%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV779_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 : n008.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 09:00:33 AM UTC 2026
% Result : Theorem 33.75s 22.30s
% Output : Refutation 34.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 116
% Syntax : Number of formulae : 234 ( 84 unt; 0 typ; 0 def)
% Number of atoms : 1515 ( 342 equ; 0 cnn)
% Maximal formula atoms : 36 ( 6 avg)
% Number of connectives : 6231 ( 83 ~; 39 |; 94 &;5811 @)
% ( 34 <=>; 170 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 10 con; 0-5 aty)
% Number of variables : 788 ( 0 ^; 770 !; 18 ?; 788 :)
% Comments :
%------------------------------------------------------------------------------
thf(event_type,type,
event: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(agent_type,type,
agent: $tType ).
thf(msg_type,type,
msg: $tType ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) @ ( TB @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(gets_decl,type,
gets: agent > msg > event ).
thf(initState_decl,type,
initState: agent > ( bool @ ( msg @ fun ) ) ).
thf(knows_decl,type,
knows: agent > ( event @ list ) > ( bool @ ( msg @ fun ) ) ).
thf(append_decl,type,
append:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(foldl_decl,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( TB @ ( TA @ fun ) @ ( TB @ fun ) ) > TB > ( TA @ list ) > TB ) ).
thf(insert1_decl,type,
insert1:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ fun ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_all_decl,type,
list_all:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(rev_decl,type,
rev:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(spy_decl,type,
spy: agent ).
thf(nS_Sha254967238shared_decl,type,
nS_Sha254967238shared: bool @ ( event @ list @ fun ) ).
thf(nS_Sha993195050haredp_decl,type,
nS_Sha993195050haredp: ( event @ list ) > $o ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
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(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(46,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_insert__code) ).
thf(320,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 @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(44,axiom,
! [A: msg,B: agent,C: msg,D: agent] :
( ( ( C @ ( D @ gets ) )
= ( A @ ( B @ gets ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_event_Osimps_I2_J) ).
thf(299,plain,
! [A: msg,B: agent,C: msg,D: agent] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ gets ) )
= ( A @ ( B @ gets ) ) ) )
& ( ( ( C @ ( D @ gets ) )
= ( A @ ( B @ gets ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(94,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list] :
( ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( C
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rev__eq__Cons__iff) ).
thf(525,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list] :
( ( ( C
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) )
=> ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( TA @ rev ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( C
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(78,axiom,
! [A: event @ list] :
( ( A @ nS_Sha993195050haredp )
<=> ( nS_Sha254967238shared @ ( A @ ( event @ list @ member @ ( bool @ ( bool @ ( event @ list @ fun ) @ fun ) @ ( event @ list @ aa ) ) ) @ ( bool @ ( bool @ ( event @ list @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_ns__sharedp__ns__shared__eq) ).
thf(450,plain,
! [A: event @ list] :
( ( ( nS_Sha254967238shared @ ( A @ ( event @ list @ member @ ( bool @ ( bool @ ( event @ list @ fun ) @ fun ) @ ( event @ list @ aa ) ) ) @ ( bool @ ( bool @ ( event @ list @ fun ) @ aa ) ) ) @ pp )
=> ( A @ nS_Sha993195050haredp ) )
& ( ( A @ nS_Sha993195050haredp )
=> ( nS_Sha254967238shared @ ( A @ ( event @ list @ member @ ( bool @ ( bool @ ( event @ list @ fun ) @ fun ) @ ( event @ list @ aa ) ) ) @ ( bool @ ( bool @ ( event @ list @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(71,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_splice_Osimps_I1_J) ).
thf(418,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(7,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(138,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)],[7]) ).
thf(53,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_insert__compr) ).
thf(347,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(50,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_list_Oinject) ).
thf(333,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_list_Osimps_I4_J) ).
