%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP094^1 : 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 : n018.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 08:06:44 AM UTC 2026
% Result : Theorem 69.26s 29.07s
% Output : Refutation 70.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 256
% Syntax : Number of formulae : 820 ( 448 unt; 0 typ; 8 def)
% Number of atoms : 2041 (1117 equ; 33 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 4794 ( 627 ~; 279 |; 186 &;3235 @)
% ( 0 <=>; 467 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 152 ( 152 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 19 con; 0-6 aty)
% Number of variables : 1331 ( 129 ^;1093 !; 101 ?;1331 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(poly_poly_poly_real_type,type,
poly_poly_poly_real: $tType ).
thf(set_poly_poly_real_type,type,
set_poly_poly_real: $tType ).
thf(poly_poly_real_type,type,
poly_poly_real: $tType ).
thf(poly_poly_nat_type,type,
poly_poly_nat: $tType ).
thf(set_poly_real_type,type,
set_poly_real: $tType ).
thf(poly_real_type,type,
poly_real: $tType ).
thf(poly_nat_type,type,
poly_nat: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(inverse_inverse_real_decl,type,
inverse_inverse_real: real > real ).
thf(finite_finite_nat_decl,type,
finite_finite_nat: set_nat > $o ).
thf(finite1810960971y_real_decl,type,
finite1810960971y_real: set_poly_real > $o ).
thf(finite_finite_real_decl,type,
finite_finite_real: set_real > $o ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(one_one_poly_real_decl,type,
one_one_poly_real: poly_real ).
thf(one_one_real_decl,type,
one_one_real: real ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(zero_z1423781445y_real_decl,type,
zero_z1423781445y_real: poly_poly_real ).
thf(zero_zero_poly_real_decl,type,
zero_zero_poly_real: poly_real ).
thf(zero_zero_real_decl,type,
zero_zero_real: real ).
thf(ring_1690226883y_real_decl,type,
ring_1690226883y_real: set_poly_real ).
thf(ring_1_Ints_real_decl,type,
ring_1_Ints_real: set_real ).
thf(suc_decl,type,
suc: nat > nat ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_poly_real_decl,type,
ord_less_poly_real: poly_real > poly_real > $o ).
thf(ord_less_real_decl,type,
ord_less_real: real > real > $o ).
thf(ord_less_eq_real_decl,type,
ord_less_eq_real: real > real > $o ).
thf(algebraic_real_decl,type,
algebraic_real: real > $o ).
thf(algebraic_int_real_decl,type,
algebraic_int_real: real > $o ).
thf(cr_poly_real_decl,type,
cr_poly_real: ( nat > real ) > poly_real > $o ).
thf(degree_real_decl,type,
degree_real: poly_real > nat ).
thf(divide1561404011n_real_decl,type,
divide1561404011n_real: real > poly_real > poly_real > poly_real > nat > nat > poly_real ).
thf(is_zero_real_decl,type,
is_zero_real: poly_real > $o ).
thf(order_poly_real_decl,type,
order_poly_real: poly_real > poly_poly_real > nat ).
thf(order_real_decl,type,
order_real: real > poly_real > nat ).
thf(pcr_poly_real_real_decl,type,
pcr_poly_real_real: ( real > real > $o ) > ( nat > real ) > poly_real > $o ).
thf(pderiv_real_decl,type,
pderiv_real: poly_real > poly_real ).
thf(poly_poly_real2_decl,type,
poly_poly_real2: poly_poly_real > poly_real > poly_real ).
thf(poly_real2_decl,type,
poly_real2: poly_real > real > real ).
thf(coeff_real_decl,type,
coeff_real: poly_real > nat > real ).
thf(poly_cutoff_real_decl,type,
poly_cutoff_real: nat > poly_real > poly_real ).
thf(poly_shift_real_decl,type,
poly_shift_real: nat > poly_real > poly_real ).
thf(reflect_poly_real_decl,type,
reflect_poly_real: poly_real > poly_real ).
thf(rsquar1555552848y_real_decl,type,
rsquar1555552848y_real: poly_poly_real > $o ).
thf(rsquarefree_real_decl,type,
rsquarefree_real: poly_real > $o ).
thf(synthetic_div_real_decl,type,
synthetic_div_real: poly_real > real > poly_real ).
thf(field_1537545994s_real_decl,type,
field_1537545994s_real: set_real ).
thf(dvd_dvd_nat_decl,type,
dvd_dvd_nat: nat > nat > $o ).
