TSTP Solution File: SWW470_5 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW470_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 : Fri May 19 12:24:01 EDT 2023
% Result : Theorem 90.22s 56.73s
% Output : Refutation 90.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 167
% Syntax : Number of formulae : 295 ( 63 unt; 41 typ; 0 def)
% Number of atoms : 3150 ( 258 equ; 0 cnn)
% Maximal formula atoms : 57 ( 12 avg)
% Number of connectives : 12550 ( 137 ~; 51 |; 96 &;11971 @)
% ( 21 <=>; 274 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 12 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 14 con; 0-6 aty)
% Number of variables : 964 ( 0 ^; 877 !; 52 ?; 964 :)
% ( 35 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(com_type,type,
com: $tType ).
thf(state_type,type,
state: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ TB @ ( fun @ TC @ TA ) ) ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( fun @ TC @ TB ) @ ( fun @ TC @ TA ) ) ) ).
thf(skip_type,type,
skip: com ).
thf(semi_type,type,
semi: com > com > com ).
thf(finite_finite1_type,type,
finite_finite1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > $o ) ).
thf(finite_fold1_type,type,
finite_fold1:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ TA ) ) > ( fun @ ( fun @ TA @ bool ) @ TA ) ) ).
thf(finite_fold1Set_type,type,
finite_fold1Set:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ TA ) ) > ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(finite_fold_graph_type,type,
finite_fold_graph:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TA ) ) > TA > ( fun @ TB @ bool ) > TA > $o ) ).
thf(finite_folding_one_type,type,
finite_folding_one:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ TA ) ) > ( fun @ ( fun @ TA @ bool ) @ TA ) > $o ) ).
thf(finite2073411215e_idem_type,type,
finite2073411215e_idem:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ TA ) ) > ( fun @ ( fun @ TA @ bool ) @ TA ) > $o ) ).
thf(the_type,type,
the:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA ) ).
thf(hoare_992312373derivs_type,type,
hoare_992312373derivs:
!>[TA: $tType] : ( ( fun @ ( hoare_28830079triple @ TA ) @ bool ) > ( fun @ ( hoare_28830079triple @ TA ) @ bool ) > $o ) ).
thf(hoare_1841697145triple_type,type,
hoare_1841697145triple:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ state @ bool ) ) > com > ( fun @ TA @ ( fun @ state @ bool ) ) > ( hoare_28830079triple @ TA ) ) ).
thf(hoare_376461865e_case_type,type,
hoare_376461865e_case:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ TA ) ) ) > ( hoare_28830079triple @ TB ) > TA ) ).
thf(hoare_678420151le_rec_type,type,
hoare_678420151le_rec:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ TA ) ) ) > ( hoare_28830079triple @ TB ) > TA ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fNot_type,type,
fNot: fun @ bool @ bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fdisj_type,type,
fdisj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(fimplies_type,type,
fimplies: fun @ bool @ ( fun @ bool @ bool ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(g_type,type,
g: fun @ ( hoare_28830079triple @ a ) @ bool ).
thf(p_type,type,
p: fun @ a @ ( fun @ state @ bool ) ).
thf(b_type,type,
b: fun @ state @ bool ).
thf(c_type,type,
c: com ).
thf(52,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(347,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(30,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ TA @ ( fun @ state @ bool ),C: fun @ TA @ ( fun @ state @ bool ),D: com,E: fun @ TA @ ( fun @ state @ bool ),F: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ E @ D @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ! [G: TA,H: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ B @ G ) @ H ) )
=> ! [I: state] :
( ! [J: TA] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ E @ J ) @ H ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ C @ J ) @ I ) ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ G ) @ I ) ) ) )
=> ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ B @ D @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_conseq12) ).
thf(234,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ TA @ ( fun @ state @ bool ),C: fun @ TA @ ( fun @ state @ bool ),D: com,E: fun @ TA @ ( fun @ state @ bool ),F: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ E @ D @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ! [G: TA,H: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ B @ G ) @ H ) )
=> ! [I: state] :
( ! [J: TA] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ E @ J ) @ H ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ C @ J ) @ I ) ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ G ) @ I ) ) ) )
=> ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ B @ D @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(110,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(555,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(58,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_emptyE) ).
thf(365,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(6,axiom,
! [A: com,B: com] :
( skip
!= ( semi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_com_Osimps_I12_J) ).
thf(138,plain,
! [A: com,B: com] :
( skip
!= ( semi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
| ~ ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(217,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
| ~ ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_singleton__inject) ).
thf(308,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(83,axiom,
bot @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(449,plain,
bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(81,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ TA @ ( fun @ state @ bool ),C: com,D: fun @ TA @ ( fun @ state @ bool ),E: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ E @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ C @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ! [F: TA,G: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ F ) @ G ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ D @ F ) @ G ) ) )
=> ( hoare_992312373derivs @ TA @ E @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ A @ C @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_conseq1) ).