thf(481,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB,C: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [D: TA,E: TA,F: TB] :
( ( E @ ( D @ ( F @ ( C @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( E @ ( F @ ( C @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( TA @ rev ) @ ( B @ ( C @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_foldl__rev) ).
thf(408,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB,C: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [D: TA,E: TA,F: TB] :
( ( E @ ( D @ ( F @ ( C @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( E @ ( F @ ( C @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( TA @ rev ) @ ( B @ ( C @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(93,axiom,
! [A: event,B: event @ list,C: agent] : ( B @ ( A @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( C @ knows ) @ ( B @ ( C @ knows ) @ ( bool @ ( msg @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_knows__subset__knows__Cons) ).
thf(523,plain,
! [A: event,B: event @ list,C: agent] : ( B @ ( A @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( C @ knows ) @ ( B @ ( C @ knows ) @ ( bool @ ( msg @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
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(120,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_ex1 ) ) )
<=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_list__ex1__simps_I2_J) ).
thf(269,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) )
=> ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_ex1 ) ) )
=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(22,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_splice_Osimps_I3_J) ).
thf(202,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ~ ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ~ ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_equalityE) ).
thf(384,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ~ ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ~ ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(81,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( B @ ( TA @ rev ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_rev__append) ).
thf(472,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ append ) ) @ ( TA @ rev ) )
= ( B @ ( TA @ rev ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_rev_Osimps_I1_J) ).
thf(538,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(102,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_list__all__simps_I2_J) ).
thf(570,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(17,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_equalityI) ).
thf(184,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(59,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 @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( 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_93_set__rev__mp) ).
thf(372,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 @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( 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)],[59]) ).
thf(113,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rev__cases) ).
thf(619,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA @ list,C: TA] :
( A
!= ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(20,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(196,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)],[20]) ).
thf(72,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B @ ( TA @ rev ) )
= ( A @ ( TA @ rev ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_rev__is__rev__conv) ).
thf(421,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B = A )
=> ( ( B @ ( TA @ rev ) )
= ( A @ ( TA @ rev ) ) ) )
& ( ( ( B @ ( TA @ rev ) )
= ( A @ ( TA @ rev ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(110,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( B @ ( A @ ( TA @ append ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_self__append__conv2) ).
thf(606,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( B @ ( A @ ( TA @ append ) ) ) ) )
& ( ( B
= ( B @ ( A @ ( TA @ append ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(38,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(284,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(28,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_equalityD1) ).
thf(228,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(40,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( C @ ( TA @ insert ) ) )
= ( A @ ( C @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_insert__commute) ).
thf(289,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( C @ ( TA @ insert ) ) )
= ( A @ ( C @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_foldl__Cons) ).
thf(261,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(82,axiom,
! [A: event @ list,B: agent] : ( A @ ( B @ knows ) @ ( B @ initState @ ( bool @ ( msg @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_initState__subset__knows) ).
thf(475,plain,
! [A: event @ list,B: agent] : ( A @ ( B @ knows ) @ ( B @ initState @ ( bool @ ( msg @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(92,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Nil__is__append__conv) ).
thf(514,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(55,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_append__assoc) ).
thf(353,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ append ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ append ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_append__eq__append__conv2) ).
thf(147,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list] :
( ( ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ append ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append ) ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ? [E: TA @ list] :
( ( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ append ) ) )
= B ) )
| ( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ append ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(26,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(221,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)],[26]) ).
thf(70,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B @ ( TA @ rev ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( B
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_rev__singleton__conv) ).
thf(411,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( B @ ( TA @ rev ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( B @ ( TA @ rev ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( B
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(73,axiom,
nS_Sha254967238shared @ ( event @ nil @ ( event @ list @ member @ ( bool @ ( bool @ ( event @ list @ fun ) @ fun ) @ ( event @ list @ aa ) ) ) @ ( bool @ ( bool @ ( event @ list @ fun ) @ aa ) ) ) @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_ns__shared_ONil) ).
