%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV573_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 : n012.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 08:59:55 AM UTC 2026
% Result : Theorem 5.31s 2.22s
% Output : Refutation 5.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 145
% Syntax : Number of formulae : 292 ( 152 unt; 0 typ; 0 def)
% Number of atoms : 620 ( 208 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 2102 ( 56 ~; 17 |; 55 &;1739 @)
% ( 32 <=>; 203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 6 con; 0-4 aty)
% Number of variables : 405 ( 0 ^; 399 !; 6 ?; 405 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex1_type,type,
complex1: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
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(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_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(real_algebra_1_decl,type,
real_algebra_1:
!>[TA: $tType] : $o ).
thf(real_normed_vector_decl,type,
real_normed_vector:
!>[TA: $tType] : $o ).
thf(real_n2089651433ebra_1_decl,type,
real_n2089651433ebra_1:
!>[TA: $tType] : $o ).
thf(im_decl,type,
im: complex1 > real ).
thf(re_decl,type,
re: complex1 > real ).
thf(complex_decl,type,
complex: real > real > complex1 ).
thf(complex_case_decl,type,
complex_case:
!>[TA: $tType] : ( ( TA @ ( real @ fun ) @ ( real @ fun ) ) > complex1 > TA ) ).
thf(complex_rec_decl,type,
complex_rec:
!>[TA: $tType] : ( ( TA @ ( real @ fun ) @ ( real @ fun ) ) > complex1 > TA ) ).
thf(complex_size_decl,type,
complex_size: complex1 > nat ).
thf(ii_decl,type,
ii: complex1 ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
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(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(norm_norm_decl,type,
norm_norm:
!>[TA: $tType] : ( TA > real ) ).
thf(of_real_decl,type,
of_real:
!>[TA: $tType] : ( real > TA ) ).
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(n_decl,type,
n: nat ).
thf(38,axiom,
nat @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(257,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(45,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_97_order__eq__iff) ).
thf(270,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)],[45]) ).
thf(121,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: nat] :
( ( A @ ( real @ semiring_1_of_nat ) @ ( TA @ of_real ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_of__real__of__nat__eq) ).
thf(541,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: nat] :
( ( A @ ( real @ semiring_1_of_nat ) @ ( TA @ of_real ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(143,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_less__zeroE) ).
thf(629,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(69,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_less__nat__zero__code) ).
thf(365,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(61,axiom,
! [A: real] :
( ( A @ ( complex1 @ of_real ) )
= ( real @ zero_zero @ ( A @ complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_complex__of__real__def) ).
thf(333,plain,
! [A: real] :
( ( A @ ( complex1 @ of_real ) )
= ( real @ zero_zero @ ( A @ complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(34,axiom,
int @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).
thf(249,plain,
int @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(26,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(217,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ( ( real @ zero_zero @ ( TA @ of_real ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_of__real__0) ).
thf(511,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ( ( real @ zero_zero @ ( TA @ of_real ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(44,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(269,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(73,axiom,
( ( complex1 @ zero_zero @ re )
= ( real @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_complex__Re__zero) ).
thf(384,plain,
( ( complex1 @ zero_zero @ re )
= ( real @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_73_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
thf(533,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)],[119]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_norm__zero) ).
thf(472,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(5,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_less__irrefl__nat) ).
thf(153,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(76,axiom,
! [A: nat] :
( ( A @ ( complex1 @ semiring_1_of_nat ) @ re )
= ( A @ ( real @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_complex__Re__of__nat) ).
thf(389,plain,
! [A: nat] :
( ( A @ ( complex1 @ semiring_1_of_nat ) @ re )
= ( A @ ( real @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(97,axiom,
complex1 @ real_normed_vector,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__vector) ).
thf(460,plain,
complex1 @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real,B: real] :
( ( ( B @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_of__real__eq__iff) ).