thf(440,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ TA @ ( fun @ state @ bool ),C: com,D: fun @ TA @ ( fun @ state @ bool ),E: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ E @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ C @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ! [F: TA,G: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ F ) @ G ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ D @ F ) @ G ) ) )
=> ( hoare_992312373derivs @ TA @ E @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ A @ C @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(98,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ? [B: TA,C: fun @ TA @ bool] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_nonempty__iff) ).
thf(511,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [B: TA,C: fun @ TA @ bool] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) )
& ( ? [B: TA,C: fun @ TA @ bool] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) )
=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(64,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj ) @ B ) ) @ A ) ) )
<=> ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
& ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_finite__Collect__disjI) ).
thf(385,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj ) @ B ) ) @ A ) ) )
=> ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
& ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) ) )
& ( ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
& ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) )
=> ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(7,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_finite) ).
thf(142,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(97,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ A )
<=> ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
| ? [B: fun @ TA @ bool,C: TA] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) )
& ( finite_finite1 @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_finite_Osimps) ).
thf(500,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( finite_finite1 @ TA @ A )
=> ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
| ? [B: fun @ TA @ bool,C: TA] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) )
& ( finite_finite1 @ TA @ B ) ) ) )
& ( ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
| ? [B: fun @ TA @ bool,C: TA] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) )
& ( finite_finite1 @ TA @ B ) ) )
=> ( finite_finite1 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(91,axiom,
! [TA: $tType,A: TA,B: TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ C @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_fold1Set__sing) ).
thf(472,plain,
! [TA: $tType,A: TA,B: TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ C @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ C @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(19,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_folding__one_Oinsert) ).
thf(185,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
( ( hoare_376461865e_case @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_triple_Osimps_I2_J) ).
thf(565,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
( ( hoare_376461865e_case @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(65,axiom,
finite_finite @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(389,plain,
finite_finite @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(118,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ B )
=> ( ( hoare_992312373derivs @ TA @ A @ C )
=> ( hoare_992312373derivs @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cut) ).
thf(587,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ B )
=> ( ( hoare_992312373derivs @ TA @ A @ C )
=> ( hoare_992312373derivs @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(51,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_insert__absorb2) ).
thf(344,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(105,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ A @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_empty) ).
thf(542,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ A @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(76,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ TA @ ( fun @ state @ bool ),C: com,D: fun @ TA @ ( fun @ state @ bool ),E: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ E @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ C @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ! [F: TA,G: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ B @ F ) @ G ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ F ) @ G ) ) )
=> ( hoare_992312373derivs @ TA @ E @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ C @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_conseq2) ).
thf(421,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ TA @ ( fun @ state @ bool ),C: com,D: fun @ TA @ ( fun @ state @ bool ),E: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ E @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ C @ B ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ! [F: TA,G: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ B @ F ) @ G ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ F ) @ G ) ) )
=> ( hoare_992312373derivs @ TA @ E @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ C @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(124,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) )
<=> ( finite_finite1 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_finite__insert) ).
thf(606,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) )
=> ( finite_finite1 @ TA @ A ) )
& ( ( finite_finite1 @ TA @ A )
=> ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(95,axiom,
! [TA: $tType,A: TA,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ B @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_folding__one_Osingleton) ).
thf(492,plain,
! [TA: $tType,A: TA,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ B @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(82,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_insert__ident) ).
thf(443,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( ( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(34,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ) )
=> ( ( C != B )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_insertE) ).
thf(253,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ) )
=> ( ( C != B )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) ) @ B ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) ) @ B ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Collect__conv__if2) ).
thf(485,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) ) @ B ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) ) ) @ B ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ C @ B ) @ A ) )
<=> ? [D: TA,E: fun @ TA @ bool,F: TA] :
( ( B
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ E ) )
& ( A = F )
& ( finite_fold_graph @ TA @ TA @ C @ D @ E @ F )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_fold1Set_Osimps) ).
thf(238,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ C @ B ) @ A ) )
=> ? [D: TA,E: fun @ TA @ bool,F: TA] :
( ( B
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ E ) )
& ( A = F )
& ( finite_fold_graph @ TA @ TA @ C @ D @ E @ F )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) )
& ( ? [D: TA,E: fun @ TA @ bool,F: TA] :
( ( B
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ E ) )
& ( A = F )
& ( finite_fold_graph @ TA @ TA @ C @ D @ E @ F )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( finite_finite1 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ! [D: TA,E: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ C @ D ) @ E ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ E ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ B @ A ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_folding__one_Oclosed) ).
thf(353,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( finite_finite1 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ! [D: TA,E: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ C @ D ) @ E ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ E ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ B @ A ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(10,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ D @ C )
= ( semi @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_com_Osimps_I3_J) ).