thf(428,plain,
nS_Sha254967238shared @ ( event @ nil @ ( event @ list @ member @ ( bool @ ( bool @ ( event @ list @ fun ) @ fun ) @ ( event @ list @ aa ) ) ) @ ( bool @ ( bool @ ( event @ list @ fun ) @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(41,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_subset__trans) ).
thf(292,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(62,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( 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_94_in__mono) ).
thf(380,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( 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)],[62]) ).
thf(91,axiom,
! [A: msg,B: agent,C: event @ list,D: agent] : ( C @ ( A @ ( B @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( D @ knows ) @ ( C @ ( D @ knows ) @ ( bool @ ( msg @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_knows__subset__knows__Gets) ).
thf(512,plain,
! [A: msg,B: agent,C: event @ list,D: agent] : ( C @ ( A @ ( B @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( D @ knows ) @ ( C @ ( D @ knows ) @ ( bool @ ( msg @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(76,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_list__ex1__simps_I1_J) ).
thf(439,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(65,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_not__Cons__self) ).
thf(392,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_foldl__Nil) ).
thf(429,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ ( TB @ fun ) @ ( TA @ fun )] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ foldl ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(85,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_eq__Nil__appendI) ).
thf(484,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B = A )
=> ( B
= ( A @ ( TA @ nil @ ( TA @ append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(115,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
<=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_append__eq__Cons__conv) ).
thf(625,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA @ list] :
( ( ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ? [E: TA @ list] :
( ( ( C @ ( E @ ( TA @ append ) ) )
= A )
& ( D
= ( E @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) )
| ( ( C
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
& ( D
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(88,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_append1__eq__conv) ).
thf(493,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA,D: TA @ list] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ append ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(79,axiom,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_list__nonempty__induct) ).
thf(456,plain,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(56,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( 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_79_insert__iff) ).
thf(356,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 ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ insert ) ) @ ( 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)],[56]) ).
thf(107,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_splice_Osimps_I2_J) ).
thf(593,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(8,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(141,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)],[8]) ).
thf(47,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(328,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)],[47]) ).
thf(86,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_splice__Nil2) ).
thf(488,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(27,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( 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_78_insertE) ).
thf(225,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( 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)],[27]) ).
thf(101,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Cons__eq__append__conv) ).
thf(554,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA] :
( ( ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) )
=> ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ( ? [E: TA @ list] :
( ( C
= ( A @ ( E @ ( TA @ append ) ) ) )
& ( ( E @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= B ) )
| ( ( ( C @ ( D @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A )
& ( B
= ( TA @ nil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(117,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert1 ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_insert__Nil) ).
thf(642,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert1 ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(100,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_neq__Nil__conv) ).
thf(547,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(114,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) @ ( TA @ rev ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_rev__rev__ident) ).
thf(622,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) @ ( TA @ rev ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(13,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 ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_insert__absorb) ).
thf(173,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 ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( 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_69_insert__subset) ).
thf(205,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( C @ ( TA @ insert ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( 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)],[23]) ).
thf(98,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_list_Osimps_I2_J) ).
thf(541,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(105,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_append__Nil) ).
thf(586,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(33,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ list_all ) ) )
<=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( TA @ list_all ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_list__all__append) ).
thf(264,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: bool @ ( TA @ fun )] :
( ( ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( TA @ list_all ) ) ) )
=> ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ list_all ) ) ) )
& ( ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ list_all ) ) )
=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( TA @ list_all ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(36,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(279,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(43,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( TA @ collect ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fimplies @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_insert__Collect) ).
thf(296,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( TA @ collect ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( fimplies @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,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(176,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)],[14]) ).
thf(67,axiom,
! [A: agent] :
( ( event @ nil @ ( A @ knows ) )
= ( A @ initState ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_knows__Nil) ).
thf(402,plain,
! [A: agent] :
( ( event @ nil @ ( A @ knows ) )
= ( A @ initState ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( A @ ( TA @ insert ) ) )
= ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_insert__compr__raw) ).
