%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW470_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:15 AM UTC 2026
% Result : Theorem 118.55s 83.44s
% Output : Refutation 119.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 126
% Syntax : Number of formulae : 254 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 3150 ( 258 equ; 0 cnn)
% Maximal formula atoms : 57 ( 12 avg)
% Number of connectives : 12382 ( 137 ~; 51 |; 96 &;11803 @)
% ( 21 <=>; 274 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 12 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 14 con; 0-6 aty)
% Number of variables : 929 ( 0 ^; 877 !; 52 ?; 929 :)
% 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_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(finite_finite_decl,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TC @ fun ) @ ( TB @ ( TC @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) ) ).
thf(skip_decl,type,
skip: com ).
thf(semi_decl,type,
semi: com > com > com ).
thf(finite_finite1_decl,type,
finite_finite1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > $o ) ).
thf(finite_fold1_decl,type,
finite_fold1:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) > ( TA @ ( bool @ ( TA @ fun ) @ fun ) ) ) ).
thf(finite_fold1Set_decl,type,
finite_fold1Set:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(finite_fold_graph_decl,type,
finite_fold_graph:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TA @ fun ) @ ( TB @ fun ) ) > TA > ( bool @ ( TB @ fun ) ) > TA > $o ) ).
thf(finite_folding_one_decl,type,
finite_folding_one:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) > ( TA @ ( bool @ ( TA @ fun ) @ fun ) ) > $o ) ).
thf(finite2073411215e_idem_decl,type,
finite2073411215e_idem:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) > ( TA @ ( bool @ ( TA @ fun ) @ fun ) ) > $o ) ).
thf(the_decl,type,
the:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > TA ) ).
thf(hoare_992312373derivs_decl,type,
hoare_992312373derivs:
!>[TA: $tType] : ( ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > $o ) ).
thf(hoare_1841697145triple_decl,type,
hoare_1841697145triple:
!>[TA: $tType] : ( ( bool @ ( state @ fun ) @ ( TA @ fun ) ) > com > ( bool @ ( state @ fun ) @ ( TA @ fun ) ) > ( TA @ hoare_28830079triple ) ) ).
thf(hoare_376461865e_case_decl,type,
hoare_376461865e_case:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) ) > ( TB @ hoare_28830079triple ) > TA ) ).
thf(hoare_678420151le_rec_decl,type,
hoare_678420151le_rec:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) ) > ( TB @ hoare_28830079triple ) > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(the_elem_decl,type,
the_elem:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > TA ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fdisj_decl,type,
fdisj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(fimplies_decl,type,
fimplies: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(g_decl,type,
g: bool @ ( a @ hoare_28830079triple @ fun ) ).
thf(p_decl,type,
p: bool @ ( state @ fun ) @ ( a @ fun ) ).
thf(b_decl,type,
b: bool @ ( state @ fun ) ).
thf(c_decl,type,
c: com ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ),C: TA,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) )
<=> ( ? [E: TB,F: bool @ ( TB @ fun ),G: TA] :
( ( G @ ( F @ ( C @ ( D @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) )
& ~ ( F @ ( E @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( G @ ( E @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
& ( B
= ( F @ ( E @ ( TB @ insert @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ aa ) ) ) ) ) )
| ( ( A = C )
& ( B
= ( bool @ ( TB @ fun ) @ bot_bot ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_fold__graph_Osimps) ).
thf(325,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ),C: TA,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( ( ? [E: TB,F: bool @ ( TB @ fun ),G: TA] :
( ( G @ ( F @ ( C @ ( D @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) )
& ~ ( F @ ( E @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( G @ ( E @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
& ( B
= ( F @ ( E @ ( TB @ insert @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ aa ) ) ) ) ) )
| ( ( A = C )
& ( B
= ( bool @ ( TB @ fun ) @ bot_bot ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) )
=> ( ? [E: TB,F: bool @ ( TB @ fun ),G: TA] :
( ( G @ ( F @ ( C @ ( D @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) )
& ~ ( F @ ( E @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( G @ ( E @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
& ( B
= ( F @ ( E @ ( TB @ insert @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ aa ) ) ) ) ) )
| ( ( A = C )
& ( B
= ( bool @ ( TB @ fun ) @ bot_bot ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(366,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(118,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( C @ ( A @ ( TA @ hoare_992312373derivs ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cut) ).
