%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM931_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 08:10:29 AM UTC 2026
% Result : Theorem 15.54s 5.92s
% Output : Refutation 16.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 117
% Syntax : Number of formulae : 236 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 822 ( 88 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 2926 ( 92 ~; 19 |; 67 &;2272 @)
% ( 34 <=>; 442 =>; 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; 5 con; 0-4 aty)
% Number of variables : 609 ( 0 ^; 601 !; 8 ?; 609 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[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(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(dense_linorder_decl,type,
dense_linorder:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(archim1727834104eiling_decl,type,
archim1727834104eiling:
!>[TA: $tType] : $o ).
thf(archimedean_ceiling_decl,type,
archimedean_ceiling:
!>[TA: $tType] : ( TA > int ) ).
thf(archim2085082626_floor_decl,type,
archim2085082626_floor:
!>[TA: $tType] : ( TA > int ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(nat_tsub_decl,type,
nat_tsub: int > int > int ).
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(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(pp_decl,type,
pp: bool > $o ).
thf(m_decl,type,
m: int ).
thf(62,axiom,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(317,plain,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(128,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( A @ ( TA @ archimedean_ceiling ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_zero__less__ceiling) ).
thf(327,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ archimedean_ceiling ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( TA @ archimedean_ceiling ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_one__reorient) ).
thf(175,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_linorder__le__less__linear) ).
thf(277,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)],[47]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_77_linorder__antisym__conv1) ).
thf(333,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)],[70]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( int @ one_one @ ( A @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less ) ) )
<=> ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_floor__less__one) ).
thf(234,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) )
=> ( int @ one_one @ ( A @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less ) ) ) )
& ( ( int @ one_one @ ( A @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ archimedean_ceiling ) @ ( B @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_ceiling__less__cancel) ).
thf(449,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ archimedean_ceiling ) @ ( B @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_order__less__not__sym) ).
thf(120,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)],[3]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_order__less__imp__not__eq2) ).
thf(202,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_order__less__imp__le) ).
thf(340,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)],[71]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_order__less__imp__not__eq) ).
thf(153,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(320,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_82_order__le__imp__less__or__eq) ).
thf(436,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)],[99]) ).
thf(22,axiom,
bool @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(174,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( C @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_pinf_I6_J) ).
thf(404,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( C @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(84,axiom,
int @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).
thf(389,plain,
int @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(13,axiom,
bool @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(157,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',fact_53_linorder__neqE__linordered__idom) ).
thf(125,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)],[5]) ).
thf(73,axiom,
~ ( m @ ( int @ one_one @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096_126_A1_A_060_061_Am_096) ).
thf(344,plain,
~ ( m @ ( int @ one_one @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',fact_78_order__neq__le__trans) ).
thf(228,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)],[37]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_linorder__not__le) ).
thf(261,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)],[44]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_order__eq__iff) ).
thf(216,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)],[35]) ).
thf(17,axiom,
bool @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(164,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(102,axiom,
! [A: int] :
( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_int__one__le__iff__zero__less) ).
thf(443,plain,
! [A: int] :
( ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(65,axiom,
int @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(321,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ( ( TA @ zero_zero @ ( TA @ archimedean_ceiling ) )
= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_ceiling__zero) ).
thf(238,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ( ( TA @ zero_zero @ ( TA @ archimedean_ceiling ) )
= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ~ ( C @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_minf_I8_J) ).
thf(514,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ~ ( C @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( D
= ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_ord__eq__le__subst) ).
thf(353,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( D
= ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(147,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_order__antisym) ).
thf(397,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)],[87]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ dense_linorder )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_dense__le) ).
thf(293,plain,
! [TA: $tType] :
( ( TA @ dense_linorder )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_not__one__less__zero) ).
thf(453,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',fact_61_ord__eq__less__trans) ).
thf(133,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)],[8]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__less__one) ).
thf(428,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(45,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ archimedean_ceiling ) @ ( B @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_ceiling__mono) ).
thf(265,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ archimedean_ceiling ) @ ( B @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',fact_59_order__less__imp__triv) ).
thf(206,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)],[29]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( C @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_pinf_I8_J) ).
thf(307,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( C @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(52,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(292,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_le__funD) ).
thf(439,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)],[100]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',fact_72_order__less__le) ).
thf(366,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)],[79]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_order__less__asym) ).
thf(160,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)],[15]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_order__trans) ).
thf(297,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)],[54]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( A @ ( TA @ archim2085082626_floor ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_one__le__floor) ).