thf(dvd_dvd_poly_real_decl,type,
dvd_dvd_poly_real: poly_real > poly_real > $o ).
thf(dvd_dvd_real_decl,type,
dvd_dvd_real: real > real > $o ).
thf(collect_nat_decl,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(collect_poly_real_decl,type,
collect_poly_real: ( poly_real > $o ) > set_poly_real ).
thf(collect_real_decl,type,
collect_real: ( real > $o ) > set_real ).
thf(member_nat_decl,type,
member_nat: nat > set_nat > $o ).
thf(member_poly_real_decl,type,
member_poly_real: poly_real > set_poly_real > $o ).
thf(member_real_decl,type,
member_real: real > set_real > $o ).
thf(n_decl,type,
n: nat ).
thf(p_decl,type,
p: poly_real ).
thf(x_decl,type,
x: real ).
thf(sk12_decl,type,
sk12: real > real ).
thf(sk25_decl,type,
sk25: ( nat > $o ) > nat ).
thf(sk26_decl,type,
sk26: ( nat > $o ) > nat ).
thf(sk30_decl,type,
sk30: nat > nat ).
thf(sk47_decl,type,
sk47: ( nat > $o ) > nat ).
thf(sk73_decl,type,
sk73: poly_real ).
thf(sk77_decl,type,
sk77: set_real > real ).
thf(sk79_decl,type,
sk79: nat ).
thf(sk80_decl,type,
sk80: nat ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: real] :
@+[B: real] :
( ( member_real @ B @ field_1537545994s_real )
& ( ord_less_real @ B @ A ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: nat > $o] :
@+[B: nat] :
~ ( ( A @ B )
=> ( A @ ( suc @ B ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: nat > $o] :
@+[B: nat] :
~ ( ( A @ B )
=> ( A @ ( suc @ B ) ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( @+[A: nat > nat] :
! [B: nat] :
( ( A @ ( suc @ B ) )
= B ) ) ) ).
thf(sk47_def,definition,
( sk47
= ( ^ [A: nat > $o] :
@+[B: nat] :
~ ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ~ ( A @ B )
=> ? [C: nat] :
( ( ord_less_nat @ C @ B )
& ~ ( A @ C ) ) ) ) ) ) ).
thf(sk73_def,definition,
( sk73
= ( @+[A: poly_real] :
~ ( ! [B: nat] : ( member_real @ ( coeff_real @ A @ B ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( poly_real2 @ A @ x )
!= zero_zero_real ) ) ) ) ) ).
thf(sk79_def,definition,
( sk79
= ( @+[A: nat] :
( one_one_nat
= ( suc @ A ) ) ) ) ).
thf(sk80_def,definition,
( sk80
= ( @+[A: nat] :
( one_one_nat
= ( suc @ A ) ) ) ) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_less__Suc__eq) ).
thf(645,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(165,axiom,
( ( (=) @ poly_real )
= ( ^ [A: poly_real,B: poly_real] :
! [C: nat] :
( ( coeff_real @ A @ C )
= ( coeff_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_poly__eq__iff) ).
thf(808,plain,
( ( (=) @ poly_real )
= ( ^ [A: poly_real,B: poly_real] :
! [C: nat] :
( ( coeff_real @ A @ C )
= ( coeff_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(809,plain,
( ( (=) @ poly_real )
= ( ^ [A: poly_real,B: poly_real] :
! [C: nat] :
( ( coeff_real @ A @ C )
= ( coeff_real @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[808]) ).
thf(113,axiom,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Collect__mem__eq) ).
thf(627,plain,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(628,plain,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[627]) ).
thf(629,plain,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[628]) ).
thf(215,axiom,
! [A: poly_real] :
( ( ( coeff_real @ A @ ( degree_real @ A ) )
= zero_zero_real )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_leading__coeff__0__iff) ).
thf(1024,plain,
! [A: poly_real] :
( ( ( coeff_real @ A @ ( degree_real @ A ) )
= zero_zero_real )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(238,axiom,
( ( pderiv_real @ one_one_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_pderiv__1) ).
thf(1104,plain,
( ( pderiv_real @ one_one_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1105,plain,
( ( pderiv_real @ one_one_poly_real )
= zero_zero_poly_real ),
inference(lifteq,[status(thm)],[1104]) ).
thf(81,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_gr0__conv__Suc) ).
thf(524,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(525,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(cnf,[status(esa)],[524]) ).
thf(526,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(lifteq,[status(thm)],[525]) ).
thf(56,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_bot__nat__0_Onot__eq__extremum) ).
thf(426,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(427,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(cnf,[status(esa)],[426]) ).
