TSTP Solution File: SWW520_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW520_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:24:58 EDT 2023
% Result : Theorem 13.99s 5.69s
% Output : Refutation 14.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 156
% Syntax : Number of formulae : 284 ( 55 unt; 30 typ; 0 def)
% Number of atoms : 861 ( 118 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 3390 ( 56 ~; 12 |; 37 &;2932 @)
% ( 20 <=>; 333 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 7 con; 0-6 aty)
% Number of variables : 731 ( 0 ^; 696 !; 8 ?; 731 :)
% ( 27 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(comple187826305attice_type,type,
comple187826305attice:
!>[TA: $tType] : $o ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(complete_Sup_Sup_type,type,
complete_Sup_Sup:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA ) ).
thf(hoare_592965047valids_type,type,
hoare_592965047valids:
!>[TA: $tType] : ( ( fun @ ( hoare_28830079triple @ TA ) @ bool ) > ( fun @ ( hoare_28830079triple @ TA ) @ bool ) > $o ) ).
thf(hoare_1633586161_valid_type,type,
hoare_1633586161_valid:
!>[TA: $tType] : ( nat > ( hoare_28830079triple @ TA ) > $o ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(semiri532925092at_aux_type,type,
semiri532925092at_aux:
!>[TA: $tType] : ( ( fun @ TA @ TA ) > nat > TA > TA ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(powp_type,type,
powp:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(inv_imagep_type,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ bool ) ) > ( fun @ TA @ TB ) > TA > TA > $o ) ).
thf(pred1_type,type,
pred1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( pred @ TA ) ) ).
thf(pred_case_type,type,
pred_case:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( fun @ TB @ bool ) @ TA ) > ( pred @ TB ) > TA ) ).
thf(pred_rec_type,type,
pred_rec:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( fun @ TB @ bool ) @ TA ) > ( pred @ TB ) > TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(ga_type,type,
ga: fun @ ( hoare_28830079triple @ a ) @ bool ).
thf(116,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
<=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
& ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_set__eq__subset) ).
thf(482,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( B = A )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
& ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ) )
& ( ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
& ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(15,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(171,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
| ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_nat__le__linear) ).
thf(138,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
| ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(249,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(468,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(115,axiom,
linorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(481,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(72,axiom,
! [TA: $tType,A: hoare_28830079triple @ TA,B: nat] :
( ( hoare_1633586161_valid @ TA @ ( suc @ B ) @ A )
=> ( hoare_1633586161_valid @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_triple__valid__Suc) ).
thf(352,plain,
! [TA: $tType,A: hoare_28830079triple @ TA,B: nat] :
( ( hoare_1633586161_valid @ TA @ ( suc @ B ) @ A )
=> ( hoare_1633586161_valid @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_bot__fun__def) ).
thf(408,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(48,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(276,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(81,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Sup__least) ).
thf(379,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(124,axiom,
comple187826305attice @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Complete__Lattices_Ocomplete__lattice) ).
thf(511,plain,
comple187826305attice @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Suc__inject) ).
thf(269,plain,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(119,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_set__mp) ).
thf(500,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(67,axiom,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_le__bot) ).
thf(340,plain,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(11,axiom,
! [TA: $tType,A: pred @ TA] :
~ ! [B: fun @ TA @ bool] :
( A
!= ( pred1 @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_pred_Oexhaust) ).
thf(153,plain,
! [TA: $tType,A: pred @ TA] :
~ ! [B: fun @ TA @ bool] :
( A
!= ( pred1 @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(94,axiom,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_empty__def) ).
thf(417,plain,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(59,axiom,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_bot__least) ).
thf(320,plain,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(84,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( ( pp @ ( aa @ TA @ bool @ B @ D ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_ball__reg) ).
thf(389,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( ( pp @ ( aa @ TA @ bool @ B @ D ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( pp @ ( aa @ TA @ bool @ B @ D ) ) )
=> ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(21,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Collect__def) ).
thf(184,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: fun @ ( fun @ TA @ bool ) @ bool,C: fun @ TA @ bool] :
( ( member @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_UnionI) ).
thf(372,plain,
! [TA: $tType,A: TA,B: fun @ ( fun @ TA @ bool ) @ bool,C: fun @ TA @ bool] :
( ( member @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(121,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_subset__refl) ).
thf(504,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_predicate1D) ).
thf(357,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( pp @ ( aa @ TA @ bool @ C @ A ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(96,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_in__mono) ).
thf(421,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(93,axiom,
preorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(416,plain,
preorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(61,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ball__empty) ).
