TSTP Solution File: SWW494_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW494_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 12:24:53 EDT 2023
% Result : Theorem 9.26s 3.29s
% Output : Refutation 9.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 140
% Syntax : Number of formulae : 254 ( 42 unt; 28 typ; 0 def)
% Number of atoms : 736 ( 81 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 2902 ( 66 ~; 17 |; 56 &;2376 @)
% ( 21 <=>; 366 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 7 con; 0-6 aty)
% Number of variables : 680 ( 0 ^; 615 !; 41 ?; 680 :)
% ( 24 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(real_type,type,
real: $tType ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(top_type,type,
top:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(dense_linorder_type,type,
dense_linorder:
!>[TA: $tType] : $o ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(isLub_type,type,
isLub:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) > TA > $o ) ).
thf(isUb_type,type,
isUb:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(leastP_type,type,
leastP:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA > $o ) ).
thf(setge_type,type,
setge:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(order_strict_mono_type,type,
order_strict_mono:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(inv_imagep_type,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ bool ) ) > ( fun @ TA @ TB ) > TA > TA > $o ) ).
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(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(p_type,type,
p: fun @ real @ bool ).
thf(y_type,type,
y: real ).
thf(thesis_type,type,
thesis: $o ).
thf(x_type,type,
x: real ).
thf(87,axiom,
! [A: fun @ real @ bool] :
( ? [B: real] : ( member @ real @ B @ A )
=> ( ? [B: real] : ( pp @ ( aa @ real @ bool @ ( isUb @ real @ ( top_top @ ( fun @ real @ bool ) ) @ A ) @ B ) )
=> ? [B: real] : ( isLub @ real @ ( top_top @ ( fun @ real @ bool ) ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_reals__complete) ).
thf(384,plain,
! [A: fun @ real @ bool] :
( ? [B: real] : ( member @ real @ B @ A )
=> ( ? [B: real] : ( pp @ ( aa @ real @ bool @ ( isUb @ real @ ( top_top @ ( fun @ real @ bool ) ) @ A ) @ B ) )
=> ? [B: real] : ( isLub @ real @ ( top_top @ ( fun @ real @ bool ) ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(393,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(76,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_less__imp__neq) ).
thf(338,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(5,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( isLub @ TA @ C @ B @ A )
<=> ( leastP @ TA @ ( isUb @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_isLub__def) ).
thf(119,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ( isLub @ TA @ C @ B @ A )
=> ( leastP @ TA @ ( isUb @ TA @ C @ B ) @ A ) )
& ( ( leastP @ TA @ ( isUb @ TA @ C @ B ) @ A )
=> ( isLub @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(79,axiom,
~ ( ? [A: real] : ( pp @ ( aa @ real @ bool @ p @ A ) )
=> ! [A: real] :
~ ! [B: real] :
( ( pp @ ( aa @ real @ bool @ p @ B ) )
=> ( ord_less @ real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__096_B_Bthesis_O_A_I_B_Bx_AY_O_A_091_124_AP_Ax_059_A_B_Bx_O_AP_Ax_A_061_061_062_Ax_A_060_AY_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(347,plain,
~ ( ? [A: real] : ( pp @ ( aa @ real @ bool @ p @ A ) )
=> ! [A: real] :
~ ! [B: real] :
( ( pp @ ( aa @ real @ bool @ p @ B ) )
=> ( ord_less @ real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(333,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(42,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_85_order__antisym) ).
thf(234,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)],[42]) ).
thf(80,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ~ ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_order__less__imp__not__less) ).
thf(352,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ~ ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(3,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( isLub @ TA @ C @ B @ A )
=> ( leastP @ TA @ ( isUb @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_isLubD3) ).
thf(115,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( isLub @ TA @ C @ B @ A )
=> ( leastP @ TA @ ( isUb @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(59,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ? [C: TA] :
( ( ord_less @ TA @ B @ C )
& ( ord_less @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_dense) ).