thf(424,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( A @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ archim2085082626_floor ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ archim2085082626_floor ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B != A )
<=> ( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_linorder__neq__iff) ).
thf(137,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)],[9]) ).
thf(18,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(165,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ( ( TA @ one_one @ ( TA @ archimedean_ceiling ) )
= ( int @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_ceiling__one) ).
thf(484,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ( ( TA @ one_one @ ( TA @ archimedean_ceiling ) )
= ( int @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_order__antisym__conv) ).
thf(252,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)],[42]) ).
thf(77,axiom,
int @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).
thf(361,plain,
int @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',fact_94_order__less__le__subst1) ).
thf(461,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)],[108]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_68_less__fun__def) ).
thf(493,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)],[114]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_order__less__imp__not__less) ).
thf(193,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)],[26]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ord__eq__le__trans) ).
thf(489,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)],[113]) ).
thf(32,axiom,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(212,plain,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( int @ zero_zero @ ( A @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_floor__less__zero) ).
thf(393,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less ) ) ) )
& ( ( int @ zero_zero @ ( A @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( A @ ( TA @ archim2085082626_floor ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_zero__le__floor) ).
thf(457,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ archim2085082626_floor ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ archim2085082626_floor ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_81_linorder__antisym__conv2) ).
thf(412,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)],[92]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( int @ one_one @ ( A @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less_eq ) ) )
<=> ( TA @ one_one @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_ceiling__le__one) ).
thf(430,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( TA @ one_one @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( int @ one_one @ ( A @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ one_one @ ( A @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less_eq ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(19,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(166,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_order__subst1) ).
thf(279,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TA,F: TA] :
( ( F @ ( E @ ( TA @ ord_less_eq ) ) )
=> ( F @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TB @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_less__imp__neq) ).
thf(149,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_order__less__asym_H) ).
thf(191,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)],[25]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_zero__le__one) ).
thf(259,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_73_less__le__not__le) ).
thf(382,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)],[82]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_93_order__le__less__subst1) ).
thf(313,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)],[61]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( int @ zero_zero @ ( A @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less_eq ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_ceiling__le__zero) ).
thf(498,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( int @ zero_zero @ ( A @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ zero_zero @ ( A @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_one__neq__zero) ).
thf(350,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_le__fun__def) ).
thf(406,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)],[90]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_zero__neq__one) ).
thf(419,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(63,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ nat_tsub ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
thf(318,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ nat_tsub ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_84_order__less__le__trans) ).
thf(434,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)],[98]) ).
thf(56,axiom,
int @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
thf(303,plain,
int @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] :
~ ( A @ ( A @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_order__less__irrefl) ).
thf(208,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] :
~ ( A @ ( A @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_order__eq__refl) ).
thf(362,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)],[78]) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',fact_85_order__le__less__trans) ).
thf(451,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)],[104]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ archim2085082626_floor ) @ ( B @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_floor__mono) ).
thf(387,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ archim2085082626_floor ) @ ( B @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(33,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(213,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_linorder__less__linear) ).
thf(130,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)],[7]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_order__refl) ).
thf(455,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_linorder__not__less) ).
thf(299,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)],[55]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_leD) ).
thf(226,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)],[36]) ).
thf(46,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_less__int__def) ).
thf(267,plain,
! [A: int,B: int] :
( ( ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(41,axiom,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( B @ pp )
<=> ( A @ pp ) ) )
=> ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ pp ) )
<=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_imp__le__cong) ).
thf(241,plain,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( A @ pp )
=> ( B @ pp ) )
& ( ( B @ pp )
=> ( A @ pp ) ) ) )
=> ( ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ pp ) )
=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ pp ) ) )
& ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ pp ) )
=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_62_ord__less__eq__trans) ).
thf(167,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)],[20]) ).
thf(110,axiom,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( B @ pp )
<=> ( A @ pp ) ) )
=> ( ( ( B @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
<=> ( ( A @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_conj__le__cong) ).
thf(473,plain,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( A @ pp )
=> ( B @ pp ) )
& ( ( B @ pp )
=> ( A @ pp ) ) ) )
=> ( ( ( ( A @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
=> ( ( B @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) )
& ( ( ( B @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
=> ( ( A @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',fact_63_order__less__trans) ).
thf(162,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)],[16]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( A @ ( TA @ archimedean_ceiling ) @ ( int @ one_one @ ( int @ ord_less ) ) )
<=> ( A @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_one__less__ceiling) ).
thf(374,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( A @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ archimedean_ceiling ) @ ( int @ one_one @ ( int @ ord_less ) ) ) )
& ( ( A @ ( TA @ archimedean_ceiling ) @ ( int @ one_one @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_linorder__le__cases) ).