thf(629,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( C @ ( A @ ( TA @ hoare_992312373derivs ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(6,axiom,
! [A: com,B: com] :
( skip
!= ( A @ ( B @ semi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_com_Osimps_I12_J) ).
thf(138,plain,
! [A: com,B: com] :
( skip
!= ( A @ ( B @ semi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) @ ( TB @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(479,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) @ ( TB @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(47,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] : ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( skip @ ( A @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( B @ ( TA @ hoare_992312373derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_hoare__derivs_OSkip) ).
thf(347,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] : ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( skip @ ( A @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( B @ ( TA @ hoare_992312373derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(82,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_insert__ident) ).
thf(468,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(49,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: TA @ hoare_28830079triple,C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( A @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( A @ ( B @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
thf(352,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: TA @ hoare_28830079triple,C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( A @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( A @ ( B @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(65,axiom,
bool @ finite_finite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(408,plain,
bool @ finite_finite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(78,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_insert__iff) ).
thf(449,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( C = B ) )
=> ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(95,axiom,
! [TA: $tType,A: TA,B: TA @ ( bool @ ( TA @ fun ) @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ finite_folding_one ) ) )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_folding__one_Osingleton) ).
thf(523,plain,
! [TA: $tType,A: TA,B: TA @ ( bool @ ( TA @ fun ) @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ finite_folding_one ) ) )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(582,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(75,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] : ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_insertI1) ).
thf(440,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] : ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(126,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(655,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(59,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_insert__compr) ).
thf(384,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ finite_finite )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_finite) ).
thf(142,plain,
! [TA: $tType] :
( ( TA @ finite_finite )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(91,axiom,
! [TA: $tType,A: TA,B: TA,C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_fold1Set__sing) ).
thf(500,plain,
! [TA: $tType,A: TA,B: TA,C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( ( B = A )
=> ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(17,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_empty__def) ).
thf(185,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(69,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_empty__iff) ).
thf(417,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_insertI2) ).
thf(257,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(55,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: com,E: bool @ ( state @ fun ) @ ( TA @ fun ),F: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( C @ ( D @ ( E @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( D @ semi ) @ ( E @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Comp) ).
thf(372,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: com,E: bool @ ( state @ fun ) @ ( TA @ fun ),F: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( C @ ( D @ ( E @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( D @ semi ) @ ( E @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(108,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_singleton__conv2) ).
thf(587,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(21,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun ),E: com,F: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( ( D @ ( E @ ( F @ ( TA @ hoare_1841697145triple ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_triple_Oinject) ).
thf(196,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun ),E: com,F: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( TA @ hoare_1841697145triple ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( TA @ hoare_1841697145triple ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(25,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(216,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(83,axiom,
bool @ bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(475,plain,
bool @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(89,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Collect__empty__eq) ).
thf(492,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(10,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( C @ ( D @ semi ) )
= ( A @ ( B @ semi ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_com_Osimps_I3_J) ).
thf(147,plain,
! [A: com,B: com,C: com,D: com] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ semi ) )
= ( A @ ( B @ semi ) ) ) )
& ( ( ( C @ ( D @ semi ) )
= ( A @ ( B @ semi ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(120,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insert__compr__raw) ).
thf(634,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(27,axiom,
! [TA: $tType] : ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ finite_finite1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_finite_OemptyI) ).
thf(221,plain,
! [TA: $tType] : ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ finite_finite1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun ),C: bool @ ( TB @ fun )] :
( ( C @ ( TB @ finite_finite1 ) )
=> ? [D: TA] : ( D @ ( C @ ( A @ ( B @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_finite__imp__fold__graph) ).
thf(132,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun ),C: bool @ ( TB @ fun )] :
( ( C @ ( TB @ finite_finite1 ) )
=> ? [D: TA] : ( D @ ( C @ ( A @ ( B @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(35,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_insert__commute) ).
thf(265,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(92,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ? [C: TA] :
( ! [D: TA] :
( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( B @ ( TA @ the ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_the1I2) ).