thf(147,plain,
! [A: com,B: com,C: com,D: com] :
( ( ( ( semi @ D @ C )
= ( semi @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( semi @ D @ C )
= ( semi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(453,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( fun @ TA @ TA ),C: fun @ TB @ bool] :
( ( finite_finite1 @ TB @ C )
=> ? [D: TA] : ( finite_fold_graph @ TB @ TA @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_finite__imp__fold__graph) ).
thf(132,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( fun @ TA @ TA ),C: fun @ TB @ bool] :
( ( finite_finite1 @ TB @ C )
=> ? [D: TA] : ( finite_fold_graph @ TB @ TA @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_finite_OinsertI) ).
thf(396,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(101,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ~ ! [C: fun @ TA @ bool] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Set_Oset__insert) ).
thf(527,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ~ ! [C: fun @ TA @ bool] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_insertI2) ).
thf(248,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(201,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) @ B ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) @ B ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Collect__conv__if) ).
thf(534,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) @ B ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) @ B ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_singletonE) ).
thf(334,plain,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_singleton__iff) ).
thf(302,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(122,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_the__elem__eq) ).
thf(598,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(40,axiom,
! [TA: $tType,A: hoare_28830079triple @ TA] :
~ ! [B: fun @ TA @ ( fun @ state @ bool ),C: com,D: fun @ TA @ ( fun @ state @ bool )] :
( A
!= ( hoare_1841697145triple @ TA @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_triple_Oexhaust) ).
thf(297,plain,
! [TA: $tType,A: hoare_28830079triple @ TA] :
~ ! [B: fun @ TA @ ( fun @ state @ bool ),C: com,D: fun @ TA @ ( fun @ state @ bool )] :
( A
!= ( hoare_1841697145triple @ TA @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(77,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_the__sym__eq__trivial) ).
thf(424,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_equals0D) ).
thf(165,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(57,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ ( hoare_28830079triple @ TA ) @ bool,D: fun @ TA @ ( fun @ state @ bool )] :
( ! [E: TA,F: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ D @ E ) @ F ) )
=> ? [G: fun @ TA @ ( fun @ state @ bool ),H: fun @ TA @ ( fun @ state @ bool )] :
( ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ G @ B @ H ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
& ! [I: state] :
( ! [J: TA] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ G @ J ) @ F ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ H @ J ) @ I ) ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ E ) @ I ) ) ) ) )
=> ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_conseq) ).
thf(361,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ ( hoare_28830079triple @ TA ) @ bool,D: fun @ TA @ ( fun @ state @ bool )] :
( ! [E: TA,F: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ D @ E ) @ F ) )
=> ? [G: fun @ TA @ ( fun @ state @ bool ),H: fun @ TA @ ( fun @ state @ bool )] :
( ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ G @ B @ H ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
& ! [I: state] :
( ! [J: TA] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ G @ J ) @ F ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ H @ J ) @ I ) ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ E ) @ I ) ) ) ) )
=> ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( C = A ) )
=> ( ( the @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_the__equality) ).
thf(522,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( C = A ) )
=> ( ( the @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(87,axiom,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(461,plain,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(86,axiom,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( ! [C: TA,D: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ D )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ D ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ D ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_finite__induct) ).
thf(456,plain,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( ! [C: TA,D: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ D )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ D ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ D ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(99,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(519,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
( ( hoare_678420151le_rec @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_triple_Orecs) ).
thf(403,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
( ( hoare_678420151le_rec @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(20,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_equals0I) ).
thf(188,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(55,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: com,E: fun @ TA @ ( fun @ state @ bool ),F: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ E @ D @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ E @ ( semi @ D @ B ) @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Comp) ).
thf(356,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: com,E: fun @ TA @ ( fun @ state @ bool ),F: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ E @ D @ C ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( hoare_992312373derivs @ TA @ F @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ E @ ( semi @ D @ B ) @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(14,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ ( hoare_28830079triple @ TA ) @ bool,D: fun @ TA @ ( fun @ state @ bool )] :
( ! [E: TA,F: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ D @ E ) @ F ) )
=> ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ ( combk @ ( fun @ state @ bool ) @ TA @ ( aa @ state @ ( fun @ state @ bool ) @ ( aa @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( combc @ state @ state @ bool ) @ ( fequal @ state ) ) @ F ) ) @ B @ ( combk @ ( fun @ state @ bool ) @ TA @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ E ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) )
=> ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_escape) ).