thf(428,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(lifteq,[status(thm)],[427]) ).
thf(3434,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(rewrite,[status(thm)],[526,428]) ).
thf(241,axiom,
( ( pderiv_real @ p )
!= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062pderiv_Ap_A_092_060noteq_062_A0_092_060close_062) ).
thf(1110,plain,
( ( pderiv_real @ p )
!= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(33,axiom,
! [A: nat] :
~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
& ( zero_zero_nat != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_gcd__nat_Oextremum__strict) ).
thf(352,plain,
! [A: nat] :
~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
& ( zero_zero_nat != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(37,axiom,
! [A: poly_poly_real] :
( ( zero_z1423781445y_real = A )
= ( A = zero_z1423781445y_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zero__reorient) ).
thf(363,plain,
! [A: poly_poly_real] :
( ( zero_z1423781445y_real = A )
= ( A = zero_z1423781445y_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(364,plain,
! [A: poly_poly_real] :
( ( zero_z1423781445y_real = A )
= ( A = zero_z1423781445y_real ) ),
inference(cnf,[status(esa)],[363]) ).
thf(365,plain,
! [A: poly_poly_real] :
( ( zero_z1423781445y_real = A )
= ( A = zero_z1423781445y_real ) ),
inference(lifteq,[status(thm)],[364]) ).
thf(121,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_old_Onat_Oinducts) ).
thf(653,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(654,plain,
! [A: nat > $o] :
( ( A @ zero_zero_nat )
=> ( ! [B: nat] :
( ( A @ B )
=> ( A @ ( suc @ B ) ) )
=> ! [B: nat] : ( A @ B ) ) ),
inference(miniscope,[status(thm)],[653]) ).
thf(655,plain,
! [B: nat,A: nat > $o] :
( ( ~ ( A @ zero_zero_nat )
| ( A @ ( sk25 @ A ) )
| ( A @ B ) )
& ( ~ ( A @ zero_zero_nat )
| ~ ( A @ ( suc @ ( sk25 @ A ) ) )
| ( A @ B ) ) ),
inference(cnf,[status(esa)],[654]) ).
thf(656,plain,
! [B: nat,A: nat > $o] :
( ~ ( A @ zero_zero_nat )
| ( A @ ( sk25 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[655]) ).
thf(658,plain,
! [A: nat] :
( ( zero_zero_nat != zero_zero_nat )
| ( zero_zero_nat
= ( sk25 @ ( (=) @ nat @ zero_zero_nat ) ) )
| ( zero_zero_nat = A ) ),
inference(replace_leibeq,[status(thm)],[656:[bind(A,$thf( (=) @ nat @ zero_zero_nat ))]]) ).
thf(660,plain,
! [A: nat] :
( ( zero_zero_nat != zero_zero_nat )
| ( ( sk25 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat )
| ( zero_zero_nat = A ) ),
inference(lifteq,[status(thm)],[658]) ).
thf(661,plain,
! [A: nat] :
( ( ( sk25 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat )
| ( zero_zero_nat = A ) ),
inference(simp,[status(thm)],[660]) ).
thf(55,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Zero__neq__Suc) ).
thf(422,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(423,plain,
~ ? [A: nat] :
( zero_zero_nat
= ( suc @ A ) ),
inference(miniscope,[status(thm)],[422]) ).
thf(424,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(cnf,[status(esa)],[423]) ).
thf(425,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(lifteq,[status(thm)],[424]) ).
thf(1821,plain,
! [B: nat,A: nat] :
( ( ( sk25 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat )
| ( zero_zero_nat != zero_zero_nat )
| ( A
!= ( suc @ B ) ) ),
inference(paramod_ordered,[status(thm)],[661,425]) ).
thf(1822,plain,
! [B: nat,A: nat] :
( ( ( sk25 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat )
| ( A
!= ( suc @ B ) ) ),
inference(simp,[status(thm)],[1821]) ).
thf(1823,plain,
( ( sk25 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat ),
inference(pattern_uni,[status(thm)],[1822:[bind(A,$thf( suc @ C )),bind(B,$thf( C ))]]) ).
thf(104,axiom,
member_real @ one_one_real @ ring_1_Ints_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Ints__1) ).
thf(592,plain,
member_real @ one_one_real @ ring_1_Ints_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(236,axiom,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Collect__mem__eq) ).
thf(1098,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1099,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[1098]) ).
thf(1100,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[1099]) ).
