%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW521_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:44 AM UTC 2026
% Result : Theorem 47.99s 30.29s
% Output : Refutation 48.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 122
% Syntax : Number of formulae : 246 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 1127 ( 130 equ; 0 cnn)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 4451 ( 37 ~; 14 |; 51 &;3965 @)
% ( 30 <=>; 354 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 36 usr; 9 con; 0-6 aty)
% Number of variables : 713 ( 0 ^; 708 !; 5 ?; 713 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[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(boolean_algebra_decl,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
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 ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(hoare_992312373derivs_decl,type,
hoare_992312373derivs:
!>[TA: $tType] : ( ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > $o ) ).
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(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(order_strict_mono_decl,type,
order_strict_mono:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > $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(ord_atLeast_decl,type,
ord_atLeast:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) ) ).
thf(ord_atMost_decl,type,
ord_atMost:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) ) ).
thf(ord_greaterThan_decl,type,
ord_greaterThan:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) ) ).
thf(ord_lessThan_decl,type,
ord_lessThan:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) ) ).
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(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(ga_decl,type,
ga: bool @ ( a @ hoare_28830079triple @ fun ) ).
thf(ts_decl,type,
ts: bool @ ( a @ hoare_28830079triple @ fun ) ).
thf(tsa_decl,type,
tsa: bool @ ( a @ hoare_28830079triple @ fun ) ).
thf(80,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( 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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Compl__iff) ).
thf(416,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(82,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( 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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_ComplD) ).
thf(423,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( 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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(72,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_74_mem__def) ).
thf(391,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)],[72]) ).
thf(16,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_le__refl) ).
thf(182,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
nat @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(154,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(65,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 ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_subsetI) ).
thf(365,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 ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_neg__equal__iff__equal) ).
thf(138,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ ord_atLeast ) )
= ( A @ ( TA @ ord_atLeast ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_atLeast__eq__iff) ).
thf(276,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ ord_atLeast ) )
= ( A @ ( TA @ ord_atLeast ) ) ) )
& ( ( ( B @ ( TA @ ord_atLeast ) )
= ( A @ ( TA @ ord_atLeast ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ linorder ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun )] :
( ( C @ ( TB @ ( TA @ order_strict_mono ) ) )
=> ( ( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_strict__mono__eq) ).
thf(440,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ linorder ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun )] :
( ( C @ ( TB @ ( TA @ order_strict_mono ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ ord_atMost ) )
= ( A @ ( TA @ ord_atMost ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_atMost__eq__iff) ).
thf(269,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ ord_atMost ) )
= ( A @ ( TA @ ord_atMost ) ) ) )
& ( ( ( B @ ( TA @ ord_atMost ) )
= ( A @ ( TA @ ord_atMost ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ ord_atMost ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_atMost__iff) ).
thf(408,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ ord_atMost ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( TA @ ord_atMost ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(12,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(170,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ boolean_algebra )
=> ( TA @ ( TB @ fun ) @ boolean_algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Oboolean__algebra) ).
thf(533,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ boolean_algebra )
=> ( TA @ ( TB @ fun ) @ boolean_algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(108,axiom,
bool @ boolean_algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Oboolean__algebra) ).
thf(500,plain,
bool @ boolean_algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ ord_greaterThan ) @ ( B @ ( TA @ ord_greaterThan ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_greaterThan__subset__iff) ).
thf(472,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ ord_greaterThan ) @ ( B @ ( TA @ ord_greaterThan ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ ord_greaterThan ) @ ( B @ ( TA @ ord_greaterThan ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(57,axiom,
bool @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(340,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_order__eq__refl) ).
thf(174,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)],[14]) ).
thf(77,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_14_equalityD1) ).
thf(404,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)],[77]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',fact_22_order__eq__iff) ).
thf(184,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)],[17]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',fact_38_ord__le__eq__subst) ).
thf(357,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)],[64]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_39_Powp__mono) ).
thf(460,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)],[95]) ).
thf(106,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_30_equalityD2) ).
thf(492,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)],[106]) ).
thf(103,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_double__complement) ).
thf(485,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(114,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_26_set__mp) ).
thf(514,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)],[114]) ).
thf(62,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_asm) ).
thf(353,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(74,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_25_subset__trans) ).
thf(397,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)],[74]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_eq__imp__le) ).
thf(265,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(111,axiom,
ts @ ( ga @ ( a @ hoare_992312373derivs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(507,plain,
ts @ ( ga @ ( a @ hoare_992312373derivs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
<=> ( B @ ( A @ suc @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_not__less__eq__eq) ).
