%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL792_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 : n014.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 07:52:55 AM UTC 2026
% Result : Theorem 26.94s 13.82s
% Output : Refutation 27.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 136
% Syntax : Number of formulae : 274 ( 128 unt; 0 typ; 0 def)
% Number of atoms : 669 ( 200 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 2439 ( 26 ~; 10 |; 64 &;2037 @)
% ( 32 <=>; 270 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 7 con; 0-4 aty)
% Number of variables : 479 ( 0 ^; 465 !; 14 ?; 479 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(char1_type,type,
char1: $tType ).
thf(literal_type,type,
literal: $tType ).
thf(nibble_type,type,
nibble: $tType ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : $o ).
thf(sgn_if_decl,type,
sgn_if:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(sgn_sgn_decl,type,
sgn_sgn:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bool_size_decl,type,
bool_size: bool > nat ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(it_decl,type,
it: dB > $o ).
thf(nat1_decl,type,
nat1: int > nat ).
thf(ring_1_of_int_decl,type,
ring_1_of_int:
!>[TA: $tType] : ( int > TA ) ).
thf(lift_decl,type,
lift: dB > nat > dB ).
thf(nat_case_decl,type,
nat_case:
!>[TA: $tType] : ( TA > ( TA @ ( nat @ fun ) ) > nat > TA ) ).
thf(nat_size_decl,type,
nat_size: nat > nat ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(semiri532925092at_aux_decl,type,
semiri532925092at_aux:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) ) > nat > TA > TA ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(nat_tsub_decl,type,
nat_tsub: int > int > int ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(char_decl,type,
char: nibble > nibble > char1 ).
thf(char_case_decl,type,
char_case:
!>[TA: $tType] : ( ( TA @ ( nibble @ fun ) @ ( nibble @ fun ) ) > char1 > TA ) ).
thf(char_rec_decl,type,
char_rec:
!>[TA: $tType] : ( ( TA @ ( nibble @ fun ) @ ( nibble @ fun ) ) > char1 > TA ) ).
thf(char_size_decl,type,
char_size: char1 > nat ).
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(t_decl,type,
t: dB ).
thf(u_decl,type,
u: dB ).
thf(ua_decl,type,
ua: dB ).
thf(107,axiom,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_nat_Osize_I1_J) ).
thf(499,plain,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',fact_74_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
thf(515,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)],[111]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_zle__int) ).
thf(479,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(62,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(333,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int] :
( ( A @ ( TA @ ring_1_of_int ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_of__int__0__le__iff) ).
thf(468,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int] :
( ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ ring_1_of_int ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ ring_1_of_int ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(34,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(234,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',fact_47_conj__le__cong) ).
thf(555,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)],[122]) ).
thf(72,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(365,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1,conjecture,
nat @ zero_zero @ ( u @ lift ) @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( nat @ zero_zero @ ( u @ lift ) @ it ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(138,plain,
~ ( nat @ zero_zero @ ( u @ lift ) @ it ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_int__int__eq) ).
thf(170,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(128,axiom,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_bool_Osize_I3_J) ).
thf(582,plain,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_transfer__int__nat__relations_I1_J) ).
thf(276,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(110,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_nonneg__eq__int) ).
thf(511,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(43,axiom,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char ) @ ( C @ ( TA @ char_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_char_Osimps_I2_J) ).
thf(269,plain,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char ) @ ( C @ ( TA @ char_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(26,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(202,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(78,axiom,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ ( B @ lift ) @ it ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_lift__IT) ).
thf(384,plain,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ ( B @ lift ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(99,axiom,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_size__bool) ).
thf(472,plain,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',fact_82_le__funI) ).
thf(153,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)],[7]) ).
thf(18,axiom,
! [A: char1] :
~ ! [B: nibble,C: nibble] :
( A
!= ( C @ ( B @ char ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_char_Oexhaust) ).
thf(185,plain,
! [A: char1] :
~ ! [B: nibble,C: nibble] :
( A
!= ( C @ ( B @ char ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(47,axiom,
bool @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(288,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(58,axiom,
int @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).
