2103299360e_tree @ TA] :
? [B: abstra2103299360e_tree @ TA] :
( ( A = B )
& ! [C: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ C @ ( abstra1749095923e_cont @ TA @ B ) )
=> ( abstra668420080finite @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_tfinite_Osimps) ).
thf(151,plain,
! [TA: $tType] :
( ( abstra668420080finite @ TA )
= ( ^ [A: abstra2103299360e_tree @ TA] :
? [B: abstra2103299360e_tree @ TA] :
( ( A = B )
& ! [C: abstra2103299360e_tree @ TA] :
( ( fmember @ ( abstra2103299360e_tree @ TA ) @ C @ ( abstra1749095923e_cont @ TA @ B ) )
=> ( abstra668420080finite @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(106,axiom,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ? [C: nat] : ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_minWait__ex) ).
thf(432,plain,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ? [C: nat] : ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_pred__equals__eq2) ).
thf(410,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: nat,B: stream @ TB,C: stream @ TA] :
( ( sdrop @ ( product_prod @ TB @ TA ) @ A @ ( szip @ TB @ TA @ B @ C ) )
= ( szip @ TB @ TA @ ( sdrop @ TB @ A @ B ) @ ( sdrop @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_sdrop__szip) ).
thf(405,plain,
! [TA: $tType,TB: $tType,A: nat,B: stream @ TB,C: stream @ TA] :
( ( sdrop @ ( product_prod @ TB @ TA ) @ A @ ( szip @ TB @ TA @ B @ C ) )
= ( szip @ TB @ TA @ ( sdrop @ TB @ A @ B ) @ ( sdrop @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(101,axiom,
abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ rs @ s2 ) @ steps,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_i) ).
thf(422,plain,
abstra313004635_ipath @ ( product_prod @ state @ rule ) @ ( abstra1225283448mkTree @ rule @ state @ eff @ rs @ s2 ) @ steps,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(47,axiom,
abstra928354080m_fair @ rule @ rules @ rs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_rs) ).
thf(273,plain,
abstra928354080m_fair @ rule @ rules @ rs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: stream @ TB,F: abstra2103299360e_tree @ ( product_prod @ TA @ TB )] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( abstra928354080m_fair @ TB @ B @ E )
=> ( ( fmember @ ( abstra2103299360e_tree @ ( product_prod @ TA @ TB ) ) @ F @ ( abstra1749095923e_cont @ ( product_prod @ TA @ TB ) @ ( abstra1225283448mkTree @ TB @ TA @ A @ E @ D ) ) )
=> ? [G: fset @ TA,H: TA] :
( ( member @ TA @ H @ C )
& ( A @ ( shd @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ E @ D ) ) @ D @ G )
& ( fmember @ TA @ H @ G )
& ( F
= ( abstra1225283448mkTree @ TB @ TA @ A @ ( stl @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ E @ D ) ) @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_RuleSystem_Oin__cont__mkTree) ).
thf(210,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA,E: stream @ TB,F: abstra2103299360e_tree @ ( product_prod @ TA @ TB )] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( abstra928354080m_fair @ TB @ B @ E )
=> ( ( fmember @ ( abstra2103299360e_tree @ ( product_prod @ TA @ TB ) ) @ F @ ( abstra1749095923e_cont @ ( product_prod @ TA @ TB ) @ ( abstra1225283448mkTree @ TB @ TA @ A @ E @ D ) ) )
=> ? [G: fset @ TA,H: TA] :
( ( member @ TA @ H @ C )
& ( A @ ( shd @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ E @ D ) ) @ D @ G )
& ( fmember @ TA @ H @ G )
& ( F
= ( abstra1225283448mkTree @ TB @ TA @ A @ ( stl @ TB @ ( abstra1259602206m_trim @ TB @ TA @ A @ E @ D ) ) @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(72,axiom,
! [A: stream @ rule,B: state] :
( ( abstra1259602206m_trim @ rule @ state @ eff @ A @ B )
= ( sdrop_while @ rule
@ ^ [C: rule] :
~ ( abstra1874422341nabled @ rule @ state @ eff @ C @ B )
@ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_trim__def) ).