thf(286,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B @ ( A @ ( TA @ insert ) ) )
= ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( TA @ fequal @ ( bool @ ( TA @ ( TA @ combc ) ) ) @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(104,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( TA @ rev ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Nil__is__rev__conv) ).
thf(579,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( TA @ nil )
= ( A @ ( TA @ rev ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( TA @ rev ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1,conjecture,
( ( event @ nil @ ( spy @ knows ) )
= ( event @ nil @ ( event @ rev ) @ ( spy @ knows ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( event @ nil @ ( spy @ knows ) )
!= ( event @ nil @ ( event @ rev ) @ ( spy @ knows ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
( ( event @ nil @ ( spy @ knows ) )
!= ( event @ nil @ ( event @ rev ) @ ( spy @ knows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_append__Cons) ).
thf(281,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ append ) ) )
= ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(31,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] : ( A @ ( B @ ( TA @ insert ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insertI1) ).
thf(259,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] : ( A @ ( B @ ( TA @ insert ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(116,axiom,
event @ nil @ nS_Sha993195050haredp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_ns__sharedp_ONil) ).
thf(641,plain,
event @ nil @ nS_Sha993195050haredp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(63,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 ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_insertI2) ).
thf(382,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 ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(103,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TA @ rev ) ) )
<=> ( A
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_singleton__rev__conv) ).
thf(572,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( A
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) )
=> ( ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TA @ rev ) ) ) )
& ( ( ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TA @ rev ) ) )
=> ( A
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(45,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 ) ) )
= ( A @ ( C @ ( TA @ insert ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__ident) ).
thf(313,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 ) ) )
= ( A @ ( C @ ( TA @ insert ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ insert ) ) )
= ( A @ ( C @ ( TA @ insert ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(54,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 @ 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(350,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 @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(18,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 @ 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(187,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 @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [E: TA,F: TA,G: TB] :
( ( F @ ( E @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( F @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_foldl__fun__comm) ).
thf(377,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ! [E: TA,F: TA,G: TB] :
( ( F @ ( E @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( F @ ( G @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( D @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(90,axiom,
! [A: event @ list,B: msg,C: agent] :
( ( A @ ( B @ ( C @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( spy @ knows ) )
= ( A @ ( spy @ knows ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_knows__Spy__Gets) ).
thf(509,plain,
! [A: event @ list,B: msg,C: agent] :
( ( A @ ( B @ ( C @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( spy @ knows ) )
= ( A @ ( spy @ knows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(112,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) )
= ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ ( TA @ list @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rev__foldl__cons) ).
thf(616,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rev ) )
= ( A @ ( TA @ nil @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ ( TA @ combc ) ) ) @ ( TA @ ( TA @ list @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(109,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= A )
<=> ( B
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_append__self__conv2) ).
thf(599,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) )
= A ) )
& ( ( ( A @ ( B @ ( TA @ append ) ) )
= A )
=> ( B
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(83,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( TA @ rev ) @ ( B @ ( TA @ list_all ) ) )
<=> ( A @ ( B @ ( TA @ list_all ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_list__all__rev) ).
thf(477,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TA @ list_all ) ) )
=> ( A @ ( TA @ rev ) @ ( B @ ( TA @ list_all ) ) ) )
& ( ( A @ ( TA @ rev ) @ ( B @ ( TA @ list_all ) ) )
=> ( A @ ( B @ ( TA @ list_all ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( 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_72_subsetD) ).
thf(345,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( 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)],[52]) ).
thf(96,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_append__Nil2) ).
thf(535,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(48,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(330,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(106,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ list @ fun )] :
( ( TA @ nil @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append ) ) @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rev__induct) ).
thf(589,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ list @ fun )] :
( ( TA @ nil @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( TA @ nil @ ( C @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ append ) ) @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(60,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 @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(374,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 @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( 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_92_set__mp) ).
thf(145,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( 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)],[10]) ).
thf(51,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_insert__absorb2) ).