thf(320,plain,
int @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(68,axiom,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_transfer__int__nat__numerals_I1_J) ).
thf(357,plain,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(22,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(196,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(19,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ nat1 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_nat__int) ).
thf(189,plain,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ nat1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(46,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_67_order__eq__refl) ).
thf(284,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)],[46]) ).
thf(48,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(289,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_le__antisym) ).
thf(448,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(56,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_69_linorder__linear) ).
thf(316,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)],[56]) ).
thf(39,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(261,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(100,axiom,
t @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
thf(475,plain,
t @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(59,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_60_le__funE) ).
thf(321,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)],[59]) ).
thf(38,axiom,
! [A: int,B: int,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ nat1 )
= ( A @ ( B @ ( C @ ( int @ if ) ) ) @ nat1 ) ) )
& ( ( C @ pp )
=> ( ( B @ nat1 )
= ( A @ ( B @ ( C @ ( int @ if ) ) ) @ nat1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_nat__if__cong) ).
thf(253,plain,
! [A: int,B: int,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ nat1 )
= ( A @ ( B @ ( C @ ( int @ if ) ) ) @ nat1 ) ) )
& ( ( C @ pp )
=> ( ( B @ nat1 )
= ( A @ ( B @ ( C @ ( int @ if ) ) ) @ nat1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(103,axiom,
nat @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(485,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(36,axiom,
! [A: nibble,B: nibble,C: nibble,D: nibble] :
( ( ( C @ ( D @ char ) )
= ( A @ ( B @ char ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_char_Oinject) ).
thf(238,plain,
! [A: nibble,B: nibble,C: nibble,D: nibble] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ char ) )
= ( A @ ( B @ char ) ) ) )
& ( ( ( C @ ( D @ char ) )
= ( A @ ( B @ char ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(124,axiom,
( ( int @ zero_zero @ nat1 )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_nat__0) ).
thf(574,plain,
( ( int @ zero_zero @ nat1 )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(134,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zero__le__imp__of__nat) ).
thf(602,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(31,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_61_order__trans) ).
thf(221,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)],[31]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_order__refl) ).
thf(293,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nat__le__linear) ).
thf(527,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(50,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(292,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(115,axiom,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_nat__size) ).
thf(529,plain,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(25,axiom,
int @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(201,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(76,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(381,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(117,axiom,
ua @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
thf(534,plain,
ua @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(33,axiom,
int @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).
thf(233,plain,
int @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(95,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_le__refl) ).
thf(452,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(30,axiom,
bool @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(220,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(73,axiom,
nat @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(366,plain,
nat @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ ring_1_of_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_of__nat__nat) ).
thf(334,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ ring_1_of_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(67,axiom,
! [A: bool @ ( nat @ fun )] :
( ! [B: nat] : ( B @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
<=> ! [B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ nat1 @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_all__nat) ).
thf(349,plain,
! [A: bool @ ( nat @ fun )] :
( ( ! [B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ nat1 @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ! [B: nat] : ( B @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
& ( ! [B: nat] : ( B @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ! [B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ nat1 @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_of__nat__le__iff) ).
thf(598,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(11,axiom,
bool @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(165,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_of__int__of__nat__eq) ).
thf(192,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(84,axiom,
! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_int__eq__0__conv) ).
thf(407,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(123,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_le__0__eq) ).
thf(566,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) ) )
& ( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(37,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(252,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(23,axiom,
int @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(197,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(70,axiom,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char ) @ ( char1 @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_char_Osize_I2_J) ).
thf(361,plain,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char ) @ ( char1 @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(65,axiom,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_size__literal__def) ).
thf(339,plain,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(119,axiom,
! [A: bool @ ( int @ fun )] :
( ! [B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) )
<=> ! [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_transfer__int__nat__quantifiers_I1_J) ).
thf(537,plain,
! [A: bool @ ( int @ fun )] :
( ( ! [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
=> ! [B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ) )
& ( ! [B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) )
=> ! [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( ( int @ zero_zero @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_of__int__0) ).
