%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW520_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:44 AM UTC 2026
% Result : Theorem 15.06s 6.56s
% Output : Refutation 15.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 126
% Syntax : Number of formulae : 254 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 861 ( 118 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 3341 ( 56 ~; 12 |; 37 &;2883 @)
% ( 20 <=>; 333 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 7 con; 0-6 aty)
% Number of variables : 704 ( 0 ^; 696 !; 8 ?; 704 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(comple187826305attice_decl,type,
comple187826305attice:
!>[TA: $tType] : $o ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(complete_Sup_Sup_decl,type,
complete_Sup_Sup:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > TA ) ).
thf(hoare_592965047valids_decl,type,
hoare_592965047valids:
!>[TA: $tType] : ( ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > $o ) ).
thf(hoare_1633586161_valid_decl,type,
hoare_1633586161_valid:
!>[TA: $tType] : ( nat > ( TA @ hoare_28830079triple ) > $o ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(semiri532925092at_aux_decl,type,
semiri532925092at_aux:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) ) > nat > TA > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(powp_decl,type,
powp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( bool @ ( TA @ fun ) @ fun ) ) ) ).
thf(inv_imagep_decl,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) @ ( TB @ fun ) ) > ( TB @ ( TA @ fun ) ) > TA > TA > $o ) ).
thf(pred1_decl,type,
pred1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ pred ) ) ).
thf(pred_case_decl,type,
pred_case:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( bool @ ( TB @ fun ) @ fun ) ) > ( TB @ pred ) > TA ) ).
thf(pred_rec_decl,type,
pred_rec:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( bool @ ( TB @ fun ) @ fun ) ) > ( TB @ pred ) > TA ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( 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(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(ga_decl,type,
ga: bool @ ( a @ hoare_28830079triple @ fun ) ).
thf(64,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_equalityD1) ).
thf(347,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)],[64]) ).
thf(115,axiom,
bool @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(515,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_nat_Oinject) ).
thf(217,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(54,axiom,
! [TA: $tType] : ( TA @ pred @ comple187826305attice ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Predicate_Opred___Complete__Lattices_Ocomplete__lattice) ).
thf(308,plain,
! [TA: $tType] : ( TA @ pred @ comple187826305attice ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(247,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(114,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( A @ ( C @ ( TA @ member ) ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_subsetI) ).
thf(511,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( A @ ( C @ ( TA @ member ) ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(25,axiom,
nat @ bot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
thf(202,plain,
nat @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(500,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(538,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_order__trans) ).
thf(153,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
nat @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(174,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(48,axiom,
nat @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(288,plain,
nat @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(39,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(257,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(20,axiom,
! [A: nat] :
~ ( A @ ( A @ suc @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Suc__n__not__le__n) ).
thf(184,plain,
! [A: nat] :
~ ( A @ ( A @ suc @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(122,axiom,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( B @ ( TA @ member ) ) )
=> ~ ! [C: bool @ ( TA @ fun )] :
( ( C @ ( B @ ( TA @ member ) ) )
=> ~ ( A @ ( C @ ( bool @ ( TA @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_UnionE) ).
thf(542,plain,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( B @ ( TA @ member ) ) )
=> ~ ! [C: bool @ ( TA @ fun )] :
( ( C @ ( B @ ( TA @ member ) ) )
=> ~ ( A @ ( C @ ( bool @ ( TA @ fun ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_order__subst2) ).
thf(284,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(49,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Suc__leD) ).
thf(289,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(97,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_predicate1I) ).
thf(448,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_le__funE) ).
thf(492,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',fact_46_equalityE) ).
thf(321,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)],[57]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',fact_42_subset__trans) ).
thf(376,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)],[75]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TB @ ( bool @ ( TA @ fun ) @ fun )] :
( ( A @ ( TA @ pred1 ) @ ( B @ ( TB @ ( TA @ pred_case ) ) ) )
= ( A @ ( B @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_pred_Osimps_I2_J) ).
thf(485,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TB @ ( bool @ ( TA @ fun ) @ fun )] :
( ( A @ ( TA @ pred1 ) @ ( B @ ( TB @ ( TA @ pred_case ) ) ) )
= ( A @ ( B @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Suc__le__mono) ).