thf(284,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real,B: real] :
( ( ( B = A )
=> ( ( B @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) ) ) )
& ( ( ( B @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(4,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(152,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,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_55_order__le__less__trans) ).
thf(316,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)],[56]) ).
thf(103,axiom,
real @ real_algebra_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__algebra__1) ).
thf(475,plain,
real @ real_algebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(59,axiom,
! [A: real,B: real] :
( ( ( A @ ( B @ complex ) )
= ( complex1 @ zero_zero ) )
<=> ( ( A
= ( real @ zero_zero ) )
& ( B
= ( real @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Complex__eq__0) ).
thf(321,plain,
! [A: real,B: real] :
( ( ( ( A
= ( real @ zero_zero ) )
& ( B
= ( real @ zero_zero ) ) )
=> ( ( A @ ( B @ complex ) )
= ( complex1 @ zero_zero ) ) )
& ( ( ( A @ ( B @ complex ) )
= ( complex1 @ zero_zero ) )
=> ( ( A
= ( real @ zero_zero ) )
& ( B
= ( real @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
<=> ( A
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_zero__less__norm__iff) ).
thf(514,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) ) )
& ( ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ( A
!= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(108,axiom,
! [A: real,B: real] :
( ( A @ ( B @ complex ) @ re )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Re) ).
thf(492,plain,
! [A: real,B: real] :
( ( A @ ( B @ complex ) @ re )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(12,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(164,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
( ( n @ ( complex1 @ semiring_1_of_nat ) )
= ( real @ zero_zero @ ( n @ ( real @ semiring_1_of_nat ) @ complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( n @ ( complex1 @ semiring_1_of_nat ) )
!= ( real @ zero_zero @ ( n @ ( real @ semiring_1_of_nat ) @ complex ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(147,plain,
( ( n @ ( complex1 @ semiring_1_of_nat ) )
!= ( real @ zero_zero @ ( n @ ( real @ semiring_1_of_nat ) @ complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(79,axiom,
! [A: real,B: real] :
( ( A @ ( B @ ( real @ ord_less_eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( real @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_less__eq__real__def) ).
thf(397,plain,
! [A: real,B: real] :
( ( ( ( B = A )
| ( A @ ( B @ ( real @ ord_less ) ) ) )
=> ( A @ ( B @ ( real @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( real @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( real @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_le__neq__implies__less) ).
thf(280,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(145,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zero__less__int__conv) ).
thf(634,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_nat__neq__iff) ).
thf(221,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',fact_2_of__nat__eq__iff) ).
thf(453,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)],[96]) ).
thf(89,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_less__eq__nat_Osimps_I1_J) ).
thf(428,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(42,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_57_order__le__neq__trans) ).
thf(265,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)],[42]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_less__imp__of__nat__less) ).
thf(507,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(40,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(260,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(8,axiom,
bool @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(160,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(77,axiom,
! [A: real,B: real] :
( ( A @ ( B @ complex ) @ ( complex1 @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_complex_Osize_I2_J) ).
thf(392,plain,
! [A: real,B: real] :
( ( A @ ( B @ complex ) @ ( complex1 @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_zless__int) ).
thf(407,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(13,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_eq__imp__le) ).
thf(165,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(36,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_98_order__eq__refl) ).
thf(252,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)],[36]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_order__refl) ).
thf(197,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(461,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)],[98]) ).
thf(126,axiom,
complex1 @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Nat_Osemiring__char__0) ).
thf(551,plain,
complex1 @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',fact_81_le__trans) ).
thf(156,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)],[6]) ).
thf(66,axiom,
! [A: real,B: real] :
( ( A @ ( B @ complex ) @ complex_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_complex_Osize_I1_J) ).
thf(356,plain,
! [A: real,B: real] :
( ( A @ ( B @ complex ) @ complex_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(169,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(137,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_not__less0) ).
thf(593,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_zero__le__imp__of__nat) ).
thf(420,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)],[85]) ).
