%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW496_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:41 AM UTC 2026
% Result : Theorem 11.02s 4.30s
% Output : Refutation 11.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 120
% Syntax : Number of formulae : 242 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 803 ( 98 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 2812 ( 95 ~; 24 |; 51 &;2250 @)
% ( 22 <=>; 370 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 9 con; 0-4 aty)
% Number of variables : 629 ( 0 ^; 613 !; 16 ?; 629 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(real_type,type,
real: $tType ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(isLub_decl,type,
isLub:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) > TA > $o ) ).
thf(isUb_decl,type,
isUb:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) > TA > $o ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(l_decl,type,
l: real ).
thf(p_decl,type,
p: bool @ ( real @ fun ) ).
thf(y1_decl,type,
y1: real ).
thf(x_decl,type,
x: real ).
thf(y_decl,type,
y: real ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_order__le__less) ).
thf(436,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(138,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,axiom,
? [A: real] : ( A @ ( p @ ( real @ collect ) @ ( bool @ ( real @ fun ) @ top_top @ ( real @ isLub ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24__096EX_At_O_AisLub_AUNIV_A_ICollect_AP_J_At_096) ).
thf(234,plain,
? [A: real] : ( A @ ( p @ ( real @ collect ) @ ( bool @ ( real @ fun ) @ top_top @ ( real @ isLub ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_order__less__asym_H) ).
thf(481,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(72,axiom,
~ ( ? [A: real] : ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ! [A: real] :
~ ! [B: real] :
( ( B @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( real @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__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(352,plain,
~ ( ? [A: real] : ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ! [A: real] :
~ ! [B: real] :
( ( B @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( real @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_order__less__trans) ).
thf(408,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_order__less__asym) ).
thf(276,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_linorder__le__less__linear) ).
thf(202,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_linorder__neqE__linordered__idom) ).
thf(384,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(8,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_linorder__le__cases) ).
thf(142,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_order__refl) ).
thf(153,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(85,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_psubset__imp__subset) ).
thf(389,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_linorder__cases) ).
thf(372,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(70,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_equalityD2) ).
thf(344,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(65,axiom,
! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( y1 @ ( A @ ( real @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_Y) ).
thf(325,plain,
! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( y1 @ ( A @ ( real @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_order__le__less__subst2) ).
thf(228,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ~ ( B @ ( A @ ( TA @ ord_less ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_linorder__antisym__conv3) ).
thf(289,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) )
& ( ~ ( B @ ( A @ ( TA @ ord_less ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_ord__less__eq__trans) ).
thf(448,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_linorder__antisym__conv2) ).
thf(316,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(44,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(261,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(17,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(164,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(79,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_UNIV__I) ).
thf(376,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( A
!= ( TA @ top_top ) )
<=> ( TA @ top_top @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__top) ).
thf(211,plain,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( ( TA @ top_top @ ( A @ ( TA @ ord_less ) ) )
=> ( A
!= ( TA @ top_top ) ) )
& ( ( A
!= ( TA @ top_top ) )
=> ( TA @ top_top @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_order__less__le__subst1) ).
thf(348,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(114,axiom,
real @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(480,plain,
real @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( D @ ( TA @ isLub ) ) ) )
=> ( ( A @ ( C @ ( D @ ( TA @ isUb ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_isLub__le__isUb) ).
thf(147,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( D @ ( TA @ isLub ) ) ) )
=> ( ( A @ ( C @ ( D @ ( TA @ isUb ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_ord__eq__less__trans) ).
thf(221,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ isLub ) ) ) )
=> ( A @ ( B @ ( C @ ( TA @ isUb ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_isLub__isUb) ).
thf(132,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ isLub ) ) ) )
=> ( A @ ( B @ ( C @ ( TA @ isUb ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_order__neq__le__trans) ).
thf(428,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(61,axiom,
real @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oorder) ).
thf(312,plain,
real @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(105,axiom,
? [A: real] :
! [B: real] :
( ( B @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( real @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_bz) ).
thf(452,plain,
? [A: real] :
! [B: real] :
( ( B @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( real @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(81,axiom,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_top1I) ).
thf(380,plain,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(32,axiom,
y1 @ ( l @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22__096L_A_060_061_AY_096) ).
thf(220,plain,
y1 @ ( l @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_order__less__imp__not__less) ).
thf(366,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B != A )
<=> ( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_linorder__neq__iff) ).
thf(334,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_ord__le__eq__trans) ).
thf(160,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(110,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_subsetD) ).
thf(467,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_linorder__linear) ).
thf(197,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(119,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_psubset__subset__trans) ).
thf(493,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_linorder__less__linear) ).
thf(456,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] :
~ ( A @ ( A @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_order__less__irrefl) ).
thf(285,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] :
~ ( A @ ( A @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_order__less__le) ).