thf(507,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ? [C: TA] :
( ! [D: TA] :
( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( B @ ( TA @ the ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_singletonE) ).
thf(349,plain,
! [TA: $tType,A: TA,B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(73,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fold1Set__nonempty) ).
thf(429,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(12,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ ( bool @ ( TA @ fun ) @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ finite_folding_one ) ) )
=> ( ( A @ ( TA @ finite_finite1 ) )
=> ( ( A @ ( B @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TA @ finite_fold1 ) @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_folding__one_Oeq__fold) ).
thf(165,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ ( bool @ ( TA @ fun ) @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ finite_folding_one ) ) )
=> ( ( A @ ( TA @ finite_finite1 ) )
=> ( ( A @ ( B @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( TA @ finite_fold1 ) @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite1 ) )
<=> ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite1 ) )
& ( B @ ( TA @ collect ) @ ( TA @ finite_finite1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_finite__Collect__disjI) ).
thf(403,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite1 ) )
& ( B @ ( TA @ collect ) @ ( TA @ finite_finite1 ) ) )
=> ( A @ ( B @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite1 ) ) )
& ( ( A @ ( B @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite1 ) )
=> ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite1 ) )
& ( B @ ( TA @ collect ) @ ( TA @ finite_finite1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA,D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TA @ finite_fold_graph ) ) ) ) ) )
=> ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_fold1Set_Ointros) ).
thf(188,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA,D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TA @ finite_fold_graph ) ) ) ) ) )
=> ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(87,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(488,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
<=> ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_doubleton__eq__iff) ).
thf(225,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
=> ( ( ( C = B )
& ( D = A ) )
| ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_equals0I) ).
thf(193,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_bot__fun__def) ).
thf(476,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(96,axiom,
! [TA: $tType,A: TA,B: TA,C: bool] :
( ( ~ ( C @ pp )
=> ( A
= ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ the ) ) ) )
& ( ( C @ pp )
=> ( B
= ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ the ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_If__def) ).
thf(526,plain,
! [TA: $tType,A: TA,B: TA,C: bool] :
( ( ~ ( C @ pp )
=> ( A
= ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ the ) ) ) )
& ( ( C @ pp )
=> ( B
= ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ the ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(121,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot )
!= ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_empty__not__insert) ).
thf(637,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot )
!= ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(109,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite1 ) )
| ( B @ ( TA @ collect ) @ ( TA @ finite_finite1 ) ) )
=> ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_finite__Collect__conjI) ).
thf(590,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite1 ) )
| ( B @ ( TA @ collect ) @ ( TA @ finite_finite1 ) ) )
=> ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Collect__conv__if2) ).
thf(515,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(79,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ? [B: TA] :
( ! [C: TA] :
( ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C = B ) )
& ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( TA @ the ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_theI_H) ).
thf(457,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ? [B: TA] :
( ! [C: TA] :
( ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C = B ) )
& ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( TA @ the ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(3,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(129,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: com,B: com] :
( ( A @ ( B @ semi ) )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_com_Osimps_I13_J) ).
thf(134,plain,
! [A: com,B: com] :
( ( A @ ( B @ semi ) )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(51,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_insert__absorb2) ).