thf(1,conjecture,
( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ A )
= zero_zero_real ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(250,plain,
~ ( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(2434,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
!= ( collect_real
@ ^ [B: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ B )
= zero_zero_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[1100,250]) ).
thf(2439,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( ( ^ [B: real] : ( member_real @ B @ A ) )
!= ( ^ [B: real] :
( ( poly_real2 @ ( pderiv_real @ p ) @ B )
= zero_zero_real ) ) ) ),
inference(simp,[status(thm)],[2434]) ).
thf(2448,plain,
! [A: set_real] :
( ( ( member_real @ ( sk77 @ A ) @ A )
!= ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
= zero_zero_real ) )
| ~ ( finite_finite_real @ A ) ),
inference(func_ext,[status(esa)],[2439]) ).
thf(2449,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ~ ( member_real @ ( sk77 @ A ) @ A )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= zero_zero_real ) ),
inference(bool_ext,[status(thm)],[2448]) ).
thf(2462,plain,
! [A: set_real] :
( ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= zero_zero_real )
| ~ ( finite_finite_real @ A )
| ~ ( member_real @ ( sk77 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[2449]) ).
thf(4166,plain,
! [A: set_real] :
( ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= zero_zero_real )
| ~ ( finite_finite_real @ A )
| ~ $true
| ( ( member_real @ ( sk77 @ A ) @ A )
!= ( member_real @ one_one_real @ ring_1_Ints_real ) ) ),
inference(paramod_ordered,[status(thm)],[592,2462]) ).
thf(4167,plain,
! [A: set_real] :
( ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= zero_zero_real )
| ~ ( finite_finite_real @ A )
| ( ( member_real @ ( sk77 @ A ) @ A )
!= ( member_real @ one_one_real @ ring_1_Ints_real ) ) ),
inference(simp,[status(thm)],[4166]) ).
thf(4170,plain,
! [A: set_real] :
( ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= zero_zero_real )
| ~ ( finite_finite_real @ A )
| ( ( sk77 @ A )
!= one_one_real )
| ( A != ring_1_Ints_real ) ),
inference(simp,[status(thm)],[4167]) ).
thf(4183,plain,
( ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ ring_1_Ints_real ) )
!= zero_zero_real )
| ~ ( finite_finite_real @ ring_1_Ints_real )
| ( ( sk77 @ ring_1_Ints_real )
!= one_one_real ) ),
inference(simp,[status(thm)],[4170]) ).
thf(218,axiom,
! [A: poly_real,B: real] :
( ( ( poly_real2 @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_poly_real )
| ( ( order_real @ B @ A )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_order__root) ).
thf(1031,plain,
! [A: poly_real,B: real] :
( ( ( poly_real2 @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_poly_real )
| ( ( order_real @ B @ A )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(228,axiom,
! [A: nat] :
( ( coeff_real @ zero_zero_poly_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_coeff__0) ).
thf(1066,plain,
! [A: nat] :
( ( coeff_real @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1067,plain,
! [A: nat] :
( ( coeff_real @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(cnf,[status(esa)],[1066]) ).
thf(1068,plain,
! [A: nat] :
( ( coeff_real @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(lifteq,[status(thm)],[1067]) ).
thf(177,axiom,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_real @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_lift__Suc__mono__less__iff) ).
thf(873,plain,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_real @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(41,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( poly_shift_real @ A @ one_one_poly_real )
= one_one_poly_real ) )
& ( ( A != zero_zero_nat )
=> ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_poly__shift__1) ).
thf(373,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( poly_shift_real @ A @ one_one_poly_real )
= one_one_poly_real ) )
& ( ( A != zero_zero_nat )
=> ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(374,plain,
( ! [A: nat] :
( ( A = zero_zero_nat )
=> ( ( poly_shift_real @ A @ one_one_poly_real )
= one_one_poly_real ) )
& ! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) ) ),
inference(miniscope,[status(thm)],[373]) ).
thf(375,plain,
! [B: nat,A: nat] :
( ( ( A != zero_zero_nat )
| ( ( poly_shift_real @ A @ one_one_poly_real )
= one_one_poly_real ) )
& ( ( B = zero_zero_nat )
| ( ( poly_shift_real @ B @ one_one_poly_real )
= zero_zero_poly_real ) ) ),
inference(cnf,[status(esa)],[374]) ).
thf(376,plain,
! [A: nat] :
( ( A != zero_zero_nat )
| ( ( poly_shift_real @ A @ one_one_poly_real )
= one_one_poly_real ) ),
inference(cnfConj,[status(thm)],[375]) ).