thf(276,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ? [C: TA] :
( ( ord_less @ TA @ B @ C )
& ( ord_less @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(48,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ B @ A )
<=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_linorder__not__less) ).
thf(247,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less_eq @ TA @ A @ B ) )
& ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(27,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_76_mem__def) ).
thf(185,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)],[27]) ).
thf(61,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(288,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(53,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_order__less__trans) ).
thf(257,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(89,axiom,
dense_linorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Odense__linorder) ).
thf(389,plain,
dense_linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(85,axiom,
! [A: fun @ real @ bool] :
( ? [B: real] : ( member @ real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member @ real @ C @ A )
=> ( ord_less @ real @ C @ B ) )
=> ? [B: real] :
! [C: real] :
( ? [D: real] :
( ( member @ real @ D @ A )
& ( ord_less @ real @ C @ D ) )
<=> ( ord_less @ real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_posreal__complete) ).
thf(372,plain,
! [A: fun @ real @ bool] :
( ? [B: real] : ( member @ real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member @ real @ C @ A )
=> ( ord_less @ real @ C @ B ) )
=> ? [B: real] :
! [C: real] :
( ( ? [D: real] :
( ( member @ real @ D @ A )
& ( ord_less @ real @ C @ D ) )
=> ( ord_less @ real @ C @ B ) )
& ( ( ord_less @ real @ C @ B )
=> ? [D: real] :
( ( member @ real @ D @ A )
& ( ord_less @ real @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(78,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ B @ A )
<=> ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_linorder__not__le) ).
thf(344,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) )
& ( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(31,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_leI) ).
thf(196,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(72,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_order__refl) ).
thf(325,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB] :
( ( order_strict_mono @ TA @ TB @ C )
=> ( ( ord_less @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( aa @ TA @ TB @ C @ A ) )
<=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_strict__mono__less) ).
thf(289,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB] :
( ( order_strict_mono @ TA @ TB @ C )
=> ( ( ( ord_less @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( aa @ TA @ TB @ C @ A ) )
=> ( ord_less @ TA @ B @ A ) )
& ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(70,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
| ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_linorder__le__less__linear) ).
thf(316,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
| ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( B = A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_ord__less__eq__trans) ).
thf(164,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( B = A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(44,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_gt__ex) ).
thf(238,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(94,axiom,
? [A: real] : ( pp @ ( aa @ real @ bool @ p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_ex) ).
thf(397,plain,
? [A: real] : ( pp @ ( aa @ real @ bool @ p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(38,axiom,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_top__greatest) ).
thf(221,plain,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(100,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( fun @ TA @ bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_UNIV__eq__I) ).
thf(411,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( fun @ TA @ bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(109,axiom,
? [A: real] : ( isLub @ real @ ( top_top @ ( fun @ real @ bool ) ) @ ( collect @ real @ p ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096EX_At_O_AisLub_AUNIV_A_ICollect_AP_J_At_096) ).
thf(428,plain,
? [A: real] : ( isLub @ real @ ( top_top @ ( fun @ real @ bool ) ) @ ( collect @ real @ p ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(67,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_order__less__imp__not__eq2) ).
thf(307,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(63,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ C @ B ) @ A ) )
=> ( ( setge @ TA @ A @ ( collect @ TA @ ( isUb @ TA @ C @ B ) ) )
=> ( isLub @ TA @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_isLubI2) ).
thf(292,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ C @ B ) @ A ) )
=> ( ( setge @ TA @ A @ ( collect @ TA @ ( isUb @ TA @ C @ B ) ) )
=> ( isLub @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(4,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( leastP @ TA @ B @ A )
=> ( setge @ TA @ A @ ( collect @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_leastPD2) ).
thf(117,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( leastP @ TA @ B @ A )
=> ( setge @ TA @ A @ ( collect @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,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(270,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)],[56]) ).
thf(84,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_82_order__antisym__conv) ).