thf(104,axiom,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_transfer__int__nat__numerals_I1_J) ).
thf(476,plain,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(136,axiom,
! [A: nat] :
( ( A @ ( complex1 @ semiring_1_of_nat ) @ im )
= ( real @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_complex__Im__of__nat) ).
thf(590,plain,
! [A: nat] :
( ( A @ ( complex1 @ semiring_1_of_nat ) @ im )
= ( real @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(124,axiom,
real @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
thf(547,plain,
real @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(101,axiom,
complex1 @ real_n2089651433ebra_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1) ).
thf(471,plain,
complex1 @ real_n2089651433ebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(37,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(256,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_of__nat__0) ).
thf(371,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)],[71]) ).
thf(140,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real] :
( ( ( A @ ( TA @ of_real ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( real @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_of__real__eq__0__iff) ).
thf(605,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real] :
( ( ( A
= ( real @ zero_zero ) )
=> ( ( A @ ( TA @ of_real ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ of_real ) )
= ( TA @ zero_zero ) )
=> ( A
= ( real @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(52,axiom,
int @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).
thf(298,plain,
int @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_norm__le__zero__iff) ).
thf(430,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) ) )
& ( ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(9,axiom,
nat @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(161,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_less__imp__le__nat) ).
thf(296,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(149,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(49,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(291,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(24,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_nat__less__cases) ).
thf(204,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_norm__not__less__zero) ).
thf(545,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(81,axiom,
! [A: complex1] : ( A @ ( complex1 @ norm_norm ) @ ( A @ re @ ( real @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_complex__Re__le__cmod) ).
thf(413,plain,
! [A: complex1] : ( A @ ( complex1 @ norm_norm ) @ ( A @ re @ ( real @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] : ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_norm__ge__zero) ).
thf(445,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] : ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',fact_92_transfer__int__nat__quantifiers_I2_J) ).
thf(572,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)],[133]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_less__or__eq__imp__le) ).
thf(236,plain,
! [A: nat,B: nat] :
( ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_nat__less__le) ).
thf(187,plain,
! [A: nat,B: nat] :
( ( ( ( B != A )
& ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__eq__less__or__eq) ).
thf(172,plain,
! [A: nat,B: nat] :
( ( ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(84,axiom,
real @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(419,plain,
real @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(68,axiom,
! [A: real] :
( ( A @ ( complex1 @ of_real ) @ re )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Re__complex__of__real) ).
thf(362,plain,
! [A: real] :
( ( A @ ( complex1 @ of_real ) @ re )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(33,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_95_le__fun__def) ).
thf(245,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)],[33]) ).
thf(57,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(318,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(113,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_int__0) ).
thf(509,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(139,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(599,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(75,axiom,
( ( ii @ re )
= ( real @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_complex__Re__i) ).
thf(387,plain,
( ( ii @ re )
= ( real @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_of__nat__0__less__iff) ).
thf(552,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(142,axiom,
! [A: real] :
( ( A @ ( complex1 @ of_real ) @ im )
= ( real @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Im__complex__of__real) ).
thf(626,plain,
! [A: real] :
( ( A @ ( complex1 @ of_real ) @ im )
= ( real @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_norm__eq__zero) ).
thf(521,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) )
& ( ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(53,axiom,
bool @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(299,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(111,axiom,
( ( complex1 @ zero_zero )
= ( real @ zero_zero @ ( real @ zero_zero @ complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_complex__zero__def) ).
thf(505,plain,
( ( complex1 @ zero_zero )
= ( real @ zero_zero @ ( real @ zero_zero @ complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(87,axiom,
real @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oord) ).
thf(426,plain,
real @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(10,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(162,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(125,axiom,
! [A: nat] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_int__less__0__conv) ).
thf(548,plain,
! [A: nat] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(72,axiom,
! [A: real,B: real,C: real] :
( ( ( B @ ( C @ complex ) )
= ( A @ ( complex1 @ of_real ) ) )
<=> ( ( B
= ( real @ zero_zero ) )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_complex__eq__cancel__iff2) ).
