%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP078^2 : TPTP v9.3.1. Released v7.5.0.
% 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 : n015.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 : Wed Sep 30 08:06:40 AM UTC 2026
% Result : Theorem 124.60s 96.70s
% Output : Refutation 125.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 329
% Syntax : Number of formulae : 660 ( 271 unt; 0 typ; 0 def)
% Number of atoms : 1815 ( 631 equ; 4 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 6667 ( 138 ~; 5 |; 60 &;5818 @)
% ( 0 <=>; 646 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 304 ( 304 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 8 con; 0-6 aty)
% Number of variables : 1749 ( 62 ^;1641 !; 46 ?;1749 :)
% Comments :
%------------------------------------------------------------------------------
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(a_type,type,
a: $tType ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(dioid_decl,type,
dioid:
!>[TA: $tType] : $o ).
thf(size_decl,type,
size:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(field_decl,type,
field:
!>[TA: $tType] : $o ).
thf(ring_1_decl,type,
ring_1:
!>[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(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(wellorder_decl,type,
wellorder:
!>[TA: $tType] : $o ).
thf(division_ring_decl,type,
division_ring:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_field_decl,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(boolean_algebra_decl,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_decl,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(archim1804426504_field_decl,type,
archim1804426504_field:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(inverse_inverse_decl,type,
inverse_inverse:
!>[TA: $tType] : ( TA > TA ) ).
thf(bij_betw_decl,type,
bij_betw:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) > $o ) ).
thf(comp_decl,type,
comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TC ) > TA > TB ) ).
thf(inj_on_decl,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > $o ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(nat2_decl,type,
nat2: int > nat ).
thf(ring_1_of_int_decl,type,
ring_1_of_int:
!>[TA: $tType] : ( int > TA ) ).
thf(gen_length_decl,type,
gen_length:
!>[TA: $tType] : ( nat > ( list @ TA ) > nat ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(list_ex_decl,type,
list_ex:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(map_tailrec_decl,type,
map_tailrec:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(nth_decl,type,
nth:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA ) ).
thf(upt_decl,type,
upt: nat > nat > ( list @ nat ) ).
thf(image_mset_decl,type,
image_mset:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( multiset @ TB ) > ( multiset @ TA ) ) ).
thf(is_empty_decl,type,
is_empty:
!>[TA: $tType] : ( ( multiset @ TA ) > $o ) ).
thf(mset_decl,type,
mset:
!>[TA: $tType] : ( ( list @ TA ) > ( multiset @ TA ) ) ).
thf(mset_set_decl,type,
mset_set:
!>[TA: $tType] : ( ( set @ TA ) > ( multiset @ TA ) ) ).
thf(size_multiset_decl,type,
size_multiset:
!>[TA: $tType] : ( ( TA > nat ) > ( multiset @ TA ) > nat ) ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > 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(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(set_or1433837966ssThan_decl,type,
set_or1433837966ssThan:
!>[TA: $tType] : ( TA > TA > ( set @ TA ) ) ).
thf(set_ord_lessThan_decl,type,
set_ord_lessThan:
!>[TA: $tType] : ( TA > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(f_decl,type,
f: nat > nat ).
thf(xs_decl,type,
xs: list @ a ).
thf(ys_decl,type,
ys: list @ a ).
thf(275,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_equal__neg__zero) ).
thf(1105,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_inj__on__imageI) ).
thf(347,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(195,axiom,
( ( zero_zero @ nat )
= ( nat2 @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_nat__zero__as__int) ).
thf(846,plain,
( ( zero_zero @ nat )
= ( nat2 @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(210,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_24) ).
thf(893,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(267,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_of__nat__0) ).
thf(1083,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(227,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_of__nat__le__iff) ).
thf(941,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(298,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: multiset @ TA] :
( A
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Multiset_Ois__empty__def) ).
thf(1179,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: multiset @ TA] :
( A
= ( zero_zero @ ( multiset @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_inj__on__def) ).
thf(481,plain,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__cong) ).
thf(333,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(253,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_neg__0__le__iff__le) ).
thf(1031,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(174,axiom,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_size__neq__size__imp__neq) ).
thf(777,plain,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Sup_OSUP__image) ).
thf(555,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(171,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nat__less__induct) ).
thf(762,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(263,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_of__nat__less__imp__less) ).
thf(1073,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( semiring_char_0 @ TA )
=> ( semiring_char_0 @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Nat_Osemiring__char__0) ).
thf(511,plain,
! [TA: $tType,TB: $tType] :
( ( semiring_char_0 @ TA )
=> ( semiring_char_0 @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(201,axiom,
( ( mset @ a @ ( map @ nat @ a @ ( comp @ nat @ a @ nat @ ( nth @ a @ ys ) @ f ) @ ( upt @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) )
= ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( image_mset @ nat @ nat @ f @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062mset_A_Imap_A_I_I_B_J_Ays_A_092_060circ_062_Af_J_A_0910_O_O_060length_Axs_093_J_A_061_Aimage__mset_A_I_I_B_J_Ays_J_A_Iimage__mset_Af_A_Imset__set_A_1230_O_O_060length_Axs_125_J_J_092_060close_062) ).
thf(861,plain,
( ( mset @ a @ ( map @ nat @ a @ ( comp @ nat @ a @ nat @ ( nth @ a @ ys ) @ f ) @ ( upt @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) )
= ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( image_mset @ nat @ nat @ f @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(34,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_psubsetD) ).
thf(408,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(240,axiom,
! [TA: $tType,A: TA > nat,B: multiset @ TA] :
( ( ( size_multiset @ TA @ A @ B )
= ( zero_zero @ nat ) )
= ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_size__multiset__eq__0__iff__empty) ).
thf(977,plain,
! [TA: $tType,A: TA > nat,B: multiset @ TA] :
( ( ( size_multiset @ TA @ A @ B )
= ( zero_zero @ nat ) )
= ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(205,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_length__induct) ).
thf(873,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(307,axiom,
! [A: int] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat2 @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_zero__less__nat__eq) ).
thf(1205,plain,
! [A: int] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat2 @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(51,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_compl__less__swap1) ).
thf(449,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(265,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_of__nat__less__iff) ).
thf(1078,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(92,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_mem__Collect__eq) ).
thf(550,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(293,axiom,
! [TA: $tType,A: TA > nat] :
( ( size_multiset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_size__multiset__empty) ).
thf(1164,plain,
! [TA: $tType,A: TA > nat] :
( ( size_multiset @ TA @ A @ ( zero_zero @ ( multiset @ TA ) ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(60,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_less__minus__iff) ).
thf(472,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(310,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_inverse__negative__iff__negative) ).
thf(1222,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(322,axiom,
( ( uminus_uminus @ int @ ( zero_zero @ int ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_uminus__int__code_I1_J) ).
thf(1260,plain,
( ( uminus_uminus @ int @ ( zero_zero @ int ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(146,axiom,
order @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_41) ).
thf(698,plain,
order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(166,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_less__nat__zero__code) ).
thf(747,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(217,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: set @ nat,B: set @ TA] :
( ( bij_betw @ nat @ TA @ ( semiring_1_of_nat @ TA ) @ A @ B )
= ( ( image @ nat @ TA @ ( semiring_1_of_nat @ TA ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_bij__betw__of__nat) ).
thf(913,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: set @ nat,B: set @ TA] :
( ( bij_betw @ nat @ TA @ ( semiring_1_of_nat @ TA ) @ A @ B )
= ( ( image @ nat @ TA @ ( semiring_1_of_nat @ TA ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(260,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_less__not__refl2) ).
thf(1063,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_image__eqI) ).
thf(340,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(212,axiom,
! [A: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( nat2 @ A )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_nat__le__0) ).
thf(898,plain,
! [A: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( nat2 @ A )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(37,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0_42) ).
thf(417,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( inj_on @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_bij__betw__imp__inj__on) ).
thf(565,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( inj_on @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(46,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Oring__char__0_13) ).
thf(436,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(324,axiom,
dioid @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Odioid) ).
thf(1265,plain,
dioid @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(312,axiom,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) )
= ( gen_length @ TA @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_length__code) ).
thf(1228,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) )
= ( gen_length @ TA @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(651,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(190,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_less__imp__inverse__less__neg) ).
thf(829,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(32,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero_16) ).
thf(404,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
= ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_comp__inj__on__iff) ).
thf(719,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
= ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comp__eq__dest__lhs) ).
thf(372,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType] :
( ( group_add @ TA )
=> ( group_add @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ogroup__add) ).
thf(702,plain,
! [TA: $tType,TB: $tType] :
( ( group_add @ TA )
=> ( group_add @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( bij_betw @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA,C: set @ TB] :
? [D: TB > TA] :
( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( member @ TB @ ( A @ E ) @ C )
& ( ( D @ ( A @ E ) )
= E ) ) )
& ! [E: TB] :
( ( member @ TB @ E @ C )
=> ( ( member @ TA @ ( D @ E ) @ B )
& ( ( A @ ( D @ E ) )
= E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_bij__betw__iff__bijections) ).