thf(366,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)],[84]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( ord_less @ TB @ D @ C )
=> ( ( ord_less @ TA @ ( aa @ TB @ TA @ B @ C ) @ A )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( aa @ TB @ TA @ B @ E ) @ ( aa @ TB @ TA @ B @ F ) ) )
=> ( ord_less @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_order__less__subst2) ).
thf(297,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( ord_less @ TB @ D @ C )
=> ( ( ord_less @ TA @ ( aa @ TB @ TA @ B @ C ) @ A )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( aa @ TB @ TA @ B @ E ) @ ( aa @ TB @ TA @ B @ F ) ) )
=> ( ord_less @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(98,axiom,
? [A: real] : ( pp @ ( aa @ real @ bool @ ( isUb @ real @ ( top_top @ ( fun @ real @ bool ) ) @ ( collect @ real @ p ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_thY) ).
thf(407,plain,
? [A: real] : ( pp @ ( aa @ real @ bool @ ( isUb @ real @ ( top_top @ ( fun @ real @ bool ) ) @ ( collect @ real @ p ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(58,axiom,
linorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(275,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(12,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_83_ord__eq__le__trans) ).
thf(137,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)],[12]) ).
thf(50,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: bool,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( pp @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_order__less__imp__triv) ).
thf(252,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: bool,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( pp @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(113,axiom,
! [A: real] :
( ( isLub @ real @ ( top_top @ ( fun @ real @ bool ) ) @ ( collect @ real @ p ) @ A )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(435,plain,
! [A: real] :
( ( isLub @ real @ ( top_top @ ( fun @ real @ bool ) ) @ ( collect @ real @ p ) @ A )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( ord_less @ TB @ D @ ( aa @ TA @ TB @ C @ B ) )
=> ( ( ord_less @ TA @ B @ A )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( aa @ TA @ TB @ C @ E ) @ ( aa @ TA @ TB @ C @ F ) ) )
=> ( ord_less @ TB @ D @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_order__less__subst1) ).
thf(188,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB,D: TB] :
( ( ord_less @ TB @ D @ ( aa @ TA @ TB @ C @ B ) )
=> ( ( ord_less @ TA @ B @ A )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( aa @ TA @ TB @ C @ E ) @ ( aa @ TA @ TB @ C @ F ) ) )
=> ( ord_less @ TB @ D @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(82,axiom,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
<=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_top__unique) ).
thf(356,plain,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) )
& ( ( A
= ( top_top @ TA ) )
=> ( ord_less_eq @ TA @ ( top_top @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(141,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(105,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_UNIV__witness) ).
thf(420,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(7,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( leastP @ TA @ ( isUb @ TA @ C @ B ) @ A )
=> ( isLub @ TA @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_isLubI1) ).
thf(124,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( leastP @ TA @ ( isUb @ TA @ C @ B ) @ A )
=> ( isLub @ TA @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(40,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
<=> ( ( ord_less_eq @ TA @ B @ A )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_order__less__le) ).
thf(225,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ( ord_less @ TA @ B @ A )
=> ( ( ord_less_eq @ TA @ B @ A )
& ( B != A ) ) )
& ( ( ( ord_less_eq @ TA @ B @ A )
& ( B != A ) )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(43,axiom,
preorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(237,plain,
preorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(47,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_linorder__neqE__linordered__idom) ).
thf(244,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(68,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_73_linorder__linear) ).
thf(311,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)],[68]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( top_top @ ( fun @ TB @ TA ) ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_top__apply) ).
thf(425,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( top_top @ ( fun @ TB @ TA ) ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(110,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_iso__tuple__UNIV__I) ).
thf(430,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( ord_less @ TB @ D @ C )
=> ( ( ( aa @ TB @ TA @ B @ C )
= A )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( aa @ TB @ TA @ B @ E ) @ ( aa @ TB @ TA @ B @ F ) ) )
=> ( ord_less @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_ord__less__eq__subst) ).
