TSTP Solution File: ITP142^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP142^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 07:48:11 EDT 2024
% Result : Theorem 150.89s 131.02s
% Output : Refutation 151.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 314
% Syntax : Number of formulae : 580 ( 212 unt; 50 typ; 0 def)
% Number of atoms : 3364 ( 726 equ; 2 cnn)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 14245 ( 304 ~; 42 |; 134 &;13061 @)
% ( 0 <=>; 704 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 411 ( 411 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 11 con; 0-5 aty)
% Number of variables : 2679 ( 14 ^2532 !; 92 ?;2679 :)
% ( 41 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(state_type,type,
state: $tType ).
thf(com_type,type,
com: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(bind_type,type,
bind:
!>[TA: $tType,TB: $tType] : ( ( list @ TB ) > ( TB > ( list @ TA ) ) > ( list @ TA ) ) ).
thf(butlast_type,type,
butlast:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(concat_type,type,
concat:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(last_type,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(lenlex_type,type,
lenlex:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) ) ).
thf(lex_type,type,
lex:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) ) ).
thf(lexord_type,type,
lexord:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(list_update_type,type,
list_update:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA > ( list @ TA ) ) ).
thf(listrel_type,type,
listrel:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) ) ) ).
thf(listrel1_type,type,
listrel1:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) ) ).
thf(maps_type,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( TB > ( list @ TA ) ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(measures_type,type,
measures:
!>[TA: $tType] : ( ( list @ ( TA > nat ) ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(nth_type,type,
nth:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA ) ).
thf(product_lists_type,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(rotate1_type,type,
rotate1:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(subseqs_type,type,
subseqs:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(take_type,type,
take:
!>[TA: $tType] : ( nat > ( list @ TA ) > ( list @ TA ) ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(pHoare1053570893_exec1_type,type,
pHoare1053570893_exec1: set @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) ).
thf(pHoare1053570959_execs_type,type,
pHoare1053570959_execs: state > ( list @ com ) > state > $o ).
thf(pHoare1335526537termis_type,type,
pHoare1335526537termis: ( list @ com ) > state > $o ).
thf(cond_type,type,
cond: ( state > $o ) > com > com > com ).
thf(do_type,type,
do: ( state > ( set @ state ) ) > com ).
thf(semi_type,type,
semi: com > com > com ).
thf(while_type,type,
while: ( state > $o ) > com > com ).
thf(exec_type,type,
exec: state > com > state > $o ).
thf(termi_type,type,
termi: com > state > $o ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(produc2004651681e_prod_type,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_prod_type,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(irrefl_type,type,
irrefl:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(transitive_rtrancl_type,type,
transitive_rtrancl:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(c_type,type,
c: com ).
thf(c2_type,type,
c2: com ).
thf(cs_type,type,
cs: list @ com ).
thf(s_type,type,
s: state ).
thf(s2_type,type,
s2: state ).
thf(29,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_append__is__Nil__conv) ).
thf(347,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(259,axiom,
! [A: state > $o,B: state,C: com] :
( ( A @ B )
=> ( ( termi @ C @ B )
=> ( ! [D: state] :
( ( exec @ B @ C @ D )
=> ( termi @ ( while @ A @ C ) @ D ) )
=> ( termi @ ( while @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_termi_OWhileTrue) ).
thf(1237,plain,
! [A: state > $o,B: state,C: com] :
( ( A @ B )
=> ( ( termi @ C @ B )
=> ( ! [D: state] :
( ( exec @ B @ C @ D )
=> ( termi @ ( while @ A @ C ) @ D ) )
=> ( termi @ ( while @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(168,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_strict__sorted_Oinduct) ).
thf(893,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(188,axiom,
! [TA: $tType] :
( ( concat @ TA @ ( nil @ ( list @ TA ) ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_concat_Osimps_I1_J) ).
thf(962,plain,
! [TA: $tType] :
( ( concat @ TA @ ( nil @ ( list @ TA ) ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(6,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: TA] :
( ( size_size @ ( list @ TA ) @ ( list_update @ TA @ A @ B @ C ) )
= ( size_size @ ( list @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_length__list__update) ).
thf(276,plain,
! [TA: $tType,A: list @ TA,B: nat,C: TA] :
( ( size_size @ ( list @ TA ) @ ( list_update @ TA @ A @ B @ C ) )
= ( size_size @ ( list @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(223,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_list_OdiscI) ).
thf(1068,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(199,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ B ) @ ( append @ TA @ A @ C ) ) @ ( lexord @ TA @ D ) )
=> ( ! [E: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ E ) @ D )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ C ) @ ( lexord @ TA @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_lexord__append__leftD) ).
thf(994,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ B ) @ ( append @ TA @ A @ C ) ) @ ( lexord @ TA @ D ) )
=> ( ! [E: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ E ) @ D )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ C ) @ ( lexord @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(157,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA] :
( ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ A )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ B ) @ ( lexord @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_lexord__irreflexive) ).
thf(861,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA] :
( ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ A )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ B ) @ ( lexord @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(162,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_71_prod__induct7) ).
thf(878,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)],[162]) ).
thf(58,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lex @ TA @ C ) )
=> ~ ! [D: nat] :
( ( ord_less @ nat @ D @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( ord_less @ nat @ D @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ( take @ TA @ D @ A )
= ( take @ TA @ D @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( nth @ TA @ A @ D ) @ ( nth @ TA @ B @ D ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_lex__take__index) ).
thf(440,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lex @ TA @ C ) )
=> ~ ! [D: nat] :
( ( ord_less @ nat @ D @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( ord_less @ nat @ D @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ( take @ TA @ D @ A )
= ( take @ TA @ D @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( nth @ TA @ A @ D ) @ ( nth @ TA @ B @ D ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA > TA > $o] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ! [E: TA] : ( D @ E @ E )
=> ( ! [E: TA,F: TA,G: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( D @ E @ F )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ G ) @ C )
=> ( D @ E @ G ) ) ) )
=> ( D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_rtrancl_Oinducts) ).
thf(511,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA > TA > $o] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ! [E: TA] : ( D @ E @ E )
=> ( ! [E: TA,F: TA,G: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( D @ E @ F )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ G ) @ C )
=> ( D @ E @ G ) ) ) )
=> ( D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(227,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rtrancl__trans) ).
thf(1078,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_bind__simps_I2_J) ).
thf(384,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(141,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA,D: list @ TA] :
( ! [E: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ E ) @ A )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) ) @ ( lex @ TA @ A ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ D ) @ ( lex @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_lex__append__leftD) ).
thf(797,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA,D: list @ TA] :
( ! [E: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ E ) @ A )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) ) @ ( lex @ TA @ A ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ D ) @ ( lex @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(67,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lex @ TA @ C ) )
=> ( ( ( size_size @ ( list @ TA ) @ D )
= ( size_size @ ( list @ TA ) @ E ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ E ) @ ( append @ TA @ B @ D ) ) @ ( lex @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_lex__append__rightI) ).
thf(472,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lex @ TA @ C ) )
=> ( ( ( size_size @ ( list @ TA ) @ D )
= ( size_size @ ( list @ TA ) @ E ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ E ) @ ( append @ TA @ B @ D ) ) @ ( lex @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(257,axiom,
member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ s ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c2 @ cs ) @ s2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1233,plain,
member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ s ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c2 @ cs ) @ s2 ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(179,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A )
=> ( irrefl @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_irreflI) ).
thf(930,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A )
=> ( irrefl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(150,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_29_prod__cases) ).
thf(841,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)],[150]) ).
thf(10,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_list__eq__iff__nth__eq) ).
thf(288,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(85,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_listrel1__eq__len) ).
thf(565,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(106,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( B != A )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rtrancl_Ocases) ).
thf(651,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( B != A )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(146,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ A ) @ ( listrel @ TB @ TA @ B ) )
=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_listrel__Nil1) ).
thf(829,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ A ) @ ( listrel @ TB @ TA @ B ) )
=> ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(231,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_16_prod__cases3) ).
thf(1095,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)],[231]) ).
thf(46,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_3) ).
thf(404,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(192,axiom,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ( ! [B: TA > TA > $o,C: TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_successively_Ocases) ).
thf(973,plain,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ( ! [B: TA > TA > $o,C: TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(165,axiom,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: list @ TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_shuffles_Ocases) ).
thf(885,plain,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: list @ TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(216,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA,D: list @ TA] :
( ( irrefl @ TA @ A )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) ) @ ( lenlex @ TA @ A ) )
= ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ D ) @ ( lenlex @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_lenlex__append2) ).
thf(1046,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA,D: list @ TA] :
( ( irrefl @ TA @ A )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) ) @ ( lenlex @ TA @ A ) )
= ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ D ) @ ( lenlex @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(219,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_15_old_Oprod_Oinject) ).
thf(1055,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)],[219]) ).
thf(123,axiom,
! [TA: $tType] :
( ( irrefl @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_irrefl__def) ).
thf(719,plain,
! [TA: $tType] :
( ( irrefl @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(137,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_min__list_Ocases) ).
thf(785,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(149,axiom,
! [A: state > $o,B: state,C: com] :
( ~ ( A @ B )
=> ( exec @ B @ ( while @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_exec_OWhileFalse) ).
thf(838,plain,
! [A: state > $o,B: state,C: com] :
( ~ ( A @ B )
=> ( exec @ B @ ( while @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(175,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_last__ConsR) ).
thf(917,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(28,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ ( butlast @ TA @ B ) ) )
=> ( ( nth @ TA @ ( butlast @ TA @ B ) @ A )
= ( nth @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_nth__butlast) ).
thf(344,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ ( butlast @ TA @ B ) ) )
=> ( ( nth @ TA @ ( butlast @ TA @ B ) @ A )
= ( nth @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(169,axiom,
! [TA: $tType,A: TA,B: set @ ( product_prod @ TA @ TA )] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( transitive_rtrancl @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_rtrancl_Ortrancl__refl) ).
thf(902,plain,
! [TA: $tType,A: TA,B: set @ ( product_prod @ TA @ TA )] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( transitive_rtrancl @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(155,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_list_Oexhaust) ).
thf(853,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(229,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
= ( ? [D: TA] :
( ( A = D )
& ( B = D ) )
| ? [D: TA,E: TA,F: TA] :
( ( A = D )
& ( B = F )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ ( transitive_rtrancl @ TA @ C ) )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_rtrancl_Osimps) ).
thf(1087,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
= ( ? [D: TA] :
( ( A = D )
& ( B = D ) )
| ? [D: TA,E: TA,F: TA] :
( ( A = D )
& ( B = F )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ ( transitive_rtrancl @ TA @ C ) )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(53,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_last__append) ).
thf(421,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(68,axiom,
ord @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_1) ).
thf(475,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(71,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_transpose_Ocases) ).
thf(492,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ D ) @ ( cons @ TA @ B @ D ) ) @ ( listrel1 @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_listrel1I1) ).