thf(169,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ ( hoare_28830079triple @ TA ) @ bool,D: fun @ TA @ ( fun @ state @ bool )] :
( ! [E: TA,F: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ D @ E ) @ F ) )
=> ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ ( combk @ ( fun @ state @ bool ) @ TA @ ( aa @ state @ ( fun @ state @ bool ) @ ( aa @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( fun @ state @ ( fun @ state @ bool ) ) @ ( combc @ state @ state @ bool ) @ ( fequal @ state ) ) @ F ) ) @ B @ ( combk @ ( fun @ state @ bool ) @ TA @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ E ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) )
=> ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ D @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(50,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ D @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) ) @ A ) )
=> ~ ! [E: TA,F: fun @ TA @ bool] :
( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ E ) @ F ) )
=> ( ( finite_fold_graph @ TA @ TA @ D @ E @ F @ A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_insert__fold1SetE) ).
thf(339,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ D @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) ) @ A ) )
=> ~ ! [E: TA,F: fun @ TA @ bool] :
( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ E ) @ F ) )
=> ( ( finite_fold_graph @ TA @ TA @ D @ E @ F @ A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(547,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(26,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_singleton__conv) ).
thf(212,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(45,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(328,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(35,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_insert__commute) ).
thf(256,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TB @ TA @ C @ B @ ( bot_bot @ ( fun @ TB @ bool ) ) @ A )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_empty__fold__graphE) ).
thf(393,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TB @ TA @ C @ B @ ( bot_bot @ ( fun @ TB @ bool ) ) @ A )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(3,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(129,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: com,B: com] :
( ( semi @ B @ A )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_com_Osimps_I13_J) ).
thf(134,plain,
! [A: com,B: com] :
( ( semi @ B @ A )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
hoare_992312373derivs @ a @ g @ ( aa @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( aa @ ( hoare_28830079triple @ a ) @ ( fun @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ a ) ) @ ( hoare_1841697145triple @ a @ ( combk @ ( fun @ state @ bool ) @ a @ ( combk @ bool @ state @ fFalse ) ) @ c @ ( aa @ ( fun @ state @ bool ) @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combc @ a @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ a @ ( combs @ state @ bool @ bool ) ) @ ( aa @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ a @ ( combb @ bool @ ( fun @ bool @ bool ) @ state @ fconj ) ) @ p ) ) ) @ ( aa @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) @ ( combb @ bool @ bool @ state @ fNot ) @ b ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( hoare_992312373derivs @ a @ g @ ( aa @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( aa @ ( hoare_28830079triple @ a ) @ ( fun @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ a ) ) @ ( hoare_1841697145triple @ a @ ( combk @ ( fun @ state @ bool ) @ a @ ( combk @ bool @ state @ fFalse ) ) @ c @ ( aa @ ( fun @ state @ bool ) @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combc @ a @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ a @ ( combs @ state @ bool @ bool ) ) @ ( aa @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ a @ ( combb @ bool @ ( fun @ bool @ bool ) @ state @ fconj ) ) @ p ) ) ) @ ( aa @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) @ ( combb @ bool @ bool @ state @ fNot ) @ b ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ( hoare_992312373derivs @ a @ g @ ( aa @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( aa @ ( hoare_28830079triple @ a ) @ ( fun @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ a ) ) @ ( hoare_1841697145triple @ a @ ( combk @ ( fun @ state @ bool ) @ a @ ( combk @ bool @ state @ fFalse ) ) @ c @ ( aa @ ( fun @ state @ bool ) @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ a @ ( fun @ state @ bool ) ) ) @ ( combc @ a @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ a @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) ) @ a @ ( combs @ state @ bool @ bool ) ) @ ( aa @ ( fun @ a @ ( fun @ state @ bool ) ) @ ( fun @ a @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ a @ ( combb @ bool @ ( fun @ bool @ bool ) @ state @ fconj ) ) @ p ) ) ) @ ( aa @ ( fun @ state @ bool ) @ ( fun @ state @ bool ) @ ( combb @ bool @ bool @ state @ fNot ) @ b ) ) ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ bool,C: TA,D: fun @ TB @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TB @ TA @ D @ C @ B @ A )
<=> ( ( ( B
= ( bot_bot @ ( fun @ TB @ bool ) ) )
& ( A = C ) )
| ? [E: TB,F: fun @ TB @ bool,G: TA] :
( ( B
= ( aa @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( insert @ TB ) @ E ) @ F ) )
& ( A
= ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ E ) @ G ) )
& ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ F ) )
& ( finite_fold_graph @ TB @ TA @ D @ C @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_fold__graph_Osimps) ).