thf(148,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TA,B: fun @ TB @ TA,C: TB,D: TB] :
( ( ord_less @ TB @ D @ C )
=> ( ( ( aa @ TB @ TA @ B @ C )
= A )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( aa @ TB @ TA @ B @ E ) @ ( aa @ TB @ TA @ B @ F ) ) )
=> ( ord_less @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(60,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
<=> ( ( ord_less @ TA @ B @ A )
| ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_linorder__neq__iff) ).
thf(279,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ( B != A )
=> ( ( ord_less @ TA @ B @ A )
| ( ord_less @ TA @ A @ B ) ) )
& ( ( ( ord_less @ TA @ B @ A )
| ( ord_less @ TA @ A @ B ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(107,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_top1I) ).
thf(423,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(54,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_74_order__eq__iff) ).
thf(259,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)],[54]) ).
thf(29,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_80_order__eq__refl) ).
thf(191,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)],[29]) ).
thf(96,axiom,
! [A: real,B: real,C: fun @ real @ bool,D: fun @ real @ bool] :
( ( isLub @ real @ D @ C @ B )
=> ( ( isLub @ real @ D @ C @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_real__isLub__unique) ).
thf(402,plain,
! [A: real,B: real,C: fun @ real @ bool,D: fun @ real @ bool] :
( ( isLub @ real @ D @ C @ B )
=> ( ( isLub @ real @ D @ C @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(391,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(86,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_UNIV__I) ).
thf(382,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(69,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ B @ A )
=> ( ( B != A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_linorder__cases) ).
thf(313,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ B @ A )
=> ( ( B != A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(75,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
| ( B = A )
| ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_linorder__less__linear) ).
thf(335,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
| ( B = A )
| ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(25,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ~ ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_order__less__asym) ).
thf(181,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ~ ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_order__less__irrefl) ).
thf(219,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(104,axiom,
pp @ ( aa @ real @ bool @ p @ x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_x) ).
thf(419,plain,
pp @ ( aa @ real @ bool @ p @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(83,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
<=> ( ( ord_less_eq @ TA @ B @ A )
& ~ ( ord_less_eq @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_less__le__not__le) ).
thf(362,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ( ord_less @ 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 ) )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(71,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
<=> ( ( ord_less @ TA @ B @ A )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_order__le__less) ).
thf(318,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ( ord_less_eq @ TA @ B @ A )
=> ( ( ord_less @ TA @ B @ A )
| ( B = A ) ) )
& ( ( ( ord_less @ TA @ B @ A )
| ( B = A ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(112,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(434,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(45,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ~ ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_order__less__not__sym) ).
thf(240,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ~ ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(18,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_72_le__fun__def) ).
thf(155,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)],[18]) ).
thf(32,axiom,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( top_top @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_not__top__less) ).
thf(198,plain,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( top_top @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(9,axiom,
ord @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(130,plain,
ord @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(95,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_59_in__inv__imagep) ).
thf(399,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)],[95]) ).
thf(39,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( isLub @ TA @ C @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_isLub__isUb) ).
thf(223,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( isLub @ TA @ C @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(11,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_81_le__funD) ).
thf(135,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)],[11]) ).
thf(20,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( isLub @ TA @ D @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_isLubD2) ).
thf(162,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( isLub @ TA @ D @ C @ B )
=> ( ( member @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(52,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( isLub @ TA @ D @ C @ B )
=> ( ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ D @ C ) @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_isLub__le__isUb) ).
thf(255,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( isLub @ TA @ D @ C @ B )
=> ( ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ D @ C ) @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(35,axiom,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( A
!= ( top_top @ TA ) )
<=> ( ord_less @ TA @ A @ ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_less__top) ).
thf(209,plain,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( ( A
!= ( top_top @ TA ) )
=> ( ord_less @ TA @ A @ ( top_top @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( top_top @ TA ) )
=> ( A
!= ( top_top @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(77,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_86_order__trans) ).
thf(342,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)],[77]) ).
thf(15,axiom,
ord @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oord) ).
thf(145,plain,
ord @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(101,axiom,
preorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Opreorder) ).