thf(344,plain,
! [TA: $tType,TB: $tType] :
( ( bij_betw @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA,C: set @ TB] :
? [D: TB > TA] :
( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( member @ TB @ ( A @ E ) @ C )
& ( ( D @ ( A @ E ) )
= E ) ) )
& ! [E: TB] :
( ( member @ TB @ E @ C )
=> ( ( member @ TA @ ( D @ E ) @ B )
& ( ( A @ ( D @ E ) )
= E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(302,axiom,
! [TA: $tType] :
( ( size_size @ ( multiset @ TA ) @ ( zero_zero @ ( multiset @ TA ) ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_size__empty) ).
thf(1191,plain,
! [TA: $tType] :
( ( size_size @ ( multiset @ TA ) @ ( zero_zero @ ( multiset @ TA ) ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(284,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
= ( ( zero_zero @ TA )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_neg__0__equal__iff__equal) ).
thf(1132,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
= ( ( zero_zero @ TA )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(89,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_compl__less__compl__iff) ).
thf(542,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(55,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_neg__less__iff__less) ).
thf(460,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(96,axiom,
zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_45) ).
thf(559,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(269,axiom,
inj_on @ nat @ nat @ f @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__C1_C) ).
thf(1087,plain,
inj_on @ nat @ nat @ f @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(289,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_of__nat__le__0__iff) ).
thf(1147,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(318,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_le__zero__eq) ).
thf(1247,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(204,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_neg__less__0__iff__less) ).
thf(870,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(36,axiom,
group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add_40) ).
thf(416,plain,
group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(273,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_not__gr0) ).
thf(1100,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(237,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_neg__less__pos) ).
thf(969,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(117,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int] :
( ( ring_1_of_int @ TA @ ( uminus_uminus @ int @ A ) )
= ( uminus_uminus @ TA @ ( ring_1_of_int @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_of__int__minus) ).
thf(606,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int] :
( ( ring_1_of_int @ TA @ ( uminus_uminus @ int @ A ) )
= ( uminus_uminus @ TA @ ( ring_1_of_int @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(61,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Collect__mem__eq) ).
thf(475,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(68,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_31) ).
thf(492,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(169,axiom,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Skolem__list__nth) ).
thf(756,plain,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(178,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_of__int__0__le__iff) ).
thf(789,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(110,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom_36) ).
thf(591,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(19,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_nat__int__comparison_I1_J) ).
thf(376,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(192,axiom,
! [A: nat,B: int] :
( ( ord_less @ nat @ A @ ( nat2 @ B ) )
= ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_zless__nat__eq__int__zless) ).
thf(834,plain,
! [A: nat,B: int] :
( ( ord_less @ nat @ A @ ( nat2 @ B ) )
= ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(79,axiom,
field @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Ofield) ).
thf(514,plain,
field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(250,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
& ( ord_less @ TA @ C @ A )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_field__lbound__gt__zero) ).
thf(1020,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
& ( ord_less @ TA @ C @ A )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(236,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( A
!= ( zero_zero @ ( multiset @ TA ) ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( multiset @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_nonempty__has__size) ).
thf(966,plain,
! [TA: $tType,A: multiset @ TA] :
( ( A
!= ( zero_zero @ ( multiset @ TA ) ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( multiset @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(300,axiom,
! [TA: $tType,TB: $tType] :
( ( zero @ TB )
=> ( ( zero_zero @ ( TA > TB ) )
= ( ^ [A: TA] : ( zero_zero @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_zero__fun__def) ).
thf(1183,plain,
! [TA: $tType,TB: $tType] :
( ( zero @ TB )
=> ( ( zero_zero @ ( TA > TB ) )
= ( ^ [A: TA] : ( zero_zero @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(187,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ ( uminus_uminus @ TA @ A ) )
= ( uminus_uminus @ TA @ ( inverse_inverse @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_nonzero__inverse__minus__eq) ).
thf(821,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ ( uminus_uminus @ TA @ A ) )
= ( uminus_uminus @ TA @ ( inverse_inverse @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: TB > TA,D: set @ TA] :
( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( bij_betw @ TB @ TA @ B @ A @ D )
= ( bij_betw @ TB @ TA @ C @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_bij__betw__cong) ).
thf(397,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: TB > TA,D: set @ TA] :
( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( bij_betw @ TB @ TA @ B @ A @ D )
= ( bij_betw @ TB @ TA @ C @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on @ TA @ TA @ C @ A )
=> ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
= ( inj_on @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_inj__on__image__iff) ).
thf(634,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on @ TA @ TA @ C @ A )
=> ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
= ( inj_on @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(160,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_list__eq__iff__nth__eq) ).
thf(734,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(232,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_of__nat__0__eq__iff) ).
thf(956,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_measure__induct) ).
thf(453,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(29,axiom,
ring_1 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oring__1_44) ).
thf(396,plain,
ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Sup_OSUP__cong) ).
thf(660,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( image @ TB @ TA @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_bij__betw__imp__surj__on) ).
thf(428,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( image @ TB @ TA @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(197,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_inverse__zero__imp__zero) ).
thf(849,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(86,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_equation__minus__iff) ).
thf(527,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(279,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_less__zeroE) ).
thf(1119,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(173,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ( ( set_or1433837966ssThan @ TA @ A @ B )
= ( set_or1433837966ssThan @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_atLeastLessThan__eq__iff) ).
thf(774,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ( ( set_or1433837966ssThan @ TA @ A @ B )
= ( set_or1433837966ssThan @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
( ( ( image @ TD @ TC @ A @ B )
= ( image @ TA @ TC @ C @ D ) )
=> ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_image__eq__imp__comp) ).
thf(380,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
( ( ( image @ TD @ TC @ A @ B )
= ( image @ TA @ TC @ C @ D ) )
=> ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: list @ TA] :
( ( map @ TC @ TB @ A @ ( map @ TA @ TC @ B @ C ) )
= ( map @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_map__map) ).
thf(678,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: list @ TA] :
( ( map @ TC @ TB @ A @ ( map @ TA @ TC @ B @ C ) )
= ( map @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: list @ TB,C: TA > TC,D: list @ TA] :
( ( ( map @ TB @ TC @ A @ B )
= ( map @ TA @ TC @ C @ D ) )
=> ( ( size_size @ ( list @ TB ) @ B )
= ( size_size @ ( list @ TA ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_map__eq__imp__length__eq) ).
thf(925,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: list @ TB,C: TA > TC,D: list @ TA] :
( ( ( map @ TB @ TC @ A @ B )
= ( map @ TA @ TC @ C @ D ) )
=> ( ( size_size @ ( list @ TB ) @ B )
= ( size_size @ ( list @ TA ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(305,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_less__eq__neg__nonpos) ).
thf(1199,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(291,axiom,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ B ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_int__if) ).
thf(1153,plain,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ B ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) )
= ( semiring_1_of_nat @ int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(183,axiom,
( xs
= ( map @ nat @ a @ ( comp @ nat @ a @ nat @ ( nth @ a @ ys ) @ f ) @ ( upt @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__092_060open_062xs_A_061_Amap_A_I_I_B_J_Ays_A_092_060circ_062_Af_J_A_0910_O_O_060length_Axs_093_092_060close_062) ).
thf(810,plain,
( xs
= ( map @ nat @ a @ ( comp @ nat @ a @ nat @ ( nth @ a @ ys ) @ f ) @ ( upt @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_inj__onI) ).
thf(534,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(261,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_inverse__zero) ).
thf(1067,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(181,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_infinite__descent) ).
thf(798,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(216,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( zero_zero @ TA )
= ( ring_1_of_int @ TA @ A ) )
= ( A
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_of__int__0__eq__iff) ).
thf(910,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( zero_zero @ TA )
= ( ring_1_of_int @ TA @ A ) )
= ( A
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(211,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ nat @ ( nat2 @ B ) @ ( nat2 @ A ) )
= ( ord_less @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_nat__mono__iff) ).
thf(894,plain,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ nat @ ( nat2 @ B ) @ ( nat2 @ A ) )
= ( ord_less @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(10,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_29) ).
thf(349,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(296,axiom,
! [A: nat,B: nat] :
( ( ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_negative__eq__positive) ).
thf(1174,plain,
! [A: nat,B: nat] :
( ( ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ ( TB > TA ) )
= ( ^ [A: nat,B: TB] : ( semiring_1_of_nat @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_of__nat__fun__apply) ).
thf(598,plain,
! [TA: $tType,TB: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ ( TB > TA ) )
= ( ^ [A: nat,B: TB] : ( semiring_1_of_nat @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_comp__assoc) ).
thf(630,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(185,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_inverse__less__iff__less__neg) ).
thf(815,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(315,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_neq0__conv) ).