thf(341,plain,
! [A: stream @ rule,B: state] :
( ( abstra1259602206m_trim @ rule @ state @ eff @ A @ B )
= ( sdrop_while @ rule
@ ^ [C: rule] :
~ ( abstra1874422341nabled @ rule @ state @ eff @ C @ B )
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(51,axiom,
! [A: stream @ rule,B: state] :
( ( abstra1332369113inWait @ rule @ state @ eff @ A @ B )
= ( ord_Least @ nat
@ ^ [C: nat] : ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_minWait__def) ).
thf(283,plain,
! [A: stream @ rule,B: state] :
( ( abstra1332369113inWait @ rule @ state @ eff @ A @ B )
= ( ord_Least @ nat
@ ^ [C: nat] : ( abstra1874422341nabled @ rule @ state @ eff @ ( shd @ rule @ ( sdrop @ rule @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',fact_203_ssubst__Pair__rhs) ).
thf(395,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)],[90]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ? [E: TB] :
( ( member @ TB @ E @ ( sset @ TB @ B ) )
& ? [F: fset @ TA] : ( A @ E @ D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_RuleSystem_Oenabled__R) ).
thf(332,plain,
! [TA: $tType,TB: $tType,A: TB > TA > ( fset @ TA ) > $o,B: stream @ TB,C: set @ TA,D: TA] :
( ( abstra1326562878System @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ? [E: TB] :
( ( member @ TB @ E @ ( sset @ TB @ B ) )
& ? [F: fset @ TA] : ( A @ E @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(103,axiom,
abstra1326562878System @ rule @ state @ eff @ rules @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_RuleSystem__axioms) ).
thf(427,plain,
abstra1326562878System @ rule @ state @ eff @ rules @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(8,axiom,
! [TA: $tType,A: fset @ TA] :
( ( fimage @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_fset_Omap__ident) ).
thf(131,plain,
! [TA: $tType,A: fset @ TA] :
( ( fimage @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',fact_225_prod__cases) ).
thf(277,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)],[49]) ).
thf(82,axiom,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( member @ rule @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) @ ( sset @ rule @ rules ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_trim__in__R) ).
thf(369,plain,
! [A: state,B: stream @ rule] :
( ( member @ state @ A @ s )
=> ( ( abstra928354080m_fair @ rule @ rules @ B )
=> ( member @ rule @ ( shd @ rule @ ( abstra1259602206m_trim @ rule @ state @ eff @ B @ A ) ) @ ( sset @ rule @ rules ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(441,plain,
$false,
inference(e,[status(thm)],[138,234,352,408,379,385,142,288,301,174,404,184,372,110,344,357,157,416,325,316,261,216,321,121,221,293,428,312,248,201,366,349,429,229,435,388,169,109,124,193,134,237,148,279,296,375,423,286,291,118,204,413,191,402,391,382,335,159,187,172,274,419,245,303,271,323,140,240,198,399,306,299,438,162,355,145,263,310,338,359,177,182,154,314,231,363,319,114,418,235,207,346,151,432,410,405,422,273,210,341,283,395,332,427,131,277,369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : COM156^1 : TPTP v8.1.2. Released v7.0.0.
% 0.16/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n015.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 6 16:48:39 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.84/1.16 % [INFO] Parsing done (270ms).
% 2.03/1.17 % [INFO] Running in sequential loop mode.
% 2.66/1.39 % [INFO] eprover registered as external prover.
% 2.66/1.39 % [INFO] cvc4 registered as external prover.
% 2.66/1.39 % [INFO] Scanning for conjecture ...
% 2.91/1.49 % [INFO] Found a conjecture and 299 axioms. Running axiom selection ...
% 3.26/1.59 % [INFO] Axiom selection finished. Selected 106 axioms (removed 193 axioms).
% 3.89/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 3.99/1.77 % [INFO] Type checking passed.
% 3.99/1.77 % [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 ...
% 138.13/102.93 % External prover 'e' found a proof!
% 138.13/102.93 % [INFO] Killing All external provers ...