thf(206,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)],[22]) ).
thf(47,axiom,
! [A: nat] :
( ! [B: a @ hoare_28830079triple] :
( ( ga @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) )
=> ! [B: a @ hoare_28830079triple] :
( ( ts @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(307,plain,
! [A: nat] :
( ! [B: a @ hoare_28830079triple] :
( ( ga @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) )
=> ! [B: a @ hoare_28830079triple] :
( ( ts @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(91,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_73_ext) ).
thf(452,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)],[91]) ).
thf(68,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Compl__eq) ).
thf(380,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(512,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_52_le__trans) ).
thf(201,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)],[20]) ).
thf(25,axiom,
! [A: nat] :
( ( A @ suc @ ( nat @ ord_lessThan ) )
= ( A @ ( nat @ ord_atMost ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_lessThan__Suc__atMost) ).
thf(220,plain,
! [A: nat] :
( ( A @ suc @ ( nat @ ord_lessThan ) )
= ( A @ ( nat @ ord_atMost ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(60,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_27_set__rev__mp) ).
thf(349,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)],[60]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
<=> ( ( B
= ( A @ suc ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_le__Suc__eq) ).
thf(160,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)],[11]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ ord_atLeast ) @ ( B @ ( TA @ ord_atLeast ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_atLeast__subset__iff) ).
thf(429,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ ord_atLeast ) @ ( B @ ( TA @ ord_atLeast ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ ord_atLeast ) @ ( B @ ( TA @ ord_atLeast ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_37_order__subst2) ).
thf(467,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)],[98]) ).
thf(102,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(484,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
( ( A @ ( TA @ ord_atMost ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ ord_greaterThan ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Compl__atMost) ).
thf(435,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
( ( A @ ( TA @ ord_atMost ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ ord_greaterThan ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fact_9_le__funD) ).
thf(456,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)],[93]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',fact_32_le__funI) ).
thf(324,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)],[53]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_65_lift__Suc__mono__le) ).
thf(519,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)],[116]) ).
thf(50,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Compl__anti__mono) ).
thf(317,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(10,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Suc__n__not__n) ).
thf(156,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(76,axiom,
bool @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(403,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(71,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(388,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)],[71]) ).
thf(81,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 @ 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(420,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 @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(104,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_subset__refl) ).
thf(488,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1,conjecture,
! [A: nat] :
( ! [B: a @ hoare_28830079triple] :
( ( tsa @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) )
| ? [B: a @ hoare_28830079triple] :
( ~ ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) )
& ( ga @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(2,negated_conjecture,
~ ! [A: nat] :
( ! [B: a @ hoare_28830079triple] :
( ( tsa @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) )
| ? [B: a @ hoare_28830079triple] :
( ~ ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) )
& ( ga @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(124,plain,
~ ! [A: nat] :
( ! [B: a @ hoare_28830079triple] :
( ( tsa @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) ) )
| ? [B: a @ hoare_28830079triple] :
( ~ ( B @ ( A @ ( a @ hoare_1633586161_valid ) ) )
& ( ga @ ( B @ ( a @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ fun ) @ ( a @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(121,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_12_set__eq__subset) ).
thf(537,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)],[121]) ).
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 @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [D: TA @ hoare_28830079triple] :
( ( A @ ( D @ ( TA @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_hoare__valids__def) ).
thf(476,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 @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [D: TA @ hoare_28830079triple] :
( ( A @ ( D @ ( TA @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( 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 @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [D: TA @ hoare_28830079triple] :
( ( A @ ( D @ ( TA @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(122,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_weaken) ).
thf(547,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(23,axiom,
nat @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(212,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(55,axiom,
! [TA: $tType,A: nat,B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( A @ suc @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( TA @ hoare_1633586161_valid ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_triples__valid__Suc) ).
thf(328,plain,
! [TA: $tType,A: nat,B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( A @ suc @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( A @ ( TA @ hoare_1633586161_valid ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(99,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(471,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(35,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Suc__le__mono) ).
thf(256,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)],[35]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_compl__eq__compl__iff) ).
thf(129,plain,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ ord_lessThan ) @ ( B @ ( TA @ ord_lessThan ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_lessThan__subset__iff) ).
thf(503,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ ord_lessThan ) @ ( B @ ( TA @ ord_lessThan ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ ord_lessThan ) @ ( B @ ( TA @ ord_lessThan ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ linorder ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun )] :
( ( C @ ( TB @ ( TA @ order_strict_mono ) ) )
=> ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_strict__mono__less__eq) ).