thf(311,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ bool,C: TA,D: fun @ TB @ ( fun @ TA @ TA )] :
( ( ( finite_fold_graph @ TB @ TA @ D @ C @ B @ A )
=> ( ( ( B
= ( bot_bot @ ( fun @ TB @ bool ) ) )
& ( A = C ) )
| ? [E: TB,F: fun @ TB @ bool,G: TA] :
( ( B
= ( aa @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( insert @ TB ) @ E ) @ F ) )
& ( A
= ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ E ) @ G ) )
& ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ F ) )
& ( finite_fold_graph @ TB @ TA @ D @ C @ F @ G ) ) ) )
& ( ( ( ( B
= ( bot_bot @ ( fun @ TB @ bool ) ) )
& ( A = C ) )
| ? [E: TB,F: fun @ TB @ bool,G: TA] :
( ( B
= ( aa @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( insert @ TB ) @ E ) @ F ) )
& ( A
= ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ E ) @ G ) )
& ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ F ) )
& ( finite_fold_graph @ TB @ TA @ D @ C @ F @ G ) ) )
=> ( finite_fold_graph @ TB @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(69,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_empty__iff) ).
thf(398,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(17,axiom,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_empty__def) ).
thf(180,plain,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(123,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_empty__Collect__eq) ).
thf(601,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite2073411215e_idem @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_folding__one__idem_Oinsert__idem) ).
thf(562,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite2073411215e_idem @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(21,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ ( fun @ state @ bool ),E: com,F: fun @ TA @ ( fun @ state @ bool )] :
( ( ( hoare_1841697145triple @ TA @ F @ E @ D )
= ( hoare_1841697145triple @ TA @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_triple_Oinject) ).
thf(191,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ ( fun @ state @ bool ),E: com,F: fun @ TA @ ( fun @ state @ bool )] :
( ( ( ( hoare_1841697145triple @ TA @ F @ E @ D )
= ( hoare_1841697145triple @ TA @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( hoare_1841697145triple @ TA @ F @ E @ D )
= ( hoare_1841697145triple @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( collect @ TA @ A ) )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fimplies ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ fNot ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_insert__Collect) ).
thf(204,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( collect @ TA @ A ) )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fimplies ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ fNot ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(36,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( C = A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ ( the @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_theI) ).
thf(259,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( C = A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ ( the @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(74,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_ex__in__conv) ).
thf(413,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(126,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(611,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(8,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(144,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(350,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(72,axiom,
! [TA: $tType,A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
<=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_bot__empty__eq) ).
thf(406,plain,
! [TA: $tType,A: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ? [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ D ) )
=> ( D = C ) ) )
=> ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( the @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_the1__equality) ).
thf(172,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ? [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ D ) )
=> ( D = C ) ) )
=> ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
=> ( ( the @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
<=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_doubleton__eq__iff) ).
thf(219,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) )
& ( ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(39,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool,D: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ C )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) )
<=> ( ( ( D = B )
=> ( C = A ) )
& ( ( D != B )
=> ? [E: fun @ TA @ bool] :
( ( C
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ E ) )
& ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_insert__eq__iff) ).
thf(274,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool,D: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ C )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) )
=> ( ( ( D = B )
=> ( C = A ) )
& ( ( D != B )
=> ? [E: fun @ TA @ bool] :
( ( C
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ E ) )
& ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ) ) )
& ( ( ( ( D = B )
=> ( C = A ) )
& ( ( D != B )
=> ? [E: fun @ TA @ bool] :
( ( C
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ E ) )
& ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ D ) @ C )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(75,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_insertI1) ).
thf(419,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(62,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_all__not__in__conv) ).
thf(377,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(79,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ B ) )
& ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( C = B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( the @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_theI_H) ).
thf(434,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ B ) )
& ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ A @ C ) )
=> ( C = B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( the @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ ( fun @ TA @ TA ),D: fun @ TB @ bool,E: TB] :
( ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ D ) )
=> ( ( finite_fold_graph @ TB @ TA @ C @ B @ D @ A )
=> ( finite_fold_graph @ TB @ TA @ C @ B @ ( aa @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( insert @ TB ) @ E ) @ D ) @ ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_fold__graph_OinsertI) ).
thf(609,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ ( fun @ TA @ TA ),D: fun @ TB @ bool,E: TB] :
( ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ D ) )
=> ( ( finite_fold_graph @ TB @ TA @ C @ B @ D @ A )
=> ( finite_fold_graph @ TB @ TA @ C @ B @ ( aa @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ TB @ bool ) ) @ ( insert @ TB ) @ E ) @ D ) @ ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ C @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(46,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(330,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(59,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_insert__compr) ).
thf(367,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(109,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
| ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) )
=> ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_finite__Collect__conjI) ).
thf(552,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
| ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) )
=> ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) @ A ) )
<=> ( ( C = A )
| ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_insert__code) ).
thf(267,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) @ A ) )
=> ( ( C = A )
| ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) )
& ( ( ( C = A )
| ( pp @ ( aa @ TA @ bool @ B @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ( finite_finite @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(438,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ( finite_finite @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(94,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(490,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(589,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(9,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_finite__code) ).