thf(325,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A )
<=> ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_le__fun__def) ).
thf(448,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A )
=> ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) )
& ( ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) )
=> ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(19,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_linorder__le__cases) ).
thf(179,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(238,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) )
=> ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_le__funI) ).
thf(514,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) )
=> ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(70,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_empty__subsetI) ).
thf(348,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(105,axiom,
order @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(453,plain,
order @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_le__trans) ).
thf(132,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(85,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_subsetD) ).
thf(396,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ C @ B )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_le__funD) ).
thf(411,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ C @ B )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(37,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat,B: nat,C: fun @ nat @ TA] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( aa @ nat @ TA @ C @ D ) @ ( aa @ nat @ TA @ C @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ TA @ ( aa @ nat @ TA @ C @ B ) @ ( aa @ nat @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_lift__Suc__mono__le) ).
thf(243,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat,B: nat,C: fun @ nat @ TA] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( aa @ nat @ TA @ C @ D ) @ ( aa @ nat @ TA @ C @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ TA @ ( aa @ nat @ TA @ C @ B ) @ ( aa @ nat @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(99,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_mem__def) ).
thf(428,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(57,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ~ ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ~ ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_equalityE) ).
thf(307,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ~ ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ~ ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(53,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_order__antisym) ).
thf(292,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(39,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(248,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(125,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( powp @ TA @ B ) @ ( powp @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Powp__mono) ).
thf(512,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( powp @ TA @ B ) @ ( powp @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( D
= ( aa @ TA @ TB @ C @ B ) )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ E ) @ ( aa @ TA @ TB @ C @ F ) ) )
=> ( ord_less_eq @ TB @ D @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_ord__eq__le__subst) ).
thf(220,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( D
= ( aa @ TA @ TB @ C @ B ) )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ E ) @ ( aa @ TA @ TB @ C @ F ) ) )
=> ( ord_less_eq @ TB @ D @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(55,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_order__antisym__conv) ).
thf(297,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
=> ( ( ( ord_less_eq @ TA @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(13,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Suc__n__not__n) ).
thf(165,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_bot__apply) ).
thf(361,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ C @ B )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_le__funE) ).
thf(461,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ C @ B )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(12,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_order__eq__iff) ).
thf(156,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) )
& ( ( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(88,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ bool] :
( ! [C: fun @ TA @ bool] :
( ( member @ ( fun @ TA @ bool ) @ C @ B )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Union__least) ).
thf(403,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ bool] :
( ! [C: fun @ TA @ bool] :
( ( member @ ( fun @ TA @ bool ) @ C @ B )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(14,axiom,
! [TA: $tType] : ( preorder @ ( pred @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Predicate_Opred___Orderings_Opreorder) ).
thf(169,plain,
! [TA: $tType] : ( preorder @ ( pred @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(95,axiom,
bot @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(420,plain,
bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( ord_less_eq @ TB @ D @ C )
=> ( ( ( aa @ TB @ TA @ B @ C )
= A )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ E ) @ ( aa @ TB @ TA @ B @ F ) ) )
=> ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_ord__le__eq__subst) ).
thf(256,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( ord_less_eq @ TB @ D @ C )
=> ( ( ( aa @ TB @ TA @ B @ C )
= A )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ E ) @ ( aa @ TB @ TA @ B @ F ) ) )
=> ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_nat_Oinject) ).
thf(212,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( suc @ B )
= ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(107,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ B @ ( complete_Sup_Sup @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Sup__upper) ).
thf(457,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
=> ( ord_less_eq @ TA @ B @ ( complete_Sup_Sup @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(17,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
| ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_linorder__linear) ).
thf(173,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
| ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(134,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,axiom,
! [TA: $tType] : ( bot @ ( pred @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Predicate_Opred___Orderings_Obot) ).
thf(205,plain,
! [TA: $tType] : ( bot @ ( pred @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(86,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_empty__iff) ).