thf(487,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)],[112]) ).
thf(72,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_minf_I6_J) ).
thf(342,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_le__funE) ).
thf(331,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)],[69]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_not__one__le__zero) ).
thf(441,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( A @ ( TA @ archimedean_ceiling ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_one__le__ceiling) ).
thf(502,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ archimedean_ceiling ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ archimedean_ceiling ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_74_order__le__less) ).
thf(465,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)],[109]) ).
thf(38,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ( ( TA @ one_one @ ( TA @ archim2085082626_floor ) )
= ( int @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_floor__one) ).
thf(231,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ( ( TA @ one_one @ ( TA @ archim2085082626_floor ) )
= ( int @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(57,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(304,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(14,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(158,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',fact_83_order__le__neq__trans) ).
thf(390,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)],[85]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_linorder__neqE) ).
thf(171,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)],[21]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( int @ one_one @ ( A @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_ceiling__less__one) ).
thf(346,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( int @ one_one @ ( A @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less ) ) ) )
& ( ( int @ one_one @ ( A @ ( TA @ archimedean_ceiling ) @ ( int @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_le__funI) ).
thf(290,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1,conjecture,
int @ zero_zero @ ( m @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( int @ zero_zero @ ( m @ ( int @ ord_less_eq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(119,plain,
~ ( int @ zero_zero @ ( m @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( A @ ( TA @ archim2085082626_floor ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zero__less__floor) ).
thf(378,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( A @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ archim2085082626_floor ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( TA @ archim2085082626_floor ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_leI) ).
thf(214,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)],[34]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ( ( TA @ zero_zero @ ( TA @ archim2085082626_floor ) )
= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_floor__zero) ).
thf(287,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ( ( TA @ zero_zero @ ( TA @ archim2085082626_floor ) )
= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_not__leE) ).
thf(410,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)],[91]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_not__less__iff__gr__or__eq) ).
thf(183,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)],[24]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ archim2085082626_floor ) @ ( B @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_floor__less__cancel) ).
thf(422,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ archim2085082626_floor ) @ ( B @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_linorder__linear) ).
thf(305,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)],[58]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(210,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(67,axiom,
int @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(326,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(117,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zero__reorient) ).
thf(506,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ~ ( B @ ( A @ ( TA @ ord_less ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_linorder__antisym__conv3) ).
thf(195,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)],[27]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_order__subst2) ).
thf(400,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ order )
& ( TA @ order ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_ord__le__eq__trans) ).
thf(283,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)],[49]) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',fact_97_order__le__less__subst2) ).
thf(322,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)],[66]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_linorder__cases) ).
thf(122,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)],[4]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( int @ zero_zero @ ( A @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less_eq ) ) )
<=> ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_floor__le__zero) ).
thf(309,plain,
! [TA: $tType] :
( ( TA @ archim1727834104eiling )
=> ! [A: TA] :
( ( ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ zero_zero @ ( A @ ( TA @ archim2085082626_floor ) @ ( int @ ord_less_eq ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(521,plain,
$false,
inference(e,[status(thm)],[317,128,327,175,277,333,234,449,120,202,340,153,320,436,174,404,389,157,125,344,228,261,216,164,443,321,238,514,353,147,397,293,453,133,428,265,206,307,292,439,366,160,297,424,137,165,484,252,361,461,493,193,489,212,393,457,412,430,166,279,149,191,259,382,313,498,350,406,419,318,434,303,208,362,451,387,213,130,455,299,226,267,241,167,473,162,374,487,342,331,441,502,465,231,304,158,390,171,346,290,119,378,214,287,410,183,422,305,210,326,506,195,400,283,322,122,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM931_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.20/0.44 % Computer : n020.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sat Sep 26 04:22:18 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.44 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.45/1.35 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.75/1.83 % [INFO] Parsing done (476ms).
% 2.75/1.85 % [INFO] Running in sequential loop mode.
% 3.97/2.47 % [INFO] eprover registered as external prover.
% 3.97/2.48 % [INFO] Scanning for conjecture ...
% 4.39/2.67 % [INFO] Found a conjecture (or negated_conjecture) and 116 axioms. Running axiom selection ...
% 4.78/2.83 % [INFO] Axiom selection finished. Selected 116 axioms (removed 0 axioms).
% 5.64/3.14 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.64/3.19 % [INFO] Type checking passed.
% 5.79/3.20 % [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 ...
% 15.54/5.91 % External prover 'e' found a proof!
% 15.54/5.91 % [INFO] Killing All external provers ...