thf(145,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( finite_finite1 @ TA @ A )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ B @ A )
= ( aa @ ( fun @ TA @ bool ) @ TA @ ( finite_fold1 @ TA @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_folding__one_Oeq__fold) ).
thf(162,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( finite_finite1 @ TA @ A )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ B @ A )
= ( aa @ ( fun @ TA @ bool ) @ TA @ ( finite_fold1 @ TA @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(102,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(531,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(111,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ ( fun @ TA @ TA )] :
( ( aa @ ( fun @ TA @ bool ) @ TA @ ( finite_fold1 @ TA @ B ) @ A )
= ( the @ TA @ ( finite_fold1Set @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_fold1__def) ).
thf(557,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ ( fun @ TA @ TA )] :
( ( aa @ ( fun @ TA @ bool ) @ TA @ ( finite_fold1 @ TA @ B ) @ A )
= ( the @ TA @ ( finite_fold1Set @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(73,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ C @ B ) @ A ) )
=> ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_fold1Set__nonempty) ).
thf(409,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ C @ B ) @ A ) )
=> ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(37,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ? [C: fun @ TA @ bool] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_mk__disjoint__insert) ).
thf(263,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ? [C: fun @ TA @ bool] :
( ( A
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(16,axiom,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_the__eq__trivial) ).
thf(177,plain,
! [TA: $tType,A: TA] :
( ( the @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_bot__apply) ).
thf(370,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(88,axiom,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(463,plain,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(544,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(90,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(470,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(117,axiom,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ! [C: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( ! [C: TA,D: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ D )
=> ( ( D
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ D ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ D ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_finite__ne__induct) ).
thf(576,plain,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ! [C: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( ! [C: TA,D: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ D )
=> ( ( D
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ D ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ D ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(127,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(613,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( C = A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_insertCI) ).
thf(571,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( C = A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(121,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( bot_bot @ ( fun @ TA @ bool ) )
!= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_empty__not__insert) ).
thf(595,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( bot_bot @ ( fun @ TA @ bool ) )
!= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_bot__fun__def) ).
thf(450,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(104,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_insert__absorb) ).
thf(539,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(96,axiom,
! [TA: $tType,A: TA,B: TA,C: bool] :
( ( ( pp @ C )
=> ( B
= ( the @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ C ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ ( aa @ bool @ bool @ fNot @ C ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) ) ) )
& ( ~ ( pp @ C )
=> ( A
= ( the @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ C ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ ( aa @ bool @ bool @ fNot @ C ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_If__def) ).
thf(495,plain,
! [TA: $tType,A: TA,B: TA,C: bool] :
( ( ( pp @ C )
=> ( B
= ( the @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ C ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ ( aa @ bool @ bool @ fNot @ C ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) ) ) )
& ( ~ ( pp @ C )
=> ( A
= ( the @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ C ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ B ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( combb @ bool @ bool @ TA @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ ( aa @ bool @ bool @ fNot @ C ) ) ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( combb @ TB @ TC @ TA @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(250,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( combb @ TB @ TC @ TA @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(89,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Collect__empty__eq) ).
thf(465,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ ( fun @ TA @ TA ),C: fun @ ( fun @ TA @ bool ) @ TA] :
( ( C
= ( finite_fold1 @ TA @ B ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_fold1__singleton__def) ).
thf(158,plain,
! [TA: $tType,A: TA,B: fun @ TA @ ( fun @ TA @ TA ),C: fun @ ( fun @ TA @ bool ) @ TA] :
( ( C
= ( finite_fold1 @ TA @ B ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(66,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [C: TA] : ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_finite__nonempty__imp__fold1Set) ).
thf(390,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [C: TA] : ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(115,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( hoare_28830079triple @ TA ) @ bool,E: bool] :
( ( ( pp @ E )
=> ( hoare_992312373derivs @ TA @ D @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) )
=> ( hoare_992312373derivs @ TA @ D @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ ( aa @ bool @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( fun @ bool @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combc @ TA @ bool @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ bool @ ( fun @ state @ bool ) ) @ TA @ ( combc @ state @ bool @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ TA @ ( combb @ bool @ ( fun @ bool @ bool ) @ state @ fconj ) ) @ C ) ) ) @ E ) @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_constant) ).