thf(508,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ linorder ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun )] :
( ( C @ ( TB @ ( TA @ order_strict_mono ) ) )
=> ( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
& ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',fact_8_le__fun__def) ).
thf(311,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)],[48]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',fact_35_order__subst1) ).
thf(412,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)],[79]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ ord_atLeast ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_atLeast__iff) ).
thf(425,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ ord_atLeast ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( TA @ ord_atLeast ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ ord_lessThan ) )
= ( A @ ( TA @ ord_lessThan ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_lessThan__eq__iff) ).
thf(296,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ ord_lessThan ) )
= ( A @ ( TA @ ord_lessThan ) ) ) )
& ( ( ( B @ ( TA @ ord_lessThan ) )
= ( A @ ( TA @ ord_lessThan ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Suc__inject) ).
thf(149,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_nat__le__linear) ).
thf(230,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)],[28]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',fact_16_order__trans) ).
thf(303,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)],[45]) ).
thf(70,axiom,
ts @ ( tsa @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(387,plain,
ts @ ( tsa @ ( bool @ ( a @ hoare_28830079triple @ fun ) @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',fact_34_Collect__mono) ).
thf(345,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)],[59]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(535,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',fact_20_order__antisym__conv) ).
thf(213,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)],[24]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_17_order__antisym) ).
thf(251,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)],[33]) ).
thf(9,axiom,
nat @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(155,plain,
nat @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [A: nat] :
( ( A @ suc @ ( nat @ ord_atLeast ) )
= ( A @ ( nat @ ord_greaterThan ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_atLeast__Suc__greaterThan) ).
thf(198,plain,
! [A: nat] :
( ( A @ suc @ ( nat @ ord_atLeast ) )
= ( A @ ( nat @ ord_greaterThan ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(96,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_5_equalityI) ).
thf(462,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)],[96]) ).
thf(117,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ! [C: nat] :
( ! [D: nat] :
( ( C @ ( D @ suc @ ( nat @ ord_less_eq ) ) )
=> ( D @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_full__nat__induct) ).
thf(521,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ! [C: nat] :
( ! [D: nat] :
( ( C @ ( D @ suc @ ( nat @ ord_less_eq ) ) )
=> ( D @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ ord_atMost ) @ ( B @ ( TA @ ord_atMost ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_atMost__subset__iff) ).
thf(399,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ ord_atMost ) @ ( B @ ( TA @ ord_atMost ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ ord_atMost ) @ ( B @ ( TA @ ord_atMost ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(92,axiom,
bool @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(455,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( B
= ( A @ suc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_le__SucE) ).
thf(223,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)],[26]) ).
thf(27,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_n__not__Suc__n) ).
thf(226,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(87,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(438,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(32,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_nat_Oinject) ).
thf(241,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)],[32]) ).
thf(105,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( 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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_ComplE) ).
thf(490,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( 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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
( ( A @ ( TA @ ord_atLeast ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ ord_lessThan ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Compl__atLeast) ).
thf(516,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
( ( A @ ( TA @ ord_atLeast ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ ord_lessThan ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(355,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',fact_46_triple__valid__Suc) ).
thf(458,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)],[94]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_compl__le__compl__iff) ).
thf(194,plain,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ? [C: nat] :
( A
= ( C @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Suc__le__D) ).
thf(145,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)],[6]) ).
thf(118,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_24_equalityE) ).
thf(525,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)],[118]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_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)],[37]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',fact_13_rev__predicate1D) ).
thf(465,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)],[97]) ).
thf(90,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(450,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(21,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Collect__def) ).
thf(203,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
( ( A @ ( TA @ ord_lessThan ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ ord_atLeast ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Compl__lessThan) ).
thf(319,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
( ( A @ ( TA @ ord_lessThan ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ ord_atLeast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(61,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_4_subsetD) ).
thf(351,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)],[61]) ).
thf(13,axiom,
! [A: nat] :
~ ( A @ ( A @ suc @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Suc__n__not__le__n) ).
thf(171,plain,
! [A: nat] :
~ ( A @ ( A @ suc @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_neg__le__iff__le) ).
thf(235,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(85,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(433,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',fact_40_in__inv__imagep) ).
thf(383,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)],[69]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
( ( A @ ( TA @ ord_greaterThan ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ ord_atMost ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Compl__greaterThan) ).