thf(1238,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(165,axiom,
size @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(746,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(271,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( comp @ ( list @ TB ) @ ( list @ TC ) @ ( list @ TA ) @ ( map @ TB @ TC @ A ) @ ( map @ TA @ TB @ B ) )
= ( map @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_List_Omap_Ocomp) ).
thf(1091,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( comp @ ( list @ TB ) @ ( list @ TC ) @ ( list @ TA ) @ ( map @ TB @ TC @ A ) @ ( map @ TA @ TB @ B ) )
= ( map @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_comp__inj__on) ).
thf(484,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(13,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_neg__le__iff__le) ).
thf(361,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(206,axiom,
bij_betw @ nat @ nat @ f @ ( set_ord_lessThan @ nat @ ( size_size @ ( list @ a ) @ xs ) ) @ ( set_ord_lessThan @ nat @ ( size_size @ ( list @ a ) @ ys ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_assms_I1_J) ).
thf(879,plain,
bij_betw @ nat @ nat @ f @ ( set_ord_lessThan @ nat @ ( size_size @ ( list @ a ) @ xs ) ) @ ( set_ord_lessThan @ nat @ ( size_size @ ( list @ a ) @ ys ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType] :
( ( dioid @ TA )
=> ( dioid @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Rings_Odioid_6) ).
thf(493,plain,
! [TA: $tType,TB: $tType] :
( ( dioid @ TA )
=> ( dioid @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(141,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_of__nat__eq__iff) ).
thf(682,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(282,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: multiset @ TA] :
( ( image_mset @ TC @ TB @ A @ ( image_mset @ TA @ TC @ B @ C ) )
= ( image_mset @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_image__mset_Ocompositionality) ).
thf(1128,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: multiset @ TA] :
( ( image_mset @ TC @ TB @ A @ ( image_mset @ TA @ TC @ B @ C ) )
= ( image_mset @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: multiset @ TA] :
( ( ( image_mset @ TA @ TB @ A @ B )
= ( zero_zero @ ( multiset @ TB ) ) )
= ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_image__mset__is__empty__iff) ).
thf(916,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: multiset @ TA] :
( ( ( image_mset @ TA @ TB @ A @ B )
= ( zero_zero @ ( multiset @ TB ) ) )
= ( B
= ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(467,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(198,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zero__less__iff__neq__zero) ).
thf(852,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(45,axiom,
preorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Opreorder_5) ).
thf(435,plain,
preorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_inj__onD) ).
thf(583,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ! [D: TB] :
( ( member @ TB @ D @ B )
=> ( member @ TA @ ( A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_bij__betwE) ).
thf(522,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ! [D: TB] :
( ( member @ TB @ D @ B )
=> ( member @ TA @ ( A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(314,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_neq__if__length__neq) ).
thf(1234,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(327,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_inverse__nonnegative__iff__nonnegative) ).
thf(1270,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(249,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_gr0I) ).
thf(1017,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(277,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_zero__less__imp__eq__int) ).
thf(1111,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( comp @ ( list @ TB ) @ ( list @ TC ) @ ( list @ TA ) @ ( map @ TB @ TC @ A ) @ ( map @ TA @ TB @ B ) )
= ( map @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_map__comp__map) ).
thf(725,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( comp @ ( list @ TB ) @ ( list @ TC ) @ ( list @ TA ) @ ( map @ TB @ TC @ A ) @ ( map @ TA @ TB @ B ) )
= ( map @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(244,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add_17) ).
thf(1006,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(24,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( multiset @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Orderings_Opreorder) ).
thf(388,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( multiset @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(286,axiom,
! [A: int,B: int] :
( ( ord_less @ nat @ ( nat2 @ A ) @ ( nat2 @ B ) )
= ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
& ( ord_less @ int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_zless__nat__conj) ).
thf(1138,plain,
! [A: int,B: int] :
( ( ord_less @ nat @ ( nat2 @ A ) @ ( nat2 @ B ) )
= ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
& ( ord_less @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(112,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( order @ ( multiset @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Orderings_Oorder_46) ).
thf(593,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( order @ ( multiset @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_image__iff) ).
thf(519,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(106,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( ring_1_of_int @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_of__int__eq__iff) ).
thf(578,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( ring_1_of_int @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(241,axiom,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less @ nat @ ( size_size @ TA @ A ) @ ( size_size @ TA @ C ) )
=> ( A != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_mbs_Oless__not__eq) ).
thf(980,plain,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less @ nat @ ( size_size @ TA @ A ) @ ( size_size @ TA @ C ) )
=> ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(31,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom) ).
thf(403,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(176,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_of__int__le__0__iff) ).
thf(783,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(39,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_3) ).
thf(420,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(252,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_neg__less__eq__nonneg) ).
thf(1028,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: list @ TA] :
( ( map @ TC @ TB @ A @ ( map @ TA @ TC @ B @ C ) )
= ( map @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_list_Omap__comp) ).
thf(488,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: list @ TA] :
( ( map @ TC @ TB @ A @ ( map @ TA @ TC @ B @ C ) )
= ( map @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(6,axiom,
boolean_algebra @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_28) ).
thf(339,plain,
boolean_algebra @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(224,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ C ) ) )
= ( ! [C: nat] :
( ( member @ nat @ C @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ A ) )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_all__nat__less__eq) ).
thf(933,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ C ) ) )
= ( ! [C: nat] :
( ( member @ nat @ C @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ A ) )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(168,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_less__not__refl) ).
thf(753,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(299,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_4) ).
thf(1182,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(128,axiom,
linord1659791738miring @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_33) ).
thf(642,plain,
linord1659791738miring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_comp__eq__elim) ).
thf(547,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(213,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set_or1433837966ssThan @ TA @ A @ B ) @ ( set_or1433837966ssThan @ TA @ C @ D ) )
= ( ( ord_less_eq @ TA @ B @ A )
| ( ( ord_less_eq @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_ivl__subset) ).
thf(901,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set_or1433837966ssThan @ TA @ A @ B ) @ ( set_or1433837966ssThan @ TA @ C @ D ) )
= ( ( ord_less_eq @ TA @ B @ A )
| ( ( ord_less_eq @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_inverse__positive__imp__positive) ).
thf(1075,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(193,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_inverse__positive__iff__positive) ).
thf(837,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(27,axiom,
preorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_1) ).
thf(393,plain,
preorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(283,axiom,
wellorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(1131,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(242,axiom,
! [A: real > $o,B: real] :
( ! [C: real,D: real] :
( ( ord_less @ real @ C @ D )
=> ( ( A @ C )
=> ( A @ D ) ) )
=> ( ! [C: nat] :
( ( C
!= ( zero_zero @ nat ) )
=> ( A @ ( inverse_inverse @ real @ ( semiring_1_of_nat @ real @ C ) ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_forall__pos__mono) ).
thf(984,plain,
! [A: real > $o,B: real] :
( ! [C: real,D: real] :
( ( ord_less @ real @ C @ D )
=> ( ( A @ C )
=> ( A @ D ) ) )
=> ( ! [C: nat] :
( ( C
!= ( zero_zero @ nat ) )
=> ( A @ ( inverse_inverse @ real @ ( semiring_1_of_nat @ real @ C ) ) ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_inj__on__imageI2) ).
thf(569,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(17,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Olinorder) ).
thf(371,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(80,axiom,
ord @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_43) ).
thf(515,plain,
ord @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(290,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( inverse_inverse @ TA @ B ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_nonzero__inverse__eq__imp__eq) ).
thf(1150,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( inverse_inverse @ TA @ B ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(325,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_23) ).
thf(1266,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(313,axiom,
! [A: nat,B: nat] :
( ( image @ nat @ int @ ( semiring_1_of_nat @ int ) @ ( set_or1433837966ssThan @ nat @ A @ B ) )
= ( set_or1433837966ssThan @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_image__int__atLeastLessThan) ).
thf(1231,plain,
! [A: nat,B: nat] :
( ( image @ nat @ int @ ( semiring_1_of_nat @ int ) @ ( set_or1433837966ssThan @ nat @ A @ B ) )
= ( set_or1433837966ssThan @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(268,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder_20) ).
thf(1086,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(316,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( comp @ ( multiset @ TB ) @ ( multiset @ TC ) @ ( multiset @ TA ) @ ( image_mset @ TB @ TC @ A ) @ ( image_mset @ TA @ TB @ B ) )
= ( image_mset @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_image__mset_Ocomp) ).
thf(1241,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( comp @ ( multiset @ TB ) @ ( multiset @ TC ) @ ( multiset @ TA ) @ ( image_mset @ TB @ TC @ A ) @ ( image_mset @ TA @ TB @ B ) )
= ( image_mset @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(126,axiom,
semiring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Osemiring__char__0_37) ).
thf(633,plain,
semiring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(295,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_less__not__refl3) ).
thf(1170,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(95,axiom,
linord219039673up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add_34) ).
thf(558,plain,
linord219039673up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(294,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ ( inverse_inverse @ TA @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_nonzero__inverse__inverse__eq) ).
thf(1167,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ ( inverse_inverse @ TA @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_rev__image__eqI) ).