% 15.54/5.91 % Time passed: 5245ms (effective reasoning time: 4049ms)
% 15.54/5.91 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 15.54/5.92 % Axioms used in derivation (116): fact_71_linorder__le__less__linear, fact_36_zero__less__floor, fact_93_order__le__less__subst1, fact_20_floor__mono, arity_HOL_Obool___Orderings_Oorder, arity_Int_Oint___Groups_Oone, fact_70_linorder__not__le, fact_40_order__subst1, arity_HOL_Obool___Orderings_Oord, fact_96_dense__le, arity_HOL_Obool___Orderings_Opreorder, fact_8_not__one__le__zero, arity_Int_Oint___Orderings_Oorder, fact_61_ord__eq__less__trans, fact_32_order__eq__refl, arity_Int_Oint___Rings_Olinordered__idom, fact_23_zero__reorient, fact_46_one__less__ceiling, fact_55_order__less__not__sym, fact_95_pinf_I6_J, fact_51_linorder__antisym__conv3, fact_21_zero__neq__one, fact_25_le__funE, fact_43_floor__less__zero, fact_49_not__less__iff__gr__or__eq, fact_58_order__less__imp__not__eq2, fact_97_order__le__less__subst2, fact_13_ceiling__zero, arity_fun___Orderings_Oord, fact_53_linorder__neqE__linordered__idom, arity_Int_Oint___Orderings_Oord, arity_Int_Oint___Orderings_Opreorder, fact_37_one__le__ceiling, fact_27_order__antisym, fact_47_order__less__irrefl, fact_57_order__less__imp__not__eq, fact_16_one__le__floor, fact_85_order__le__less__trans, fact_92_less__int__def, fact_59_order__less__imp__triv, fact_52_linorder__neqE, fact_29_ord__eq__le__trans, arity_HOL_Obool___Orderings_Olinorder, fact_14_floor__one, fact_1_order__refl, fact_73_less__le__not__le, fact_30_order__antisym__conv, fact_35_ceiling__less__one, fact_3_conj__le__cong, fact_86_not__one__less__zero, fact_18_one__reorient, fact_67_linorder__cases, fact_48_linorder__neq__iff, fact_54_less__imp__neq, fact_89_minf_I8_J, fact_65_ceiling__less__cancel, fact_38_floor__le__zero, fact_82_order__le__imp__less__or__eq, arity_fun___Orderings_Oorder, fact_74_order__le__less, fact_34_le__funI, fact_87_zero__less__one, fact_19_ceiling__mono, fact_72_order__less__le, arity_fun___Orderings_Opreorder, fact_64_order__less__asym, fact_28_ord__le__eq__trans, fact_31_le__funD, fact_2_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_63_order__less__trans, fact_90_pinf_I8_J, fact_15_ceiling__one, fact_60_order__less__asym_H, arity_Int_Oint___Orderings_Olinorder, fact_66_floor__less__cancel, fact_24_linorder__le__cases, fact_69_linorder__not__less, fact_56_order__less__imp__not__less, fact_91_minf_I6_J, fact_26_order__trans, fact_84_order__less__le__trans, fact_17_ceiling__le__one, fact_7_ceiling__le__zero, fact_33_order__eq__iff, fact_78_order__neq__le__trans, fact_76_not__leE, fact_88_int__one__le__iff__zero__less, fact_0__096_126_A1_A_060_061_Am_096, fact_77_linorder__antisym__conv1, fact_22_one__neq__zero, fact_80_order__less__imp__le, arity_Int_Oint___Rings_Ozero__neq__one, fact_11_linorder__linear, fact_83_order__le__neq__trans, fact_41_ord__eq__le__subst, fact_79_leD, fact_75_leI, fact_94_order__less__le__subst1, fact_10_le__fun__def, fact_12_floor__zero, fact_42_order__subst2, fact_4_imp__le__cong, fact_62_ord__less__eq__trans, fact_50_linorder__less__linear, help_pp_1_1_U, fact_81_linorder__antisym__conv2, fact_44_zero__less__ceiling, fact_6_zero__le__floor, fact_45_floor__less__one, arity_Int_Oint___Groups_Ozero, fact_39_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J, fact_9_zero__le__one, help_pp_2_1_U, arity_Int_Oint___Rings_Olinordered__semidom, fact_5_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_68_less__fun__def
% 15.54/5.92 % No. of inferences in proof: 236
% 15.54/5.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5245 ms resp. 4049 ms w/o parsing
% 16.16/6.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.16/6.12 % [INFO] Killing All external provers ...
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