thf(549,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
( ( A @ ( TA @ ord_greaterThan ) @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( TA @ ord_atMost ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ ord_greaterThan ) )
= ( A @ ( TA @ ord_greaterThan ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_greaterThan__eq__iff) ).
thf(287,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ ord_greaterThan ) )
= ( A @ ( TA @ ord_greaterThan ) ) ) )
& ( ( ( B @ ( TA @ ord_greaterThan ) )
= ( A @ ( TA @ ord_greaterThan ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_67_of__nat__aux_Osimps_I2_J) ).
thf(447,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)],[89]) ).
thf(49,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_29_in__mono) ).
thf(315,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)],[49]) ).
thf(36,axiom,
nat @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(262,plain,
nat @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(67,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( B @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Compl__eq__Compl__iff) ).
thf(373,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( B = A )
=> ( ( B @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) ) ) )
& ( ( ( B @ ( bool @ ( TA @ fun ) @ uminus_uminus ) )
= ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_le__SucI) ).
thf(305,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)],[46]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_28_predicate1D) ).
thf(326,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)],[54]) ).
thf(31,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( C @ ( A @ ( TA @ hoare_992312373derivs ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_cut) ).
thf(239,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( C @ ( A @ ( TA @ hoare_992312373derivs ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(58,axiom,
! [A: bool @ ( nat @ fun ),B: nat,C: nat] :
( ( B @ ( C @ suc @ ( nat @ ord_less_eq ) ) )
=> ( ! [D: nat] :
( ( D @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( D @ suc @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Suc__le__D__lemma) ).
thf(341,plain,
! [A: bool @ ( nat @ fun ),B: nat,C: nat] :
( ( B @ ( C @ suc @ ( nat @ ord_less_eq ) ) )
=> ( ! [D: nat] :
( ( D @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( D @ suc @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',fact_19_ord__eq__le__trans) ).
thf(283,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)],[41]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_linorder__le__cases) ).
thf(294,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)],[43]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Suc__leD) ).
thf(136,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)],[4]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',fact_10_le__funE) ).
thf(395,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)],[73]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',fact_36_ord__eq__le__subst) ).
thf(332,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)],[56]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',fact_18_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)],[15]) ).
thf(109,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_ComplI) ).
thf(501,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(66,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( B @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Compl__subset__Compl__iff) ).
thf(369,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( B @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( B @ ( bool @ ( TA @ fun ) @ uminus_uminus ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_linorder__linear) ).
thf(254,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)],[34]) ).
thf(52,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_thin) ).
thf(322,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun ),C: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( B @ ( C @ ( TA @ hoare_992312373derivs ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ hoare_992312373derivs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_33_predicate1I) ).
thf(496,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)],[107]) ).
thf(29,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_le__antisym) ).
thf(232,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)],[29]) ).
thf(552,plain,
$false,
inference(e,[status(thm)],[416,423,391,182,154,365,138,276,440,269,408,170,533,500,472,340,174,404,184,357,460,492,485,514,353,397,265,507,206,307,452,380,512,201,220,349,160,429,467,484,435,456,324,519,317,156,403,388,420,488,124,537,476,547,212,328,471,256,129,503,508,311,412,425,296,149,230,303,387,345,535,213,251,155,198,462,521,399,455,223,226,438,241,490,516,355,458,194,145,525,263,465,450,203,319,351,171,235,433,383,549,287,447,315,262,373,305,326,239,341,283,294,136,395,332,178,501,369,254,322,496,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW521_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
% 0.18/0.42 % Computer : n004.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 16:10:22 UTC 2026
% 0.18/0.42 % CPUTime :
% 0.18/0.42 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.89/1.32 % [INFO] Parsing done (328ms).
% 1.89/1.34 % [INFO] Running in sequential loop mode.
% 2.67/1.72 % [INFO] eprover registered as external prover.
% 2.67/1.73 % [INFO] Scanning for conjecture ...
% 3.04/1.91 % [INFO] Found a conjecture (or negated_conjecture) and 121 axioms. Running axiom selection ...
% 3.36/2.04 % [INFO] Axiom selection finished. Selected 121 axioms (removed 0 axioms).
% 3.82/2.25 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.82/2.29 % [INFO] Type checking passed.
% 3.82/2.30 % [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 ...
% 47.99/30.28 % External prover 'e' found a proof!
% 47.99/30.29 % [INFO] Killing All external provers ...