thf(374,plain,
! [A: real,B: real,C: real] :
( ( ( ( B
= ( real @ zero_zero ) )
& ( C = A ) )
=> ( ( B @ ( C @ complex ) )
= ( A @ ( complex1 @ of_real ) ) ) )
& ( ( ( B @ ( C @ complex ) )
= ( A @ ( complex1 @ of_real ) ) )
=> ( ( B
= ( real @ zero_zero ) )
& ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(129,axiom,
! [A: real,B: real] :
( ( A @ ( B @ complex ) @ im )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Im) ).
thf(557,plain,
! [A: real,B: real] :
( ( A @ ( B @ complex ) @ im )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(134,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_zero__reorient) ).
thf(580,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)],[134]) ).
thf(146,axiom,
! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_int__eq__0__conv) ).
thf(640,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)],[146]) ).
thf(21,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(199,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_less__not__refl2) ).
thf(182,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(60,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_le0) ).
thf(331,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(92,axiom,
real @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(441,plain,
real @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(110,axiom,
! [TA: $tType,A: real,B: real,C: TA @ ( real @ fun ) @ ( real @ fun )] :
( ( A @ ( B @ complex ) @ ( C @ ( TA @ complex_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( TA @ ( real @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_complex_Orecs) ).
thf(502,plain,
! [TA: $tType,A: real,B: real,C: TA @ ( real @ fun ) @ ( real @ fun )] :
( ( A @ ( B @ complex ) @ ( C @ ( TA @ complex_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( TA @ ( real @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_int__int__eq) ).
thf(338,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)],[63]) ).
thf(100,axiom,
real @ real_normed_vector,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__vector) ).
thf(470,plain,
real @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(67,axiom,
( ii
!= ( complex1 @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_complex__i__not__zero) ).
thf(359,plain,
( ii
!= ( complex1 @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(122,axiom,
real @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Nat_Osemiring__char__0) ).
thf(544,plain,
real @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_of__nat__less__0__iff) ).
thf(336,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(74,axiom,
complex1 @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__1) ).
thf(386,plain,
complex1 @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(132,axiom,
real @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Opreorder) ).
thf(571,plain,
real @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(141,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( C @ ( D @ complex ) )
= ( A @ ( B @ complex ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_complex_Oinject) ).
thf(612,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ complex ) )
= ( A @ ( B @ complex ) ) ) )
& ( ( ( C @ ( D @ complex ) )
= ( A @ ( B @ complex ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(35,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_96_linorder__linear) ).
thf(250,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)],[35]) ).
thf(128,axiom,
complex1 @ real_algebra_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__algebra__1) ).
thf(556,plain,
complex1 @ real_algebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(120,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(539,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(23,axiom,
int @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(203,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_91_transfer__int__nat__quantifiers_I1_J) ).
thf(495,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)],[109]) ).
thf(27,axiom,
! [A: complex1,B: complex1] :
( ( ( B @ re )
= ( A @ re ) )
=> ( ( ( B @ im )
= ( A @ im ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_complex__eqI) ).
thf(218,plain,
! [A: complex1,B: complex1] :
( ( ( B @ re )
= ( A @ re ) )
=> ( ( ( B @ im )
= ( A @ im ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(70,axiom,
! [TA: $tType,A: real,B: real,C: TA @ ( real @ fun ) @ ( real @ fun )] :
( ( A @ ( B @ complex ) @ ( C @ ( TA @ complex_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( TA @ ( real @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_complex_Osimps_I2_J) ).
thf(368,plain,
! [TA: $tType,A: real,B: real,C: TA @ ( real @ fun ) @ ( real @ fun )] :
( ( A @ ( B @ complex ) @ ( C @ ( TA @ complex_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( TA @ ( real @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(135,axiom,
( ( complex1 @ zero_zero @ im )
= ( real @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_complex__Im__zero) ).