thf(530,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(231,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ A )
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_nonzero__imp__inverse__nonzero) ).
thf(953,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ A )
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_inj__on__inverseI) ).
thf(586,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(306,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_zero__reorient) ).
thf(1202,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(179,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( member @ TA @ A @ ( set_or1433837966ssThan @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ B @ A )
& ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_atLeastLessThan__iff) ).
thf(792,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( member @ TA @ A @ ( set_or1433837966ssThan @ TA @ B @ C ) )
= ( ( ord_less_eq @ TA @ B @ A )
& ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(285,axiom,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( multiset @ TA ) @ ( mset @ TA @ A ) )
= ( size_size @ ( list @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_size__mset) ).
thf(1135,plain,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( multiset @ TA ) @ ( mset @ TA @ A ) )
= ( size_size @ ( list @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(167,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA )
= ( ^ [A: int] : ( if @ TA @ ( ord_less @ int @ A @ ( zero_zero @ int ) ) @ ( uminus_uminus @ TA @ ( semiring_1_of_nat @ TA @ ( nat2 @ ( uminus_uminus @ int @ A ) ) ) ) @ ( semiring_1_of_nat @ TA @ ( nat2 @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_of__int__of__nat) ).
thf(750,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA )
= ( ^ [A: int] : ( if @ TA @ ( ord_less @ int @ A @ ( zero_zero @ int ) ) @ ( uminus_uminus @ TA @ ( semiring_1_of_nat @ TA @ ( nat2 @ ( uminus_uminus @ int @ A ) ) ) ) @ ( semiring_1_of_nat @ TA @ ( nat2 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( bij_betw @ TA @ TB @ A @ B @ ( image @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_inj__on__imp__bij__betw) ).
thf(618,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( bij_betw @ TA @ TB @ A @ B @ ( image @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType] :
( ( ring_char_0 @ TA )
=> ( ring_char_0 @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Nat_Oring__char__0) ).
thf(425,plain,
! [TA: $tType,TB: $tType] :
( ( ring_char_0 @ TA )
=> ( ring_char_0 @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(78,axiom,
ord @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oord_14) ).
thf(513,plain,
ord @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(274,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: set @ nat] : ( inj_on @ nat @ TA @ ( semiring_1_of_nat @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_inj__on__of__nat) ).
thf(1103,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: set @ nat] : ( inj_on @ nat @ TA @ ( semiring_1_of_nat @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(188,axiom,
( ( mset @ a @ xs )
= ( mset @ a @ ( map @ nat @ a @ ( comp @ nat @ a @ nat @ ( nth @ a @ ys ) @ f ) @ ( upt @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__092_060open_062mset_Axs_A_061_Amset_A_Imap_A_I_I_B_J_Ays_A_092_060circ_062_Af_J_A_0910_O_O_060length_Axs_093_J_092_060close_062) ).
thf(824,plain,
( ( mset @ a @ xs )
= ( mset @ a @ ( map @ nat @ a @ ( comp @ nat @ a @ nat @ ( nth @ a @ ys ) @ f ) @ ( upt @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(328,axiom,
! [TA: $tType,A: multiset @ TA] :
( ( ( size_size @ ( multiset @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_size__eq__0__iff__empty) ).
thf(1273,plain,
! [TA: $tType,A: multiset @ TA] :
( ( ( size_size @ ( multiset @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ ( multiset @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(104,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_26) ).
thf(573,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_bex__imageD) ).
thf(689,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_imageI) ).
thf(601,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(245,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_of__nat__0__less__iff) ).
thf(1007,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(163,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_22) ).
thf(743,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(281,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_gr__implies__not0) ).
thf(1124,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(90,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_27) ).
thf(545,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(214,axiom,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
= ( ? [B: nat] :
( ( B
!= ( zero_zero @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( inverse_inverse @ real @ ( semiring_1_of_nat @ real @ B ) ) )
& ( ord_less @ real @ ( inverse_inverse @ real @ ( semiring_1_of_nat @ real @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_real__arch__inverse) ).
thf(904,plain,
! [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
= ( ? [B: nat] :
( ( B
!= ( zero_zero @ nat ) )
& ( ord_less @ real @ ( zero_zero @ real ) @ ( inverse_inverse @ real @ ( semiring_1_of_nat @ real @ B ) ) )
& ( ord_less @ real @ ( inverse_inverse @ real @ ( semiring_1_of_nat @ real @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(239,axiom,
( ( set_ord_lessThan @ nat )
= ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_lessThan__atLeast0) ).
thf(975,plain,
( ( set_ord_lessThan @ nat )
= ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType,A: TB > nat,B: TA > TB] :
( ( comp @ ( multiset @ TB ) @ nat @ ( multiset @ TA ) @ ( size_multiset @ TB @ A ) @ ( image_mset @ TA @ TB @ B ) )
= ( size_multiset @ TA @ ( comp @ TB @ nat @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_size__multiset__o__map) ).
thf(826,plain,
! [TA: $tType,TB: $tType,A: TB > nat,B: TA > TB] :
( ( comp @ ( multiset @ TB ) @ nat @ ( multiset @ TA ) @ ( size_multiset @ TB @ A ) @ ( image_mset @ TA @ TB @ B ) )
= ( size_multiset @ TA @ ( comp @ TB @ nat @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(152,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_psubset__trans) ).
thf(711,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ C @ B )
=> ( ord_less @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_inj__on__strict__subset) ).
thf(391,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ C @ B )
=> ( ord_less @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(225,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_inverse__le__iff__le) ).
thf(936,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(259,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_pos__int__cases) ).
thf(1058,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( size_size @ ( list @ TB ) @ ( map @ TA @ TB @ A @ B ) )
= ( size_size @ ( list @ TA ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_length__map) ).
thf(919,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( size_size @ ( list @ TB ) @ ( map @ TA @ TB @ A @ B ) )
= ( size_size @ ( list @ TA ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(229,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_neg__le__0__iff__le) ).
thf(947,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Inf_OINF__cong) ).
thf(350,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(153,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_minus__equation__iff) ).
thf(713,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(71,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_int__int__eq) ).
thf(498,plain,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(321,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_not__less__zero) ).
thf(1258,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(149,axiom,
ring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oring__1_15) ).
thf(704,plain,
ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(303,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_inverse__le__iff__le__neg) ).
thf(1194,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(191,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_add_Oinverse__neutral) ).
thf(831,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(140,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_2) ).
thf(681,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(247,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_nat__neq__iff) ).
thf(1011,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(288,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_not__gr__zero) ).
thf(1144,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(161,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_neg__equal__zero) ).
thf(737,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(280,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_inverse__less__imp__less__neg) ).
thf(1122,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(202,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ TA @ ( inverse_inverse @ TA @ ( semiring_1_of_nat @ TA @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_ex__inverse__of__nat__less) ).
thf(863,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ TA @ ( inverse_inverse @ TA @ ( semiring_1_of_nat @ TA @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(52,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: nat] : ( ord_less @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_reals__Archimedean2) ).
thf(451,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA )
=> ! [A: TA] :
? [B: nat] : ( ord_less @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(100,axiom,
ordered_ab_group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add_35) ).
thf(567,plain,
ordered_ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(76,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_linordered__field__no__lb) ).
thf(509,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(207,axiom,
! [A: int] :
( ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) )
=> ~ ! [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( A
!= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_int__cases4) ).
thf(880,plain,
! [A: int] :
( ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) )
=> ~ ! [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( A
!= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(209,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_neg__equal__0__iff__equal) ).
thf(890,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(118,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set_ord_lessThan @ TA @ A ) @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_lessThan__subset__iff) ).
thf(609,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set_ord_lessThan @ TA @ A ) @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(292,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_inverse__less__imp__less) ).
thf(1162,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(196,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0_19) ).
thf(848,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(235,axiom,
! [TA: $tType] : ( size @ ( list @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_32) ).
thf(964,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(123,axiom,
linordered_field @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).
thf(626,plain,
linordered_field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(297,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_less__imp__of__nat__less) ).
thf(1177,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(200,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_inverse__nonzero__iff__nonzero) ).
thf(858,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(15,axiom,
semiring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Osemiring__char__0_9) ).
thf(367,plain,
semiring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(330,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_of__nat__less__0__iff) ).
thf(1293,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(135,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less @ int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_of__int__less__iff) ).
thf(668,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(142,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Inf_OINF__image) ).
thf(685,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(233,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_positive__imp__inverse__positive) ).
thf(959,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(255,axiom,
! [A: int] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= A ) )
& ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_int__nat__eq) ).
thf(1044,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= A ) )
& ( ~ ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( semiring_1_of_nat @ int @ ( nat2 @ A ) )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(28,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ord @ ( multiset @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Orderings_Oord_47) ).
thf(394,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ord @ ( multiset @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(98,axiom,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Oboolean__algebra_25) ).
thf(563,plain,
! [TA: $tType] : ( boolean_algebra @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(319,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_less__neg__neg) ).