% 47.99/30.29 % Time passed: 29721ms (effective reasoning time: 28945ms)
% 47.99/30.29 % 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)>
% 47.99/30.29 % Axioms used in derivation (121): arity_HOL_Obool___Orderings_Oorder, fact_10_le__funE, arity_Nat_Onat___Orderings_Oord, fact_31_subsetI, fact_90_ComplE, arity_HOL_Obool___Orderings_Oord, arity_HOL_Obool___Orderings_Opreorder, fact_51_le__antisym, fact_18_ord__le__eq__trans, fact_5_equalityI, fact_46_triple__valid__Suc, arity_Nat_Onat___Rings_Osemiring__1, fact_97_neg__equal__iff__equal, fact_15_linorder__le__cases, arity_fun___Orderings_Oord, fact_49_lessThan__subset__iff, arity_Nat_Onat___Orderings_Opreorder, fact_38_ord__le__eq__subst, fact_80_lessThan__Suc__atMost, fact_74_mem__def, fact_32_le__funI, fact_83_ComplI, fact_93_Compl__eq, fact_13_rev__predicate1D, arity_HOL_Obool___Lattices_Oboolean__algebra, fact_54_nat__le__linear, fact_88_Compl__lessThan, fact_8_le__fun__def, fact_16_order__trans, fact_26_set__mp, fact_47_nat_Oinject, fact_63_Suc__n__not__n, fact_6_order__refl, help_fNot_2_1_U, fact_27_set__rev__mp, fact_94_neg__le__iff__le, fact_66_Suc__le__D, fact_0_asm, fact_87_Compl__atLeast, help_fNot_1_1_U, arity_HOL_Obool___Orderings_Olinorder, fact_29_in__mono, fact_44_greaterThan__eq__iff, fact_45_strict__mono__eq, fact_67_of__nat__aux_Osimps_I2_J, fact_9_le__funD, fact_76_atLeast__eq__iff, fact_61_Suc__leD, fact_7_hoare__valids__def, help_COMBB_1_1_U, fact_89_Compl__anti__mono, fact_86_Compl__subset__Compl__iff, fact_85_Compl__iff, conj_2, fact_55_le__refl, fact_23_linorder__linear, arity_fun___Orderings_Oorder, fact_72_atMost__eq__iff, arity_Nat_Onat___Orderings_Olinorder, fact_91_ComplD, fact_64_n__not__Suc__n, fact_24_equalityE, fact_68_full__nat__induct, fact_62_Suc__inject, fact_35_order__subst1, fact_78_atLeast__iff, fact_58_le__Suc__eq, arity_fun___Orderings_Opreorder, fact_73_ext, fact_42_strict__mono__less__eq, fact_3_cut, fact_56_Suc__n__not__le__n, fact_39_Powp__mono, fact_77_atMost__iff, fact_79_atLeast__Suc__greaterThan, fact_92_double__complement, fact_1_weaken, fact_53_eq__imp__le, fact_84_Compl__eq__Compl__iff, fact_59_le__SucI, fact_17_order__antisym, fact_48_Suc__le__mono, fact_11_subset__refl, fact_2_thin, fact_19_ord__eq__le__trans, fact_95_compl__le__compl__iff, fact_36_ord__eq__le__subst, fact_41_triples__valid__Suc, arity_fun___Lattices_Oboolean__algebra, fact_22_order__eq__iff, fact_21_order__eq__refl, help_COMBC_1_1_U, fact_14_equalityD1, fact_69_atLeast__subset__iff, fact_37_order__subst2, conj_1, fact_34_Collect__mono, fact_75_Collect__def, fact_28_predicate1D, fact_70_atMost__subset__iff, fact_30_equalityD2, fact_4_subsetD, fact_43_greaterThan__subset__iff, arity_Nat_Onat___Orderings_Oorder, fact_20_order__antisym__conv, fact_82_Compl__greaterThan, fact_40_in__inv__imagep, fact_81_Compl__atMost, fact_60_le__SucE, fact_12_set__eq__subset, help_pp_1_1_U, fact_57_not__less__eq__eq, fact_50_lessThan__eq__iff, fact_33_predicate1I, fact_96_compl__eq__compl__iff, fact_65_lift__Suc__mono__le, conj_0, help_pp_2_1_U, fact_25_subset__trans, fact_71_Suc__le__D__lemma, fact_52_le__trans
% 47.99/30.29 % No. of inferences in proof: 246
% 47.99/30.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 29721 ms resp. 28945 ms w/o parsing
% 48.86/30.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 48.86/30.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------