thf(591,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ D ) @ ( cons @ TA @ B @ D ) ) @ ( listrel1 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(20,axiom,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( rotate1 @ TA @ A ) )
= ( size_size @ ( list @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_length__rotate1) ).
thf(321,plain,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( rotate1 @ TA @ A ) )
= ( size_size @ ( list @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(102,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lexord @ TA @ B ) )
= ( ? [C: TA,D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_lexord__Nil__left) ).
thf(623,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lexord @ TA @ B ) )
= ( ? [C: TA,D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(31,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( B
= ( append @ TA @ E @ C ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( last @ TA @ D )
!= ( last @ TA @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_longest__common__suffix) ).
thf(353,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( B
= ( append @ TA @ E @ C ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( last @ TA @ D )
!= ( last @ TA @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(70,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A != B )
=> ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ? [C: list @ TA,D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( D != F )
& ( A
= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ D @ ( nil @ TA ) ) @ E ) ) )
& ( B
= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ F @ ( nil @ TA ) ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_same__length__different) ).
thf(485,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A != B )
=> ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ? [C: list @ TA,D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( D != F )
& ( A
= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ D @ ( nil @ TA ) ) @ E ) ) )
& ( B
= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ F @ ( nil @ TA ) ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(238,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_27_old_Oprod_Oexhaust) ).
thf(1136,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)],[238]) ).
thf(207,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_rotate1__is__Nil__conv) ).
thf(1020,plain,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(88,axiom,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_list__ex1__simps_I1_J) ).
thf(574,plain,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(132,axiom,
! [A: state,B: state > ( set @ state ),C: state] :
( ( member @ state @ A @ ( B @ C ) )
=> ( exec @ C @ ( do @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_exec_ODo) ).
thf(766,plain,
! [A: state,B: state > ( set @ state ),C: state] :
( ( member @ state @ A @ ( B @ C ) )
=> ( exec @ C @ ( do @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(244,axiom,
! [A: state] : ( pHoare1335526537termis @ ( nil @ com ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_termis_Osimps_I1_J) ).
thf(1169,plain,
! [A: state] : ( pHoare1335526537termis @ ( nil @ com ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(118,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ E ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ D ) @ ( cons @ TA @ B @ E ) ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_rtrancl__listrel1__ConsI2) ).
thf(692,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ E ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ D ) @ ( cons @ TA @ B @ E ) ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_maps__simps_I2_J) ).
thf(866,plain,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(135,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_rev__nonempty__induct) ).
thf(774,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(43,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( irrefl @ TA @ A )
=> ( irrefl @ ( list @ TA ) @ ( lex @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_irrefl__lex) ).
thf(396,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( irrefl @ TA @ A )
=> ( irrefl @ ( list @ TA ) @ ( lex @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(201,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ C ) @ ( listrel1 @ TA @ D ) )
=> ( ! [E: TA] :
( ( C
= ( cons @ TA @ E @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ E ) @ D ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ A @ E ) )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ E ) @ ( listrel1 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Cons__listrel1E1) ).
thf(998,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ C ) @ ( listrel1 @ TA @ D ) )
=> ( ! [E: TA] :
( ( C
= ( cons @ TA @ E @ B ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ E ) @ D ) )
=> ~ ! [E: list @ TA] :
( ( C
= ( cons @ TA @ A @ E ) )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ E ) @ ( listrel1 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(17,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_append_Oleft__neutral) ).
thf(312,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(253,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_last_Osimps) ).
thf(1215,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(105,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA > $o] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( D @ A )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ E ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ C )
=> ( ( D @ E )
=> ( D @ F ) ) ) )
=> ( D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rtrancl__induct) ).
thf(634,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA > $o] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( D @ A )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ E ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ C )
=> ( ( D @ E )
=> ( D @ F ) ) ) )
=> ( D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(224,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA,F: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ ( cons @ TA @ A @ E ) ) @ ( append @ TA @ D @ ( cons @ TA @ B @ F ) ) ) @ ( lexord @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_lexord__append__left__rightI) ).
thf(1072,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA,F: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ ( cons @ TA @ A @ E ) ) @ ( append @ TA @ D @ ( cons @ TA @ B @ F ) ) ) @ ( lexord @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(61,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_append__self__conv2) ).
thf(453,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(225,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ D ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_listrel__rtrancl__trans) ).
thf(1074,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ D ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(176,axiom,
! [A: state,B: list @ com,C: state,D: state > ( list @ com ) > state > $o] :
( ( pHoare1053570959_execs @ A @ B @ C )
=> ( ! [E: state] : ( D @ E @ ( nil @ com ) @ E )
=> ( ! [E: state,F: com,G: state,H: list @ com,I: state] :
( ( exec @ E @ F @ G )
=> ( ( pHoare1053570959_execs @ G @ H @ I )
=> ( ( D @ G @ H @ I )
=> ( D @ E @ ( cons @ com @ F @ H ) @ I ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_execs_Oinducts) ).
thf(920,plain,
! [A: state,B: list @ com,C: state,D: state > ( list @ com ) > state > $o] :
( ( pHoare1053570959_execs @ A @ B @ C )
=> ( ! [E: state] : ( D @ E @ ( nil @ com ) @ E )
=> ( ! [E: state,F: com,G: state,H: list @ com,I: state] :
( ( exec @ E @ F @ G )
=> ( ( pHoare1053570959_execs @ G @ H @ I )
=> ( ( D @ G @ H @ I )
=> ( D @ E @ ( cons @ com @ F @ H ) @ I ) ) ) )
=> ( D @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(113,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_73_prod__induct5) ).
thf(678,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)],[113]) ).
thf(4,axiom,
! [TA: $tType,A: nat,B: nat,C: list @ TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( nth @ TA @ ( take @ TA @ B @ C ) @ A )
= ( nth @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_nth__take) ).
thf(270,plain,
! [TA: $tType,A: nat,B: nat,C: list @ TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( nth @ TA @ ( take @ TA @ B @ C ) @ A )
= ( nth @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(109,axiom,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_sorted__wrt_Ocases) ).
thf(661,plain,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(79,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_successively_Oinduct) ).
thf(546,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(38,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( nth @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ C ) ) @ ( size_size @ ( list @ TA ) @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_nth__append__length) ).
thf(381,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( nth @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ C ) ) @ ( size_size @ ( list @ TA ) @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TB @ TA @ C ) )
= ( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [D: nat] :
( ( ord_less @ nat @ D @ ( size_size @ ( list @ TB ) @ A ) )
=> ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ ( nth @ TB @ A @ D ) @ ( nth @ TA @ B @ D ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_listrel__iff__nth) ).
thf(366,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TB @ TA @ C ) )
= ( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [D: nat] :
( ( ord_less @ nat @ D @ ( size_size @ ( list @ TB ) @ A ) )
=> ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ ( nth @ TB @ A @ D ) @ ( nth @ TA @ B @ D ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(24,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( butlast @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_butlast__snoc) ).
thf(334,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( butlast @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: list @ TA,E: list @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ D @ E ) @ ( listrel @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( cons @ TA @ A @ D ) @ ( cons @ TB @ B @ E ) ) @ ( listrel @ TA @ TB @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_listrel_OCons) ).
thf(910,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: list @ TA,E: list @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ D @ E ) @ ( listrel @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( cons @ TA @ A @ D ) @ ( cons @ TB @ B @ E ) ) @ ( listrel @ TA @ TB @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(186,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA] :
( ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ A )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ B ) @ ( lenlex @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_lenlex__irreflexive) ).
thf(957,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA] :
( ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ A )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ B ) @ ( lenlex @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(215,axiom,
! [A: state > ( set @ state ),B: state > $o,C: com,D: com] :
( ( do @ A )
!= ( cond @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_com_Odistinct_I3_J) ).
thf(1042,plain,
! [A: state > ( set @ state ),B: state > $o,C: com,D: com] :
( ( do @ A )
!= ( cond @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(234,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA] :
( ( irrefl @ TA @ A )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ B ) @ ( lex @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_lexl__not__refl) ).
thf(1123,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA] :
( ( irrefl @ TA @ A )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ B ) @ ( lex @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(138,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_17_prod__cases4) ).
thf(788,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)],[138]) ).
thf(66,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
| ( ( size_size @ ( list @ TA ) @ C )
= ( size_size @ ( list @ TA ) @ D ) ) )
=> ( ( ( append @ TA @ A @ C )
= ( append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_append__eq__append__conv) ).
thf(467,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
| ( ( size_size @ ( list @ TA ) @ C )
= ( size_size @ ( list @ TA ) @ D ) ) )
=> ( ( ( append @ TA @ A @ C )
= ( append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(212,axiom,
! [A: state,B: state > ( set @ state ),C: state,D: list @ com] :
( ( member @ state @ A @ ( B @ C ) )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( do @ B ) @ D ) @ C ) @ ( product_Pair @ ( list @ com ) @ state @ D @ A ) ) @ pHoare1053570893_exec1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_exec1_ODo) ).
thf(1032,plain,
! [A: state,B: state > ( set @ state ),C: state,D: list @ com] :
( ( member @ state @ A @ ( B @ C ) )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( do @ B ) @ D ) @ C ) @ ( product_Pair @ ( list @ com ) @ state @ D @ A ) ) @ pHoare1053570893_exec1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(131,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_list_Oinducts) ).
thf(757,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(236,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_18_prod__cases5) ).
thf(1128,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)],[236]) ).
thf(62,axiom,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_butlast_Osimps_I1_J) ).
thf(456,plain,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(21,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_same__append__eq) ).
thf(324,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(204,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) )] :
( ! [B: TB > TA,C: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ C ) ) )
=> ~ ! [B: TB > TA,C: TB,D: list @ TB,E: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( cons @ TB @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_map__tailrec__rev_Ocases) ).
thf(1012,plain,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) )] :
( ! [B: TB > TA,C: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ C ) ) )
=> ~ ! [B: TB > TA,C: TB,D: list @ TB,E: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( cons @ TB @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(9,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_append__Cons) ).
thf(285,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(115,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_product__lists_Osimps_I1_J) ).
thf(682,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(251,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_76_prod__cases7) ).
thf(1195,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)],[251]) ).
thf(99,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( listrel1 @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_not__Nil__listrel1) ).
thf(615,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( listrel1 @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(125,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( cons @ TA @ B @ C ) ) @ ( listrel1 @ TA @ D ) )
=> ( ! [E: TA] :
( ( A
= ( cons @ TA @ E @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ B ) @ D ) )
=> ~ ! [E: list @ TA] :
( ( A
= ( cons @ TA @ B @ E ) )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ E @ C ) @ ( listrel1 @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Cons__listrel1E2) ).