thf(568,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( hoare_28830079triple @ TA ) @ bool,E: bool] :
( ( ( pp @ E )
=> ( hoare_992312373derivs @ TA @ D @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) )
=> ( hoare_992312373derivs @ TA @ D @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ ( aa @ bool @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( fun @ bool @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( combc @ TA @ bool @ ( fun @ state @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ bool @ ( fun @ state @ bool ) ) ) @ ( combb @ ( fun @ state @ ( fun @ bool @ bool ) ) @ ( fun @ bool @ ( fun @ state @ bool ) ) @ TA @ ( combc @ state @ bool @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ TA @ ( fun @ state @ ( fun @ bool @ bool ) ) ) @ ( combb @ ( fun @ state @ bool ) @ ( fun @ state @ ( fun @ bool @ bool ) ) @ TA @ ( combb @ bool @ ( fun @ bool @ bool ) @ state @ fconj ) ) @ C ) ) ) @ E ) @ B @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(24,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( the_elem @ TA @ A )
= ( the @ TA @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ bool ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fequal @ ( fun @ TA @ bool ) ) @ A ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_the__elem__def) ).
thf(207,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( the_elem @ TA @ A )
= ( the @ TA @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ bool ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fequal @ ( fun @ TA @ bool ) ) @ A ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(92,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ? [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ D ) )
=> ( D = C ) ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( the @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_the1I2) ).
thf(478,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ? [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
& ! [D: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ D ) )
=> ( D = C ) ) )
=> ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ ( the @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( fun @ TA @ TA )] : ( finite_fold_graph @ TB @ TA @ B @ A @ ( bot_bot @ ( fun @ TB @ bool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_fold__graph_OemptyI) ).
thf(383,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( fun @ TA @ TA )] : ( finite_fold_graph @ TB @ TA @ B @ A @ ( bot_bot @ ( fun @ TB @ bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(108,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_singleton__conv2) ).
thf(549,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(41,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(300,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TA @ TA @ D @ C @ B @ A )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ D @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_fold1Set_Ointros) ).
thf(183,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TA @ TA @ D @ C @ B @ A )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ D @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ C ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(373,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(25,axiom,
! [A: bool,B: bool] :
( ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(210,plain,
! [A: bool,B: bool] :
( ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ ( fun @ TA @ TA )] :
( ( aa @ ( fun @ TA @ bool ) @ TA @ ( finite_fold1 @ TA @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_fold1__singleton) ).
thf(358,plain,
! [TA: $tType,A: TA,B: fun @ TA @ ( fun @ TA @ TA )] :
( ( aa @ ( fun @ TA @ bool ) @ TA @ ( finite_fold1 @ TA @ B ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(70,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A )
!= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_insert__not__empty) ).
thf(400,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A )
!= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(47,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ B @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ A @ skip @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_hoare__derivs_OSkip) ).
thf(332,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ B @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ ( hoare_1841697145triple @ TA @ A @ skip @ A ) ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(78,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ) )
<=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_insert__iff) ).
thf(427,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ) )
=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(49,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: hoare_28830079triple @ TA,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ B ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ( hoare_992312373derivs @ TA @ C @ A )
=> ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
thf(337,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: hoare_28830079triple @ TA,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ B ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ( hoare_992312373derivs @ TA @ C @ A )
=> ( hoare_992312373derivs @ TA @ C @ ( aa @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) @ ( insert @ ( hoare_28830079triple @ TA ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(27,axiom,
! [TA: $tType] : ( finite_finite1 @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_finite_OemptyI) ).
thf(215,plain,
! [TA: $tType] : ( finite_finite1 @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ ( fun @ TA @ TA )] :
~ ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_empty__fold1SetE) ).
thf(560,plain,
! [TA: $tType,A: TA,B: fun @ TA @ ( fun @ TA @ TA )] :
~ ( pp @ ( aa @ TA @ bool @ ( finite_fold1Set @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(120,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_insert__compr__raw) ).
thf(592,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( insert @ TA ) @ A ) @ B )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj ) @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ TA @ bool ) @ ( fequal @ TA ) ) @ A ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(615,plain,
$false,
inference(e,[status(thm)],[347,234,555,365,138,217,308,449,440,511,385,142,500,472,185,565,389,587,344,542,421,606,492,443,253,485,238,353,147,453,132,396,527,248,201,534,334,302,598,297,424,165,361,522,461,456,519,403,188,356,169,339,547,212,328,256,393,129,134,128,311,398,180,601,562,191,204,259,413,611,144,350,406,172,219,274,419,377,434,609,330,367,552,267,438,490,589,145,162,531,557,409,263,177,370,463,544,470,576,613,571,595,450,539,495,250,465,158,390,568,207,478,383,549,300,183,373,210,358,400,332,427,337,215,560,592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW470_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n020.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 : Thu May 18 22:22:18 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.00/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.58/1.15 % [INFO] Parsing done (234ms).
% 1.58/1.15 % [INFO] Running in sequential loop mode.
% 2.37/1.36 % [INFO] eprover registered as external prover.
% 2.37/1.36 % [INFO] cvc4 registered as external prover.
% 2.37/1.37 % [INFO] Scanning for conjecture ...
% 2.87/1.50 % [INFO] Found a conjecture and 125 axioms. Running axiom selection ...