thf(1250,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( ( image @ TB @ TA @ A @ B )
= C )
=> ( bij_betw @ TB @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_bij__betw__imageI) ).
thf(431,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( ( image @ TB @ TA @ A @ B )
= C )
=> ( bij_betw @ TB @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_comp__apply) ).
thf(653,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(220,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Ex__list__of__length) ).
thf(922,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ordered_ab_group_add @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Oordered__ab__group__add) ).
thf(658,plain,
! [TA: $tType,TB: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ordered_ab_group_add @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(74,axiom,
division_ring @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Odivision__ring) ).
thf(505,plain,
division_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(48,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_neg__equal__iff__equal) ).
thf(438,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: multiset @ TA] :
( ( image_mset @ TC @ TB @ A @ ( image_mset @ TA @ TC @ B @ C ) )
= ( image_mset @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_multiset_Omap__comp) ).
thf(722,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: multiset @ TA] :
( ( image_mset @ TC @ TB @ A @ ( image_mset @ TA @ TC @ B @ C ) )
= ( image_mset @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(254,axiom,
! [A: int] :
( ( A
!= ( zero_zero @ int ) )
=> ( ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) )
=> ~ ! [B: nat] :
( ( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_int__cases3) ).
thf(1034,plain,
! [A: int] :
( ( A
!= ( zero_zero @ int ) )
=> ( ! [B: nat] :
( ( A
= ( semiring_1_of_nat @ int @ B ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) )
=> ~ ! [B: nat] :
( ( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_inj__on__contraD) ).
thf(675,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(308,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_infinite__descent0__measure) ).
thf(1208,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(228,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_inverse__less__iff__less) ).
thf(944,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(180,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( set_or1433837966ssThan @ int @ ( zero_zero @ int ) @ A )
= ( image @ nat @ int @ ( semiring_1_of_nat @ int ) @ ( set_ord_lessThan @ nat @ ( nat2 @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_image__atLeastZeroLessThan__int) ).
thf(795,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( set_or1433837966ssThan @ int @ ( zero_zero @ int ) @ A )
= ( image @ nat @ int @ ( semiring_1_of_nat @ int ) @ ( set_ord_lessThan @ nat @ ( nat2 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(184,axiom,
! [A: nat,B: nat] :
( ( mset @ nat @ ( upt @ A @ B ) )
= ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_mset__upt) ).
thf(812,plain,
! [A: nat,B: nat] :
( ( mset @ nat @ ( upt @ A @ B ) )
= ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(266,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_int__ops_I1_J) ).
thf(1081,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_comp__eq__dest) ).
thf(516,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(226,axiom,
( ( image @ nat @ nat @ f @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) )
= ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ ys ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__C2_C) ).
thf(939,plain,
( ( image @ nat @ nat @ f @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) )
= ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ ys ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType] :
( ( zero @ TA )
=> ( zero @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ozero) ).
thf(553,plain,
! [TA: $tType,TB: $tType] :
( ( zero @ TA )
=> ( zero @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: set @ TC,C: set @ TB,D: TB > TA,E: set @ TA] :
( ( bij_betw @ TC @ TB @ A @ B @ C )
=> ( ( bij_betw @ TB @ TA @ D @ C @ E )
=> ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ D @ A ) @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_bij__betw__trans) ).
thf(525,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: set @ TC,C: set @ TB,D: TB > TA,E: set @ TA] :
( ( bij_betw @ TC @ TB @ A @ B @ C )
=> ( ( bij_betw @ TB @ TA @ D @ C @ E )
=> ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ D @ A ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(199,axiom,
! [A: nat] :
( ( nat2 @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_nat__zminus__int) ).
thf(855,plain,
! [A: nat] :
( ( nat2 @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(251,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ xs ) )
=> ( ( nth @ a @ xs @ A )
= ( nth @ a @ ys @ ( f @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I2_J) ).
thf(1025,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ xs ) )
=> ( ( nth @ a @ xs @ A )
= ( nth @ a @ ys @ ( f @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(262,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( zero_zero @ int ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_of__int__0) ).
thf(1070,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( zero_zero @ int ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(705,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(311,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_inverse__negative__imp__negative) ).
thf(1225,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(208,axiom,
! [A: nat > $o,B: int] :
( ( A @ ( nat2 @ B ) )
= ( ! [C: nat] :
( ( B
= ( semiring_1_of_nat @ int @ C ) )
=> ( A @ C ) )
& ( ( ord_less @ int @ B @ ( zero_zero @ int ) )
=> ( A @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_split__nat) ).
thf(887,plain,
! [A: nat > $o,B: int] :
( ( A @ ( nat2 @ B ) )
= ( ! [C: nat] :
( ( B
= ( semiring_1_of_nat @ int @ C ) )
=> ( A @ C ) )
& ( ( ord_less @ int @ B @ ( zero_zero @ int ) )
=> ( A @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(326,axiom,
! [TA: $tType,TB: $tType,A: nat,B: list @ TA,C: TA > TB] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TB @ ( map @ TA @ TB @ C @ B ) @ A )
= ( C @ ( nth @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_nth__map) ).
thf(1267,plain,
! [TA: $tType,TB: $tType,A: nat,B: list @ TA,C: TA > TB] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TB @ ( map @ TA @ TB @ C @ B ) @ A )
= ( C @ ( nth @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(257,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_not__less0) ).
thf(1053,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(137,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_verit__comp__simplify1_I1_J) ).
thf(673,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ball__imageD) ).
thf(441,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(73,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ( set_ord_lessThan @ TA @ A )
= ( set_ord_lessThan @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_lessThan__eq__iff) ).
thf(502,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ( set_ord_lessThan @ TA @ A )
= ( set_ord_lessThan @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(194,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_infinite__descent__measure) ).
thf(840,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(323,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_gr__zeroI) ).
thf(1262,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(56,axiom,
! [TA: $tType] : ( zero @ ( multiset @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Groups_Ozero_48) ).
thf(463,plain,
! [TA: $tType] : ( zero @ ( multiset @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(5,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(338,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(309,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_gr__implies__not__zero) ).
thf(1218,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_image__cong) ).
thf(643,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(215,axiom,
! [A: int] :
( ( ( nat2 @ A )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_nat__0__iff) ).
thf(907,plain,
! [A: int] :
( ( ( nat2 @ A )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1,conjecture,
( ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( image_mset @ nat @ nat @ f @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ) )
= ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ ys ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( image_mset @ nat @ nat @ f @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ) )
!= ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ ys ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(331,plain,
( ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( image_mset @ nat @ nat @ f @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ) )
!= ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ ys ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(301,axiom,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ( ord_less @ int @ E @ ( zero_zero @ int ) )
=> ( A @ ( uminus_uminus @ int @ D ) @ ( uminus_uminus @ int @ E ) ) )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_norm__frac_Oinduct) ).
thf(1186,plain,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ( ord_less @ int @ E @ ( zero_zero @ int ) )
=> ( A @ ( uminus_uminus @ int @ D ) @ ( uminus_uminus @ int @ E ) ) )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(164,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_negative__imp__inverse__negative) ).
thf(744,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(336,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(287,axiom,
! [TA: $tType] :
( ( list_ex @ TA )
= ( ^ [A: TA > $o,B: list @ TA] :
? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_list__ex__length) ).
thf(1141,plain,
! [TA: $tType] :
( ( list_ex @ TA )
= ( ^ [A: TA > $o,B: list @ TA] :
? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(132,axiom,
! [TA: $tType] : ( size @ ( multiset @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Multiset_Omultiset___Nat_Osize_49) ).
thf(656,plain,
! [TA: $tType] : ( size @ ( multiset @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(256,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_18) ).
thf(1052,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(103,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) ) @ ( semiring_1_of_nat @ int @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_negative__zle) ).
thf(571,plain,
! [A: nat,B: nat] : ( ord_less_eq @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ A ) ) @ ( semiring_1_of_nat @ int @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(595,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_measure__induct__rule) ).
thf(612,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(272,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_nth__equalityI) ).
thf(1094,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(23,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_linordered__field__no__ub) ).
thf(386,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( semiring_1 @ TA )
=> ( semiring_1 @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Rings_Osemiring__1) ).
thf(465,plain,
! [TA: $tType,TB: $tType] :
( ( semiring_1 @ TA )
=> ( semiring_1 @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(124,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_of__int__le__iff) ).
thf(627,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(223,axiom,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_less__int__code_I1_J) ).
thf(931,plain,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType] :
( ( dioid @ TA )
=> ( canoni770627133id_add @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ocanonically__ordered__monoid__add) ).
thf(671,plain,
! [TA: $tType,TB: $tType] :
( ( dioid @ TA )
=> ( canoni770627133id_add @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(143,axiom,
linord1659791738miring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__nonzero__semiring) ).
thf(688,plain,
linord1659791738miring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(70,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA] :
( ( member @ TA @ A @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_lessThan__iff) ).