thf(725,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( cons @ TA @ B @ C ) ) @ ( listrel1 @ TA @ D ) )
=> ( ! [E: TA] :
( ( A
= ( cons @ TA @ E @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ B ) @ D ) )
=> ~ ! [E: list @ TA] :
( ( A
= ( cons @ TA @ B @ E ) )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ E @ C ) @ ( listrel1 @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_not__Cons__self2) ).
thf(1006,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(95,axiom,
! [A: state,B: com,C: state,D: list @ com,E: state] :
( ( exec @ A @ B @ C )
=> ( ( pHoare1053570959_execs @ C @ D @ E )
=> ( pHoare1053570959_execs @ A @ ( cons @ com @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_execs_Ointros_I2_J) ).
thf(593,plain,
! [A: state,B: com,C: state,D: list @ com,E: state] :
( ( exec @ A @ B @ C )
=> ( ( pHoare1053570959_execs @ C @ D @ E )
=> ( pHoare1053570959_execs @ A @ ( cons @ com @ B @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(160,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( nil @ TA ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_butlast_Osimps_I2_J) ).
thf(869,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( nil @ TA ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(197,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_rev__exhaust) ).
thf(989,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(120,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA] :
( ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ A )
| ( D = E )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ A ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ C ) @ ( lexord @ TA @ A ) )
| ( B = C )
| ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ B ) @ ( lexord @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_lexord__linear) ).
thf(697,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA] :
( ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ A )
| ( D = E )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ A ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ C ) @ ( lexord @ TA @ A ) )
| ( B = C )
| ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ B ) @ ( lexord @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(258,axiom,
! [A: state > $o,B: state,C: com] :
( ~ ( A @ B )
=> ( termi @ ( while @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_termi_OWhileFalse) ).
thf(1234,plain,
! [A: state > $o,B: state,C: com] :
( ~ ( A @ B )
=> ( termi @ ( while @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(210,axiom,
! [TA: $tType,A: TA,B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( measures @ TA @ ( nil @ ( TA > nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_in__measures_I1_J) ).
thf(1028,plain,
! [TA: $tType,A: TA,B: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( measures @ TA @ ( nil @ ( TA > nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: list @ TA,D: ( list @ TB ) > ( list @ TC ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( ( size_size @ ( list @ TC ) @ B )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: list @ TB,G: TC,H: list @ TC,I: TA,J: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ F )
= ( size_size @ ( list @ TC ) @ H ) )
=> ( ( ( size_size @ ( list @ TC ) @ H )
= ( size_size @ ( list @ TA ) @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons @ TB @ E @ F ) @ ( cons @ TC @ G @ H ) @ ( cons @ TA @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_list__induct3) ).
thf(476,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: list @ TA,D: ( list @ TB ) > ( list @ TC ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( ( size_size @ ( list @ TC ) @ B )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: list @ TB,G: TC,H: list @ TC,I: TA,J: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ F )
= ( size_size @ ( list @ TC ) @ H ) )
=> ( ( ( size_size @ ( list @ TC ) @ H )
= ( size_size @ ( list @ TA ) @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons @ TB @ E @ F ) @ ( cons @ TC @ G @ H ) @ ( cons @ TA @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(81,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ? [D: TA,E: list @ TA] :
( A
= ( cons @ TA @ D @ E ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( append @ TA @ B @ A ) ) @ ( lexord @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_lexord__append__rightI) ).
thf(554,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ? [D: TA,E: list @ TA] :
( A
= ( cons @ TA @ D @ E ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( append @ TA @ B @ A ) ) @ ( lexord @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(130,axiom,
! [A: state > ( set @ state ),B: list @ com,C: state,D: list @ com,E: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( do @ A ) @ B ) @ C ) @ ( product_Pair @ ( list @ com ) @ state @ D @ E ) ) @ pHoare1053570893_exec1 )
=> ~ ( ( D = B )
=> ~ ( member @ state @ E @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_exec1E_I2_J) ).
thf(753,plain,
! [A: state > ( set @ state ),B: list @ com,C: state,D: list @ com,E: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( do @ A ) @ B ) @ C ) @ ( product_Pair @ ( list @ com ) @ state @ D @ E ) ) @ pHoare1053570893_exec1 )
=> ~ ( ( D = B )
=> ~ ( member @ state @ E @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_map__tailrec__rev_Oinduct) ).
thf(1039,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(191,axiom,
! [A: state > $o,B: com,C: state > $o,D: com] :
( ( ( while @ A @ B )
= ( while @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_com_Oinject_I4_J) ).
thf(970,plain,
! [A: state > $o,B: com,C: state > $o,D: com] :
( ( ( while @ A @ B )
= ( while @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(42,axiom,
! [TA: $tType,A: list @ TA,B: list @ ( list @ TA )] :
( ( concat @ TA @ ( cons @ ( list @ TA ) @ A @ B ) )
= ( append @ TA @ A @ ( concat @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_concat_Osimps_I2_J) ).
thf(393,plain,
! [TA: $tType,A: list @ TA,B: list @ ( list @ TA )] :
( ( concat @ TA @ ( cons @ ( list @ TA ) @ A @ B ) )
= ( append @ TA @ A @ ( concat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(263,axiom,
! [A: state > $o,B: state,C: com,D: com] :
( ( A @ B )
=> ( ( termi @ C @ B )
=> ( termi @ ( cond @ A @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_termi_OIfTrue) ).
thf(1249,plain,
! [A: state > $o,B: state,C: com,D: com] :
( ( A @ B )
=> ( ( termi @ C @ B )
=> ( termi @ ( cond @ A @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(237,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_28_Pair__inject) ).
thf(1131,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)],[237]) ).
thf(250,axiom,
! [A: list @ com,B: state,C: list @ com,D: state,E: list @ com] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ A @ E ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ C @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_app__execs) ).
thf(1192,plain,
! [A: list @ com,B: state,C: list @ com,D: state,E: list @ com] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ A @ E ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ C @ E ) @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(262,axiom,
! [A: state > $o,B: com,C: state,D: state] :
( ( termi @ ( while @ A @ B ) @ C )
=> ( ( A @ C )
=> ( ( exec @ C @ B @ D )
=> ( termi @ ( while @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_while__termiE2) ).
thf(1246,plain,
! [A: state > $o,B: com,C: state,D: state] :
( ( termi @ ( while @ A @ B ) @ C )
=> ( ( A @ C )
=> ( ( exec @ C @ B @ D )
=> ( termi @ ( while @ A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(36,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( butlast @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( append @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_butlast__append) ).
thf(371,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( butlast @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( append @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(32,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_last__appendR) ).
thf(360,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_listrel__eq__len) ).
thf(508,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: set @ ( product_prod @ TB @ TA )] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(82,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( lexord @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_lexord__Nil__right) ).
thf(558,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( lexord @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(248,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_74_prod__induct4) ).
thf(1187,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)],[248]) ).
thf(140,axiom,
! [A: state > $o,B: state,C: com,D: state,E: com] :
( ~ ( A @ B )
=> ( ( exec @ B @ C @ D )
=> ( exec @ B @ ( cond @ A @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_exec_OIfFalse) ).
thf(794,plain,
! [A: state > $o,B: state,C: com,D: state,E: com] :
( ~ ( A @ B )
=> ( ( exec @ B @ C @ D )
=> ( exec @ B @ ( cond @ A @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(166,axiom,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ A @ ( transitive_rtrancl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_r__into__rtrancl) ).
thf(888,plain,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ A @ ( transitive_rtrancl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(177,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( cons @ TA @ D @ B ) ) @ ( listrel1 @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_listrel1I2) ).
thf(926,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( cons @ TA @ D @ B ) ) @ ( listrel1 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(260,axiom,
! [A: state,B: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ A ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c2 @ cs ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( ( termi @ c @ A )
=> ( ( termi @ c2 @ B )
& ! [C: state] :
( ( exec @ B @ c2 @ C )
=> ( pHoare1335526537termis @ cs @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(1241,plain,
! [A: state,B: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c @ ( nil @ com ) ) @ A ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ c2 @ cs ) @ B ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( ( termi @ c @ A )
=> ( ( termi @ c2 @ B )
& ! [C: state] :
( ( exec @ B @ c2 @ C )
=> ( pHoare1335526537termis @ cs @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1,conjecture,
termi @ c2 @ s2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(2,negated_conjecture,
~ ( termi @ c2 @ s2 ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(266,plain,
~ ( termi @ c2 @ s2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ B ) @ ( append @ TA @ C @ D ) ) @ ( lexord @ TA @ E ) )
=> ( ( A != C )
=> ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( ( size_size @ ( list @ TA ) @ B )
= ( size_size @ ( list @ TA ) @ D ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ C ) @ ( lexord @ TA @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_lexord__sufE) ).
thf(398,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ B ) @ ( append @ TA @ C @ D ) ) @ ( lexord @ TA @ E ) )
=> ( ( A != C )
=> ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( ( size_size @ ( list @ TA ) @ B )
= ( size_size @ ( list @ TA ) @ D ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ C ) @ ( lexord @ TA @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(213,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA,F: list @ TA,G: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( ( D
= ( append @ TA @ E @ ( cons @ TA @ A @ F ) ) )
=> ( ( G
= ( append @ TA @ E @ ( cons @ TA @ B @ F ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ G ) @ ( listrel1 @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_listrel1I) ).
thf(1035,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA,F: list @ TA,G: list @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( ( D
= ( append @ TA @ E @ ( cons @ TA @ A @ F ) ) )
=> ( ( G
= ( append @ TA @ E @ ( cons @ TA @ B @ F ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ G ) @ ( listrel1 @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(209,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_rtrancl_Ortrancl__into__rtrancl) ).
thf(1026,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(243,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_listrel__reflcl__if__listrel1) ).
thf(1167,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(13,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_nth__equalityI) ).
thf(298,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(50,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_append__same__eq) ).
thf(412,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(189,axiom,
! [A: com,B: state,C: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ A @ ( nil @ com ) ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( exec @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_exec1s__impl__exec) ).
thf(965,plain,
! [A: com,B: state,C: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ A @ ( nil @ com ) ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( exec @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(156,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( A != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rtranclE) ).
thf(856,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( A != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(7,axiom,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA] :
( ( A != B )
=> ( ( nth @ TA @ ( list_update @ TA @ C @ A @ D ) @ B )
= ( nth @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_nth__list__update__neq) ).
thf(279,plain,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA] :
( ( A != B )
=> ( ( nth @ TA @ ( list_update @ TA @ C @ A @ D ) @ B )
= ( nth @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(126,axiom,
! [A: list @ com,B: state,C: list @ com,D: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( ( pHoare1335526537termis @ A @ B )
=> ( pHoare1335526537termis @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_execs__pres__termis) ).