% 3.27/1.59 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 3.75/1.77 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.75/1.79 % [INFO] Type checking passed.
% 3.75/1.79 % [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 ...
% 5.69/2.36 % [INFO] [Domain constraints] Detected constraint on bool
% 5.69/2.36 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 90.22/56.72 % External prover 'e' found a proof!
% 90.22/56.72 % [INFO] Killing All external provers ...
% 90.22/56.73 % Time passed: 56193ms (effective reasoning time: 55567ms)
% 90.22/56.73 % 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)>
% 90.22/56.73 % Axioms used in derivation (125): fact_4_constant, arity_HOL_Obool___Finite__Set_Ofinite, fact_45_bot__fun__def, fact_23_insert__absorb, help_fimplies_2_1_U, help_COMBS_1_1_U, fact_19_empty__iff, fact_84_finite, help_fconj_3_1_U, arity_fun___Orderings_Obot, fact_95_finite__imp__fold__graph, fact_13_insertE, fact_96_fold1Set_Osimps, fact_51_com_Osimps_I12_J, fact_47_Comp, fact_89_fold1__singleton__def, fact_83_folding__one_Oeq__fold, fact_3_hoare__derivs_Oinsert, fact_41_the__elem__eq, fact_69_fold1Set__nonempty, fact_60_theI_H, fact_71_fold1Set_Ointros, fact_56_Set_Oset__insert, fact_12_insert__iff, fact_39_Collect__conv__if, fact_67_folding__one_Osingleton, fact_50_com_Osimps_I13_J, fact_15_all__not__in__conv, help_fNot_2_1_U, fact_74_finite__code, fact_1_empty, help_fNot_1_1_U, fact_46_hoare__derivs_OSkip, help_fFalse_1_1_T, fact_2_cut, fact_72_folding__one_Oinsert, fact_21_ex__in__conv, fact_7_escape, help_COMBB_1_1_U, fact_64_nonempty__iff, fact_31_insertI1, fact_97_fold__graph_Osimps, fact_0_triple_Oinject, fact_62_equals0I, fact_27_insert__code, fact_93_finite_Osimps, fact_11_insert__absorb2, help_fdisj_1_1_U, fact_87_fold__graph_OemptyI, fact_36_singleton__iff, help_fconj_2_1_U, fact_6_singleton__conv, fact_17_emptyE, fact_68_the1I2, fact_40_Collect__conv__if2, fact_85_fold__graph_OinsertI, fact_35_doubleton__eq__iff, fact_26_insert__ident, fact_52_the__elem__def, fact_79_finite__Collect__disjI, fact_58_theI, fact_43_triple_Orecs, fact_37_insert__not__empty, fact_25_insert__eq__iff, help_fequal_1_1_T, arity_fun___Finite__Set_Ofinite, fact_65_bot__empty__eq, fact_14_insertCI, fact_8_conseq2, fact_61_mk__disjoint__insert, fact_44_bot__apply, fact_76_mem__def, fact_22_empty__def, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_70_empty__fold1SetE, fact_38_empty__not__insert, fact_10_conseq12, fact_28_insert__commute, fact_34_singletonE, fact_63_conseq, fact_53_the__sym__eq__trivial, fact_73_fold1__def, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, help_fequal_2_1_T, fact_81_finite_OinsertI, fact_99_finite__ne__induct, fact_24_insertI2, fact_48_triple_Oexhaust, help_fconj_1_1_U, help_fdisj_3_1_U, fact_54_the__eq__trivial, fact_86_empty__fold__graphE, fact_32_insert__compr__raw, fact_91_insert__fold1SetE, help_fFalse_1_1_U, fact_49_com_Osimps_I3_J, fact_77_Collect__def, fact_57_the__equality, fact_9_conseq1, fact_90_folding__one_Oclosed, fact_78_finite__Collect__conjI, fact_55_If__def, fact_94_finite__induct, help_pp_1_1_U, fact_88_fold1__singleton, fact_5_singleton__conv2, fact_16_empty__Collect__eq, help_fimplies_1_1_U, fact_98_folding__one__idem_Oinsert__idem, fact_75_ext, help_fimplies_3_1_U, fact_66_fold1Set__sing, fact_82_finite__insert, help_pp_2_1_U, fact_92_finite__nonempty__imp__fold1Set, fact_59_the1__equality, fact_29_insert__Collect, fact_18_Collect__empty__eq, fact_80_finite_OemptyI, fact_42_triple_Osimps_I2_J, fact_30_insert__compr, fact_20_equals0D, fact_33_singleton__inject
% 90.22/56.73 % No. of inferences in proof: 254
% 90.22/56.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 56193 ms resp. 55567 ms w/o parsing
% 90.66/56.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 90.66/56.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------