thf(420,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( ( B != A )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_le__funE) ).
thf(499,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_order__less__imp__le) ).
thf(225,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ top_top @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ top_top ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_top__apply) ).
thf(328,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ top_top @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ top_top ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_not__leE) ).
thf(256,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) )
<=> ( A
= ( TA @ top_top ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_top__unique) ).
thf(173,plain,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( ( A
= ( TA @ top_top ) )
=> ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ top_top ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_order__antisym) ).
thf(129,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_ord__eq__le__trans) ).
thf(134,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
<=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_set__eq__subset) ).
thf(244,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_linorder__not__le) ).
thf(205,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ ord_less ) ) )
=> ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
& ( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(92,axiom,
real @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Opreorder) ).
thf(412,plain,
real @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(46,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_equalityD1) ).
thf(264,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B = A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(102,axiom,
l @ ( p @ ( real @ collect ) @ ( bool @ ( real @ fun ) @ top_top @ ( real @ isLub ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_L) ).
thf(444,plain,
l @ ( p @ ( real @ collect ) @ ( bool @ ( real @ fun ) @ top_top @ ( real @ isLub ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_order__trans) ).
thf(149,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(78,axiom,
bool @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(375,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_order__eq__iff) ).
thf(180,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_linorder__antisym__conv1) ).
thf(296,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_less__imp__neq) ).
thf(402,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(27,axiom,
bool @ top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(204,plain,
bool @ top,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(93,axiom,
bool @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(413,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(391,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(445,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(82,axiom,
! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( y1 @ ( A @ ( real @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Y_H) ).
thf(382,plain,
! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( y1 @ ( A @ ( real @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_linorder__neqE) ).
thf(313,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(9,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(144,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_not__less__iff__gr__or__eq) ).
thf(236,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( ( B = A )
| ( B @ ( A @ ( TA @ ord_less ) ) ) )
=> ~ ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( B = A )
| ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(89,axiom,
? [A: real] : ( A @ ( p @ ( real @ collect ) @ ( bool @ ( real @ fun ) @ top_top @ ( real @ isUb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_thY) ).
thf(406,plain,
? [A: real] : ( A @ ( p @ ( real @ collect ) @ ( bool @ ( real @ fun ) @ top_top @ ( real @ isUb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(49,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_subset__refl) ).
thf(274,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(96,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(419,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(58,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_UNIV__def) ).
thf(303,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(84,axiom,
! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( ( A @ ( y @ ( real @ ord_less ) ) )
=> ( l @ ( y @ ( real @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096_B_Bz_O_A_091_124_AP_Az_059_Ay_A_060_Az_A_124_093_A_061_061_062_Ay_A_060_AL_096) ).
thf(387,plain,
! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( ( A @ ( y @ ( real @ ord_less ) ) )
=> ( l @ ( y @ ( real @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(64,axiom,
? [A: real] : ( p @ ( real @ collect ) @ ( A @ ( real @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_thx) ).
thf(323,plain,
? [A: real] : ( p @ ( real @ collect ) @ ( A @ ( real @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(140,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_order__less__imp__not__eq) ).
thf(483,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ top_top ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_top__le) ).
thf(155,plain,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
( ( A @ ( TA @ top_top @ ( TA @ ord_less_eq ) ) )
=> ( A
= ( TA @ top_top ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(51,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(278,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(99,axiom,
? [A: real] : ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_ex) ).
thf(431,plain,
? [A: real] : ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_order__eq__refl) ).
thf(167,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(87,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_psubset__eq) ).
thf(394,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( B != A )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less ) ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less ) ) )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_order__less__le__subst2) ).
thf(306,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less ) ) )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less ) ) )
<=> ( ~ ( B @ ( A @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_less__fun__def) ).
thf(473,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( ( ~ ( B @ ( A @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less ) ) )
=> ( ~ ( B @ ( A @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
& ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(29,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rev__predicate1D) ).
thf(209,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_order__le__less__subst1) ).
thf(487,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(52,axiom,
real @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(282,plain,
real @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(94,axiom,
y1 @ ( x @ ( real @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_xY) ).
thf(414,plain,
y1 @ ( x @ ( real @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(66,axiom,
bool @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(327,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_in__mono) ).
thf(310,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( B @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(24,axiom,
x @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_x) ).
thf(199,plain,
x @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(68,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_equalityI) ).
thf(331,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(76,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_set__rev__mp) ).
thf(370,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_order__less__imp__not__eq2) ).
thf(463,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(120,axiom,
( ( l @ ( y @ ( real @ ord_less ) ) )
=> ~ ! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ~ ( A @ ( y @ ( real @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096_091_124_Ay_A_060_AL_059_AALL_Az_O_AP_Az_A_N_N_062_A_126_Ay_A_060_Az_A_124_093_A_061_061_062_AFalse_096) ).