thf(733,plain,
! [A: list @ com,B: state,C: list @ com,D: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( ( pHoare1335526537termis @ A @ B )
=> ( pHoare1335526537termis @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TB,C: list @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ ( cons @ TB @ B @ C ) ) @ ( listrel @ TA @ TB @ D ) )
=> ~ ! [E: TA,F: list @ TA] :
( ( A
= ( cons @ TA @ E @ F ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ B ) @ D )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ C ) @ ( listrel @ TA @ TB @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_listrel__Cons2) ).
thf(584,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TB,C: list @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ ( cons @ TB @ B @ C ) ) @ ( listrel @ TA @ TB @ D ) )
=> ~ ! [E: TA,F: list @ TA] :
( ( A
= ( cons @ TA @ E @ F ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ B ) @ D )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ C ) @ ( listrel @ TA @ TB @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(170,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Cons__eq__append__conv) ).
thf(904,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(119,axiom,
! [A: state > $o,B: state,C: com,D: state,E: state] :
( ( A @ B )
=> ( ( exec @ B @ C @ D )
=> ( ( exec @ D @ ( while @ A @ C ) @ E )
=> ( exec @ B @ ( while @ A @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_exec_OWhileTrue) ).
thf(694,plain,
! [A: state > $o,B: state,C: com,D: state,E: state] :
( ( A @ B )
=> ( ( exec @ B @ C @ D )
=> ( ( exec @ D @ ( while @ A @ C ) @ E )
=> ( exec @ B @ ( while @ A @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(255,axiom,
! [A: com,B: state,C: com] :
( ( termi @ A @ B )
=> ( ! [D: state] :
( ( exec @ B @ A @ D )
=> ( termi @ C @ D ) )
=> ( termi @ ( semi @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_termi_OSemi) ).
thf(1226,plain,
! [A: com,B: state,C: com] :
( ( termi @ A @ B )
=> ( ! [D: state] :
( ( exec @ B @ A @ D )
=> ( termi @ C @ D ) )
=> ( termi @ ( semi @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(151,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( lenlex @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_Nil__lenlex__iff2) ).
thf(843,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( lenlex @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(235,axiom,
! [A: state > $o,B: state,C: com,D: com,E: list @ com] :
( ~ ( A @ B )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ A @ C @ D ) @ E ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ D @ E ) @ B ) ) @ pHoare1053570893_exec1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_exec1_OIfFalse) ).
thf(1125,plain,
! [A: state > $o,B: state,C: com,D: com,E: list @ com] :
( ~ ( A @ B )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ A @ C @ D ) @ E ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ D @ E ) @ B ) ) @ pHoare1053570893_exec1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(161,axiom,
! [A: state,B: com,C: state,D: com,E: state] :
( ( exec @ A @ B @ C )
=> ( ( exec @ C @ D @ E )
=> ( exec @ A @ ( semi @ B @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_exec_OSemi) ).
thf(875,plain,
! [A: state,B: com,C: state,D: com,E: state] :
( ( exec @ A @ B @ C )
=> ( ( exec @ C @ D @ E )
=> ( exec @ A @ ( semi @ B @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(145,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_com_Oinject_I2_J) ).
thf(826,plain,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(90,axiom,
! [A: state] : ( pHoare1053570959_execs @ A @ ( nil @ com ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_execs_Ointros_I1_J) ).
thf(579,plain,
! [A: state] : ( pHoare1053570959_execs @ A @ ( nil @ com ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(11,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_append__assoc) ).
thf(291,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(239,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lex @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ A ) @ ( append @ TA @ D @ B ) ) @ ( lex @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_lex__append__leftI) ).
thf(1139,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lex @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ A ) @ ( append @ TA @ D @ B ) ) @ ( lex @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(220,axiom,
! [A: state > $o,B: com,C: com,D: state > $o,E: com,F: com] :
( ( ( cond @ A @ B @ C )
= ( cond @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_com_Oinject_I3_J) ).
thf(1058,plain,
! [A: state > $o,B: com,C: com,D: state > $o,E: com,F: com] :
( ( ( cond @ A @ B @ C )
= ( cond @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: set @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) )] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Pair @ TA @ TB @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ E ) )
=> ( ( ( product_Pair @ TA @ TB @ A @ B )
!= ( product_Pair @ TA @ TB @ C @ D ) )
=> ~ ! [F: TA,G: TB] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Pair @ TA @ TB @ F @ G ) ) @ E )
=> ~ ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ F @ G ) @ ( product_Pair @ TA @ TB @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_converse__rtranclE2) ).
thf(1090,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB,E: set @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) )] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Pair @ TA @ TB @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ E ) )
=> ( ( ( product_Pair @ TA @ TB @ A @ B )
!= ( product_Pair @ TA @ TB @ C @ D ) )
=> ~ ! [F: TA,G: TB] :
( ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Pair @ TA @ TB @ F @ G ) ) @ E )
=> ~ ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ F @ G ) @ ( product_Pair @ TA @ TB @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TA @ TB ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(144,axiom,
! [A: state > $o,B: com,C: list @ com,D: state,E: list @ com,F: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ A @ B ) @ C ) @ D ) @ ( product_Pair @ ( list @ com ) @ state @ E @ F ) ) @ pHoare1053570893_exec1 )
=> ( ( ( E = C )
=> ( ( F = D )
=> ( A @ D ) ) )
=> ~ ( ( E
= ( cons @ com @ B @ ( cons @ com @ ( while @ A @ B ) @ C ) ) )
=> ( ( F = D )
=> ~ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_exec1E_I5_J) ).
thf(804,plain,
! [A: state > $o,B: com,C: list @ com,D: state,E: list @ com,F: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ A @ B ) @ C ) @ D ) @ ( product_Pair @ ( list @ com ) @ state @ E @ F ) ) @ pHoare1053570893_exec1 )
=> ( ( ( E = C )
=> ( ( F = D )
=> ( A @ D ) ) )
=> ~ ( ( E
= ( cons @ com @ B @ ( cons @ com @ ( while @ A @ B ) @ C ) ) )
=> ( ( F = D )
=> ~ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(121,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_rev__induct) ).
thf(704,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(184,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_remdups__adj_Ocases) ).
thf(947,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(30,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( last @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_last__snoc) ).
thf(350,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( last @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(122,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ~ ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ C )
=> ! [F: list @ TA,G: list @ TA] :
( ( A
= ( append @ TA @ F @ ( cons @ TA @ D @ G ) ) )
=> ( B
!= ( append @ TA @ F @ ( cons @ TA @ E @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_listrel1E) ).
thf(713,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
=> ~ ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ C )
=> ! [F: list @ TA,G: list @ TA] :
( ( A
= ( append @ TA @ F @ ( cons @ TA @ D @ G ) ) )
=> ( B
!= ( append @ TA @ F @ ( cons @ TA @ E @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(73,axiom,
! [TA: $tType,A: TA,B: TA,C: TA > nat,D: list @ ( TA > nat )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( measures @ TA @ ( cons @ ( TA > nat ) @ C @ D ) ) )
= ( ( ord_less @ nat @ ( C @ A ) @ ( C @ B ) )
| ( ( ( C @ A )
= ( C @ B ) )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( measures @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_in__measures_I2_J) ).
thf(498,plain,
! [TA: $tType,A: TA,B: TA,C: TA > nat,D: list @ ( TA > nat )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( measures @ TA @ ( cons @ ( TA > nat ) @ C @ D ) ) )
= ( ( ord_less @ nat @ ( C @ A ) @ ( C @ B ) )
| ( ( ( C @ A )
= ( C @ B ) )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( measures @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(194,axiom,
! [TA: $tType] :
( ( rotate1 @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_rotate1_Osimps_I1_J) ).
thf(979,plain,
! [TA: $tType] :
( ( rotate1 @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(48,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_append__Nil2) ).
thf(406,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(14,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Ex__list__of__length) ).
thf(303,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(158,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lenlex @ TA @ C ) )
=> ( ( ( size_size @ ( list @ TA ) @ D )
= ( size_size @ ( list @ TA ) @ E ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ D ) @ ( append @ TA @ B @ E ) ) @ ( lenlex @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_lenlex__append1) ).
thf(863,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lenlex @ TA @ C ) )
=> ( ( ( size_size @ ( list @ TA ) @ D )
= ( size_size @ ( list @ TA ) @ E ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ D ) @ ( append @ TA @ B @ E ) ) @ ( lenlex @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(37,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_last__appendL) ).
thf(377,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(200,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( lex @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_Nil2__notin__lex) ).
thf(996,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( lex @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ B ) @ ( listrel @ TA @ TB @ C ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TB ) ) )
| ? [D: TA,E: TB,F: list @ TA,G: list @ TB] :
( ( A
= ( cons @ TA @ D @ F ) )
& ( B
= ( cons @ TB @ E @ G ) )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ G ) @ ( listrel @ TA @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_listrel_Osimps) ).
thf(737,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ B ) @ ( listrel @ TA @ TB @ C ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TB ) ) )
| ? [D: TA,E: TB,F: list @ TA,G: list @ TB] :
( ( A
= ( cons @ TA @ D @ F ) )
& ( B
= ( cons @ TB @ E @ G ) )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ G ) @ ( listrel @ TA @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(19,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( lenlex @ TA @ E ) )
= ( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ B ) @ ( size_size @ ( list @ TA ) @ D ) )
| ( ( ( size_size @ ( list @ TA ) @ B )
= ( size_size @ ( list @ TA ) @ D ) )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( lenlex @ TA @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_Cons__lenlex__iff) ).
thf(318,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( lenlex @ TA @ E ) )
= ( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ B ) @ ( size_size @ ( list @ TA ) @ D ) )
| ( ( ( size_size @ ( list @ TA ) @ B )
= ( size_size @ ( list @ TA ) @ D ) )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( lenlex @ TA @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(163,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( listrel1 @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_not__listrel1__Nil) ).
thf(880,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ ( nil @ TA ) ) @ ( listrel1 @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(56,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_append__Nil) ).
thf(434,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ ( nil @ TB ) ) @ ( listrel @ TA @ TB @ B ) )
=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_listrel__Nil2) ).
thf(890,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ ( nil @ TB ) ) @ ( listrel @ TA @ TB @ B ) )
=> ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(40,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_self__append__conv2) ).
thf(387,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(228,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
& ( D = E ) )
| ( ( A = B )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ E ) @ ( listrel1 @ TA @ C ) ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ D ) @ ( append @ TA @ B @ E ) ) @ ( listrel1 @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_append__listrel1I) ).
thf(1080,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA,E: list @ TA] :
( ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
& ( D = E ) )
| ( ( A = B )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ E ) @ ( listrel1 @ TA @ C ) ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ D ) @ ( append @ TA @ B @ E ) ) @ ( listrel1 @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(104,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_30_surj__pair) ).
thf(631,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)],[104]) ).
thf(97,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_78_old_Oprod_Orec) ).
thf(609,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)],[97]) ).
thf(153,axiom,
! [A: list @ com,B: state,C: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( pHoare1053570959_execs @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_exec1s__impl__execs) ).