thf(414,plain,
preorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(73,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ B @ A )
=> ( ~ ( ord_less @ TA @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_linorder__antisym__conv3) ).
thf(327,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ B @ A )
=> ( ( ~ ( ord_less @ TA @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ~ ( ord_less @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(99,axiom,
? [A: real] : ( member @ real @ A @ ( collect @ real @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_thx) ).
thf(409,plain,
? [A: real] : ( member @ real @ A @ ( collect @ real @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(14,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_87_le__funE) ).
thf(143,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)],[14]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB] :
( ( order_strict_mono @ TA @ TB @ C )
=> ( ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( aa @ TA @ TB @ C @ A ) )
<=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_strict__mono__less__eq) ).
thf(175,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB] :
( ( order_strict_mono @ TA @ TB @ C )
=> ( ( ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( aa @ TA @ TB @ C @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) )
& ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(88,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(386,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(49,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ D @ C ) @ B ) )
=> ( ( member @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_isUbD) ).
thf(250,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ D @ C ) @ B ) )
=> ( ( member @ TA @ A @ C )
=> ( ord_less_eq @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB] :
( ( order_strict_mono @ TA @ TB @ C )
=> ( ( ( aa @ TA @ TB @ C @ B )
= ( aa @ TA @ TB @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_strict__mono__eq) ).
thf(203,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB] :
( ( order_strict_mono @ TA @ TB @ C )
=> ( ( ( ( aa @ TA @ TB @ C @ B )
= ( aa @ TA @ TB @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ TA @ TB @ C @ B )
= ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ord__eq__less__trans) ).
thf(158,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(90,axiom,
order @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oorder) ).
thf(390,plain,
order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(114,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(103,axiom,
top @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(418,plain,
top @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(66,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ B @ A )
<=> ( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_not__less__iff__gr__or__eq) ).
thf(300,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ B @ A )
=> ( ( ord_less @ TA @ A @ B )
| ( B = A ) ) )
& ( ( ( ord_less @ TA @ A @ B )
| ( B = A ) )
=> ~ ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(111,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_subset__UNIV) ).
thf(432,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( top_top @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(22,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 @ TA @ B @ A )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( aa @ TA @ TB @ C @ E ) @ ( aa @ TA @ TB @ C @ F ) ) )
=> ( ord_less @ TB @ D @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_ord__eq__less__subst) ).
thf(168,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 @ TA @ B @ A )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( aa @ TA @ TB @ C @ E ) @ ( aa @ TA @ TB @ C @ F ) ) )
=> ( ord_less @ TB @ D @ ( aa @ TA @ TB @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( isLub @ TA @ C @ B @ A )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_isLubD1a) ).
thf(146,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( isLub @ TA @ C @ B @ A )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(97,axiom,
! [A: fun @ real @ bool] :
( ( ? [B: real] : ( member @ real @ B @ A )
& ? [B: real] : ( pp @ ( aa @ real @ bool @ ( isUb @ real @ ( top_top @ ( fun @ real @ bool ) ) @ A ) @ B ) ) )
=> ? [B: real] : ( isLub @ real @ ( top_top @ ( fun @ real @ bool ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_lemma__reals__complete) ).
thf(405,plain,
! [A: fun @ real @ bool] :
( ( ? [B: real] : ( member @ real @ B @ A )
& ? [B: real] : ( pp @ ( aa @ real @ bool @ ( isUb @ real @ ( top_top @ ( fun @ real @ bool ) ) @ A ) @ B ) ) )
=> ? [B: real] : ( isLub @ real @ ( top_top @ ( fun @ real @ bool ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ C @ B ) @ A ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_isUbD2a) ).
thf(183,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( pp @ ( aa @ TA @ bool @ ( isUb @ TA @ C @ B ) @ A ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(106,axiom,
linorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(422,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(57,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ~ ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_order__less__asym_H) ).
thf(273,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ~ ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB] :
( ( order_strict_mono @ TA @ TB @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( aa @ TA @ TB @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_strict__monoD) ).