thf(342,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ insert ) ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_append__eq__appendI) ).
thf(123,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA @ list] :
( ( ( D @ ( E @ ( TA @ append ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_list_Osimps_I5_J) ).
thf(199,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,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(182,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)],[16]) ).
thf(49,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(331,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)],[49]) ).
thf(77,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) )
<=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_append__is__Nil__conv) ).
thf(441,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) )
=> ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( B @ ( TA @ append ) ) )
= ( TA @ nil ) )
=> ( ( A
= ( TA @ nil ) )
& ( B
= ( TA @ nil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(89,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_rev__is__Nil__conv) ).
thf(502,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(5,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Cons__eq__appendI) ).
thf(127,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list,D: TA @ list,E: TA] :
( ( ( D @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= C )
=> ( ( B
= ( A @ ( D @ ( TA @ append ) ) ) )
=> ( ( B @ ( E @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(99,axiom,
! [A: event @ list,B: msg,C: agent] :
( ( C != spy )
=> ( ( A @ ( B @ ( C @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( C @ knows ) )
= ( A @ ( C @ knows ) @ ( B @ ( msg @ insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_knows__Gets) ).
thf(544,plain,
! [A: event @ list,B: msg,C: agent] :
( ( C != spy )
=> ( ( A @ ( B @ ( C @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( C @ knows ) )
= ( A @ ( C @ knows ) @ ( B @ ( msg @ insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(111,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ rev ) )
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_rev_Osimps_I2_J) ).
thf(613,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ rev ) )
= ( TA @ nil @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ rev ) @ ( TA @ append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(9,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(143,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)],[9]) ).
thf(30,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 ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) )
<=> ( ( ( 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 ) ) ) )
& ~ ( E @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( C
= ( E @ ( B @ ( TA @ insert ) ) ) ) ) )
& ( ( D = B )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_insert__eq__iff) ).
thf(235,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 ) ) ) )
& ~ ( E @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( C
= ( E @ ( B @ ( TA @ insert ) ) ) ) ) )
& ( ( D = B )
=> ( C = A ) ) )
=> ( ( C @ ( D @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) ) )
=> ( ( ( 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 ) ) ) )
& ~ ( E @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( C
= ( E @ ( B @ ( TA @ insert ) ) ) ) ) )
& ( ( D = B )
=> ( C = A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(25,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_same__append__eq) ).
thf(214,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append ) ) )
= ( A @ ( C @ ( TA @ append ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(75,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A @ ( B @ ( TA @ append ) ) )
= B )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_append__self__conv) ).
thf(432,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TA @ append ) ) )
= B ) )
& ( ( ( A @ ( B @ ( TA @ append ) ) )
= B )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(68,axiom,
! [A: msg,B: agent,C: event @ list] :
( ( event @ nil @ ( A @ ( B @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( C @ ( event @ append ) ) @ ( spy @ knows ) )
= ( C @ ( spy @ knows ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_spies__Gets__rev) ).
thf(405,plain,
! [A: msg,B: agent,C: event @ list] :
( ( event @ nil @ ( A @ ( B @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( C @ ( event @ append ) ) @ ( spy @ knows ) )
= ( C @ ( spy @ knows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(19,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 ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_insertCI) ).
thf(190,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 ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(24,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_equalityD2) ).
thf(210,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(42,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_subset__refl) ).
thf(294,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(95,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_list_Oexhaust) ).
thf(532,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(66,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( B
= ( A @ ( B @ ( TA @ append ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_self__append__conv) ).
thf(395,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( B
= ( A @ ( B @ ( TA @ append ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ append ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(80,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B @ ( TA @ rev ) )
= A )
<=> ( B
= ( A @ ( TA @ rev ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_rev__swap) ).
thf(464,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B
= ( A @ ( TA @ rev ) ) )
=> ( ( B @ ( TA @ rev ) )
= A ) )
& ( ( ( B @ ( TA @ rev ) )
= A )
=> ( B
= ( A @ ( TA @ rev ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(108,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list_Osimps_I3_J) ).