thf(848,plain,
! [A: list @ com,B: state,C: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) )
=> ( pHoare1053570959_execs @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(111,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_neq__Nil__conv) ).
thf(668,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(142,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_26_old_Oprod_Oinducts) ).
thf(799,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)],[142]) ).
thf(242,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: set @ ( product_prod @ TB @ TA ),D: ( list @ TB ) > ( list @ TA ) > $o] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: TA,G: list @ TB,H: list @ TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ E @ F ) @ C )
=> ( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ G @ H ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TB @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) )
=> ( D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_listrel_Oinducts) ).
thf(1162,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: set @ ( product_prod @ TB @ TA ),D: ( list @ TB ) > ( list @ TA ) > $o] :
( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: TA,G: list @ TB,H: list @ TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ E @ F ) @ C )
=> ( ( member @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ G @ H ) @ ( listrel @ TB @ TA @ C ) )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TB @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) )
=> ( D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(103,axiom,
! [A: com,B: com,C: list @ com,D: state,E: list @ com,F: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( semi @ A @ B ) @ C ) @ D ) @ ( product_Pair @ ( list @ com ) @ state @ E @ F ) ) @ pHoare1053570893_exec1 )
=> ~ ( ( E
= ( cons @ com @ A @ ( cons @ com @ B @ C ) ) )
=> ( F != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_exec1E_I3_J) ).
thf(626,plain,
! [A: com,B: com,C: list @ com,D: state,E: list @ com,F: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( semi @ A @ B ) @ C ) @ D ) @ ( product_Pair @ ( list @ com ) @ state @ E @ F ) ) @ pHoare1053570893_exec1 )
=> ~ ( ( E
= ( cons @ com @ A @ ( cons @ com @ B @ C ) ) )
=> ( F != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(174,axiom,
! [TA: $tType,A: TA > nat,B: TA,C: TA,D: list @ ( TA > nat )] :
( ( ord_less @ nat @ ( A @ B ) @ ( A @ C ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( measures @ TA @ ( cons @ ( TA > nat ) @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_measures__less) ).
thf(915,plain,
! [TA: $tType,A: TA > nat,B: TA,C: TA,D: list @ ( TA > nat )] :
( ( ord_less @ nat @ ( A @ B ) @ ( A @ C ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( measures @ TA @ ( cons @ ( TA > nat ) @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(64,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( irrefl @ TA @ A )
=> ( irrefl @ ( list @ TA ) @ ( lexord @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_lexord__irrefl) ).
thf(462,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( irrefl @ TA @ A )
=> ( irrefl @ ( list @ TA ) @ ( lexord @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(180,axiom,
! [A: state,B: com,C: state,D: list @ com] :
( ( exec @ A @ B @ C )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ B @ D ) @ A ) @ ( product_Pair @ ( list @ com ) @ state @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_exec__impl__execs) ).
thf(932,plain,
! [A: state,B: com,C: state,D: list @ com] :
( ( exec @ A @ B @ C )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ B @ D ) @ A ) @ ( product_Pair @ ( list @ com ) @ state @ D @ C ) ) @ ( transitive_rtrancl @ ( product_prod @ ( list @ com ) @ state ) @ pHoare1053570893_exec1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(221,axiom,
! [A: state > ( set @ state ),B: state > $o,C: com] :
( ( do @ A )
!= ( while @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_com_Odistinct_I5_J) ).
thf(1061,plain,
! [A: state > ( set @ state ),B: state > $o,C: com] :
( ( do @ A )
!= ( while @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(252,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ B ) @ ( listrel @ TA @ TB @ C ) )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( nil @ TB ) ) )
=> ~ ! [D: TA,E: TB,F: list @ TA] :
( ( A
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TB] :
( ( B
= ( cons @ TB @ E @ G ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ G ) @ ( listrel @ TA @ TB @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_listrel_Ocases) ).
thf(1198,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: list @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ A @ B ) @ ( listrel @ TA @ TB @ C ) )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( nil @ TB ) ) )
=> ~ ! [D: TA,E: TB,F: list @ TA] :
( ( A
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TB] :
( ( B
= ( cons @ TB @ E @ G ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ F @ G ) @ ( listrel @ TA @ TB @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(187,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_append1__eq__conv) ).
thf(959,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(133,axiom,
! [A: state > $o,B: state,C: com,D: list @ com] :
( ~ ( A @ B )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ A @ C ) @ D ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ D @ B ) ) @ pHoare1053570893_exec1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_exec1_OWhileFalse) ).
thf(768,plain,
! [A: state > $o,B: state,C: com,D: list @ com] :
( ~ ( A @ B )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ A @ C ) @ D ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ D @ B ) ) @ pHoare1053570893_exec1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(205,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_list_Odistinct_I1_J) ).
thf(1015,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_converse__rtrancl__into__rtrancl) ).
thf(563,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ ( transitive_rtrancl @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(3,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: TA,D: TA] :
( ( list_update @ TA @ ( list_update @ TA @ A @ B @ C ) @ B @ D )
= ( list_update @ TA @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_list__update__overwrite) ).
thf(267,plain,
! [TA: $tType,A: list @ TA,B: nat,C: TA,D: TA] :
( ( list_update @ TA @ ( list_update @ TA @ A @ B @ C ) @ B @ D )
= ( list_update @ TA @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(55,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_append_Oright__neutral) ).
thf(431,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(108,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_220_internal__case__prod__conv) ).
thf(658,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)],[108]) ).
thf(173,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_14_prod_Oinject) ).
thf(912,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)],[173]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA,E: set @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ),F: TB > TA > $o] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ E ) )
=> ( ( F @ C @ D )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ E )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ I @ J ) @ ( product_Pair @ TB @ TA @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ E ) )
=> ( ( F @ I @ J )
=> ( F @ G @ H ) ) ) )
=> ( F @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_converse__rtrancl__induct2) ).
thf(685,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA,E: set @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ),F: TB > TA > $o] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ E ) )
=> ( ( F @ C @ D )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ E )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ I @ J ) @ ( product_Pair @ TB @ TA @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ E ) )
=> ( ( F @ I @ J )
=> ( F @ G @ H ) ) ) )
=> ( F @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(245,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_min__list_Oinduct) ).
thf(1171,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(196,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( transitive_rtrancl @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( transitive_rtrancl @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_rtrancl__idemp) ).
thf(986,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( transitive_rtrancl @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( transitive_rtrancl @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(15,axiom,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ ( list @ TA )] :
( ( concat @ TA @ ( append @ ( list @ TA ) @ A @ B ) )
= ( append @ TA @ ( concat @ TA @ A ) @ ( concat @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_concat__append) ).
thf(306,plain,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ ( list @ TA )] :
( ( concat @ TA @ ( append @ ( list @ TA ) @ A @ B ) )
= ( append @ TA @ ( concat @ TA @ A ) @ ( concat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(226,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lex @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_Nil__notin__lex) ).
thf(1076,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lex @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(124,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( listrel1 @ TA @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Cons__listrel1__Cons) ).
thf(722,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( listrel1 @ TA @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(93,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] : ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ A ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_listrel__rtrancl__refl) ).
thf(589,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] : ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ A ) @ ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(114,axiom,
( pHoare1053570959_execs
= ( ^ [A: state,B: list @ com,C: state] :
( ? [D: state] :
( ( A = D )
& ( B
= ( nil @ com ) )
& ( C = D ) )
| ? [D: state,E: com,F: state,G: list @ com,H: state] :
( ( A = D )
& ( B
= ( cons @ com @ E @ G ) )
& ( C = H )
& ( exec @ D @ E @ F )
& ( pHoare1053570959_execs @ F @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_execs_Osimps) ).
thf(680,plain,
( pHoare1053570959_execs
= ( ^ [A: state,B: list @ com,C: state] :
( ? [D: state] :
( ( A = D )
& ( B
= ( nil @ com ) )
& ( C = D ) )
| ? [D: state,E: com,F: state,G: list @ com,H: state] :
( ( A = D )
& ( B
= ( cons @ com @ E @ G ) )
& ( C = H )
& ( exec @ D @ E @ F )
& ( pHoare1053570959_execs @ F @ G @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(100,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lex @ TA @ C ) )
= ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) )
& ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_lexord__lex) ).
thf(617,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lex @ TA @ C ) )
= ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) )
& ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(246,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(1181,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(217,axiom,
! [A: state > ( set @ state ),B: com,C: com] :
( ( do @ A )
!= ( semi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_com_Odistinct_I1_J) ).
thf(1049,plain,
! [A: state > ( set @ state ),B: com,C: com] :
( ( do @ A )
!= ( semi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(78,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_remdups__adj_Oinduct) ).
thf(531,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: product_prod @ ( TA > TB ) @ ( list @ TA )] :
( ! [B: TA > TB,C: TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [B: TA > TB,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ~ ! [B: TA > TB] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_arg__min__list_Ocases) ).
thf(944,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: product_prod @ ( TA > TB ) @ ( list @ TA )] :
( ! [B: TA > TB,C: TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [B: TA > TB,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ~ ! [B: TA > TB] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(241,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA > $o] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( D @ B )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( D @ F )
=> ( D @ E ) ) ) )
=> ( D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_converse__rtrancl__induct) ).
thf(1145,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA ),D: TA > $o] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( D @ B )
=> ( ! [E: TA,F: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( D @ F )
=> ( D @ E ) ) ) )
=> ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(206,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_72_prod__induct6) ).
thf(1018,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)],[206]) ).
thf(117,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TA @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_rtrancl__listrel1__if__listrel) ).
thf(690,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel @ TA @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(8,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: TA] :
( ( ( list_update @ TA @ A @ B @ C )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_list__update__nonempty) ).
thf(282,plain,
! [TA: $tType,A: list @ TA,B: nat,C: TA] :
( ( ( list_update @ TA @ A @ B @ C )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_eq__Nil__appendI) ).
thf(327,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(264,axiom,
termi @ c @ s,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(1252,plain,
termi @ c @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(232,axiom,
! [A: state > $o,B: com,C: com,D: list @ com,E: state,F: list @ com,G: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ A @ B @ C ) @ D ) @ E ) @ ( product_Pair @ ( list @ com ) @ state @ F @ G ) ) @ pHoare1053570893_exec1 )
=> ( ( ( F
= ( cons @ com @ B @ D ) )
=> ( ( G = E )
=> ~ ( A @ E ) ) )
=> ~ ( ( F
= ( cons @ com @ C @ D ) )
=> ( ( G = E )
=> ( A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_exec1E_I4_J) ).