thf(147,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ suc @ ( B @ suc @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ suc @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_le__trans) ).
thf(133,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) )
= A )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_ord__le__eq__subst) ).
thf(265,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) )
= A )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( TA @ complete_Sup_Sup ) @ ( B @ ( TA @ complete_Sup_Sup ) @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Sup__subset__mono) ).
thf(452,plain,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( TA @ complete_Sup_Sup ) @ ( B @ ( TA @ complete_Sup_Sup ) @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(118,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member ) ) )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_all__not__in__conv) ).
thf(529,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( A @ ( B @ ( TA @ member ) ) ) )
& ( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member ) ) )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(123,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_emptyE) ).
thf(546,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(77,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_subset__empty) ).
thf(381,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(366,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: nat,C: TA @ ( TA @ fun )] :
( ( A @ ( B @ suc @ ( C @ ( TA @ semiri532925092at_aux ) ) ) )
= ( A @ ( C @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ semiri532925092at_aux ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_of__nat__aux_Osimps_I2_J) ).
thf(260,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: nat,C: TA @ ( TA @ fun )] :
( ( A @ ( B @ suc @ ( C @ ( TA @ semiri532925092at_aux ) ) ) )
= ( A @ ( C @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ semiri532925092at_aux ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(80,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_empty__Collect__eq) ).
thf(392,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(105,axiom,
bool @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(484,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: nat,B: nat,C: TA @ ( nat @ fun )] :
( ! [D: nat] : ( D @ suc @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_lift__Suc__mono__le) ).
thf(252,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: nat,B: nat,C: TA @ ( nat @ fun )] :
( ! [D: nat] : ( D @ suc @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_le__funD) ).
thf(435,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) )
<=> ( A
= ( TA @ bot_bot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_bot__unique) ).
thf(329,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( ( A
= ( TA @ bot_bot ) )
=> ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ bot_bot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_le__funI) ).
thf(551,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_equals0D) ).
thf(317,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(78,axiom,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: bool @ ( bool @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( B @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Union__mono) ).
thf(388,plain,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: bool @ ( bool @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( B @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ bot_bot ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_le__bot) ).
thf(356,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_eq__imp__le) ).
thf(141,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(86,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_empty__iff) ).
thf(420,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
=> ( A @ ( TA @ complete_Sup_Sup ) @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Sup__upper) ).
thf(488,plain,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
=> ( A @ ( TA @ complete_Sup_Sup ) @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(117,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member ) ) )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_equals0I) ).
thf(526,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member ) ) )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(29,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(212,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ complete_Sup_Sup ) @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Sup__least) ).
thf(398,plain,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ complete_Sup_Sup ) @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1,conjecture,
! [A: nat] :
( ! [B: a @ hoare_28830079triple] :
( ( bool @ ( a @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( a @ hoare_28830079triple @ member ) ) )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) )
| ? [B: a @ hoare_28830079triple] :
( ~ ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) )
& ( ga @ ( B @ ( a @ hoare_28830079triple @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: nat] :
( ! [B: a @ hoare_28830079triple] :
( ( bool @ ( a @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( a @ hoare_28830079triple @ member ) ) )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) )
| ? [B: a @ hoare_28830079triple] :
( ~ ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) )
& ( ga @ ( B @ ( a @ hoare_28830079triple @ member ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ! [A: nat] :
( ! [B: a @ hoare_28830079triple] :
( ( bool @ ( a @ hoare_28830079triple @ fun ) @ bot_bot @ ( B @ ( a @ hoare_28830079triple @ member ) ) )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) )
| ? [B: a @ hoare_28830079triple] :
( ~ ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) )
& ( ga @ ( B @ ( a @ hoare_28830079triple @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ pred @ bot_bot )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ pred1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_bot__pred__def) ).
thf(343,plain,
! [TA: $tType] :
( ( TA @ pred @ bot_bot )
= ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ pred1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(52,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( B @ ( TA @ pred1 ) )
= ( A @ ( TA @ pred1 ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_pred_Oinject) ).