thf(495,plain,
( ( l @ ( y @ ( real @ ord_less ) ) )
=> ~ ! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ~ ( A @ ( y @ ( real @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_le__funD) ).
thf(218,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(75,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(368,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_order__le__neq__trans) ).
thf(258,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(158,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] : ( TA @ top_top @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_top__greatest) ).
thf(171,plain,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] : ( TA @ top_top @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_order__less__not__sym) ).
thf(378,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_order__le__imp__less__or__eq) ).
thf(433,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_predicate1D) ).
thf(478,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
~ ( A @ ( TA @ top_top @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_not__top__less) ).
thf(287,plain,
! [TA: $tType] :
( ( TA @ top )
=> ! [A: TA] :
~ ( A @ ( TA @ top_top @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(151,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: bool,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( C @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_order__less__imp__triv) ).
thf(410,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: bool,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( C @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(45,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_order__le__less__trans) ).
thf(262,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_order__antisym__conv) ).
thf(190,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(48,axiom,
real @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oord) ).
thf(273,plain,
real @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( ~ ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_less__le__not__le) ).
thf(268,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( ( ~ ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ~ ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(73,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_subset__iff__psubset__eq) ).
thf(358,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( B = A )
| ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less ) ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_leD) ).
thf(283,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_le__fun__def) ).
thf(415,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(108,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_linorder__not__less) ).
thf(459,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ~ ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(25,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_leI) ).
thf(200,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1,conjecture,
( ? [A: real] :
( ( A @ ( y @ ( real @ ord_less ) ) )
& ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp ) )
<=> ( l @ ( y @ ( real @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ? [A: real] :
( ( A @ ( y @ ( real @ ord_less ) ) )
& ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp ) )
<=> ( l @ ( y @ ( real @ ord_less ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(122,plain,
~ ( ( ( l @ ( y @ ( real @ ord_less ) ) )
=> ? [A: real] :
( ( A @ ( y @ ( real @ ord_less ) ) )
& ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp ) ) )
& ( ? [A: real] :
( ( A @ ( y @ ( real @ ord_less ) ) )
& ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp ) )
=> ( l @ ( y @ ( real @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(111,axiom,
~ ! [A: real] :
~ ( A @ ( p @ ( real @ collect ) @ ( bool @ ( real @ fun ) @ top_top @ ( real @ isLub ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23__096_B_Bthesis_O_A_I_B_BL_O_AisLub_AUNIV_A_ICollect_AP_J_AL_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(469,plain,
~ ! [A: real] :
~ ( A @ ( p @ ( real @ collect ) @ ( bool @ ( real @ fun ) @ top_top @ ( real @ isLub ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_order__less__le__trans) ).
thf(491,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(106,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_subset__UNIV) ).
thf(454,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(37,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_iso__tuple__UNIV__I) ).
thf(232,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(41,axiom,
! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( l @ ( A @ ( real @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_L_H) ).
thf(254,plain,
! [A: real] :
( ( A @ ( p @ ( bool @ ( real @ aa ) ) ) @ pp )
=> ( l @ ( A @ ( real @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(35,axiom,
bool @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(227,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(521,plain,
$false,
inference(e,[status(thm)],[436,138,234,481,352,408,276,202,384,142,153,389,372,344,325,228,289,448,316,261,164,376,211,348,480,147,221,132,428,312,452,380,220,366,334,160,467,197,493,456,285,420,499,225,328,256,173,129,134,244,205,412,264,444,149,375,180,296,402,204,413,391,445,382,313,144,236,406,274,419,303,387,323,140,483,155,278,431,167,394,306,473,209,487,282,414,327,310,199,331,370,463,495,218,368,258,158,171,378,433,478,287,151,410,262,190,273,268,358,283,415,459,200,122,469,491,454,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW496_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n011.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 16:09:14 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.83/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.26 % [INFO] Parsing done (263ms).
% 1.35/1.27 % [INFO] Running in sequential loop mode.
% 2.37/1.66 % [INFO] eprover registered as external prover.
% 2.37/1.67 % [INFO] Scanning for conjecture ...
% 2.75/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 119 axioms. Running axiom selection ...
% 2.92/1.92 % [INFO] Axiom selection finished. Selected 119 axioms (removed 0 axioms).
% 3.26/2.10 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.26/2.11 % [INFO] Type checking passed.
% 3.26/2.12 % [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 ...
% 3.87/2.39 % [INFO] [Domain constraints] Detected constraint on bool
% 3.87/2.40 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 10.40/4.29 % External prover 'e' found a proof!
% 10.40/4.29 % [INFO] Killing All external provers ...