thf(1098,plain,
! [A: state > $o,B: com,C: com,D: list @ com,E: state,F: list @ com,G: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ A @ B @ C ) @ D ) @ E ) @ ( product_Pair @ ( list @ com ) @ state @ F @ G ) ) @ pHoare1053570893_exec1 )
=> ( ( ( F
= ( cons @ com @ B @ D ) )
=> ( ( G = E )
=> ~ ( A @ E ) ) )
=> ~ ( ( F
= ( cons @ com @ C @ D ) )
=> ( ( G = E )
=> ( A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(49,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_append_Oassoc) ).
thf(409,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(256,axiom,
! [A: state > $o,B: state,C: com,D: com] :
( ~ ( A @ B )
=> ( ( termi @ C @ B )
=> ( termi @ ( cond @ A @ D @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_termi_OIfFalse) ).
thf(1230,plain,
! [A: state > $o,B: state,C: com,D: com] :
( ~ ( A @ B )
=> ( ( termi @ C @ B )
=> ( termi @ ( cond @ A @ D @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(218,axiom,
! [A: list @ com,B: state,C: list @ com,D: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ C @ D ) ) @ pHoare1053570893_exec1 )
=> ( ( pHoare1335526537termis @ A @ B )
=> ( pHoare1335526537termis @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_exec1__pres__termis) ).
thf(1053,plain,
! [A: list @ com,B: state,C: list @ com,D: state] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ C @ D ) ) @ pHoare1053570893_exec1 )
=> ( ( pHoare1335526537termis @ A @ B )
=> ( pHoare1335526537termis @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_list__induct2_H) ).
thf(791,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(23,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(331,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(26,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_append__eq__append__conv2) ).
thf(338,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(89,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA,D: list @ TA] :
( ( irrefl @ TA @ A )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) ) @ ( lexord @ TA @ A ) )
= ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ D ) @ ( lexord @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_lexord__same__pref__if__irrefl) ).
thf(576,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA,D: list @ TA] :
( ( irrefl @ TA @ A )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) ) @ ( lexord @ TA @ A ) )
= ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ D ) @ ( lexord @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(171,axiom,
! [TA: $tType] :
( ( subseqs @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_subseqs_Osimps_I1_J) ).
thf(907,plain,
! [TA: $tType] :
( ( subseqs @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(240,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_last__ConsL) ).
thf(1141,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(254,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA,E: set @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ),F: TB > TA > $o] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ E ) )
=> ( ( F @ A @ B )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ G @ H ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ E ) )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ E )
=> ( ( F @ G @ H )
=> ( F @ I @ J ) ) ) )
=> ( F @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_rtrancl__induct2) ).
thf(1221,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA,E: set @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ),F: TB > TA > $o] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ C @ D ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ E ) )
=> ( ( F @ A @ B )
=> ( ! [G: TB,H: TA,I: TB,J: TA] :
( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( product_Pair @ TB @ TA @ G @ H ) ) @ ( transitive_rtrancl @ ( product_prod @ TB @ TA ) @ E ) )
=> ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ G @ H ) @ ( product_Pair @ TB @ TA @ I @ J ) ) @ E )
=> ( ( F @ G @ H )
=> ( F @ I @ J ) ) ) )
=> ( F @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(98,axiom,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ TA,C: list @ TA] :
( ( ( concat @ TA @ A )
= ( append @ TA @ B @ C ) )
= ( ( ( A
= ( nil @ ( list @ TA ) ) )
=> ( ( B
= ( nil @ TA ) )
& ( C
= ( nil @ TA ) ) ) )
& ( ( A
!= ( nil @ ( list @ TA ) ) )
=> ? [D: list @ ( list @ TA ),E: list @ TA,F: list @ TA,G: list @ ( list @ TA )] :
( ( A
= ( append @ ( list @ TA ) @ D @ ( cons @ ( list @ TA ) @ ( append @ TA @ E @ F ) @ G ) ) )
& ( B
= ( append @ TA @ ( concat @ TA @ D ) @ E ) )
& ( C
= ( append @ TA @ F @ ( concat @ TA @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_concat__eq__append__conv) ).
thf(612,plain,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ TA,C: list @ TA] :
( ( ( concat @ TA @ A )
= ( append @ TA @ B @ C ) )
= ( ( ( A
= ( nil @ ( list @ TA ) ) )
=> ( ( B
= ( nil @ TA ) )
& ( C
= ( nil @ TA ) ) ) )
& ( ( A
!= ( nil @ ( list @ TA ) ) )
=> ? [D: list @ ( list @ TA ),E: list @ TA,F: list @ TA,G: list @ ( list @ TA )] :
( ( A
= ( append @ ( list @ TA ) @ D @ ( cons @ ( list @ TA ) @ ( append @ TA @ E @ F ) @ G ) ) )
& ( B
= ( append @ TA @ ( concat @ TA @ D ) @ E ) )
& ( C
= ( append @ TA @ F @ ( concat @ TA @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] : ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( nil @ TA ) @ ( nil @ TB ) ) @ ( listrel @ TA @ TB @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_listrel_ONil) ).
thf(656,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] : ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( nil @ TA ) @ ( nil @ TB ) ) @ ( listrel @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(208,axiom,
! [A: state,B: list @ com,C: state] :
~ ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ A ) @ ( product_Pair @ ( list @ com ) @ state @ B @ C ) ) @ pHoare1053570893_exec1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_exec1E_I1_J) ).
thf(1023,plain,
! [A: state,B: list @ com,C: state] :
~ ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( nil @ com ) @ A ) @ ( product_Pair @ ( list @ com ) @ state @ B @ C ) ) @ pHoare1053570893_exec1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_append__eq__appendI) ).
thf(446,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(87,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_sorted__wrt_Oinduct) ).
thf(571,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(152,axiom,
! [A: state > $o,B: state,C: com,D: com,E: list @ com] :
( ( A @ B )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ A @ C @ D ) @ E ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ E ) @ B ) ) @ pHoare1053570893_exec1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_exec1_OIfTrue) ).
thf(845,plain,
! [A: state > $o,B: state,C: com,D: com,E: list @ com] :
( ( A @ B )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( cond @ A @ C @ D ) @ E ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ E ) @ B ) ) @ pHoare1053570893_exec1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(60,axiom,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_Skolem__list__nth) ).
thf(450,plain,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(33,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= C )
= ( ( C
!= ( nil @ TA ) )
& ( ( butlast @ TA @ C )
= A )
& ( ( last @ TA @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_snoc__eq__iff__butlast) ).
thf(363,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= C )
= ( ( C
!= ( nil @ TA ) )
& ( ( butlast @ TA @ C )
= A )
& ( ( last @ TA @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(112,axiom,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ TA,C: list @ TA] :
( ( ( concat @ TA @ A )
= ( append @ TA @ B @ C ) )
=> ( ( A
!= ( nil @ ( list @ TA ) ) )
=> ? [D: list @ ( list @ TA ),E: list @ TA,F: list @ TA,G: list @ ( list @ TA )] :
( ( A
= ( append @ ( list @ TA ) @ D @ ( cons @ ( list @ TA ) @ ( append @ TA @ E @ F ) @ G ) ) )
& ( B
= ( append @ TA @ ( concat @ TA @ D ) @ E ) )
& ( C
= ( append @ TA @ F @ ( concat @ TA @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_concat__eq__appendD) ).
thf(671,plain,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ TA,C: list @ TA] :
( ( ( concat @ TA @ A )
= ( append @ TA @ B @ C ) )
=> ( ( A
!= ( nil @ ( list @ TA ) ) )
=> ? [D: list @ ( list @ TA ),E: list @ TA,F: list @ TA,G: list @ ( list @ TA )] :
( ( A
= ( append @ ( list @ TA ) @ D @ ( cons @ ( list @ TA ) @ ( append @ TA @ E @ F ) @ G ) ) )
& ( B
= ( append @ TA @ ( concat @ TA @ D ) @ E ) )
& ( C
= ( append @ TA @ F @ ( concat @ TA @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(193,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_append__eq__Cons__conv) ).
thf(976,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(91,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_strict__sorted_Ocases) ).
thf(581,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(72,axiom,
! [A: state > $o,B: state,C: com,D: list @ com] :
( ( A @ B )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ A @ C ) @ D ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ ( cons @ com @ ( while @ A @ C ) @ D ) ) @ B ) ) @ pHoare1053570893_exec1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_exec1_OWhileTrue) ).
thf(495,plain,
! [A: state > $o,B: state,C: com,D: list @ com] :
( ( A @ B )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( while @ A @ C ) @ D ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ C @ ( cons @ com @ ( while @ A @ C ) @ D ) ) @ B ) ) @ pHoare1053570893_exec1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(249,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_list_Oinject) ).
thf(1189,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(134,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_77_prod__cases6) ).
thf(771,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)],[134]) ).
thf(265,axiom,
! [A: com,B: list @ com,C: state] :
( ( pHoare1335526537termis @ ( cons @ com @ A @ B ) @ C )
= ( ( termi @ A @ C )
& ! [D: state] :
( ( exec @ C @ A @ D )
=> ( pHoare1335526537termis @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_termis_Osimps_I2_J) ).
thf(1253,plain,
! [A: com,B: list @ com,C: state] :
( ( pHoare1335526537termis @ ( cons @ com @ A @ B ) @ C )
= ( ( termi @ A @ C )
& ! [D: state] :
( ( exec @ C @ A @ D )
=> ( pHoare1335526537termis @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rotate1 @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_rotate1_Osimps_I2_J) ).
thf(390,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rotate1 @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(45,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_listrel__rtrancl__eq__rtrancl__listrel1) ).
thf(401,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( listrel @ TA @ TA @ ( transitive_rtrancl @ TA @ A ) )
= ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(261,axiom,
! [A: state > $o,B: com,C: state] :
( ( termi @ ( while @ A @ B ) @ C )
=> ( ( A @ C )
=> ( termi @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_while__termiE) ).
thf(1244,plain,
! [A: state > $o,B: com,C: state] :
( ( termi @ ( while @ A @ B ) @ C )
=> ( ( A @ C )
=> ( termi @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(52,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Nil__is__append__conv) ).
thf(418,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(136,axiom,
! [A: state > $o,B: com,C: com,D: state > $o,E: com] :
( ( cond @ A @ B @ C )
!= ( while @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_com_Odistinct_I19_J) ).
thf(781,plain,
! [A: state > $o,B: com,C: com,D: state > $o,E: com] :
( ( cond @ A @ B @ C )
!= ( while @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(211,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ A ) @ ( append @ TA @ D @ B ) ) @ ( lexord @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_lexord__append__leftI) ).
thf(1030,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ D @ A ) @ ( append @ TA @ D @ B ) ) @ ( lexord @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(86,axiom,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_splice_Ocases) ).
thf(568,plain,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(147,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA,D: list @ TA] :
( ! [E: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ E ) @ A )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) ) @ ( lex @ TA @ A ) )
= ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ D ) @ ( lex @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_lex__append__left__iff) ).