thf(476,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( ( int @ zero_zero @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(121,axiom,
! [A: bool @ ( int @ fun )] :
( ? [B: int] :
( ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
<=> ? [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_transfer__int__nat__quantifiers_I2_J) ).
thf(547,plain,
! [A: bool @ ( int @ fun )] :
( ( ? [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
=> ? [B: int] :
( ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) )
& ( ? [B: int] :
( ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
=> ? [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(35,axiom,
int @ ring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).
thf(237,plain,
int @ ring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(27,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_70_le__fun__def) ).
thf(205,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)],[27]) ).
thf(109,axiom,
! [TA: $tType,A: TA @ ( nat @ fun ),B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ nat_case ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_nat__case__0) ).
thf(508,plain,
! [TA: $tType,A: TA @ ( nat @ fun ),B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ nat_case ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(130,axiom,
! [A: int] :
( ( ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_int__nat__eq) ).
thf(586,plain,
! [A: int] :
( ( ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(87,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_nat__mono) ).
thf(430,plain,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(166,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,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_63_ord__le__eq__trans) ).
thf(264,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)],[41]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',fact_86_order__subst2) ).
thf(161,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)],[10]) ).
thf(5,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(149,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(129,axiom,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_bool_Osize_I2_J) ).
thf(584,plain,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int] :
( ( ( A @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( int @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_of__int__eq__0__iff) ).
thf(423,plain,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int] :
( ( ( A
= ( int @ zero_zero ) )
=> ( ( A @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) )
=> ( A
= ( int @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less_eq ) ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_of__int__le__0__iff) ).
thf(402,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less_eq ) ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(126,axiom,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_bool_Osize_I4_J) ).
thf(579,plain,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(92,axiom,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char ) @ char_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_char_Osize_I1_J) ).
thf(445,plain,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char ) @ char_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(77,axiom,
( ( nat @ zero_zero )
= ( int @ zero_zero @ nat1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_transfer__nat__int__numerals_I1_J) ).
thf(382,plain,
( ( nat @ zero_zero )
= ( int @ zero_zero @ nat1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_eq__imp__le) ).
thf(604,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(83,axiom,
nat @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(406,plain,
nat @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(94,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(451,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(318,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int] :
( ( ( TA @ zero_zero )
= ( A @ ( TA @ ring_1_of_int ) ) )
<=> ( A
= ( int @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_of__int__0__eq__iff) ).
thf(434,plain,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int] :
( ( ( A
= ( int @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( TA @ ring_1_of_int ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( TA @ ring_1_of_int ) ) )
=> ( A
= ( int @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(53,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_62_order__antisym) ).
thf(303,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)],[53]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_sgn__0__0) ).
thf(387,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(105,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(494,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_transfer__int__nat__relations_I3_J) ).
thf(367,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_of__nat__0__le__iff) ).
thf(535,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_sgn__sgn) ).
thf(323,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(131,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__trans) ).
thf(594,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_of__nat__eq__iff) ).
thf(213,plain,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(113,axiom,
! [A: bool @ ( nat @ fun )] :
( ? [B: nat] : ( B @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
<=> ? [B: int] :
( ( B @ nat1 @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_ex__nat) ).
thf(520,plain,
! [A: bool @ ( nat @ fun )] :
( ( ? [B: int] :
( ( B @ nat1 @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
=> ? [B: nat] : ( B @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
& ( ? [B: nat] : ( B @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ? [B: int] :
( ( B @ nat1 @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(8,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ring_1_of_int ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_of__int__int__eq) ).
thf(155,plain,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ring_1_of_int ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(198,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(32,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_68_order__eq__iff) ).
thf(223,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)],[32]) ).
thf(136,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_nonneg__int__cases) ).
thf(608,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(81,axiom,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( C @ pp )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_int__if__cong) ).
thf(394,plain,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( C @ pp )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',fact_85_ord__eq__le__subst) ).
thf(306,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)],[54]) ).