% 10.40/4.29 % Time passed: 3741ms (effective reasoning time: 3014ms)
% 10.40/4.29 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 11.02/4.30 % Axioms used in derivation (119): arity_RealDef_Oreal___Orderings_Oord, fact_35_ord__eq__le__trans, fact_59_not__top__less, fact_17_linorder__neqE__linordered__idom, fact_67_order__less__imp__not__eq2, arity_HOL_Obool___Orderings_Oorder, fact_53_less__le__not__le, fact_33_le__funD, fact_69_order__less__imp__not__less, arity_HOL_Obool___Orderings_Oord, fact_32_order__eq__refl, arity_HOL_Obool___Orderings_Opreorder, fact_66_order__less__imp__triv, fact_3__096_B_Bz_O_A_091_124_AP_Az_059_Ay_A_060_Az_A_124_093_A_061_061_062_Ay_A_060_AL_096, fact_65_order__less__asym_H, fact_63_ord__less__eq__trans, fact_23__096_B_Bthesis_O_A_I_B_BL_O_AisLub_AUNIV_A_ICollect_AP_J_AL_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_30_order__eq__iff, fact_82_less__fun__def, fact_31_top__le, fact_90_set__eq__subset, arity_fun___Orderings_Oord, fact_62_order__less__trans, fact_74_order__le__less__subst1, fact_18_less__imp__neq, fact_42_order__less__le__trans, fact_5_thx, fact_43_order__le__neq__trans, fact_12_linorder__neq__iff, fact_54_order__less__le, help_fTrue_1_1_T, fact_0_ex, fact_1_x, fact_4__096_091_124_Ay_A_060_AL_059_AALL_Az_O_AP_Az_A_N_N_062_A_126_Ay_A_060_Az_A_124_093_A_061_061_062_AFalse_096, fact_2_bz, fact_81_subset__UNIV, fact_57_linorder__not__less, fact_21_Y_H, fact_89_psubset__eq, fact_20_order__refl, fact_40_linorder__le__cases, fact_8_L_H, help_fTrue_1_1_U, fact_87_equalityI, fact_92_rev__predicate1D, arity_HOL_Obool___Orderings_Olinorder, fact_97_predicate1D, fact_39_le__funE, fact_56_linorder__not__le, arity_fun___Orderings_Oorder, fact_51_leI, fact_15_linorder__antisym__conv3, fact_91_subset__iff__psubset__eq, fact_96_in__mono, fact_64_ord__eq__less__trans, fact_55_linorder__le__less__linear, fact_70_thY, fact_68_order__less__imp__not__eq, arity_fun___Orderings_Opreorder, fact_78_order__less__le__subst1, fact_27_top__unique, fact_14_linorder__less__linear, fact_26_top__apply, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_80_order__less__le__subst2, arity_HOL_Obool___Orderings_Otop, fact_25_top__greatest, fact_49_linorder__antisym__conv1, fact_50_not__leE, fact_61_order__less__asym, fact_99_psubset__subset__trans, fact_29_linorder__linear, fact_76_mem__def, fact_71_top1I, fact_24__096EX_At_O_AisLub_AUNIV_A_ICollect_AP_J_At_096, fact_44_order__le__imp__less__or__eq, fact_88_subset__refl, fact_93_equalityD1, help_COMBK_1_1_U, fact_58_less__top, arity_RealDef_Oreal___Orderings_Oorder, arity_RealDef_Oreal___Orderings_Olinorder, fact_36_ord__le__eq__trans, fact_16_linorder__neqE, fact_47_leD, fact_10_xY, fact_72_UNIV__I, fact_46_order__less__imp__le, fact_98_set__rev__mp, fact_79_order__le__less__subst2, fact_41_order__le__less__trans, fact_11_order__less__irrefl, arity_RealDef_Oreal___Orderings_Opreorder, fact_45_linorder__antisym__conv2, fact_95_psubset__imp__subset, fact_38_order__trans, fact_85_isLub__isUb, fact_52_order__le__less, fact_19_order__less__not__sym, fact_84_isLub__le__isUb, fact_22__096L_A_060_061_AY_096, fact_37_order__antisym, fact_83_UNIV__def, fact_77_Collect__def, fact_13_not__less__iff__gr__or__eq, fact_86_subsetD, fact_94_equalityD2, help_pp_1_1_U, fact_73_iso__tuple__UNIV__I, fact_60_linorder__cases, fact_75_ext, arity_fun___Orderings_Otop, help_pp_2_1_U, fact_28_le__fun__def, fact_9_L, fact_34_order__antisym__conv, fact_7__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_6_Y, fact_48_order__neq__le__trans
% 11.02/4.30 % No. of inferences in proof: 242
% 11.02/4.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3741 ms resp. 3014 ms w/o parsing
% 11.44/4.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.44/4.43 % [INFO] Killing All external provers ...
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