thf(832,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: list @ TA,C: list @ TA,D: list @ TA] :
( ! [E: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ E ) @ A )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) ) @ ( lex @ TA @ A ) )
= ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ C @ D ) @ ( lex @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: list @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( cons @ TA @ A @ B ) @ C ) @ ( listrel @ TA @ TB @ D ) )
=> ~ ! [E: TB,F: list @ TB] :
( ( C
= ( cons @ TB @ E @ F ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ E ) @ D )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ B @ F ) @ ( listrel @ TA @ TB @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_listrel__Cons1) ).
thf(549,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: list @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ ( cons @ TA @ A @ B ) @ C ) @ ( listrel @ TA @ TB @ D ) )
=> ~ ! [E: TB,F: list @ TB] :
( ( C
= ( cons @ TB @ E @ F ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ E ) @ D )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TB ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TB ) @ B @ F ) @ ( listrel @ TA @ TB @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( lex @ TA @ E ) )
= ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
& ( ( size_size @ ( list @ TA ) @ B )
= ( size_size @ ( list @ TA ) @ D ) ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( lex @ TA @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_Cons__in__lex) ).
thf(620,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( lex @ TA @ E ) )
= ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
& ( ( size_size @ ( list @ TA ) @ B )
= ( size_size @ ( list @ TA ) @ D ) ) )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( lex @ TA @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(18,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( append @ TA @ ( butlast @ TA @ A ) @ ( cons @ TA @ ( last @ TA @ A ) @ ( nil @ TA ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_append__butlast__last__id) ).
thf(315,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( append @ TA @ ( butlast @ TA @ A ) @ ( cons @ TA @ ( last @ TA @ A ) @ ( nil @ TA ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(190,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(967,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(47,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_4) ).
thf(405,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(5,axiom,
! [TA: $tType,A: list @ TA,B: nat] :
( ( list_update @ TA @ A @ B @ ( nth @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_list__update__id) ).
thf(273,plain,
! [TA: $tType,A: list @ TA,B: nat] :
( ( list_update @ TA @ A @ B @ ( nth @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(127,axiom,
! [A: com,B: com,C: list @ com,D: state] : ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( semi @ A @ B ) @ C ) @ D ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ A @ ( cons @ com @ B @ C ) ) @ D ) ) @ pHoare1053570893_exec1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_exec1_OSemi) ).
thf(735,plain,
! [A: com,B: com,C: list @ com,D: state] : ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ ( semi @ A @ B ) @ C ) @ D ) @ ( product_Pair @ ( list @ com ) @ state @ ( cons @ com @ A @ ( cons @ com @ B @ C ) ) @ D ) ) @ pHoare1053570893_exec1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(185,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( C @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ E )
= ( size_size @ ( list @ TA ) @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_list__induct2) ).
thf(950,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( C @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ E )
= ( size_size @ ( list @ TA ) @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_bind__simps_I1_J) ).
thf(835,plain,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(27,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_append__self__conv) ).
thf(341,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(57,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_length__induct) ).
thf(437,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(110,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_shuffles_Oinduct) ).
thf(664,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(222,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lenlex @ TA @ B ) )
= ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_Nil__lenlex__iff1) ).
thf(1065,plain,
! [TA: $tType,A: list @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ A ) @ ( lenlex @ TA @ B ) )
= ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(12,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_neq__if__length__neq) ).
thf(294,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(143,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ C ) @ ( listrel1 @ TA @ E ) )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_snoc__listrel1__snoc__iff) ).
thf(801,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) @ ( listrel1 @ TA @ E ) )
= ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ C ) @ ( listrel1 @ TA @ E ) )
& ( B = D ) )
| ( ( A = C )
& ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(178,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( cons @ TA @ D @ B ) ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_rtrancl__listrel1__ConsI1) ).
thf(928,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA ),D: TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( cons @ TA @ D @ B ) ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(51,axiom,
! [A: state > ( set @ state ),B: state > ( set @ state )] :
( ( ( do @ A )
= ( do @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_com_Oinject_I1_J) ).
thf(415,plain,
! [A: state > ( set @ state ),B: state > ( set @ state )] :
( ( ( do @ A )
= ( do @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(129,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_induct__list012) ).
thf(740,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(65,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
= ( ? [D: TA,E: nat] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( nth @ TA @ A @ E ) @ D ) @ C )
& ( ord_less @ nat @ E @ ( size_size @ ( list @ TA ) @ A ) )
& ( B
= ( list_update @ TA @ A @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_listrel1__iff__update) ).
thf(464,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( listrel1 @ TA @ C ) )
= ( ? [D: TA,E: nat] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( nth @ TA @ A @ E ) @ D ) @ C )
& ( ord_less @ nat @ E @ ( size_size @ ( list @ TA ) @ A ) )
& ( B
= ( list_update @ TA @ A @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(54,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_Cons__eq__appendI) ).
thf(427,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(96,axiom,
! [A: state,B: list @ com,C: state] :
( ( pHoare1053570959_execs @ A @ B @ C )
=> ( ( ( B
= ( nil @ com ) )
=> ( C != A ) )
=> ~ ! [D: com,E: state,F: list @ com] :
( ( B
= ( cons @ com @ D @ F ) )
=> ( ( exec @ A @ D @ E )
=> ~ ( pHoare1053570959_execs @ E @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_execs_Ocases) ).
thf(596,plain,
! [A: state,B: list @ com,C: state] :
( ( pHoare1053570959_execs @ A @ B @ C )
=> ( ( ( B
= ( nil @ com ) )
=> ( C != A ) )
=> ~ ! [D: com,E: state,F: list @ com] :
( ( B
= ( cons @ com @ D @ F ) )
=> ( ( exec @ A @ D @ E )
=> ~ ( pHoare1053570959_execs @ E @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(77,axiom,
! [A: state > $o,B: state,C: com,D: state,E: com] :
( ( A @ B )
=> ( ( exec @ B @ C @ D )
=> ( exec @ B @ ( cond @ A @ C @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_exec_OIfTrue) ).
thf(528,plain,
! [A: state > $o,B: state,C: com,D: state,E: com] :
( ( A @ B )
=> ( ( exec @ B @ C @ D )
=> ( exec @ B @ ( cond @ A @ C @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TA > ( list @ TB ),B: TA,C: list @ TA] :
( ( maps @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TB @ ( A @ B ) @ ( maps @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_maps__simps_I1_J) ).
thf(459,plain,
! [TA: $tType,TB: $tType,A: TA > ( list @ TB ),B: TA,C: list @ TA] :
( ( maps @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TB @ ( A @ B ) @ ( maps @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(198,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_75_prod__induct3) ).
thf(992,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)],[198]) ).
thf(154,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_splice_Oinduct) ).
thf(850,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(195,axiom,
! [A: com,B: com,C: state > $o,D: com,E: com] :
( ( semi @ A @ B )
!= ( cond @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_com_Odistinct_I11_J) ).
thf(982,plain,
! [A: com,B: com,C: state > $o,D: com,E: com] :
( ( semi @ A @ B )
!= ( cond @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(233,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insert__Nil) ).
thf(1120,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(74,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_list__nonempty__induct) ).
thf(501,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(369,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(25,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(337,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(182,axiom,
! [A: com,B: com,C: state > $o,D: com] :
( ( semi @ A @ B )
!= ( while @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_com_Odistinct_I13_J) ).
thf(940,plain,
! [A: com,B: com,C: state > $o,D: com] :
( ( semi @ A @ B )
!= ( while @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(247,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( lexord @ TA @ E ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( lexord @ TA @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_lexord__cons__cons) ).
thf(1184,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA,E: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) ) @ ( lexord @ TA @ E ) )
= ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ C ) @ E )
| ( ( A = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ D ) @ ( lexord @ TA @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(16,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_self__append__conv) ).
thf(309,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(83,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) )
=> ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_rtrancl__listrel1__eq__len) ).
thf(560,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( transitive_rtrancl @ ( list @ TA ) @ ( listrel1 @ TA @ C ) ) )
=> ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_arg__min__list_Oinduct) ).
thf(882,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(181,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( A != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ C )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ ( transitive_rtrancl @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_converse__rtranclE) ).
thf(935,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( transitive_rtrancl @ TA @ C ) )
=> ( ( A != B )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ D ) @ C )
=> ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ B ) @ ( transitive_rtrancl @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(203,axiom,
! [A: list @ com,B: state,C: list @ com,D: state,E: list @ com] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ C @ D ) ) @ pHoare1053570893_exec1 )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ A @ E ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ C @ E ) @ D ) ) @ pHoare1053570893_exec1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_app__exec) ).
thf(1009,plain,
! [A: list @ com,B: state,C: list @ com,D: state,E: list @ com] :
( ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ A @ B ) @ ( product_Pair @ ( list @ com ) @ state @ C @ D ) ) @ pHoare1053570893_exec1 )
=> ( member @ ( product_prod @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) ) @ ( product_Pair @ ( product_prod @ ( list @ com ) @ state ) @ ( product_prod @ ( list @ com ) @ state ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ A @ E ) @ B ) @ ( product_Pair @ ( list @ com ) @ state @ ( append @ com @ C @ E ) @ D ) ) @ pHoare1053570893_exec1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1256,plain,
$false,
inference(e,[status(thm)],[347,1237,893,962,276,1068,994,861,878,440,511,1078,384,797,472,1233,930,841,288,565,651,829,1095,404,973,885,1046,1055,719,785,838,917,344,902,853,1087,421,475,492,591,321,623,353,485,1136,1020,574,766,1169,692,866,774,396,998,312,1215,634,1072,453,1074,920,678,270,661,546,381,366,334,910,957,1042,1123,788,467,1032,757,1128,456,324,1012,285,682,1195,615,725,1006,593,869,989,697,1234,1028,476,554,753,1039,970,393,1249,1131,1192,1246,371,360,508,558,1187,794,888,926,1241,266,398,1035,1026,1167,298,412,965,856,279,733,584,904,694,1226,843,1125,875,826,579,291,1139,1058,1090,804,704,947,350,713,498,979,406,303,863,377,996,737,318,880,434,890,387,1080,631,609,848,668,799,1162,626,915,462,932,1061,1198,959,768,1015,563,267,431,658,912,685,1171,986,306,1076,722,589,680,617,1181,1049,531,944,1145,1018,690,282,327,1252,1098,409,1230,1053,791,331,338,576,907,1141,1221,612,656,1023,446,571,845,450,363,671,976,581,495,1189,771,1253,390,401,1244,418,781,1030,568,832,549,620,315,967,405,273,735,950,835,341,437,664,1065,294,801,928,415,740,464,427,596,528,459,992,850,982,1120,501,369,337,940,1184,309,560,882,935,1009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP142^2 : TPTP v8.1.2. Released v7.5.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n024.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 14:49:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.76/1.13 % [INFO] Parsing done (264ms).
% 1.76/1.14 % [INFO] Running in sequential loop mode.