thf(28,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_64_ord__eq__le__trans) ).
thf(209,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)],[28]) ).
thf(66,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( B @ nat1 )
= ( A @ nat1 ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_eq__nat__nat__iff) ).
thf(342,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( B = A )
=> ( ( B @ nat1 )
= ( A @ nat1 ) ) )
& ( ( ( B @ nat1 )
= ( A @ nat1 ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) )
= A )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_ord__le__eq__subst) ).
thf(295,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ord )
& ( TA @ ord ) )
=> ! [A: TA,B: TA @ ( TB @ fun ),C: TB,D: TB] :
( ( C @ ( D @ ( TB @ ord_less_eq ) ) )
=> ( ( ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) )
= A )
=> ( ! [E: TB,F: TB] :
( ( F @ ( E @ ( TB @ ord_less_eq ) ) )
=> ( F @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( E @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(6,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(150,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
int @ sgn_if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Osgn__if) ).
thf(263,plain,
int @ sgn_if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(16,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(182,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(90,axiom,
u @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT) ).
thf(441,plain,
u @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(125,axiom,
! [A: char1] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_char__size) ).
thf(576,plain,
! [A: char1] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(69,axiom,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_nat_Osize_I3_J) ).
thf(359,plain,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_of__nat__0) ).
thf(544,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(79,axiom,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(386,plain,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(314,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(137,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_zero__zle__int) ).
thf(612,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(97,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ? [B: nat] :
( A
= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_zero__le__imp__eq__int) ).
thf(465,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ? [B: nat] :
( A
= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(127,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(581,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_sgn0) ).
thf(517,plain,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(9,axiom,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char ) @ ( C @ ( TA @ char_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_char_Orecs) ).
thf(158,plain,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char ) @ ( C @ ( TA @ char_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,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_65_order__antisym__conv) ).
thf(139,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)],[3]) ).
thf(49,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(290,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int,B: int] :
( ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_of__int__le__iff) ).
thf(272,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(88,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_le0) ).
thf(432,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(13,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_66_le__funD) ).
thf(168,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)],[13]) ).
thf(4,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(146,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,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_59_linorder__le__cases) ).
thf(183,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)],[17]) ).
thf(75,axiom,
! [A: int] :
( ( ( A @ nat1 )
= ( nat @ zero_zero ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_nat__0__iff) ).
thf(373,plain,
! [A: int] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ nat1 )
= ( nat @ zero_zero ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_of__int__eq__iff) ).
thf(326,plain,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) ) ) )
& ( ( ( B @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(42,axiom,
bool @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(268,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(21,axiom,
int @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
thf(195,plain,
int @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(116,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_int__0) ).
thf(532,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_zero__reorient) ).
thf(415,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)],[85]) ).
thf(132,axiom,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_bool_Osize_I1_J) ).
thf(596,plain,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',fact_84_order__subst1) ).
thf(178,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)],[15]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: TA @ ( TA @ fun )] :
( ( A @ ( nat @ zero_zero @ ( B @ ( TA @ semiri532925092at_aux ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_of__nat__aux_Osimps_I1_J) ).
thf(442,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: TA @ ( TA @ fun )] :
( ( A @ ( nat @ zero_zero @ ( B @ ( TA @ semiri532925092at_aux ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(108,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( B @ nat1 )
= ( A @ nat1 ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_transfer__nat__int__relations_I1_J) ).
thf(501,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( B = A )
=> ( ( B @ nat1 )
= ( A @ nat1 ) ) )
& ( ( ( B @ nat1 )
= ( A @ nat1 ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(104,axiom,
! [A: nat] :
( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_int__le__0__conv) ).
thf(486,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(64,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_less__eq__nat_Osimps_I1_J) ).
thf(337,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(71,axiom,
nat @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(364,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(106,axiom,
! [A: char1] :
( ( A @ ( char1 @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_size__char) ).
thf(496,plain,
! [A: char1] :
( ( A @ ( char1 @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',fact_48_imp__le__cong) ).