thf(360,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(127,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(657,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1,conjecture,
bool @ ( a @ hoare_28830079triple @ fun ) @ bot_bot @ ( b @ ( fNot @ ( state @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( p @ ( fconj @ ( state @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( a @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( a @ fun ) @ ( bool @ ( state @ fun ) @ ( a @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( state @ combs ) ) @ ( a @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( a @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( a @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ ( a @ combc ) ) @ ( bool @ ( state @ fun ) @ ( a @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( a @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( a @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( c @ ( fFalse @ ( state @ ( bool @ combk ) ) @ ( a @ ( bool @ ( state @ fun ) @ combk ) ) @ ( a @ hoare_1841697145triple ) ) ) @ ( a @ hoare_28830079triple @ insert @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( g @ ( a @ hoare_992312373derivs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( bool @ ( a @ hoare_28830079triple @ fun ) @ bot_bot @ ( b @ ( fNot @ ( state @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( p @ ( fconj @ ( state @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( a @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( a @ fun ) @ ( bool @ ( state @ fun ) @ ( a @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( state @ combs ) ) @ ( a @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( a @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( a @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ ( a @ combc ) ) @ ( bool @ ( state @ fun ) @ ( a @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( a @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( a @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( c @ ( fFalse @ ( state @ ( bool @ combk ) ) @ ( a @ ( bool @ ( state @ fun ) @ combk ) ) @ ( a @ hoare_1841697145triple ) ) ) @ ( a @ hoare_28830079triple @ insert @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( g @ ( a @ hoare_992312373derivs ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ( bool @ ( a @ hoare_28830079triple @ fun ) @ bot_bot @ ( b @ ( fNot @ ( state @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( p @ ( fconj @ ( state @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( a @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( a @ fun ) @ ( bool @ ( state @ fun ) @ ( a @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( state @ combs ) ) @ ( a @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( a @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( a @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ ( a @ combc ) ) @ ( bool @ ( state @ fun ) @ ( a @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( bool @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ fun ) @ ( a @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( a @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( c @ ( fFalse @ ( state @ ( bool @ combk ) ) @ ( a @ ( bool @ ( state @ fun ) @ combk ) ) @ ( a @ hoare_1841697145triple ) ) ) @ ( a @ hoare_28830079triple @ insert @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( g @ ( a @ hoare_992312373derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(343,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( bool @ ( TB @ fun ) @ bot_bot @ ( B @ ( C @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_empty__fold__graphE) ).
thf(412,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( bool @ ( TB @ fun ) @ bot_bot @ ( B @ ( C @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(72,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_bot__empty__eq) ).
thf(425,plain,
! [TA: $tType,A: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun )] :
( ( C
= ( B @ ( TA @ finite_fold1 ) ) )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_fold1__singleton__def) ).
thf(161,plain,
! [TA: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun )] :
( ( C
= ( B @ ( TA @ finite_fold1 ) ) )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ finite2073411215e_idem ) ) )
=> ( ( B @ ( TA @ finite_finite1 ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_folding__one__idem_Oinsert__idem) ).
thf(601,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ finite2073411215e_idem ) ) )
=> ( ( B @ ( TA @ finite_finite1 ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ? [C: TA] :
( ! [D: TA] :
( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( TA @ the ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_the1__equality) ).
thf(176,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ? [C: TA] :
( ! [D: TA] :
( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( TA @ the ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(39,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun ),D: TA] :
( ~ ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( C @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
<=> ( ( ( D != B )
=> ? [E: bool @ ( TA @ fun )] :
( ~ ( E @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( E @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
& ~ ( E @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( C
= ( E @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) )
& ( ( D = B )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_insert__eq__iff) ).
thf(286,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun ),D: TA] :
( ~ ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( ( ( D != B )
=> ? [E: bool @ ( TA @ fun )] :
( ~ ( E @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( E @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
& ~ ( E @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( C
= ( E @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) )
& ( ( D = B )
=> ( C = A ) ) )
=> ( ( C @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
=> ( ( ( D != B )
=> ? [E: bool @ ( TA @ fun )] :
( ~ ( E @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( E @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
& ~ ( E @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( C
= ( E @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) )
& ( ( D = B )
=> ( C = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(104,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_insert__absorb) ).
thf(577,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(259,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(58,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_emptyE) ).
thf(382,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(41,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(313,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C = A ) )
=> ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_insertCI) ).
thf(611,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C = A ) )
=> ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(8,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(144,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(90,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(498,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_376461865e_case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_triple_Osimps_I2_J) ).
thf(604,plain,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_376461865e_case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(14,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( TA @ hoare_28830079triple @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ! [E: TA,F: state] :
( ( F @ ( E @ ( D @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( E @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( bool @ ( state @ fun ) @ combk ) ) @ ( B @ ( F @ ( state @ fequal @ ( bool @ ( state @ ( state @ combc ) ) @ ( bool @ ( state @ fun ) @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ ( state @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( state @ aa ) ) ) @ ( TA @ ( bool @ ( state @ fun ) @ combk ) ) @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_escape) ).