thf(495,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA] :
( ( member @ TA @ A @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(170,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_of__int__eq__0__iff) ).
thf(759,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(246,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_21) ).
thf(1010,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( bij_betw @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA,C: set @ TB] :
( ( inj_on @ TA @ TB @ A @ B )
& ( ( image @ TA @ TB @ A @ B )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_bij__betw__def) ).
thf(368,plain,
! [TA: $tType,TB: $tType] :
( ( bij_betw @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA,C: set @ TB] :
( ( inj_on @ TA @ TB @ A @ B )
& ( ( image @ TA @ TB @ A @ B )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(172,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_less__irrefl__nat) ).
thf(771,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(276,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_field__class_Ofield__inverse__zero) ).
thf(1108,plain,
! [TA: $tType] :
( ( field @ TA )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(84,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(524,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder_7) ).
thf(581,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(329,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_infinite__descent0) ).
thf(1276,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(234,axiom,
! [TA: $tType,TB: $tType] :
( ( zero @ TB )
=> ( ( zero_zero @ ( TA > TB ) )
= ( ^ [A: TA] : ( zero_zero @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_zero__fun__apply) ).
thf(961,plain,
! [TA: $tType,TB: $tType] :
( ( zero @ TB )
=> ( ( zero_zero @ ( TA > TB ) )
= ( ^ [A: TA] : ( zero_zero @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(25,axiom,
ordered_ab_group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__group__add_8) ).
thf(390,plain,
ordered_ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(317,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_neg__0__less__iff__less) ).
thf(1244,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(175,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_less__imp__inverse__less) ).
thf(781,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(320,axiom,
! [A: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ~ ! [B: nat] :
( ( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_neg__int__cases) ).
thf(1253,plain,
! [A: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ~ ! [B: nat] :
( ( A
= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) )
=> ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_comp__def) ).
thf(699,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(159,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C ) ) )
= ( ? [C: nat] :
( ( member @ nat @ C @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ A ) )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ex__nat__less__eq) ).
thf(731,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C ) ) )
= ( ? [C: nat] :
( ( member @ nat @ C @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ A ) )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(38,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_verit__negate__coefficient_I2_J) ).
thf(418,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(177,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_bot__nat__0_Oextremum__strict) ).
thf(786,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(101,axiom,
group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add_11) ).
thf(568,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(20,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_compl__less__swap2) ).
thf(378,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(62,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: nat] :
( ( ring_1_of_int @ TA @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_of__int__of__nat__eq) ).
thf(478,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: nat] :
( ( ring_1_of_int @ TA @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( map @ TA @ TB )
= ( map_tailrec @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_map__eq__map__tailrec) ).
thf(383,plain,
! [TA: $tType,TB: $tType] :
( ( map @ TA @ TB )
= ( map_tailrec @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(154,axiom,
! [TA: $tType,A: multiset @ TA] :
? [B: list @ TA] :
( ( mset @ TA @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_ex__mset) ).
thf(716,plain,
! [TA: $tType,A: multiset @ TA] :
? [B: list @ TA] :
( ( mset @ TA @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(278,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_of__nat__eq__0__iff) ).
thf(1116,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(121,axiom,
! [A: int] :
( ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) )
=> ~ ! [B: nat] :
( A
!= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_int__cases2) ).
thf(620,plain,
! [A: int] :
( ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) )
=> ~ ! [B: nat] :
( A
!= ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(50,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: set @ TA] : ( inj_on @ TA @ TA @ ( uminus_uminus @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_inj__uminus) ).
thf(447,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: set @ TA] : ( inj_on @ TA @ TA @ ( uminus_uminus @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_inj__on__cong) ).
thf(410,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( image_mset @ TA @ TB @ A @ ( mset_set @ TA @ B ) )
= ( mset_set @ TB @ ( image @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_image__mset__mset__set) ).
thf(950,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( image_mset @ TA @ TB @ A @ ( mset_set @ TA @ B ) )
= ( mset_set @ TB @ ( image @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image_mset @ TB @ TA @ A @ ( zero_zero @ ( multiset @ TB ) ) )
= ( zero_zero @ ( multiset @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_image__mset__empty) ).
thf(818,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image_mset @ TB @ TA @ A @ ( zero_zero @ ( multiset @ TB ) ) )
= ( zero_zero @ ( multiset @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_inj__on__eq__iff) ).
thf(405,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(40,axiom,
! [A: nat] :
( ( nat2 @ ( semiring_1_of_nat @ int @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_nat__int) ).
thf(422,plain,
! [A: nat] :
( ( nat2 @ ( semiring_1_of_nat @ int @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(203,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_bot__nat__0_Onot__eq__extremum) ).
thf(867,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: set @ TC,C: set @ TB,D: TB > TA,E: set @ TA] :
( ( bij_betw @ TC @ TB @ A @ B @ C )
=> ( ( bij_betw @ TB @ TA @ D @ C @ E )
= ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ D @ A ) @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_bij__betw__comp__iff) ).
thf(603,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: set @ TC,C: set @ TB,D: TB > TA,E: set @ TA] :
( ( bij_betw @ TC @ TB @ A @ B @ C )
=> ( ( bij_betw @ TB @ TA @ D @ C @ E )
= ( bij_betw @ TC @ TA @ ( comp @ TB @ TA @ TC @ D @ A ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(75,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_add_Oinverse__inverse) ).
thf(506,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(47,axiom,
order @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oorder_12) ).
thf(437,plain,
order @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(258,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] : ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_nat__int__comparison_I2_J) ).
thf(1056,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] : ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(304,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_less__numeral__extra_I3_J) ).
thf(1197,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType] :
( ( ring_1 @ TA )
=> ( ring_1 @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Rings_Oring__1) ).
thf(696,plain,
! [TA: $tType,TB: $tType] :
( ( ring_1 @ TA )
=> ( ring_1 @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(222,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( set_or1433837966ssThan @ TA @ A @ B )
= ( set_or1433837966ssThan @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( B = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_atLeastLessThan__inj_I2_J) ).
thf(928,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( set_or1433837966ssThan @ TA @ A @ B )
= ( set_or1433837966ssThan @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( B = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(12,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_minus__less__iff) ).
thf(358,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(182,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_inverse__nonpositive__iff__nonpositive) ).
thf(807,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ? [D: TB > TA] : ( bij_betw @ TB @ TA @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_bij__betw__inv) ).
thf(624,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ? [D: TB > TA] : ( bij_betw @ TB @ TA @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(105,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ ( set @ TA ) @ ( set_ord_lessThan @ TA @ A ) @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_lessThan__strict__subset__iff) ).
thf(575,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ ( set @ TA ) @ ( set_ord_lessThan @ TA @ A ) @ ( set_ord_lessThan @ TA @ B ) )
= ( ord_less @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(42,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1_10) ).
thf(427,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(54,axiom,
linorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_38) ).
thf(459,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(243,axiom,
( ( mset @ a @ xs )
= ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( image_mset @ nat @ nat @ f @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_calculation) ).
thf(1004,plain,
( ( mset @ a @ xs )
= ( image_mset @ nat @ a @ ( nth @ a @ ys ) @ ( image_mset @ nat @ nat @ f @ ( mset_set @ nat @ ( set_or1433837966ssThan @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ a ) @ xs ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(72,axiom,
archim1804426504_field @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field) ).
thf(501,plain,
archim1804426504_field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(158,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_linorder__neqE__nat) ).
thf(728,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: multiset @ TA] :
( ( size_size @ ( multiset @ TB ) @ ( image_mset @ TA @ TB @ A @ B ) )
= ( size_size @ ( multiset @ TA ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_size__image__mset) ).
thf(740,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: multiset @ TA] :
( ( size_size @ ( multiset @ TB ) @ ( image_mset @ TA @ TB @ A @ B ) )
= ( size_size @ ( multiset @ TA ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TB] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( member @ TB @ D @ B )
=> ( member @ TA @ ( A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_bij__betw__apply) ).
thf(486,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TB] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( member @ TB @ D @ B )
=> ( member @ TA @ ( A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ ( TB > TA ) )
= ( ^ [A: nat,B: TB] : ( semiring_1_of_nat @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_of__nat__fun) ).
thf(469,plain,
! [TA: $tType,TB: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ ( TB > TA ) )
= ( ^ [A: nat,B: TB] : ( semiring_1_of_nat @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_image__comp) ).
thf(560,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(111,axiom,
semiring_1 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__1_39) ).
thf(592,plain,
semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: list @ TA] :
( ( map @ TC @ TB @ A @ ( map @ TA @ TC @ B @ C ) )
= ( map @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_List_Omap_Ocompositionality) ).
thf(364,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: list @ TA] :
( ( map @ TC @ TB @ A @ ( map @ TA @ TC @ B @ C ) )
= ( map @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(151,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_not__int__zless__negative) ).
thf(708,plain,
! [A: nat,B: nat] :
~ ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(67,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_30) ).
thf(491,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(270,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( mset @ TA @ A )
= ( mset @ TA @ B ) )
=> ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_mset__eq__length) ).