% 138.13/102.93 % Time passed: 102381ms (effective reasoning time: 101757ms)
% 138.13/102.93 % 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)>
% 138.13/102.93 % Axioms used in derivation (106): fact_79_tfinite_Osimps, fact_221_prod_Oinject, fact_61_RuleSystem__Defs_Osset__fenum, fact_78_tfinite_Ocases, fact_226_Pair__inject, fact_53_sdrop__stl, fact_128_ipath_Ointros, fact_12_trim__alt, fact_16_pickEff, fact_63_RuleSystem__Defs_Otrim__def, fact_229_prod__cases5, fact_33_Saturated__def, fact_143_fimage__eqI, fact_20_sset__fenum, fact_6_Suc_Oprems_I3_J, fact_81_tfinite, fact_231_prod__cases7, fact_22_shd__sset, fact_194_mkTree_Osimps_I1_J, fact_59_RuleSystem__def, fact_35_minWait__least, fact_29_RuleSystem__Defs_Oenabled__def, fact_182_eqfelem__imp__iff, fact_187_fset__choice, fact_207_szip_Osimps_I1_J, fact_10_trim__fair, fact_34_minWait__def, fact_238_old_Oprod_Oinducts, fact_5_sdrop__fair, fact_181_tree_Oexpand, fact_149_rev__fimage__eqI, fact_51_stl__sset, fact_62_RuleSystem__Defs_Ofair__fenum, fact_241_pred__equals__eq2, fact_209_RuleSystem__Defs_OmkTree_Osimps_I1_J, fact_57_RuleSystem_Ointro, fact_3_i, fact_41_RuleSystem_OminWait__least, fact_27_RuleSystem__Defs_OpickEff, fact_186_eq__fmem__trans, fact_235_prod__induct6, fact_127_ipath_Osimps, fact_9_RuleSystem__Defs_Osdrop__fair, fact_126_ipath_Ocases, fact_38_RuleSystem_OminWait__def, fact_254_ex__has__least__nat, fact_225_prod__cases, fact_54_RuleSystem__Defs_Ofair__stl, fact_14_minWait__ex, fact_220_old_Oprod_Oinject, fact_56_sset__induct, fact_24_RuleSystem_Otrim__fair, fact_23_RuleSystem_Oenabled__R, fact_159_fimage__cong, fact_2_Suc_Oprems_I2_J, fact_234_prod__induct5, fact_188_fequalityCE, fact_30_RuleSystem_Otrim__alt, fact_58_RuleSystem_Oeff__S, fact_179_fimage__fimage, fact_11_enabled__R, fact_142_fset_Omap__ident, fact_4_RuleSystem__axioms, fact_60_RuleSystem__Defs_OSaturated__def, fact_17_ftree__no__ipath, fact_44_stream_Ocoinduct__strong, fact_40_fair__stl, fact_130_RuleSystem__Defs_OmkTree_Osimps_I2_J, fact_227_prod__cases3, fact_7_enabled__def, fact_28_RuleSystem_OminWait__ex, fact_8_Suc_Ohyps, fact_1_rs, fact_236_prod__induct7, fact_67_RuleSystem_Oin__cont__mkTree, fact_19_trim__enabled, fact_141_fimage__ident, fact_185_eqfset__imp__iff, fact_232_prod__induct3, fact_65_in__cont__mkTree, fact_173_fimageI, fact_21_fair__fenum, fact_26_RuleSystem_Otrim__enabled, fact_32_trim__def, fact_124_mkTree_Osimps_I2_J, fact_80_tfinite_Oinducts, fact_25_RuleSystem_Otrim__in__R, fact_31_RuleSystem__Defs_Owf__ipath__epath, fact_228_prod__cases4, fact_224_surj__pair, fact_49_stream_Ocoinduct, fact_42_szip_Osimps_I2_J, fact_0_s, fact_203_ssubst__Pair__rhs, conj_0, fact_129_ipath_Ocoinduct, fact_36_eff__S, fact_13_sdrop__szip, fact_189_fset__eqI, fact_15_wf__ipath__epath, fact_174_fimageE, fact_18_trim__in__R, fact_237_old_Oprod_Oexhaust, fact_50_stream_Oexpand, fact_233_prod__induct4, fact_230_prod__cases6
% 138.13/102.93 % No. of inferences in proof: 216
% 138.13/102.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 102381 ms resp. 101757 ms w/o parsing
% 138.77/103.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 138.77/103.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------