thf(596,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_append__same__eq) ).
thf(131,plain,
! [TA: $tType,A: TA @ list,B: TA @ list,C: TA @ list] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ append ) ) )
= ( B @ ( A @ ( TA @ append ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
<=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_set__eq__subset) ).
thf(163,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(15,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(178,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)],[15]) ).
thf(35,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(277,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_foldl__append) ).
thf(369,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA @ list,C: TB,D: TB @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ append ) ) @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) @ ( D @ ( TA @ ( TB @ foldl ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(87,axiom,
! [A: msg,B: agent,C: event @ list] : ( C @ ( A @ ( B @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( spy @ knows ) @ ( C @ ( spy @ knows ) @ ( bool @ ( msg @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_knows__Spy__subset__knows__Spy__Gets) ).
thf(491,plain,
! [A: msg,B: agent,C: event @ list] : ( C @ ( A @ ( B @ gets ) @ ( event @ cons @ ( event @ list @ ( event @ list @ fun ) @ ( event @ aa ) ) ) @ ( event @ list @ ( event @ list @ aa ) ) ) @ ( spy @ knows ) @ ( C @ ( spy @ knows ) @ ( bool @ ( msg @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(57,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_all ) ) )
<=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_list__all__simps_I1_J) ).
thf(364,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_all ) ) ) )
& ( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list_all ) ) )
=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(29,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_not__Cons__self2) ).
thf(232,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(648,plain,
$false,
inference(e,[status(thm)],[320,299,525,450,418,138,347,333,481,408,523,120,269,202,384,472,538,570,184,372,619,196,421,606,284,228,289,261,475,514,353,147,221,411,428,292,380,512,439,392,429,484,625,493,456,356,593,141,328,488,225,554,642,547,622,173,205,541,586,264,279,296,176,402,286,579,118,281,259,641,382,572,313,350,187,377,509,616,599,477,345,535,330,589,374,145,342,123,199,182,331,441,502,127,544,613,143,235,214,432,405,190,210,294,532,395,464,596,131,163,178,277,369,491,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV779_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
% 0.15/5.41 % Computer : n008.cluster.edu
% 0.15/5.41 % Model : x86_64 x86_64
% 0.15/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.41 % Memory : 8046.5625MB
% 0.15/5.41 % OS : Linux 6.8.0-71-generic
% 0.15/5.41 % CPULimit : 300
% 0.15/5.41 % WCLimit : 300
% 0.15/5.41 % DateTime : Sat Sep 26 14:57:46 UTC 2026
% 0.15/5.41 % CPUTime :
% 0.15/5.41 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
% 0.18/5.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/5.93 % [INFO] Parsing done (204ms).
% 0.18/5.93 % [INFO] Running in sequential loop mode.
% 2.16/6.14 % [INFO] eprover registered as external prover.
% 2.16/6.14 % [INFO] Scanning for conjecture ...
% 2.32/6.24 % [INFO] Found a conjecture (or negated_conjecture) and 115 axioms. Running axiom selection ...
% 2.66/6.32 % [INFO] Axiom selection finished. Selected 115 axioms (removed 0 axioms).
% 3.41/6.49 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.57/6.51 % [INFO] Type checking passed.
% 3.57/6.51 % [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 ...
% 33.75/22.29 % External prover 'e' found a proof!
% 33.75/22.29 % [INFO] Killing All external provers ...