thf(1088,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( mset @ TA @ A )
= ( mset @ TA @ B ) )
=> ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(248,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( mset @ TB @ ( map @ TA @ TB @ A @ B ) )
= ( image_mset @ TA @ TB @ A @ ( mset @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mset__map) ).
thf(1014,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( mset @ TB @ ( map @ TA @ TB @ A @ B ) )
= ( image_mset @ TA @ TB @ A @ ( mset @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(238,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( set_or1433837966ssThan @ TA @ A @ B )
= ( set_or1433837966ssThan @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_atLeastLessThan__inj_I1_J) ).
thf(972,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( set_or1433837966ssThan @ TA @ A @ B )
= ( set_or1433837966ssThan @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1295,plain,
$false,
inference(e,[status(thm)],[1105,347,846,893,1083,941,1179,481,333,1031,777,555,762,1073,511,861,408,977,873,1205,449,1078,550,1164,472,1222,1260,698,747,913,1063,340,898,417,565,436,1265,1228,651,829,404,719,372,702,344,1191,1132,542,460,559,1087,1147,1247,870,416,1100,969,606,475,492,756,789,591,376,834,514,1020,966,1183,821,397,634,734,956,453,396,660,428,849,527,1119,774,380,678,925,1199,1153,810,534,1067,798,910,894,349,1174,598,630,815,1238,746,1091,484,361,879,493,682,1128,916,467,852,435,583,522,1234,1270,1017,1111,725,1006,388,1138,593,519,578,980,403,783,420,1028,488,339,933,753,1182,642,547,901,1075,837,393,1131,984,569,371,515,1150,1266,1231,1086,1241,633,1170,558,1167,530,953,586,1202,792,1135,750,618,425,513,1103,824,1273,573,689,601,1007,743,1124,545,904,975,826,711,391,936,1058,919,947,350,713,498,1258,704,1194,831,681,1011,1144,737,1122,863,451,567,509,880,890,609,1162,848,964,626,1177,858,367,1293,668,685,959,1044,394,563,1250,431,653,922,658,505,438,722,1034,675,1208,944,795,812,1081,516,939,553,525,855,1025,1070,705,1225,887,1267,1053,673,441,502,840,1262,463,338,1218,643,907,331,1186,744,336,1141,656,1052,571,595,612,1094,386,465,627,931,671,688,495,759,1010,368,771,1108,524,581,1276,961,390,1244,781,1253,699,731,418,786,568,378,478,383,716,1116,620,447,410,950,818,405,422,867,603,506,437,1056,1197,696,928,358,807,624,575,427,459,1004,501,728,740,486,469,560,592,364,708,491,1088,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP078^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:51:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.65/0.54 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.14/0.92 % [INFO] Parsing done (371ms).
% 2.14/0.93 % [INFO] Running in sequential loop mode.
% 2.85/1.18 % [INFO] eprover registered as external prover.
% 2.85/1.19 % [INFO] Scanning for conjecture ...
% 3.07/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 329 axioms. Running axiom selection ...
% 3.72/1.43 % [INFO] Axiom selection finished. Selected 328 axioms (removed 1 axioms).
% 4.51/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 4.91/1.70 % [INFO] Type checking passed.
% 4.91/1.70 % [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 ...
% 124.38/96.69 % External prover 'e' found a proof!
% 124.38/96.69 % [INFO] Killing All external provers ...
% 124.38/96.69 % Time passed: 96369ms (effective reasoning time: 95754ms)
% 124.38/96.69 % 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)>
% 124.38/96.70 % Axioms used in derivation (328): fact_83_comp__def, tcon_Real_Oreal___Rings_Osemiring__1_39, fact_27_measure__induct, fact_243_of__int__minus, tcon_Nat_Onat___Orderings_Oord_23, fact_227_neg__le__iff__le, fact_223_image__atLeastZeroLessThan__int, fact_122_psubset__trans, fact_98_image__comp, fact_76_size__image__mset, fact_179_minus__equation__iff, fact_217_less__imp__inverse__less__neg, fact_60_size__mset, tcon_fun___Orderings_Opreorder_7, fact_203_inverse__zero, tcon_Int_Oint___Groups_Oordered__ab__group__add_8, tcon_Multiset_Omultiset___Nat_Osize_49, tcon_List_Olist___Nat_Osize_32, fact_137_of__nat__0, fact_54_list__eq__iff__nth__eq, fact_120_length__code, tcon_Multiset_Omultiset___Groups_Ozero_48, fact_167_inj__uminus, fact_151_size__multiset__empty, fact_165_neg__equal__zero, fact_110_image__mset_Ocompositionality, fact_124_image__iff, fact_47_less__zeroE, tcon_Nat_Onat___Nat_Osize, fact_105_inj__on__imageI2, fact_85_inj__on__contraD, fact_182_verit__comp__simplify1_I1_J, fact_35_zero__less__iff__neq__zero, tcon_Int_Oint___Nat_Oring__char__0_13, fact_150_reals__Archimedean2, fact_188_compl__less__swap2, fact_44_Collect__mem__eq, fact_38_gr__zeroI, fact_82_comp__assoc, fact_80_comp__eq__elim, fact_6__092_060open_062mset_A_Imap_A_I_I_B_J_Ays_A_092_060circ_062_Af_J_A_0910_O_O_060length_Axs_093_J_A_061_Aimage__mset_A_I_I_B_J_Ays_J_A_Iimage__mset_Af_A_Imset__set_A_1230_O_O_060length_Axs_125_J_J_092_060close_062, fact_146_of__nat__less__imp__less, fact_183_nat__int__comparison_I1_J, fact_51_length__induct, fact_237_atLeastLessThan__iff, fact_18_list_Omap__comp, fact_114_image__eqI, fact_249_nat__le__0, fact_139_of__nat__eq__0__iff, fact_104_inj__on__image__iff, fact_129_Inf_OINF__cong, fact_93_bij__betw__cong, fact_95_bij__betwE, fact_29_nat__less__induct, fact_135_of__nat__fun__apply, tcon_Nat_Onat___Rings_Odioid, fact_75_size__empty, tcon_Int_Oint___Nat_Osemiring__char__0_9, fact_11_not__gr__zero, fact_241_of__int__le__iff, fact_126_image__cong, fact_229_ivl__subset, fact_84_inj__on__inverseI, tcon_fun___Orderings_Oord, fact_9_neq__if__length__neq, fact_202_inverse__negative__iff__negative, fact_244_of__int__of__nat__eq, fact_58_zero__reorient, fact_178_equation__minus__iff, fact_20_length__map, tcon_Real_Oreal___Nat_Osemiring__char__0_37, fact_61_lessThan__iff, tcon_HOL_Obool___Orderings_Olinorder_29, fact_236_inverse__nonnegative__iff__nonnegative, fact_96_ex__mset, fact_36_gr__implies__not__zero, fact_102_atLeastLessThan__eq__iff, fact_123_imageI, fact_59_mset__map, fact_246_of__nat__le__0__iff, fact_145_of__nat__less__0__iff, fact_147_less__imp__of__nat__less, fact_49_not__gr0, fact_164_equal__neg__zero, fact_222_nonzero__inverse__minus__eq, fact_31_linorder__neqE__nat, fact_79_comp__eq__dest__lhs, fact_99_nonempty__has__size, fact_173_int__cases2, fact_119_field__lbound__gt__zero, fact_220_negative__imp__inverse__negative, fact_57_zero__fun__def, fact_196_forall__pos__mono, fact_224_of__int__of__nat, fact_252_of__int__le__0__iff, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_18, fact_74_size__eq__0__iff__empty, fact_117_Inf_OINF__image, tcon_Nat_Onat___Groups_Ozero_24, fact_232_neg__le__0__iff__le, fact_112_bij__betw__imp__inj__on, fact_158_neg__int__cases, fact_154_less__int__code_I1_J, fact_92_bij__betw__apply, tcon_fun___Nat_Osemiring__char__0, fact_100_atLeastLessThan__inj_I2_J, fact_43_mem__Collect__eq, fact_70_comp__apply, fact_228_of__nat__le__iff, fact_71_lessThan__eq__iff, fact_157_int__ops_I1_J, fact_186_norm__frac_Oinduct, fact_16_List_Omap_Ocomp, tcon_Set_Oset___Orderings_Oord_27, fact_22__092_060open_062mset_Axs_A_061_Amset_A_Imap_A_I_I_B_J_Ays_A_092_060circ_062_Af_J_A_0910_O_O_060length_Axs_093_J_092_060close_062, tcon_Real_Oreal___Groups_Olinordered