thf(398,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1,conjecture,
! [A: nat] :
( ? [B: hoare_28830079triple @ a] :
( ( member @ ( hoare_28830079triple @ a ) @ B @ ga )
& ~ ( hoare_1633586161_valid @ a @ A @ B ) )
| ! [B: hoare_28830079triple @ a] :
( ( member @ ( hoare_28830079triple @ a ) @ B @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) )
=> ( hoare_1633586161_valid @ a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: nat] :
( ? [B: hoare_28830079triple @ a] :
( ( member @ ( hoare_28830079triple @ a ) @ B @ ga )
& ~ ( hoare_1633586161_valid @ a @ A @ B ) )
| ! [B: hoare_28830079triple @ a] :
( ( member @ ( hoare_28830079triple @ a ) @ B @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) )
=> ( hoare_1633586161_valid @ a @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ! [A: nat] :
( ? [B: hoare_28830079triple @ a] :
( ( member @ ( hoare_28830079triple @ a ) @ B @ ga )
& ~ ( hoare_1633586161_valid @ a @ A @ B ) )
| ! [B: hoare_28830079triple @ a] :
( ( member @ ( hoare_28830079triple @ a ) @ B @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) )
=> ( hoare_1633586161_valid @ a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TB] :
( ( pred_rec @ TA @ TB @ B @ ( pred1 @ TA @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ TB @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_pred_Orecs) ).
thf(343,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TB] :
( ( pred_rec @ TA @ TB @ B @ ( pred1 @ TA @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(50,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(279,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(102,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ B ) @ A )
<=> ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Sup__le__iff) ).
thf(444,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ B ) @ A )
=> ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) )
& ( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(97,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_predicate1I) ).
thf(423,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( ord_less_eq @ TB @ D @ ( aa @ TA @ TB @ C @ B ) )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ E ) @ ( aa @ TA @ TB @ C @ F ) ) )
=> ( ord_less_eq @ TB @ D @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_order__subst1) ).
thf(191,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( ord_less_eq @ TB @ D @ ( aa @ TA @ TB @ C @ B ) )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ E ) @ ( aa @ TA @ TB @ C @ F ) ) )
=> ( ord_less_eq @ TB @ D @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(52,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( pred1 @ TA @ B )
= ( pred1 @ TA @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_pred_Oinject) ).
thf(286,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( ( pred1 @ TA @ B )
= ( pred1 @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( pred1 @ TA @ B )
= ( pred1 @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_in__inv__imagep) ).
thf(413,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) )
=> ( inv_imagep @ TB @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(82,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_equalityD2) ).
thf(382,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(8,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_le__refl) ).
thf(144,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(65,axiom,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Union__empty) ).
thf(335,plain,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(34,axiom,
! [TA: $tType] : ( order @ ( pred @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Predicate_Opred___Orderings_Oorder) ).
thf(236,plain,
! [TA: $tType] : ( order @ ( pred @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(20,axiom,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Suc__n__not__le__n) ).
thf(181,plain,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(350,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ B ) @ A )
=> ? [C: nat] :
( A
= ( suc @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Suc__le__D) ).
thf(187,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ B ) @ A )
=> ? [C: nat] :
( A
= ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(406,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(16,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(172,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(104,axiom,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( member @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Union__upper) ).
thf(451,plain,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( member @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ ( suc @ A ) )
=> ( ~ ( ord_less_eq @ nat @ B @ A )
=> ( B
= ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_le__SucE) ).
thf(245,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ ( suc @ A ) )
=> ( ~ ( ord_less_eq @ nat @ B @ A )
=> ( B
= ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(123,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_emptyE) ).
thf(509,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_equals0D) ).
thf(303,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(118,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_all__not__in__conv) ).
thf(494,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_eq__imp__le) ).
thf(140,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: TA,B: nat,C: fun @ TA @ TA] :
( ( semiri532925092at_aux @ TA @ C @ ( suc @ B ) @ A )
= ( semiri532925092at_aux @ TA @ C @ B @ ( aa @ TA @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_of__nat__aux_Osimps_I2_J) ).
thf(251,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: TA,B: nat,C: fun @ TA @ TA] :
( ( semiri532925092at_aux @ TA @ C @ ( suc @ B ) @ A )
= ( semiri532925092at_aux @ TA @ C @ B @ ( aa @ TA @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(25,axiom,
bot @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
thf(198,plain,
bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(63,axiom,
ord @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(330,plain,
ord @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_le__antisym) ).
thf(135,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__SucI) ).
thf(267,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(100,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] : ( member @ TA @ B @ A )
<=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_ex__in__conv) ).
thf(431,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ? [B: TA] : ( member @ TA @ B @ A )
=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [B: TA] : ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(36,axiom,
! [TA: $tType] : ( ord @ ( pred @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Predicate_Opred___Orderings_Oord) ).
thf(241,plain,
! [TA: $tType] : ( ord @ ( pred @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(113,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Collect__empty__eq) ).
thf(473,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(98,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ B ) @ ( complete_Sup_Sup @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Sup__subset__mono) ).