thf(298,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( B = A )
=> ( ( B @ ( TA @ pred1 ) )
= ( A @ ( TA @ pred1 ) ) ) )
& ( ( ( B @ ( TA @ pred1 ) )
= ( A @ ( TA @ pred1 ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(430,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Suc__inject) ).
thf(279,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_linorder__linear) ).
thf(176,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(82,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_equalityD2) ).
thf(402,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)],[82]) ).
thf(50,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(291,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
<=> ( B @ ( A @ suc @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_not__less__eq__eq) ).
thf(204,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ suc @ ( nat @ ord_less_eq ) ) )
=> ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
& ( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( B @ ( A @ suc @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(95,axiom,
bool @ bot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(445,plain,
bool @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(121,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_subset__refl) ).
thf(540,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(21,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Collect__def) ).
thf(187,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(83,axiom,
! [TA: $tType,A: nat,B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( C @ ( A @ suc @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( C @ ( A @ ( TA @ hoare_1633586161_valid ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_triples__valid__Suc) ).
thf(406,plain,
! [TA: $tType,A: nat,B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( C @ ( A @ suc @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( C @ ( A @ ( TA @ hoare_1633586161_valid ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(14,axiom,
! [TA: $tType] : ( TA @ pred @ preorder ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Predicate_Opred___Orderings_Opreorder) ).
thf(172,plain,
! [TA: $tType] : ( TA @ pred @ preorder ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(69,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_set__rev__mp) ).
thf(362,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(34,axiom,
! [TA: $tType] : ( TA @ pred @ order ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Predicate_Opred___Orderings_Oorder) ).
thf(245,plain,
! [TA: $tType] : ( TA @ pred @ order ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( C @ ( A @ ( TA @ ord_less_eq ) ) ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( B @ ( TA @ complete_Sup_Sup ) @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__eq__Sup) ).
thf(494,plain,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( C @ ( A @ ( TA @ ord_less_eq ) ) ) )
=> ( ( B
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( B @ ( TA @ complete_Sup_Sup ) @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(11,axiom,
! [TA: $tType,A: TA @ pred] :
~ ! [B: bool @ ( TA @ fun )] :
( A
!= ( B @ ( TA @ pred1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_pred_Oexhaust) ).
thf(155,plain,
! [TA: $tType,A: TA @ pred] :
~ ! [B: bool @ ( TA @ fun )] :
( A
!= ( B @ ( TA @ pred1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_ord__eq__le__trans) ).
thf(198,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(135,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(113,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Collect__empty__eq) ).
thf(505,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ complete_Sup_Sup ) @ ( TA @ ord_less_eq ) ) )
<=> ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Sup__le__iff) ).
thf(473,plain,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: TA,B: bool @ ( TA @ fun )] :
( ( ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ complete_Sup_Sup ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TA @ complete_Sup_Sup ) @ ( TA @ ord_less_eq ) ) )
=> ! [C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ comple187826305attice )
=> ( TA @ ( TB @ fun ) @ comple187826305attice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Complete__Lattices_Ocomplete__lattice) ).
thf(490,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ comple187826305attice )
=> ( TA @ ( TB @ fun ) @ comple187826305attice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(88,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( bool @ ( TA @ fun ) @ fun )] :
( ! [C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ member ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Union__least) ).
thf(426,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( bool @ ( TA @ fun ) @ fun )] :
( ! [C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ member ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(124,axiom,
bool @ comple187826305attice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Complete__Lattices_Ocomplete__lattice) ).
thf(548,plain,
bool @ comple187826305attice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_predicate1D) ).
thf(374,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',fact_29_set__eq__subset) ).
thf(516,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)],[116]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( ( C @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( TA @ complete_Sup_Sup ) @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Sup__upper2) ).
thf(553,plain,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ! [A: TA,B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( ( C @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( TA @ complete_Sup_Sup ) @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(100,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ? [B: TA] : ( A @ ( B @ ( TA @ member ) ) )
<=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_ex__in__conv) ).
thf(458,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [B: TA] : ( A @ ( B @ ( TA @ member ) ) ) )
& ( ? [B: TA] : ( A @ ( B @ ( TA @ member ) ) )
=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_order__subst1) ).
thf(194,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le__refl) ).
thf(145,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_order__refl) ).
thf(263,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_order__antisym__conv) ).