thf(172,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( TA @ hoare_28830079triple @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ! [E: TA,F: state] :
( ( F @ ( E @ ( D @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( E @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( bool @ ( state @ fun ) @ combk ) ) @ ( B @ ( F @ ( state @ fequal @ ( bool @ ( state @ ( state @ combc ) ) @ ( bool @ ( state @ fun ) @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ ( state @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( state @ aa ) ) ) @ ( TA @ ( bool @ ( state @ fun ) @ combk ) ) @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(70,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_insert__not__empty) ).
thf(419,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(57,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( TA @ hoare_28830079triple @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ! [E: TA,F: state] :
( ( F @ ( E @ ( D @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ? [G: bool @ ( state @ fun ) @ ( TA @ fun ),H: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ! [I: state] :
( ! [J: TA] :
( ( F @ ( J @ ( G @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( I @ ( J @ ( H @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
=> ( I @ ( E @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
& ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( H @ ( B @ ( G @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_conseq) ).
thf(377,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( TA @ hoare_28830079triple @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ! [E: TA,F: state] :
( ( F @ ( E @ ( D @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ? [G: bool @ ( state @ fun ) @ ( TA @ fun ),H: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ! [I: state] :
( ! [J: TA] :
( ( F @ ( J @ ( G @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( I @ ( J @ ( H @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
=> ( I @ ( E @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
& ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( H @ ( B @ ( G @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(124,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite1 ) )
<=> ( A @ ( TA @ finite_finite1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_finite__insert) ).
thf(649,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( A @ ( TA @ finite_finite1 ) )
=> ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite1 ) ) )
& ( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite1 ) )
=> ( A @ ( TA @ finite_finite1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TA @ fun )] :
~ ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_empty__fold1SetE) ).
thf(599,plain,
! [TA: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TA @ fun )] :
~ ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_bot__apply) ).
thf(387,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(631,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(46,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(345,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(110,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(594,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(24,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ the_elem ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( bool @ ( TA @ fun ) @ fequal @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ ( TA @ fun ) @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ the ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_the__elem__def) ).
thf(213,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ the_elem ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( bool @ ( TA @ fun ) @ fequal @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( bool @ ( TA @ fun ) @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ the ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite )
& ( TA @ finite_finite ) )
=> ( TA @ ( TB @ fun ) @ finite_finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(462,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite )
& ( TA @ finite_finite ) )
=> ( TA @ ( TB @ fun ) @ finite_finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(94,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(521,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_insert__code) ).
thf(278,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(28,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( B @ pp )
| ~ ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(223,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( B @ pp )
| ~ ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(62,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_all__not__in__conv) ).
thf(394,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(101,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ! [C: bool @ ( TA @ fun )] :
( ( A
= ( C @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
=> ( C @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Set_Oset__insert) ).
thf(563,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ! [C: bool @ ( TA @ fun )] :
( ( A
= ( C @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
=> ( C @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(30,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: bool @ ( state @ fun ) @ ( TA @ fun ),C: bool @ ( state @ fun ) @ ( TA @ fun ),D: com,E: bool @ ( state @ fun ) @ ( TA @ fun ),F: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( C @ ( D @ ( E @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) )
=> ( ! [G: TA,H: state] :
( ( H @ ( G @ ( B @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ! [I: state] :
( ! [J: TA] :
( ( H @ ( J @ ( E @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( I @ ( J @ ( C @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
=> ( I @ ( G @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( D @ ( B @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_conseq12) ).
thf(241,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: bool @ ( state @ fun ) @ ( TA @ fun ),C: bool @ ( state @ fun ) @ ( TA @ fun ),D: com,E: bool @ ( state @ fun ) @ ( TA @ fun ),F: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( C @ ( D @ ( E @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) )
=> ( ! [G: TA,H: state] :
( ( H @ ( G @ ( B @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ! [I: state] :
( ! [J: TA] :
( ( H @ ( J @ ( E @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( I @ ( J @ ( C @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
=> ( I @ ( G @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( D @ ( B @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( F @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA @ ( TA @ fun ) @ ( TB @ fun ),D: bool @ ( TB @ fun ),E: TB] :
( ~ ( D @ ( E @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( D @ ( B @ ( C @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) )
=> ( A @ ( E @ ( C @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( E @ ( TB @ insert @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_fold__graph_OinsertI) ).