thf(426,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ B ) @ ( complete_Sup_Sup @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(80,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_empty__Collect__eq) ).
thf(374,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_ext) ).
thf(209,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(127,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: TA] :
( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Sup__upper2) ).
thf(516,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: TA] :
( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(24,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_ord__eq__le__trans) ).
thf(194,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(54,axiom,
! [TA: $tType] : ( comple187826305attice @ ( pred @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Predicate_Opred___Complete__Lattices_Ocomplete__lattice) ).
thf(295,plain,
! [TA: $tType] : ( comple187826305attice @ ( pred @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(51,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_order__eq__refl) ).
thf(282,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(62,axiom,
! [TA: $tType] :
( ( bot_bot @ ( pred @ TA ) )
= ( pred1 @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_bot__pred__def) ).
thf(327,plain,
! [TA: $tType] :
( ( bot_bot @ ( pred @ TA ) )
= ( pred1 @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(44,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_n__not__Suc__n) ).
thf(263,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(199,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(64,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_equalityD1) ).
thf(331,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( B = A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(78,axiom,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ ( fun @ TA @ bool ) @ bool] :
( ( ord_less_eq @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ B ) @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Union__mono) ).
thf(370,plain,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ ( fun @ TA @ bool ) @ bool] :
( ( ord_less_eq @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ B ) @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(502,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(110,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( ord_less_eq @ TA @ A @ C ) )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ord_less_eq @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_less__eq__Sup) ).
thf(463,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( ord_less_eq @ TA @ A @ C ) )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ord_less_eq @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(66,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_rev__predicate1D) ).
thf(338,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(112,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ( ( complete_Sup_Sup @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Sup__empty) ).
thf(470,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ( ( complete_Sup_Sup @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(75,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_subset__trans) ).
thf(359,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(58,axiom,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
<=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_bot__unique) ).
thf(314,plain,
! [TA: $tType] :
( ( bot @ TA )
=> ! [A: TA] :
( ( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) )
& ( ( A
= ( bot_bot @ TA ) )
=> ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(18,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ( B = A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_ord__le__eq__trans) ).
thf(175,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ( B = A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(83,axiom,
! [TA: $tType,A: nat,B: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ! [C: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ C @ B )
=> ( hoare_1633586161_valid @ TA @ ( suc @ A ) @ C ) )
=> ! [C: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ C @ B )
=> ( hoare_1633586161_valid @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_triples__valid__Suc) ).
thf(386,plain,
! [TA: $tType,A: nat,B: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ! [C: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ C @ B )
=> ( hoare_1633586161_valid @ TA @ ( suc @ A ) @ C ) )
=> ! [C: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ C @ B )
=> ( hoare_1633586161_valid @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(29,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(207,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(114,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( member @ TA @ C @ A ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_subsetI) ).
thf(478,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( member @ TA @ C @ A ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(69,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_set__rev__mp) ).
thf(346,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(10,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_order__trans) ).
thf(151,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ B ) @ ( suc @ A ) )
<=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Suc__le__mono) ).
thf(146,plain,
! [A: nat,B: nat] :
( ( ( ord_less_eq @ nat @ ( suc @ B ) @ ( suc @ A ) )
=> ( ord_less_eq @ nat @ B @ A ) )
& ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ ( suc @ B ) @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( ord_less_eq @ TB @ D @ C )
=> ( ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ C ) @ A )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ E ) @ ( aa @ TB @ TA @ B @ F ) ) )
=> ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_order__subst2) ).
thf(273,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( ord_less_eq @ TB @ D @ C )
=> ( ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ C ) @ A )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ E ) @ ( aa @ TB @ TA @ B @ F ) ) )
=> ( ord_less_eq @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(122,axiom,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: TA] :
( ( member @ TA @ B @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ A ) )
=> ~ ! [C: fun @ TA @ bool] :
( ( member @ TA @ B @ C )
=> ~ ( member @ ( fun @ TA @ bool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_UnionE) ).
thf(506,plain,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: TA] :
( ( member @ TA @ B @ ( complete_Sup_Sup @ ( fun @ TA @ bool ) @ A ) )
=> ~ ! [C: fun @ TA @ bool] :
( ( member @ TA @ B @ C )
=> ~ ( member @ ( fun @ TA @ bool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(101,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_592965047valids @ TA @ B @ A )
<=> ! [C: nat] :
( ! [D: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ D @ B )
=> ( hoare_1633586161_valid @ TA @ C @ D ) )
=> ! [D: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ D @ A )
=> ( hoare_1633586161_valid @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_hoare__valids__def) ).