thf(242,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA,B: TA,C: fun @ TA @ TB] :
( ( order_strict_mono @ TA @ TB @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( aa @ TA @ TB @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(55,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_88_linorder__le__cases) ).
thf(268,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)],[55]) ).
thf(30,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(195,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(102,axiom,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_UNIV__def) ).
thf(415,plain,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(64,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_75_ext) ).
thf(294,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)],[64]) ).
thf(8,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( leastP @ TA @ B @ A )
<=> ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
& ( setge @ TA @ A @ ( collect @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_leastP__def) ).
thf(126,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( ( leastP @ TA @ B @ A )
=> ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
& ( setge @ TA @ A @ ( collect @ TA @ B ) ) ) )
& ( ( ( pp @ ( aa @ TA @ bool @ B @ A ) )
& ( setge @ TA @ A @ ( collect @ TA @ B ) ) )
=> ( leastP @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(93,axiom,
! [A: real] :
( ( pp @ ( aa @ real @ bool @ p @ A ) )
=> ( ord_less @ real @ A @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Y) ).
thf(395,plain,
! [A: real] :
( ( pp @ ( aa @ real @ bool @ p @ A ) )
=> ( ord_less @ real @ A @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(10,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_84_ord__le__eq__trans) ).
thf(131,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)],[10]) ).
thf(33,axiom,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_top__le) ).
thf(200,plain,
! [TA: $tType] :
( ( top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_linorder__neqE) ).
thf(178,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(51,axiom,
order @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(254,plain,
order @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( leastP @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_leastPD1) ).
thf(122,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( leastP @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(81,axiom,
? [A: real] :
! [B: real] :
( ( pp @ ( aa @ real @ bool @ p @ B ) )
=> ( ord_less @ real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_bz) ).
thf(354,plain,
? [A: real] :
! [B: real] :
( ( pp @ ( aa @ real @ bool @ p @ B ) )
=> ( ord_less @ real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(36,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_order__less__imp__not__eq) ).
thf(215,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(41,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_lt__ex) ).
thf(232,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(438,plain,
$false,
inference(e,[status(thm)],[384,393,338,119,347,333,234,352,115,276,247,185,288,257,389,372,344,196,325,289,316,164,238,397,221,411,428,307,292,117,270,366,297,407,275,137,252,435,188,356,141,420,124,225,237,244,311,425,430,148,279,423,259,191,402,391,382,313,335,181,219,419,362,318,434,240,155,198,130,399,223,135,162,255,209,342,145,414,327,409,143,175,386,250,203,158,390,114,418,300,432,168,146,405,183,422,273,242,268,195,415,294,126,395,131,200,178,254,122,354,215,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW494_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n020.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 22:07:03 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.99/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.11 % [INFO] Parsing done (220ms).
% 1.59/1.12 % [INFO] Running in sequential loop mode.
% 2.22/1.32 % [INFO] eprover registered as external prover.
% 2.22/1.32 % [INFO] cvc4 registered as external prover.
% 2.22/1.33 % [INFO] Scanning for conjecture ...
% 2.43/1.40 % [INFO] Found a conjecture and 121 axioms. Running axiom selection ...
% 2.75/1.47 % [INFO] Axiom selection finished. Selected 111 axioms (removed 10 axioms).
% 3.02/1.59 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.02/1.61 % [INFO] Type checking passed.
% 3.02/1.62 % [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 ...
% 9.26/3.28 % External prover 'e' found a proof!
% 9.26/3.28 % [INFO] Killing All external provers ...