__ab__group__add_34, fact_78_inj__on__strict__subset, tcon_fun___Nat_Oring__char__0, fact_204_inverse__nonzero__iff__nonzero, fact_106_bij__betw__imp__surj__on, fact_201_inverse__positive__iff__positive, fact_219_inverse__positive__imp__positive, fact_206_inverse__less__iff__less__neg, fact_138_of__nat__0__eq__iff, fact_212_nonzero__inverse__inverse__eq, fact_242_of__int__less__iff, fact_148_pos__int__cases, fact_33_infinite__descent__measure, fact_174_minus__less__iff, fact_141_bij__betw__of__nat, fact_168_neg__less__0__iff__less, fact_26_less__not__refl3, fact_39_infinite__descent0__measure, help_If_1_1_T, fact_172_negative__eq__positive, fact_191_zero__less__nat__eq, fact_69_comp__inj__on__iff, fact_42_gr__implies__not0, fact_207_linordered__field__no__lb, fact_177_verit__negate__coefficient_I2_J, fact_155_size__multiset__o__map, fact_162_neg__0__equal__iff__equal, fact_250_nat__0__iff, fact_248_inverse__le__iff__le__neg, fact_184_int__if, fact_81_comp__eq__dest, fact_91_bij__betw__iff__bijections, fact_199_zless__nat__eq__int__zless, fact_143_inj__on__of__nat, fact_77_mset__upt, tcon_Real_Oreal___Nat_Oring__char__0_42, tcon_Real_Oreal___Orderings_Opreorder_1, tcon_Int_Oint___Rings_Olinordered__idom, tcon_Int_Oint___Orderings_Olinorder, fact_142_image__int__atLeastLessThan, fact_116_Sup_OSUP__image, fact_221_positive__imp__inverse__positive, fact_5_assms_I1_J, tcon_Nat_Onat___Orderings_Owellorder, fact_140_of__nat__less__iff, fact_50_gr0I, fact_86_inj__on__eq__iff, fact_198_nat__mono__iff, fact_144_of__nat__fun, fact_195_nat__zero__as__int, fact_90_inj__onD, fact_10_size__neq__size__imp__neq, fact_132_map__eq__map__tailrec, fact_97_image__eq__imp__comp, fact_251_int__nat__eq, fact_208_linordered__field__no__ub, fact_193_zless__nat__conj, fact_13_less__nat__zero__code, tcon_Int_Oint___Groups_Ozero_16, fact_108_bij__betw__trans, fact_109_multiset_Omap__comp, tcon_Real_Oreal___Groups_Ozero_45, tcon_Multiset_Omultiset___Orderings_Oorder_46, fact_171_less__neg__neg, tcon_Real_Oreal___Groups_Ogroup__add_40, tcon_fun___Groups_Ogroup__add, fact_66_inj__on__imp__bij__betw, fact_118_less__numeral__extra_I3_J, tcon_Set_Oset___Orderings_Opreorder_3, tcon_Int_Oint___Orderings_Oorder_12, fact_230_lessThan__subset__iff, fact_1_calculation, tcon_Nat_Onat___Orderings_Olinorder_20, tcon_Int_Oint___Groups_Ogroup__add_11, fact_136_of__nat__eq__iff, tcon_Real_Oreal___Rings_Olinordered__idom_36, fact_238_of__int__eq__0__iff, fact_194_nat__zminus__int, tcon_Multiset_Omultiset___Orderings_Opreorder, fact_121_psubsetD, fact_25_less__not__refl2, fact_192_nat__int, help_If_3_1_T, help_If_2_1_T, tcon_Int_Oint___Orderings_Opreorder_5, fact_41_infinite__descent0, fact_67_comp__inj__on, tcon_HOL_Obool___Orderings_Oorder_30, tcon_fun___Lattices_Oboolean__algebra, tcon_fun___Groups_Ocanonically__ordered__monoid__add, fact_134_of__nat__0__less__iff, fact_153_int__int__eq, tcon_fun___Groups_Ozero, tcon_Int_Oint___Groups_Olinordered__ab__group__add, fact_156_nat__int__comparison_I2_J, fact_19_List_Omap_Ocompositionality, fact_32_measure__induct__rule, fact_107_bij__betw__comp__iff, fact_34_map__eq__imp__length__eq, fact_233_less__eq__neg__nonpos, fact_2_assms_I2_J, fact_87_inj__on__cong, fact_17_map__comp__map, tcon_HOL_Obool___Orderings_Opreorder_2, fact_209_field__class_Ofield__inverse__zero, fact_7__092_060open_062xs_A_061_Amap_A_I_I_B_J_Ays_A_092_060circ_062_Af_J_A_0910_O_O_060length_Axs_093_092_060close_062, fact_234_neg__less__eq__nonneg, fact_247_inverse__le__iff__le, tcon_Set_Oset___Orderings_Oorder_26, fact_216_inverse__less__imp__less__neg, fact_210_inverse__zero__imp__zero, fact_55_Skolem__list__nth, fact_101_atLeastLessThan__inj_I1_J, fact_231_neg__0__le__iff__le, fact_37_not__less__zero, fact_218_inverse__negative__imp__negative, fact_239_of__int__0__eq__iff, tcon_Real_Oreal___Fields_Olinordered__field, fact_160_neg__equal__iff__equal, fact_115_mbs_Oless__not__eq, fact_253_of__int__0__le__iff, fact_163_neg__equal__0__iff__equal, fact_63_lessThan__atLeast0, fact_73_image__mset__is__empty__iff, tcon_Real_Oreal___Groups_Oordered__ab__group__add_35, fact_103_lessThan__strict__subset__iff, tcon_Real_Oreal___Rings_Oring__1_44, fact_3__C2_C, fact_213_nonzero__imp__inverse__nonzero, fact_68_inj__on__imageI, tcon_Nat_Onat___Orderings_Oorder_22, fact_211_nonzero__inverse__eq__imp__eq, fact_64_bij__betw__def, fact_8_Ex__list__of__length, fact_53_ex__nat__less__eq, fact_111_image__mset_Ocomp, tcon_HOL_Obool___Lattices_Oboolean__algebra_28, fact_40_bot__nat__0_Oextremum__strict, fact_235_inverse__nonpositive__iff__nonpositive, fact_190_ex__inverse__of__nat__less, fact_45_Collect__cong, fact_214_inverse__less__imp__less, fact_161_add_Oinverse__neutral, fact_215_less__imp__inverse__less, fact_189_compl__less__compl__iff, fact_176_uminus__int__code_I1_J, fact_89_inj__onI, fact_21_nth__map, fact_152_size__multiset__eq__0__iff__empty, fact_225_of__int__eq__iff, tcon_fun___Rings_Oring__1, tcon_fun___Orderings_Oorder, fact_197_real__arch__inverse, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add_17, fact_94_bij__betw__inv, fact_181_int__cases4, tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_33, tcon_fun___Rings_Osemiring__1, fact_245_negative__zle, fact_4_zero__fun__apply, fact_180_not__int__zless__negative, fact_52_all__nat__less__eq, fact_28_less__irrefl__nat, tcon_Real_Oreal___Orderings_Oord_43, fact_127_ball__imageD, fact_175_less__minus__iff, fact_0__C1_C, fact_226_le__zero__eq, fact_88_inj__on__def, tcon_Multiset_Omultiset___Orderings_Oord_47, fact_48_not__less0, fact_130_Sup_OSUP__cong, tcon_Int_Oint___Orderings_Oord_14, tcon_Nat_Onat___Rings_Osemiring__1_21, fact_205_inverse__less__iff__less, tcon_fun___Groups_Oordered__ab__group__add, fact_30_infinite__descent, tcon_Int_Oint___Rings_Oring__1_15, tcon_fun___Rings_Odioid_6, fact_133_list__ex__length, fact_24_less__not__refl, fact_169_neg__0__less__iff__less, fact_166_neg__less__iff__less, tcon_Nat_Onat___Nat_Osemiring__char__0_19, fact_23_nat__neq__iff, fact_72_image__mset__empty, fact_56_nth__equalityI, tcon_Real_Oreal___Orderings_Oorder_41, tcon_Nat_Onat___Orderings_Opreorder_4, tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field, fact_65_bij__betw__imageI, fact_200_split__nat, fact_128_rev__image__eqI, fact_159_add_Oinverse__inverse, tcon_Set_Oset___Lattices_Oboolean__algebra_25, fact_185_int__cases3, tcon_HOL_Obool___Orderings_Oord_31, fact_125_bex__imageD, tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, fact_170_neg__less__pos, tcon_Real_Oreal___Fields_Ofield, fact_62_image__mset__mset__set, fact_113_mset__eq__length, fact_15_map__map, fact_131_Multiset_Ois__empty__def, tcon_Int_Oint___Rings_Osemiring__1_10, fact_12_bot__nat__0_Onot__eq__extremum, tcon_Real_Oreal___Fields_Odivision__ring, fact_240_of__int__0, fact_14_neq0__conv, tcon_Real_Oreal___Orderings_Olinorder_38, fact_187_compl__less__swap1, fact_149_zero__less__imp__eq__int
% 124.38/96.70 % No. of inferences in proof: 660
% 124.60/96.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 96369 ms resp. 95754 ms w/o parsing
% 125.35/96.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 125.35/96.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------