thf(454,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)],[96]) ).
thf(884,plain,
$false,
inference(e,[status(thm)],[499,515,479,333,468,234,555,365,138,170,582,276,511,269,202,384,472,153,185,288,320,357,196,189,284,289,448,316,261,475,321,253,485,238,574,602,221,293,527,292,529,201,381,534,233,452,220,366,334,349,598,165,192,407,566,252,197,361,339,537,476,547,237,205,508,586,430,166,264,161,149,584,423,402,579,445,382,604,406,451,318,434,303,387,494,367,535,323,594,213,520,155,198,223,608,394,306,209,342,295,150,263,182,441,576,359,544,386,314,612,465,581,517,158,139,290,272,432,168,146,183,373,326,268,195,532,415,596,178,442,501,486,337,364,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL792_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.12 % 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
% 0.26/5.52 % Computer : n014.cluster.edu
% 0.26/5.52 % Model : x86_64 x86_64
% 0.26/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/5.52 % Memory : 8046.5625MB
% 0.26/5.52 % OS : Linux 6.8.0-71-generic
% 0.26/5.52 % CPULimit : 300
% 0.26/5.52 % WCLimit : 300
% 0.26/5.52 % DateTime : Fri Sep 25 23:34:38 UTC 2026
% 0.26/5.52 % CPUTime :
% 0.26/5.52 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
% 1.41/6.32 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.38/6.78 % [INFO] Parsing done (449ms).
% 2.87/6.80 % [INFO] Running in sequential loop mode.
% 4.01/7.39 % [INFO] eprover registered as external prover.
% 4.27/7.41 % [INFO] Scanning for conjecture ...
% 4.64/7.61 % [INFO] Found a conjecture (or negated_conjecture) and 135 axioms. Running axiom selection ...
% 4.82/7.78 % [INFO] Axiom selection finished. Selected 135 axioms (removed 0 axioms).
% 5.74/8.08 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.74/8.10 % [INFO] Type checking passed.
% 5.74/8.11 % [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 ...
% 6.71/8.48 % [INFO] [Domain constraints] Detected constraint on bool
% 6.71/8.48 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 7.29/8.78 % [INFO] [Domain constraints] Detected constraint on bool
% 7.29/8.78 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 7.54/8.87 % [INFO] [Domain constraints] Detected constraint on bool
% 7.54/8.87 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 26.94/13.81 % External prover 'e' found a proof!
% 26.94/13.81 % [INFO] Killing All external provers ...
% 26.94/13.81 % Time passed: 8099ms (effective reasoning time: 7007ms)
% 26.94/13.81 % 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)>
% 26.94/13.82 % Axioms used in derivation (135): fact_68_order__eq__iff, fact_20_transfer__int__nat__numerals_I1_J, fact_1_Var_I3_J, fact_13_nat_Osize_I3_J, fact_79_of__int__le__iff, fact_49_le0, arity_HOL_Obool___Orderings_Oorder, fact_66_le__funD, fact_12_size__literal__def, fact_32_char_Oexhaust, fact_34_char_Osimps_I2_J, fact_59_linorder__le__cases, arity_HOL_Obool___Orderings_Oord, arity_Int_Oint___Rings_Olinordered__idom, arity_HOL_Obool___Orderings_Opreorder, fact_51_le__0__eq, arity_Nat_Onat___Rings_Osemiring__1, arity_Int_Oint___Orderings_Oorder, arity_Int_Oint___Int_Oring__char__0, fact_86_order__subst2, arity_fun___Orderings_Oord, arity_Int_Oint___Orderings_Oord, fact_9_size__char, fact_85_ord__eq__le__subst, arity_Nat_Onat___Orderings_Opreorder, arity_Int_Oint___Orderings_Opreorder, fact_43_zero__zle__int, fact_91_transfer__nat__int__numerals_I1_J, fact_31_sgn__0__0, fact_8_nat_Osize_I1_J, fact_81_of__int__int__eq, help_fTrue_1_1_T, fact_35_int__le__0__conv, fact_69_linorder__linear, fact_61_order__trans, fact_2_uIT, fact_19_char_Osize_I1_J, fact_47_conj__le__cong, fact_76_of__int__eq__0__iff, fact_50_less__eq__nat_Osimps_I1_J, fact_29_int__if__cong, fact_72_of__int__0__le__iff, help_fTrue_1_1_U, fact_45_zero__le__imp__eq__int, fact_42_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, arity_Int_Oint___Rings_Osemiring__1, arity_HOL_Obool___Orderings_Olinorder, fact_7_char__size, fact_26_char_Oinject, fact_0__096IT_At_096, fact_87_of__nat__nat, fact_14_of__nat__0, fact_33_char_Orecs, fact_71_of__int__le__0__iff, fact_27_int__int__eq, help_fFalse_1_1_T, help_If_1_1_T, fact_41_transfer__int__nat__quantifiers_I2_J, arity_Int_Oint___Rings_Oring__1, arity_fun___Orderings_Oorder, fact_18_char_Osize_I2_J, arity_Nat_Onat___Orderings_Olinorder, arity_fun___Orderings_Opreorder, fact_55_nat__le__linear, fact_75_of__int__eq__iff, fact_30_sgn__sgn, fact_21_int__0, fact_5_bool_Osize_I1_J, fact_39_of__nat__0__le__iff, fact_36_of__nat__le__iff, fact_80_of__int__of__nat__eq, fact_97_nat__if__cong, arity_Nat_Onat___Rings_Olinordered__semidom, fact_92_ex__nat, arity_Int_Oint___Orderings_Olinorder, fact_57_transfer__int__nat__relations_I3_J, fact_84_order__subst1, fact_23_of__nat__aux_Osimps_I1_J, fact_95_eq__nat__nat__iff, fact_46_order__refl, arity_Nat_Onat___Groups_Ozero, fact_56_le__refl, arity_Nat_Onat___Orderings_Oord, help_If_3_1_T, fact_40_transfer__int__nat__quantifiers_I1_J, fact_70_le__fun__def, fact_93_all__nat, fact_28_transfer__int__nat__relations_I1_J, help_If_2_1_T, fact_65_order__antisym__conv, fact_10_bool_Osize_I3_J, fact_78_of__int__0, fact_73_nonneg__int__cases, fact_3_lift__IT, fact_22_int__eq__0__conv, arity_Nat_Onat___Nat_Osemiring__char__0, fact_37_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_16_nat__size, fact_6_bool_Osize_I2_J, fact_83_ord__le__eq__subst, fact_53_le__trans, fact_90_int__nat__eq, fact_96_nat__mono, help_fFalse_1_1_U, fact_44_nonneg__eq__int, fact_89_nat__0__iff, arity_Nat_Onat___Orderings_Oorder, fact_25_sgn0, arity_Int_Oint___Groups_Osgn__if, fact_88_nat__0, fact_60_le__funE, fact_77_of__int__0__eq__iff, fact_38_zero__le__imp__of__nat, help_pp_1_1_U, fact_98_nat__int, fact_82_le__funI, fact_63_ord__le__eq__trans, fact_94_transfer__nat__int__relations_I1_J, fact_11_bool_Osize_I4_J, fact_58_zle__int, fact_15_of__nat__eq__iff, arity_Int_Oint___Groups_Ozero, arity_Int_Oint___Nat_Osemiring__char__0, fact_52_le__antisym, help_pp_2_1_U, arity_Int_Oint___Rings_Olinordered__semidom, fact_62_order__antisym, fact_67_order__eq__refl, fact_64_ord__eq__le__trans, fact_24_nat__case__0, fact_48_imp__le__cong, fact_54_eq__imp__le, fact_4_zero__reorient, fact_17_size__bool, fact_74_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J
% 26.94/13.82 % No. of inferences in proof: 274
% 26.94/13.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8099 ms resp. 7007 ms w/o parsing
% 27.42/13.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.42/13.94 % [INFO] Killing All external provers ...
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