thf(653,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA @ ( TA @ fun ) @ ( TB @ fun ),D: bool @ ( TB @ fun ),E: TB] :
( ~ ( D @ ( E @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( D @ ( B @ ( C @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) )
=> ( A @ ( E @ ( C @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( E @ ( TB @ insert @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(88,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(490,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ finite_fold1 ) @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_fold1__singleton) ).
thf(374,plain,
! [TA: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ finite_fold1 ) @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(117,axiom,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite1 ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ! [C: TA] : ( bool @ ( TA @ fun ) @ bot_bot @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: bool @ ( TA @ fun )] :
( ( D @ ( TA @ finite_finite1 ) )
=> ( ( D
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ~ ( D @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ) )
=> ( B @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_finite__ne__induct) ).
thf(617,plain,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite1 ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ! [C: TA] : ( bool @ ( TA @ fun ) @ bot_bot @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: bool @ ( TA @ fun )] :
( ( D @ ( TA @ finite_finite1 ) )
=> ( ( D
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ~ ( D @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ) )
=> ( B @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(99,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(553,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ finite_finite )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_finite__code) ).
thf(145,plain,
! [TA: $tType] :
( ( TA @ finite_finite )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C = A ) )
=> ( ( B @ ( TA @ the ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_the__equality) ).
thf(557,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C = A ) )
=> ( ( B @ ( TA @ the ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(105,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun )] : ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( TA @ hoare_992312373derivs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_empty) ).
thf(580,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun )] : ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( TA @ hoare_992312373derivs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(122,axiom,
! [TA: $tType,A: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ the_elem ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_the__elem__eq) ).
thf(640,plain,
! [TA: $tType,A: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ the_elem ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(66,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite1 ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [C: TA] : ( C @ ( B @ ( A @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__nonempty__imp__fold1Set) ).
thf(409,plain,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite1 ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [C: TA] : ( C @ ( B @ ( A @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(40,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple] :
~ ! [B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( A
!= ( D @ ( C @ ( B @ ( TA @ hoare_1841697145triple ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_triple_Oexhaust) ).
thf(310,plain,
! [TA: $tType,A: TA @ hoare_28830079triple] :
~ ! [B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( A
!= ( D @ ( C @ ( B @ ( TA @ hoare_1841697145triple ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(16,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ the ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_the__eq__trivial) ).
thf(182,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ the ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(585,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(123,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_empty__Collect__eq) ).
thf(643,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(98,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ? [B: TA,C: bool @ ( TA @ fun )] :
( ~ ( C @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( C @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_nonempty__iff) ).
thf(544,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ? [B: TA,C: bool @ ( TA @ fun )] :
( ~ ( C @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( C @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) )
=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [B: TA,C: bool @ ( TA @ fun )] :
( ~ ( C @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( C @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(77,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ the ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_the__sym__eq__trivial) ).
thf(446,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ the ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Collect__conv__if) ).
thf(571,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(52,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(363,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(86,axiom,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite1 ) )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: bool @ ( TA @ fun )] :
( ( D @ ( TA @ finite_finite1 ) )
=> ( ~ ( D @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) )
=> ( B @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_finite__induct) ).
thf(482,plain,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite1 ) )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: bool @ ( TA @ fun )] :
( ( D @ ( TA @ finite_finite1 ) )
=> ( ~ ( D @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) )
=> ( B @ ( A @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(26,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_singleton__conv) ).
thf(218,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(390,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] : ( A @ ( bool @ ( TB @ fun ) @ bot_bot @ ( A @ ( B @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_fold__graph_OemptyI) ).
thf(401,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] : ( A @ ( bool @ ( TB @ fun ) @ bot_bot @ ( A @ ( B @ ( TA @ ( TB @ finite_fold_graph ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(102,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(568,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ? [D: TA,E: bool @ ( TA @ fun ),F: TA] :
( ~ ( E @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( F @ ( E @ ( D @ ( C @ ( TA @ ( TA @ finite_fold_graph ) ) ) ) ) )
& ( A = F )
& ( B
= ( E @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_fold1Set_Osimps) ).