thf(310,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_linorder__le__cases) ).
thf(182,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(93,axiom,
bool @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(441,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(73,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_bot__empty__eq) ).
thf(370,plain,
! [TA: $tType,A: TA] :
( ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member ) ) )
=> ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ complete_Sup_Sup ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Sup__empty) ).
thf(502,plain,
! [TA: $tType] :
( ( TA @ comple187826305attice )
=> ( ( bool @ ( TA @ fun ) @ bot_bot @ ( TA @ complete_Sup_Sup ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_24_equalityI) ).
thf(338,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)],[60]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TB @ ( bool @ ( TA @ fun ) @ fun )] :
( ( A @ ( TA @ pred1 ) @ ( B @ ( TB @ ( TA @ pred_rec ) ) ) )
= ( A @ ( B @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_pred_Orecs) ).
thf(359,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TB @ ( bool @ ( TA @ fun ) @ fun )] :
( ( A @ ( TA @ pred1 ) @ ( B @ ( TB @ ( TA @ pred_rec ) ) ) )
= ( A @ ( B @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] : ( A @ ( TA @ bot_bot @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_bot__least) ).
thf(336,plain,
! [TA: $tType] :
( ( TA @ bot )
=> ! [A: TA] : ( A @ ( TA @ bot_bot @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(16,axiom,
nat @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(175,plain,
nat @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(96,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 ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_in__mono) ).
thf(446,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 ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(72,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple,B: nat] :
( ( A @ ( B @ suc @ ( TA @ hoare_1633586161_valid ) ) )
=> ( A @ ( B @ ( TA @ hoare_1633586161_valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_triple__valid__Suc) ).
thf(368,plain,
! [TA: $tType,A: TA @ hoare_28830079triple,B: nat] :
( ( A @ ( B @ suc @ ( TA @ hoare_1633586161_valid ) ) )
=> ( A @ ( B @ ( TA @ hoare_1633586161_valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(36,axiom,
! [TA: $tType] : ( TA @ pred @ ord ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Predicate_Opred___Orderings_Oord) ).
thf(250,plain,
! [TA: $tType] : ( TA @ pred @ ord ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(101,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( A @ ( B @ ( TA @ hoare_592965047valids ) ) )
<=> ! [C: nat] :
( ! [D: TA @ hoare_28830079triple] :
( ( B @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [D: TA @ hoare_28830079triple] :
( ( A @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_hoare__valids__def) ).
thf(465,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( ! [C: nat] :
( ! [D: TA @ hoare_28830079triple] :
( ( B @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [D: TA @ hoare_28830079triple] :
( ( A @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) ) )
=> ( A @ ( B @ ( TA @ hoare_592965047valids ) ) ) )
& ( ( A @ ( B @ ( TA @ hoare_592965047valids ) ) )
=> ! [C: nat] :
( ! [D: TA @ hoare_28830079triple] :
( ( B @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [D: TA @ hoare_28830079triple] :
( ( A @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(104,axiom,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ member ) ) )
=> ( A @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Union__upper) ).
thf(482,plain,
! [TA: $tType,A: bool @ ( bool @ ( TA @ fun ) @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ member ) ) )
=> ( A @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(26,axiom,
nat @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(203,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(40,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(258,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: bool @ ( bool @ ( TA @ fun ) @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( B @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_UnionI) ).
thf(390,plain,
! [TA: $tType,A: TA,B: bool @ ( bool @ ( TA @ fun ) @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( B @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_nat__le__linear) ).
thf(139,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(85,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 ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_subsetD) ).
thf(418,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 ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_order__eq__iff) ).
thf(158,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(65,axiom,
! [TA: $tType] :
( ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Union__empty) ).
thf(351,plain,
! [TA: $tType] :
( ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ complete_Sup_Sup ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_bot__apply) ).
thf(378,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
<=> ( ( B
= ( A @ suc ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_le__Suc__eq) ).
thf(235,plain,
! [A: nat,B: nat] :
( ( ( ( B
= ( A @ suc ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B
= ( A @ suc ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_le__fun__def) ).
thf(478,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(63,axiom,
bool @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(346,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(125,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( TA @ powp ) @ ( B @ ( TA @ powp ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Powp__mono) ).