thf(588,plain,
( ( complex1 @ zero_zero @ im )
= ( real @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(319,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(55,axiom,
! [A: complex1,B: complex1] :
( ( B = A )
<=> ( ( ( B @ im )
= ( A @ im ) )
& ( ( B @ re )
= ( A @ re ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_complex__eq__iff) ).
thf(304,plain,
! [A: complex1,B: complex1] :
( ( ( ( ( B @ im )
= ( A @ im ) )
& ( ( B @ re )
= ( A @ re ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( ( B @ im )
= ( A @ im ) )
& ( ( B @ re )
= ( A @ re ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(39,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_le__refl) ).
thf(258,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(7,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_56_order__less__le__trans) ).
thf(158,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)],[7]) ).
thf(18,axiom,
int @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
thf(186,plain,
int @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(144,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 ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_of__nat__less__imp__less) ).
thf(632,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(15,axiom,
nat @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(171,plain,
nat @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(83,axiom,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(418,plain,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(131,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_gr0I) ).
thf(568,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(30,axiom,
bool @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(235,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_44_int__if__cong) ).
thf(478,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)],[105]) ).
thf(64,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_le__0__eq) ).
thf(346,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)],[64]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_less__not__refl3) ).
thf(300,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_72_zle__int) ).
thf(447,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)],[95]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_le__antisym) ).
thf(262,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)],[41]) ).
thf(86,axiom,
! [A: complex1] :
~ ! [B: real,C: real] :
( A
!= ( C @ ( B @ complex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_complex_Oexhaust) ).
thf(422,plain,
! [A: complex1] :
~ ! [B: real,C: real] :
( A
!= ( C @ ( B @ complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(32,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_linorder__neqE__nat) ).
thf(242,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_nat__le__linear) ).
thf(294,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)],[50]) ).
thf(43,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(268,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(91,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 ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_of__nat__less__iff) ).
thf(437,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(118,axiom,
real @ real_n2089651433ebra_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1) ).
thf(532,plain,
real @ real_n2089651433ebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(47,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(283,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(82,axiom,
! [A: complex1] :
( ( A @ im @ ( A @ re @ complex ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_complex__surj) ).
thf(415,plain,
! [A: complex1] :
( ( A @ im @ ( A @ re @ complex ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(78,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zero__zle__int) ).
thf(395,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(88,axiom,
complex1 @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(427,plain,
complex1 @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(138,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: TA @ ( TA @ fun )] :
( ( A @ ( nat @ zero_zero @ ( B @ ( TA @ semiri532925092at_aux ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_of__nat__aux_Osimps_I1_J) ).
thf(596,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)],[138]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',fact_38_of__nat__le__iff) ).
thf(528,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)],[117]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ real_n2089651433ebra_1 )
=> ! [A: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ norm_norm ) )
= ( A @ ( real @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_norm__of__nat) ).
thf(442,plain,
! [TA: $tType] :
( ( TA @ real_n2089651433ebra_1 )
=> ! [A: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ norm_norm ) )
= ( A @ ( real @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(11,axiom,
nat @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(163,plain,
nat @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(200,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_gr__implies__not0) ).
thf(486,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(99,axiom,
real @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oorder) ).
thf(469,plain,
real @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_of__nat__0__le__iff) ).
thf(354,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)],[65]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(215,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(130,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_neq0__conv) ).
thf(560,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(107,axiom,
real @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(491,plain,
real @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(29,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__not__refl) ).