thf(246,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( ? [D: TA,E: bool @ ( TA @ fun ),F: TA] :
( ~ ( E @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( F @ ( E @ ( D @ ( C @ ( TA @ ( TA @ finite_fold_graph ) ) ) ) ) )
& ( A = F )
& ( B
= ( E @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) )
=> ( A @ ( B @ ( C @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ? [D: TA,E: bool @ ( TA @ fun ),F: TA] :
( ~ ( E @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( F @ ( E @ ( D @ ( C @ ( TA @ ( TA @ finite_fold_graph ) ) ) ) ) )
& ( A = F )
& ( B
= ( E @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(74,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_ex__in__conv) ).
thf(433,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(207,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_singleton__iff) ).
thf(315,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( B = A )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(19,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ finite_folding_one ) ) )
=> ( ( B @ ( TA @ finite_finite1 ) )
=> ( ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_folding__one_Oinsert) ).
thf(190,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA @ ( bool @ ( TA @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( C @ ( D @ ( TA @ finite_folding_one ) ) )
=> ( ( B @ ( TA @ finite_finite1 ) )
=> ( ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( B @ ( C @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_678420151le_rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_triple_Orecs) ).
thf(422,plain,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_678420151le_rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(37,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ? [C: bool @ ( TA @ fun )] :
( ~ ( C @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( C @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_mk__disjoint__insert) ).
thf(273,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ? [C: bool @ ( TA @ fun )] :
( ~ ( C @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( A
= ( C @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_equals0D) ).
thf(168,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(34,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C != B )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_insertE) ).
thf(262,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( C != B )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(23,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( TA @ collect ) @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( fimplies @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_insert__Collect) ).
thf(210,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( TA @ collect ) @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( fimplies @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(36,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C = A ) )
=> ( B @ ( TA @ the ) @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_theI) ).
thf(268,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C = A ) )
=> ( B @ ( TA @ the ) @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(97,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ finite_finite1 ) )
<=> ( ? [B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( TA @ finite_finite1 ) )
& ( A
= ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) )
| ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_finite_Osimps) ).
thf(532,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( ? [B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( TA @ finite_finite1 ) )
& ( A
= ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) )
| ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
=> ( A @ ( TA @ finite_finite1 ) ) )
& ( ( A @ ( TA @ finite_finite1 ) )
=> ( ? [B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( TA @ finite_finite1 ) )
& ( A
= ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) )
| ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite1 ) )
=> ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_finite_OinsertI) ).
thf(415,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite1 ) )
=> ( B @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(81,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun ),E: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( C @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( E @ ( TA @ hoare_992312373derivs ) ) )
=> ( ! [F: TA,G: state] :
( ( G @ ( F @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( G @ ( F @ ( D @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( C @ ( A @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( E @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_conseq1) ).
thf(464,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun ),E: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( C @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( E @ ( TA @ hoare_992312373derivs ) ) )
=> ( ! [F: TA,G: state] :
( ( G @ ( F @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( G @ ( F @ ( D @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( C @ ( A @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( E @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(111,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ finite_fold1 ) @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TA @ finite_fold1Set ) ) @ ( TA @ the ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_fold1__def) ).
thf(596,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ finite_fold1 ) @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TA @ finite_fold1Set ) ) @ ( TA @ the ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(76,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun ),E: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( C @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( E @ ( TA @ hoare_992312373derivs ) ) )
=> ( ! [F: TA,G: state] :
( ( G @ ( F @ ( B @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( G @ ( F @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( C @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( E @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_conseq2) ).
thf(442,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun ),E: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( C @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( E @ ( TA @ hoare_992312373derivs ) ) )
=> ( ! [F: TA,G: state] :
( ( G @ ( F @ ( B @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( G @ ( F @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( C @ ( D @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( E @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(54,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ ( bool @ ( TA @ fun ) @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ finite_folding_one ) ) )
=> ( ( A @ ( TA @ finite_finite1 ) )
=> ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ! [D: TA,E: TA] : ( bool @ ( TA @ fun ) @ bot_bot @ ( E @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( C @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( A @ ( B @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_folding__one_Oclosed) ).