% 2.62/1.35 % [INFO] eprover registered as external prover.
% 2.62/1.35 % [INFO] cvc4 registered as external prover.
% 2.62/1.36 % [INFO] Scanning for conjecture ...
% 2.96/1.46 % [INFO] Found a conjecture and 264 axioms. Running axiom selection ...
% 3.35/1.56 % [INFO] Axiom selection finished. Selected 263 axioms (removed 1 axioms).
% 4.37/1.84 % [INFO] Problem is higher-order (TPTP THF).
% 4.37/1.85 % [INFO] Type checking passed.
% 4.37/1.86 % [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 ...
% 150.89/131.02 % External prover 'e' found a proof!
% 150.89/131.02 % [INFO] Killing All external provers ...
% 150.89/131.02 % Time passed: 130488ms (effective reasoning time: 129881ms)
% 150.89/131.02 % 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)>
% 150.89/131.02 % Axioms used in derivation (263): fact_24_splice_Ocases, fact_99_com_Odistinct_I19_J, fact_17_prod__cases4, fact_133_append_Oleft__neutral, fact_245_nth__butlast, fact_208_lenlex__append2, fact_227_list__induct3, fact_72_prod__induct6, fact_246_measures__less, fact_185_rotate1_Osimps_I1_J, fact_167_listrel__rtrancl__eq__rtrancl__listrel1, fact_70_rtranclE, fact_106_exec_OSemi, fact_164_append__listrel1I, fact_137_append__eq__append__conv2, fact_90_exec1E_I5_J, fact_170_Cons__listrel1E2, fact_53_list_Oinducts, fact_5_exec1__pres__termis, fact_64_converse__rtranclE, fact_205_last__append, tcon_Nat_Onat___Orderings_Olinorder, fact_67_rtrancl__trans, fact_187_lexord__irreflexive, fact_75_prod__induct3, fact_251_length__list__update, fact_13_list_Oinject, fact_249_list__update__overwrite, fact_34_strict__sorted_Ocases, fact_66_rtrancl__induct, fact_184_butlast_Osimps_I1_J, fact_124_append__self__conv2, fact_52_neq__Nil__conv, fact_228_list__induct2, fact_141_append__eq__Cons__conv, fact_55_list_OdiscI, tcon_HOL_Obool___Orderings_Oord_4, fact_76_prod__cases7, fact_242_nth__equalityI, fact_235_Cons__lenlex__iff, fact_47_min__list_Oinduct, fact_220_internal__case__prod__conv, fact_225_Ex__list__of__length, fact_15_old_Oprod_Oinject, fact_41_remdups__adj_Ocases, fact_179_rotate1_Osimps_I2_J, fact_154_snoc__listrel1__snoc__iff, tcon_fun___Orderings_Oord, fact_103_exec_OIfTrue, tcon_Nat_Onat___Orderings_Oord_1, fact_188_butlast_Osimps_I2_J, fact_127_append__is__Nil__conv, fact_40_sorted__wrt_Oinduct, fact_60_converse__rtrancl__into__rtrancl, fact_221_append__eq__append__conv, fact_111_com_Odistinct_I1_J, fact_57_execs_Oinducts, fact_181_rotate1__is__Nil__conv, fact_207_irrefl__def, fact_153_bind__simps_I2_J, fact_68_rtrancl_Osimps, fact_189_lexord__Nil__right, fact_113_subseqs_Osimps_I1_J, fact_100_termi_OWhileFalse, fact_25_execs_Ointros_I1_J, fact_16_prod__cases3, fact_161_rtrancl__listrel1__ConsI1, fact_7_rtrancl__induct2, fact_218_lex__append__left__iff, fact_239_listrel__iff__nth, fact_91_termi_OSemi, fact_22_sorted__wrt_Ocases, fact_217_lex__append__leftD, fact_27_old_Oprod_Oexhaust, fact_233_lexord__lex, fact_219_Cons__in__lex, fact_211_Nil__notin__lex, fact_178_lexord__append__left__rightI, fact_21_successively_Ocases, fact_10_exec1s__impl__execs, fact_146_listrel__rtrancl__trans, fact_194_lexord__same__pref__if__irrefl, fact_20_arg__min__list_Ocases, fact_160_listrel1I2, fact_51_list__induct2_H, fact_222_length__rotate1, fact_142_rev__nonempty__induct, fact_199_last__snoc, fact_18_prod__cases5, fact_168_rtrancl__listrel1__if__listrel, fact_32_execs_Ointros_I2_J, fact_213_lex__append__leftI, fact_120_same__append__eq, fact_243_Skolem__list__nth, fact_135_eq__Nil__appendI, fact_84_exec1_OIfTrue, fact_78_old_Oprod_Orec, fact_157_bind__simps_I1_J, fact_132_Cons__eq__appendI, fact_108_termi_OIfTrue, fact_149_listrel__Cons2, fact_210_Nil__lenlex__iff1, fact_26_old_Oprod_Oinducts, fact_186_lexord__linear, fact_48_min__list_Ocases, conj_2, fact_38_arg__min__list_Oinduct, fact_62_converse__rtrancl__induct, fact_107_termi_OIfFalse, fact_203_last_Osimps, fact_212_Nil2__notin__lex, fact_23_shuffles_Ocases, fact_6_execs__pres__termis, fact_136_append__eq__appendI, fact_49_induct__list012, fact_238_in__measures_I2_J, fact_39_remdups__adj_Oinduct, fact_214_lenlex__irreflexive, fact_94_com_Oinject_I1_J, fact_144_listrel__Nil1, fact_56_list_Odistinct_I1_J, fact_4_exec1s__impl__exec, fact_125_self__append__conv2, fact_176_listrel1E, fact_122_append__self__conv, fact_169_maps__simps_I2_J, fact_54_list_Oexhaust, fact_96_com_Oinject_I4_J, fact_253_nth__list__update__neq, fact_89_while__termiE2, fact_224_listrel__eq__len, fact_101_com_Odistinct_I5_J, fact_88_while__termiE, fact_148_listrel__Cons1, fact_232_lenlex__append1, fact_182_lexord__cons__cons, fact_216_lexl__not__refl, fact_9_converse__rtrancl__induct2, fact_156_concat__eq__append__conv, fact_180_butlast__snoc, fact_105_exec_ODo, fact_19_map__tailrec__rev_Ocases, fact_71_prod__induct7, fact_252_list__update__id, fact_116_listrel_Oinducts, fact_37_successively_Oinduct, fact_248_lex__take__index, fact_215_Nil__lenlex__iff2, fact_174_concat__eq__appendD, fact_114_app__execs, fact_236_list__ex1__simps_I1_J, fact_155_maps__simps_I1_J, fact_172_listrel1I1, fact_85_exec1E_I4_J, fact_35_map__tailrec__rev_Oinduct, fact_2_termis_Osimps_I1_J, tcon_HOL_Obool___Orderings_Olinorder_3, fact_250_list__update__nonempty, fact_8_converse__rtranclE2, fact_204_longest__common__suffix, fact_92_termi_OWhileTrue, fact_104_com_Odistinct_I13_J, fact_177_rtrancl__listrel1__ConsI2, fact_110_com_Odistinct_I11_J, fact_138_rev__induct, fact_193_lexord__append__rightI, fact_0_exec1E_I1_J, fact_151_listrel_Ocases, fact_166_concat_Osimps_I2_J, fact_65_rtrancl_Oinducts, fact_241_nth__append__length, fact_196_snoc__eq__iff__butlast, fact_82_exec1E_I2_J, fact_87_exec1_OWhileTrue, fact_129_append1__eq__conv, fact_190_butlast__append, fact_83_exec1_OIfFalse, fact_162_not__Nil__listrel1, fact_223_listrel1__eq__len, fact_14_prod_Oinject, fact_81_exec1_ODo, fact_165_concat_Osimps_I1_J, fact_237_length__induct, fact_1_termis_Osimps_I2_J, fact_206_irreflI, fact_230_lexord__sufE, fact_77_prod__cases6, fact_61_rtrancl_Ortrancl__into__rtrancl, fact_140_Cons__eq__append__conv, fact_117_append_Oassoc, fact_195_append__butlast__last__id, fact_244_list__eq__iff__nth__eq, fact_109_com_Odistinct_I3_J, fact_80_exec1E_I3_J, fact_95_com_Oinject_I3_J, fact_119_append__same__eq, fact_50_splice_Oinduct, fact_139_rev__exhaust, conj_1, fact_134_append__Nil, fact_175_listrel1I, fact_3_exec__impl__execs, fact_42_transpose_Ocases, fact_45_Collect__mem__eq, fact_247_listrel1__iff__update, fact_11_rtrancl__idemp, fact_131_append__Cons, fact_198_last__appendL, fact_159_Cons__listrel1__Cons, fact_98_exec_OWhileTrue, fact_102_exec_OIfFalse, fact_173_listrel__reflcl__if__listrel1, fact_86_exec1_OWhileFalse, fact_130_listrel__rtrancl__refl, fact_145_listrel_ONil, fact_231_lex__append__rightI, fact_150_app__exec, fact_12_r__into__rtrancl, fact_226_neq__if__length__neq, fact_97_exec_OWhileFalse, fact_163_not__listrel1__Nil, fact_33_strict__sorted_Oinduct, fact_73_prod__induct5, fact_112_product__lists_Osimps_I1_J, fact_240_in__measures_I1_J, fact_36_list__nonempty__induct, fact_192_lexord__append__leftD, fact_152_listrel_Osimps, fact_115_insert__Nil, fact_28_Pair__inject, fact_121_append__Nil2, fact_58_execs_Osimps, fact_79_exec1_OSemi, fact_30_surj__pair, fact_126_Nil__is__append__conv, fact_143_listrel__Nil2, fact_191_lexord__append__leftI, fact_147_listrel_OCons, fact_31_not__Cons__self2, fact_63_rtrancl_Ortrancl__refl, fact_234_rtrancl__listrel1__eq__len, fact_29_prod__cases, fact_123_self__append__conv, fact_128_append_Oright__neutral, conj_0, fact_183_lexord__Nil__left, fact_93_com_Oinject_I2_J, fact_158_concat__append, fact_197_last__appendR, fact_69_rtrancl_Ocases, fact_59_execs_Ocases, fact_74_prod__induct4, fact_254_nth__take, fact_201_last__ConsR, fact_118_append__assoc, fact_209_irrefl__lex, fact_44_mem__Collect__eq, fact_200_lexord__irrefl, fact_171_Cons__listrel1E1, fact_202_last__ConsL, fact_43_shuffles_Oinduct, fact_229_same__length__different, fact_46_Collect__cong
% 150.89/131.02 % No. of inferences in proof: 530
% 150.89/131.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 130488 ms resp. 129881 ms w/o parsing
% 151.78/131.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 151.78/131.20 % [INFO] Killing All external provers ...
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