thf(549,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( TA @ powp ) @ ( B @ ( TA @ powp ) @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(119,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 ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_set__mp) ).
thf(536,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 ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',fact_73_ext) ).
thf(214,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)],[30]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_bot__fun__def) ).
thf(432,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(84,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_ball__reg) ).
thf(410,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(13,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Suc__n__not__n) ).
thf(168,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ? [C: nat] :
( A
= ( C @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Suc__le__D) ).
thf(190,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ? [C: nat] :
( A
= ( C @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(87,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( TA @ collect ) @ ( B @ ( TA @ collect ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Collect__mono) ).
thf(422,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( TA @ collect ) @ ( B @ ( TA @ collect ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(44,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_n__not__Suc__n) ).
thf(273,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_order__antisym) ).
thf(305,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(28,axiom,
! [TA: $tType] : ( TA @ pred @ bot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Predicate_Opred___Orderings_Obot) ).
thf(210,plain,
! [TA: $tType] : ( TA @ pred @ bot ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(61,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_ball__empty) ).
thf(341,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
<=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_in__inv__imagep) ).
thf(437,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_order__eq__refl) ).
thf(294,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_le__antisym) ).
thf(136,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_ord__le__eq__trans) ).
thf(178,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_le__SucI) ).
thf(277,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(94,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_empty__def) ).
thf(442,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(66,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rev__predicate1D) ).
thf(354,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(99,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mem__def) ).
thf(454,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(70,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_empty__subsetI) ).
thf(364,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( B
= ( A @ suc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_le__SucE) ).
thf(254,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( B
= ( A @ suc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( D
= ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_ord__eq__le__subst) ).
thf(227,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( D
= ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(563,plain,
$false,
inference(e,[status(thm)],[347,515,217,308,247,511,202,500,538,153,174,288,257,184,542,284,289,448,492,321,376,485,147,133,265,452,529,546,381,366,260,392,484,252,435,329,551,317,388,356,141,420,488,526,212,398,128,343,298,430,279,176,402,291,204,445,540,187,406,172,362,245,494,155,198,135,505,473,490,426,548,374,516,553,458,194,145,263,310,182,441,370,502,338,359,336,175,446,368,250,465,482,203,258,390,139,418,158,351,378,235,478,346,549,536,214,432,410,168,190,422,273,305,210,341,437,294,136,178,277,442,354,454,364,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW520_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.53 % Computer : n003.cluster.edu
% 0.13/0.53 % Model : x86_64 x86_64
% 0.13/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.53 % Memory : 8046.5625MB
% 0.13/0.53 % OS : Linux 6.8.0-71-generic
% 0.13/0.53 % CPULimit : 300
% 0.13/0.53 % WCLimit : 300
% 0.13/0.53 % DateTime : Sat Sep 26 16:12:10 UTC 2026
% 0.13/0.53 % CPUTime :
% 0.13/0.53 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/1.11 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.75/1.42 % [INFO] Parsing done (313ms).
% 1.75/1.44 % [INFO] Running in sequential loop mode.
% 2.84/1.82 % [INFO] eprover registered as external prover.
% 2.84/1.83 % [INFO] Scanning for conjecture ...
% 3.00/1.98 % [INFO] Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ...
% 3.25/2.10 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 3.67/2.29 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.92/2.33 % [INFO] Type checking passed.
% 3.92/2.33 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.34/2.94 % [INFO] [Domain constraints] Detected constraint on bool
% 5.34/2.95 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 15.06/6.55 % External prover 'e' found a proof!
% 15.06/6.55 % [INFO] Killing All external provers ...