thf(437,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( ( hoare_592965047valids @ TA @ B @ A )
=> ! [C: nat] :
( ! [D: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ D @ B )
=> ( hoare_1633586161_valid @ TA @ C @ D ) )
=> ! [D: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ D @ A )
=> ( hoare_1633586161_valid @ TA @ C @ D ) ) ) )
& ( ! [C: nat] :
( ! [D: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ D @ B )
=> ( hoare_1633586161_valid @ TA @ C @ D ) )
=> ! [D: hoare_28830079triple @ TA] :
( ( member @ ( hoare_28830079triple @ TA ) @ D @ A )
=> ( hoare_1633586161_valid @ TA @ C @ D ) ) )
=> ( hoare_592965047valids @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(87,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( collect @ TA @ B ) @ ( collect @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Collect__mono) ).
thf(400,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( collect @ TA @ B ) @ ( collect @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Complete__Lattices_Ocomplete__lattice) ).
thf(459,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq @ nat @ B @ A )
<=> ( ord_less_eq @ nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_not__less__eq__eq) ).
thf(200,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ ( suc @ A ) @ B ) )
& ( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ~ ( ord_less_eq @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(49,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ B ) @ A )
=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Suc__leD) ).
thf(277,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ B ) @ A )
=> ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(60,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_equalityI) ).
thf(322,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(73,axiom,
! [TA: $tType,A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
<=> ( member @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_bot__empty__eq) ).
thf(354,plain,
! [TA: $tType,A: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
=> ( member @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( member @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(117,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_equals0I) ).
thf(491,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TB] :
( ( pred_case @ TA @ TB @ B @ ( pred1 @ TA @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ TB @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_pred_Osimps_I2_J) ).
thf(454,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TB] :
( ( pred_case @ TA @ TB @ B @ ( pred1 @ TA @ A ) )
= ( aa @ ( fun @ TA @ bool ) @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(77,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_subset__empty) ).
thf(364,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(42,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_order__refl) ).
thf(254,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ ( suc @ A ) )
<=> ( ( ord_less_eq @ nat @ B @ A )
| ( B
= ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__Suc__eq) ).
thf(227,plain,
! [A: nat,B: nat] :
( ( ( ord_less_eq @ nat @ B @ ( suc @ A ) )
=> ( ( ord_less_eq @ nat @ B @ A )
| ( B
= ( suc @ A ) ) ) )
& ( ( ( ord_less_eq @ nat @ B @ A )
| ( B
= ( suc @ A ) ) )
=> ( ord_less_eq @ nat @ B @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(518,plain,
$false,
inference(e,[status(thm)],[482,171,138,249,468,481,352,408,276,379,511,269,500,340,153,417,320,389,184,372,504,357,421,416,325,448,179,238,514,348,453,132,396,411,243,428,307,292,248,512,220,297,165,361,461,156,403,169,420,256,212,457,173,134,205,398,128,343,279,444,423,191,286,413,382,144,335,236,181,350,187,406,172,451,245,509,303,494,140,251,198,330,135,267,431,241,473,426,374,209,516,194,295,282,327,263,199,331,370,502,463,338,470,359,314,175,386,207,478,346,151,146,273,506,437,400,459,200,277,322,354,491,454,364,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWW520_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n001.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu May 18 23:18:21 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.94/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.70/1.09 % [INFO] Parsing done (202ms).
% 1.70/1.10 % [INFO] Running in sequential loop mode.
% 2.17/1.30 % [INFO] eprover registered as external prover.
% 2.17/1.30 % [INFO] cvc4 registered as external prover.
% 2.17/1.30 % [INFO] Scanning for conjecture ...
% 2.53/1.40 % [INFO] Found a conjecture and 125 axioms. Running axiom selection ...
% 2.78/1.47 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 3.15/1.60 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.15/1.62 % [INFO] Type checking passed.
% 3.15/1.62 % [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 ...
% 4.26/1.97 % [INFO] [Domain constraints] Detected constraint on bool
% 4.26/1.97 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 13.99/5.69 % External prover 'e' found a proof!
% 13.99/5.69 % [INFO] Killing All external provers ...
% 13.99/5.69 % Time passed: 5174ms (effective reasoning time: 4590ms)
% 13.99/5.69 % 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)>
% 13.99/5.69 % 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
% 13.99/5.69 % No. of inferences in proof: 254
% 13.99/5.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5174 ms resp. 4590 ms w/o parsing
% 14.46/5.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.46/5.76 % [INFO] Killing All external provers ...
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