thf(232,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(650,plain,
$false,
inference(e,[status(thm)],[257,270,541,629,365,333,249,217,511,269,384,533,472,153,389,460,284,152,316,475,321,514,492,164,147,397,280,634,221,453,428,265,507,260,160,392,407,165,252,197,461,551,156,356,169,593,420,476,590,547,471,256,371,605,298,430,161,296,149,291,204,545,413,445,572,236,187,172,419,362,245,318,509,599,387,552,626,521,299,505,426,162,548,374,557,580,640,199,182,331,441,502,338,470,359,544,336,386,571,612,250,556,539,203,495,218,368,588,319,304,258,158,186,632,171,418,568,235,478,346,300,447,262,422,242,294,268,437,532,283,415,395,427,596,528,442,163,200,486,469,354,215,560,491,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV573_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % 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
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Sat Sep 26 14:31:35 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.33 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
% 0.38/0.61 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.64/0.76 % [INFO] Parsing done (150ms).
% 0.64/0.77 % [INFO] Running in sequential loop mode.
% 1.22/0.97 % [INFO] eprover registered as external prover.
% 1.22/0.97 % [INFO] Scanning for conjecture ...
% 1.45/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 144 axioms. Running axiom selection ...
% 1.45/1.11 % [INFO] Axiom selection finished. Selected 144 axioms (removed 0 axioms).
% 1.93/1.20 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.93/1.22 % [INFO] Type checking passed.
% 1.93/1.22 % [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 ...
% 2.23/1.34 % [INFO] [Domain constraints] Detected constraint on bool
% 2.23/1.35 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 5.31/2.22 % External prover 'e' found a proof!
% 5.31/2.22 % [INFO] Killing All external provers ...
% 5.31/2.22 % Time passed: 1821ms (effective reasoning time: 1450ms)
% 5.31/2.22 % 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)>
% 5.31/2.22 % Axioms used in derivation (144): fact_58_neq0__conv, fact_55_order__le__less__trans, arity_HOL_Obool___Orderings_Oorder, fact_77_less__not__refl3, fact_69_le__eq__less__or__eq, arity_HOL_Obool___Orderings_Oord, fact_62_less__eq__nat_Osimps_I1_J, arity_HOL_Obool___Orderings_Opreorder, fact_82_le__antisym, arity_Nat_Onat___Rings_Osemiring__1, arity_Complex_Ocomplex___Nat_Osemiring__char__0, arity_Int_Oint___Orderings_Oorder, fact_38_of__nat__le__iff, fact_17_Im, fact_93_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, fact_10_complex_Oexhaust, fact_18_norm__eq__zero, arity_Int_Oint___Orderings_Oord, fact_37_of__nat__aux_Osimps_I1_J, fact_52_norm__ge__zero, arity_fun___Orderings_Oord, fact_26_Re, arity_RealDef_Oreal___Groups_Ozero, fact_32_norm__le__zero__iff, arity_Nat_Onat___Orderings_Opreorder, fact_4_complex__Re__of__nat, arity_Int_Oint___Orderings_Opreorder, fact_21_of__real__0, fact_97_order__eq__iff, fact_8_of__real__of__nat__eq, fact_2_of__nat__eq__iff, fact_84_nat__less__cases, fact_51_norm__not__less__zero, fact_65_le__refl, fact_1_complex_Oinject, fact_92_transfer__int__nat__quantifiers_I2_J, fact_87_gr0I, fact_30_complex_Osize_I2_J, fact_11_of__real__eq__iff, fact_61_le0, arity_Int_Oint___Rings_Osemiring__1, fact_31_complex__Re__i, arity_HOL_Obool___Orderings_Olinorder, arity_RealDef_Oreal___RealVector_Oreal__algebra__1, fact_76_less__not__refl2, fact