% 9.26/3.28 % Time passed: 2744ms (effective reasoning time: 2161ms)
% 9.26/3.28 % 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)>
% 9.26/3.29 % Axioms used in derivation (111): fact_53_order__less__subst2, fact_52_ord__eq__less__subst, fact_26_order__less__imp__not__eq2, fact_1_ex, fact_97_less__le__not__le, fact_24_order__less__imp__not__less, fact_25_order__less__imp__not__eq, fact_36_not__top__less, arity_HOL_Obool___Orderings_Oorder, fact_70_isUbD, arity_HOL_Obool___Orderings_Oord, fact_72_le__fun__def, arity_HOL_Obool___Orderings_Opreorder, fact_92_top__greatest, fact_73_linorder__linear, fact_79_strict__mono__less__eq, fact_16_order__less__irrefl, fact_46_leastP__def, fact_65_strict__mono__less, arity_fun___Orderings_Oord, fact_64_isLub__le__isUb, fact_19_linorder__less__linear, fact_32_order__less__asym, fact_18_not__less__iff__gr__or__eq, fact_14__096_B_Bthesis_O_A_I_B_Bx_AY_O_A_091_124_AP_Ax_059_A_B_Bx_O_AP_Ax_A_061_061_062_Ax_A_060_AY_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_8_iso__tuple__UNIV__I, fact_2__096EX_At_O_AisLub_AUNIV_A_ICollect_AP_J_At_096, fact_78_strict__mono__eq, fact_91_top__unique, fact_29_ord__eq__less__trans, help_fTrue_1_1_U, fact_34_linorder__cases, fact_98_order__le__less, fact_7_UNIV__I, fact_38_reals__complete, arity_HOL_Obool___Orderings_Olinorder, fact_22_less__imp__neq, fact_57_ord__less__eq__subst, fact_99_leI, fact_59_in__inv__imagep, arity_RealDef_Oreal___Orderings_Oord, fact_23_order__less__not__sym, fact_58_linorder__neqE__linordered__idom, fact_30_ord__less__eq__trans, fact_3_thx, fact_83_ord__eq__le__trans, fact_42_isLubI1, arity_fun___Orderings_Oorder, arity_RealDef_Oreal___Orderings_Odense__linorder, arity_fun___Orderings_Opreorder, fact_44_UNIV__eq__I, fact_88_linorder__le__cases, fact_41_isLubD3, fact_37_isLub__isUb, fact_10_real__isLub__unique, fact_11_isLubD1a, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_13_UNIV__def, fact_0_x, arity_HOL_Obool___Orderings_Otop, fact_27_order__less__imp__triv, fact_9_top__apply, fact_45_UNIV__witness, fact_35_less__top, fact_51_order__less__subst1, fact_95_linorder__le__less__linear, fact_47_leastPD1, fact_84_ord__le__eq__trans, fact_76_mem__def, fact_20_linorder__antisym__conv3, fact_50_posreal__complete, fact_56_dense, fact_67_order__refl, help_COMBK_1_1_U, fact_6_top1I, arity_RealDef_Oreal___Orderings_Olinorder, arity_RealDef_Oreal___Orderings_Oorder, fact_4_bz, fact_15_lemma__reals__complete, fact_85_order__antisym, fact_55_lt__ex, arity_RealDef_Oreal___Orderings_Opreorder, fact_48_leastPD2, fact_96_order__less__le, fact_28_order__less__asym_H, fact_17_linorder__neq__iff, fact_21_linorder__neqE, fact_94_linorder__not__le, fact_89_subset__UNIV, fact_43_isLub__def, fact_81_le__funD, fact_80_order__eq__refl, fact_93_linorder__not__less, fact_77_Collect__def, fact_33_isUbD2a, fact_86_order__trans, fact_12_Y, fact_82_order__antisym__conv, fact_87_le__funE, fact_75_ext, arity_fun___Orderings_Otop, fact_74_order__eq__iff, conj_0, fact_5_thY, help_pp_2_1_U, fact_54_gt__ex, fact_66_strict__monoD, fact_40_isLubI2, fact_31_order__less__trans, fact_90_top__le, fact_71_isLubD2
% 9.26/3.29 % No. of inferences in proof: 226
% 9.26/3.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2744 ms resp. 2161 ms w/o parsing
% 9.58/3.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.58/3.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------