% 33.75/22.29 % Time passed: 16791ms (effective reasoning time: 16356ms)
% 33.75/22.29 % 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)>
% 33.75/22.30 % Axioms used in derivation (115): fact_38_knows__Gets, fact_22_splice_Osimps_I2_J, fact_3_rev__is__rev__conv, help_fimplies_2_1_U, fact_58_append__eq__appendI, fact_11_list_Osimps_I4_J, fact_52_list__all__simps_I2_J, help_COMBS_1_1_U, fact_92_set__mp, fact_81_insert__absorb, fact_39_append__same__eq, fact_33_foldl__rev, fact_41_append__assoc, fact_78_insertE, fact_13_not__Cons__self, fact_67_initState__subset__knows, fact_97_set__eq__subset, fact_8_ns__shared_ONil, fact_63_append__Nil, fact_56_rev__eq__Cons__iff, fact_87_insert__Collect, fact_90_equalityE, fact_50_foldl__append, help_fNot_2_1_U, fact_80_insert__absorb2, fact_96_equalityD1, fact_25_knows__Spy__Gets, help_fNot_1_1_U, fact_71_rev__cases, fact_65_Cons__eq__append__conv, fact_55_append1__eq__conv, fact_46_self__append__conv2, fact_66_knows__subset__knows__Cons, fact_45_append__is__Nil__conv, fact_12_list_Oinject, fact_27_rev__foldl__cons, fact_42_append__Cons, fact_21_insert__Nil, fact_88_insert__compr, fact_10_singleton__rev__conv, fact_95_equalityD2, help_COMBB_1_1_U, fact_72_subsetD, fact_70_rev__induct, fact_82_insertI2, fact_83_insert__eq__iff, fact_47_self__append__conv, fact_93_set__rev__mp, help_fdisj_1_1_U, fact_85_insert__code, fact_31_splice_Osimps_I1_J, fact_64_append__eq__Cons__conv, fact_54_list__all__rev, fact_89_insertI1, fact_98_subset__refl, fact_23_list__ex1__simps_I1_J, fact_60_Cons__eq__appendI, fact_9_rev__singleton__conv, fact_36_foldl__fun__comm, fact_53_list__all__append, help_fequal_1_1_T, fact_48_Nil__is__append__conv, fact_34_list__ex1__simps_I2_J, fact_14_not__Cons__self2, fact_74_insertCI, fact_76_mem__def, fact_32_splice__Nil2, fact_26_list__nonempty__induct, fact_4_rev__rev__ident, fact_57_rev_Osimps_I2_J, fact_16_list_Osimps_I5_J, fact_30_foldl__Nil, fact_79_insert__iff, help_fdisj_2_1_U, fact_59_append__eq__append__conv2, fact_18_list_Osimps_I2_J, fact_86_insert__commute, fact_69_insert__subset, fact_68_knows__subset__knows__Gets, fact_15_ns__sharedp__ns__shared__eq, help_COMBC_1_1_U, fact_43_append__self__conv2, help_fequal_2_1_T, fact_19_list_Oexhaust, fact_73_equalityI, fact_84_insert__ident, fact_1_Nil__is__rev__conv, help_fdisj_3_1_U, fact_62_append__Nil2, fact_0_rev_Osimps_I1_J, fact_61_eq__Nil__appendI, fact_49_rev__append, fact_94_in__mono, fact_77_Collect__def, fact_51_list__all__simps_I1_J, help_pp_1_1_U, fact_44_append__self__conv, fact_99_insert__compr__raw, fact_17_list_Osimps_I3_J, fact_24_splice_Osimps_I3_J, fact_40_same__append__eq, help_fimplies_1_1_U, fact_75_ext, help_fimplies_3_1_U, fact_2_rev__is__Nil__conv, help_pp_2_1_U, fact_5_rev__swap, fact_6_knows__Nil, fact_29_foldl__Cons, fact_28_event_Osimps_I2_J, fact_20_neq__Nil__conv, fact_35_spies__Gets__rev, fact_91_subset__trans, fact_37_knows__Spy__subset__knows__Spy__Gets, fact_7_ns__sharedp_ONil
% 33.75/22.30 % No. of inferences in proof: 234
% 33.75/22.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16791 ms resp. 16356 ms w/o parsing
% 34.84/22.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 34.84/22.47 % [INFO] Killing All external provers ...
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