thf(369,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA @ ( bool @ ( TA @ fun ) @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ finite_folding_one ) ) )
=> ( ( A @ ( TA @ finite_finite1 ) )
=> ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ! [D: TA,E: TA] : ( bool @ ( TA @ fun ) @ bot_bot @ ( E @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( C @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( A @ ( B @ ( TA @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(115,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: bool @ ( TA @ hoare_28830079triple @ fun ),E: bool] :
( ( ( E @ pp )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( D @ ( TA @ hoare_992312373derivs ) ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( E @ ( C @ ( fconj @ ( state @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( TA @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( TA @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( state @ combc ) ) @ ( TA @ ( bool @ ( state @ fun ) @ ( bool @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( TA @ combc ) ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( bool @ fun ) @ ( bool @ ( state @ fun ) @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( D @ ( TA @ hoare_992312373derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_constant) ).
thf(607,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: bool @ ( TA @ hoare_28830079triple @ fun ),E: bool] :
( ( ( E @ pp )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( D @ ( TA @ hoare_992312373derivs ) ) ) )
=> ( bool @ ( TA @ hoare_28830079triple @ fun ) @ bot_bot @ ( A @ ( B @ ( E @ ( C @ ( fconj @ ( state @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) @ ( TA @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( bool @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( TA @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( state @ combc ) ) @ ( TA @ ( bool @ ( state @ fun ) @ ( bool @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ combb ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( bool @ fun ) @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( bool @ ( TA @ combc ) ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( bool @ fun ) @ ( bool @ ( state @ fun ) @ ( bool @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ insert @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ ( D @ ( TA @ hoare_992312373derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_singleton__inject) ).
thf(322,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(50,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA,D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ! [E: TA,F: bool @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( F @ ( E @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
=> ( ( A @ ( F @ ( E @ ( D @ ( TA @ ( TA @ finite_fold_graph ) ) ) ) ) )
=> ( F @ ( E @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_insert__fold1SetE) ).
thf(354,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA,D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( D @ ( TA @ finite_fold1Set ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ! [E: TA,F: bool @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( F @ ( E @ ( TA @ insert @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) )
=> ( ( A @ ( F @ ( E @ ( D @ ( TA @ ( TA @ finite_fold_graph ) ) ) ) ) )
=> ( F @ ( E @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(662,plain,
$false,
inference(e,[status(thm)],[325,366,629,138,479,347,468,352,408,449,523,582,440,655,384,142,500,185,417,257,372,587,196,216,475,492,147,634,221,132,265,507,349,429,165,403,188,488,225,193,476,526,637,590,515,457,129,134,360,657,128,343,412,425,161,601,176,286,577,259,382,313,611,144,498,604,172,419,377,649,599,387,631,345,594,213,462,521,278,223,394,563,241,653,490,374,617,553,145,557,580,640,409,310,182,585,643,544,446,571,363,482,218,390,401,568,246,433,207,315,190,422,273,168,262,210,268,532,415,464,596,442,369,607,322,354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n004.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 15:58:21 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.90/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.93/1.35 % [INFO] Parsing done (372ms).
% 1.93/1.36 % [INFO] Running in sequential loop mode.
% 3.43/1.76 % [INFO] eprover registered as external prover.
% 3.43/1.77 % [INFO] Scanning for conjecture ...
% 3.98/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ...
% 4.90/2.15 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 6.15/2.48 % [INFO] Problem is typed first-order (TPTP TFF).
% 6.58/2.53 % [INFO] Type checking passed.
% 6.58/2.54 % [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 ...
% 10.63/3.59 % [INFO] [Domain constraints] Detected constraint on bool
% 10.63/3.59 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 118.55/83.43 % External prover 'e' found a proof!
% 118.55/83.43 % [INFO] Killing All external provers ...
% 118.55/83.43 % Time passed: 82888ms (effective reasoning time: 82062ms)
% 118.55/83.43 % 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)>
% 118.55/83.44 % 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
% 118.55/83.44 % No. of inferences in proof: 254
% 118.55/83.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 82888 ms resp. 82062 ms w/o parsing
% 119.53/83.61 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 119.53/83.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------