% 15.06/6.55 % Time passed: 5877ms (effective reasoning time: 5109ms)
% 15.06/6.55 % 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)>
% 15.06/6.56 % Axioms used in derivation (125): fact_76_n__not__Suc__n, fact_85_nat__le__linear, arity_Nat_Onat___Orderings_Obot, fact_86_le__refl, arity_HOL_Obool___Orderings_Oorder, fact_71_not__less__eq__eq, fact_16_Sup__empty, fact_57_bot__unique, arity_HOL_Obool___Orderings_Oord, fact_6_hoare__valids__def, fact_63_nat_Oinject, arity_HOL_Obool___Orderings_Opreorder, fact_82_le__antisym, fact_18_ball__reg, fact_93_predicate1I, fact_84_eq__imp__le, arity_Nat_Onat___Rings_Osemiring__1, arity_fun___Orderings_Obot, fact_38_predicate1D, fact_94_order__subst1, fact_25_pred_Oinject, fact_30_order__eq__iff, arity_Predicate_Opred___Orderings_Opreorder, fact_52_Sup__subset__mono, arity_fun___Orderings_Oord, arity_Nat_Onat___Orderings_Opreorder, fact_1_all__not__in__conv, fact_41_set__mp, fact_64_Sup__least, fact_51_Union__mono, fact_74_mem__def, fact_31_rev__predicate1D, fact_67_Suc__leD, fact_32_equalityD1, fact_88_Suc__le__D, arity_HOL_Obool___Complete__Lattices_Ocomplete__lattice, fact_17_bot__pred__def, fact_33_equalityD2, fact_5_emptyE, fact_58_le__bot, fact_46_equalityE, fact_34_order__eq__refl, fact_81_le__funI, fact_55_Sup__le__iff, fact_7_bot__fun__def, arity_HOL_Obool___Orderings_Olinorder, fact_14_in__inv__imagep, help_fFalse_1_1_T, fact_22_order__refl, fact_49_Union__empty, fact_48_linorder__le__cases, fact_68_le__SucE, fact_66_UnionI, fact_40_set__rev__mp, fact_78_Suc__inject, fact_95_ord__le__eq__subst, fact_28_linorder__linear, fact_21_empty__subsetI, arity_fun___Orderings_Oorder, arity_Nat_Onat___Orderings_Olinorder, fact_37_order__antisym__conv, fact_53_Sup__upper, fact_26_subset__refl, fact_13_equals0I, fact_73_ext, fact_12_ex__in__conv, arity_Predicate_Opred___Orderings_Oord, arity_fun___Orderings_Opreorder, fact_50_Sup__upper2, fact_8_bot__apply, fact_42_subset__trans, fact_79_UnionE, fact_43_ord__le__eq__trans, fact_72_Suc__n__not__le__n, fact_89_Powp__mono, fact_61_pred_Orecs, arity_fun___Complete__Lattices_Ocomplete__lattice, fact_96_order__subst2, fact_83_le__trans, fact_47_le__funE, arity_Nat_Onat___Orderings_Oord, fact_39_ord__eq__le__trans, help_COMBK_1_1_U, fact_19_triple__valid__Suc, fact_60_less__eq__Sup, fact_4_Collect__empty__eq, fact_91_of__nat__aux_Osimps_I2_J, fact_29_set__eq__subset, fact_10_empty__def, arity_Predicate_Opred___Orderings_Obot, fact_87_lift__Suc__mono__le, fact_27_le__fun__def, fact_3_empty__iff, fact_44_order__antisym, arity_HOL_Obool___Orderings_Obot, fact_35_le__funD, fact_75_Collect__def, fact_90_pred_Oexhaust, fact_92_Collect__mono, fact_54_Union__upper, fact_69_le__SucI, arity_Predicate_Opred___Orderings_Oorder, fact_97_ord__eq__le__subst, fact_9_bot__empty__eq, help_fFalse_1_1_U, arity_Nat_Onat___Orderings_Oorder, fact_23_subsetD, fact_80_Union__least, fact_11_equals0D, fact_36_in__mono, fact_15_triples__valid__Suc, fact_2_empty__Collect__eq, help_pp_1_1_U, fact_24_equalityI, fact_65_Suc__le__mono, fact_20_subset__empty, fact_45_order__trans, help_pp_2_1_U, fact_77_Suc__n__not__n, arity_Predicate_Opred___Complete__Lattices_Ocomplete__lattice, fact_59_subsetI, fact_62_pred_Osimps_I2_J, fact_56_bot__least, fact_70_le__Suc__eq, fact_0_ball__empty
% 15.06/6.56 % No. of inferences in proof: 254
% 15.06/6.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5877 ms resp. 5109 ms w/o parsing
% 15.60/6.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.60/6.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------