_27_complex__of__real__def, arity_RealDef_Oreal___Orderings_Oord, fact_91_transfer__int__nat__quantifiers_I1_J, fact_9_norm__of__nat, fact_56_order__less__le__trans, fact_13_complex__Im__zero, fact_23_complex__eq__iff, help_If_1_1_T, fact_89_zero__less__int__conv, fact_40_of__nat__0__less__iff, fact_50_of__nat__0__le__iff, arity_fun___Orderings_Oorder, arity_Nat_Onat___Orderings_Olinorder, fact_66_nat__neq__iff, fact_45_less__imp__of__nat__less, fact_24_complex__surj, fact_53_order__refl, arity_RealDef_Oreal___Rings_Osemiring__1, arity_fun___Orderings_Opreorder, fact_47_complex__Re__le__cmod, fact_90_int__less__0__conv, arity_Complex_Ocomplex___RealVector_Oreal__algebra__1, fact_46_of__nat__less__imp__less, fact_36_int__eq__0__conv, fact_73_Nat__Transfer_Otransfer__int__nat__relations_I3_J, fact_49_zero__le__imp__of__nat, fact_74_linorder__neqE__nat, fact_39_of__nat__less__iff, fact_15_complex__eq__cancel__iff2, fact_95_le__fun__def, fact_35_int__0, fact_7_complex__Im__of__nat, fact_68_nat__less__le, arity_Int_Oint___Orderings_Olinorder, fact_25_complex__eqI, arity_Nat_Onat___Rings_Olinordered__semidom, arity_RealDef_Oreal___Rings_Olinordered__semidom, fact_80_le__neq__implies__less, fact_78_eq__imp__le, fact_54_less__eq__real__def, fact_43_Nat__Transfer_Otransfer__int__nat__relations_I1_J, arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1, arity_Nat_Onat___Groups_Ozero, fact_44_int__if__cong, fact_81_le__trans, arity_Nat_Onat___Orderings_Oord, help_If_3_1_T, fact_3_zero__reorient, fact_19_norm__zero, fact_83_less__or__eq__imp__le, help_If_2_1_T, fact_14_Im__complex__of__real, arity_RealDef_Oreal___Orderings_Oorder, arity_RealDef_Oreal___Orderings_Olinorder, fact_48_of__nat__less__0__iff, fact_29_complex_Osize_I1_J, fact_16_Complex__eq__0, arity_RealDef_Oreal___RealVector_Oreal__normed__vector, fact_72_zle__int, fact_0_of__nat__0, arity_Complex_Ocomplex___Rings_Osemiring__1, fact_63_le__0__eq, fact_67_nat__le__linear, arity_RealDef_Oreal___Orderings_Opreorder, arity_Nat_Onat___Nat_Osemiring__char__0, fact_41_complex__i__not__zero, fact_6_complex_Osimps_I2_J, fact_96_linorder__linear, fact_70_zless__int, fact_28_complex__zero__def, fact_79_less__imp__le__nat, fact_22_Re__complex__of__real, arity_Nat_Onat___Orderings_Oorder, fact_64_less__not__refl, help_pp_1_1_U, fact_5_complex_Orecs, fact_34_transfer__int__nat__numerals_I1_J, arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1, fact_71_Nat__Transfer_Otransfer__int__nat__relations_I2_J, fact_57_order__le__neq__trans, fact_20_of__real__eq__0__iff, fact_94_zero__zle__int, fact_60_less__zeroE, fact_85_not__less0, fact_33_zero__less__norm__iff, arity_Int_Oint___Groups_Ozero, arity_Int_Oint___Nat_Osemiring__char__0, help_pp_2_1_U, arity_Int_Oint___Rings_Olinordered__semidom, fact_88_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_42_int__int__eq, arity_Complex_Ocomplex___Groups_Ozero, fact_59_less__nat__zero__code, fact_75_less__irrefl__nat, fact_98_order__eq__refl, arity_RealDef_Oreal___Nat_Osemiring__char__0, arity_Complex_Ocomplex___RealVector_Oreal__normed__vector, fact_12_complex__Re__zero, fact_86_gr__implies__not0
% 5.31/2.22 % No. of inferences in proof: 292
% 5.31/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1821 ms resp. 1450 ms w/o parsing
% 5.31/2.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.31/2.29 % [INFO] Killing All external provers ...
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