thf(378,plain,
! [A: nat] :
( ( A != zero_zero_nat )
| ( ( poly_shift_real @ A @ one_one_poly_real )
= one_one_poly_real ) ),
inference(lifteq,[status(thm)],[376]) ).
thf(379,plain,
( ( poly_shift_real @ zero_zero_nat @ one_one_poly_real )
= one_one_poly_real ),
inference(simp,[status(thm)],[378]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_less__SucI) ).
thf(440,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(80,axiom,
! [A: nat > $o,B: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_finite__M__bounded__by__nat) ).
thf(522,plain,
! [A: nat > $o,B: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(523,plain,
! [B: nat,A: nat > $o] :
( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( ord_less_nat @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[522]) ).
thf(150,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_less__trans__Suc) ).
thf(762,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(141,axiom,
ord_less_nat @ zero_zero_nat @ one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_zero__less__one) ).
thf(730,plain,
ord_less_nat @ zero_zero_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(13,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_zero__neq__one) ).
thf(276,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(110,axiom,
! [A: set_nat,B: set_poly_real,C: nat > poly_real > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite1810960971y_real @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: poly_real] :
( ( member_poly_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: poly_real] :
( ( member_poly_real @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_pigeonhole__infinite__rel) ).
thf(614,plain,
! [A: set_nat,B: set_poly_real,C: nat > poly_real > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite1810960971y_real @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: poly_real] :
( ( member_poly_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: poly_real] :
( ( member_poly_real @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_less__SucE) ).
thf(677,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(44,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_less__nat__zero__code) ).
thf(385,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(43,axiom,
( rsquarefree_real
= ( ^ [A: poly_real] :
( ( A != zero_zero_poly_real )
& ! [B: real] :
( ( ( order_real @ B @ A )
= zero_zero_nat )
| ( ( order_real @ B @ A )
= one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_rsquarefree__def) ).
thf(383,plain,
( rsquarefree_real
= ( ^ [A: poly_real] :
( ( A != zero_zero_poly_real )
& ! [B: real] :
( ( ( order_real @ B @ A )
= zero_zero_nat )
| ( ( order_real @ B @ A )
= one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(384,plain,
( ( ^ [A: poly_real] :
( ( A != zero_zero_poly_real )
& ! [B: real] :
( ( ( order_real @ B @ A )
= zero_zero_nat )
| ( ( order_real @ B @ A )
= one_one_nat ) ) ) )
= rsquarefree_real ),
inference(lifteq,[status(thm)],[383]) ).
thf(249,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_zero__neq__one) ).
thf(1135,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(1136,plain,
zero_zero_real != one_one_real,
inference(polarity_switch,[status(thm)],[1135]) ).
thf(1137,plain,
zero_zero_real != one_one_real,
inference(lifteq,[status(thm)],[1136]) ).
thf(84,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_One__nat__def) ).
thf(532,plain,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(533,plain,
( ( suc @ zero_zero_nat )
= one_one_nat ),
inference(lifteq,[status(thm)],[532]) ).
thf(161,axiom,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_finite__Collect__less__nat) ).
thf(796,plain,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(797,plain,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_nat @ B @ A ) ) ),
inference(cnf,[status(esa)],[796]) ).
thf(147,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_less__Suc0) ).
thf(747,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(88,axiom,
! [A: real] :
? [B: real] :
( ( member_real @ B @ field_1537545994s_real )
& ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_Rats__no__bot__less) ).
thf(541,plain,
! [A: real] :
? [B: real] :
( ( member_real @ B @ field_1537545994s_real )
& ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(542,plain,
! [A: real] :
( ( member_real @ ( sk12 @ A ) @ field_1537545994s_real )
& ( ord_less_real @ ( sk12 @ A ) @ A ) ),
inference(cnf,[status(esa)],[541]) ).
thf(544,plain,
! [A: real] : ( ord_less_real @ ( sk12 @ A ) @ A ),
inference(cnfConj,[status(thm)],[542]) ).
thf(211,axiom,
~ ( ord_less_real @ one_one_real @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_not__one__less__zero) ).
thf(1014,plain,
~ ( ord_less_real @ one_one_real @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1015,plain,
~ ( ord_less_real @ one_one_real @ zero_zero_real ),
inference(polarity_switch,[status(thm)],[1014]) ).
thf(2039,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ ( sk12 @ A ) @ A )
!= ( ord_less_real @ one_one_real @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[544,1015]) ).
thf(2040,plain,
! [A: real] :
( ( ord_less_real @ ( sk12 @ A ) @ A )
!= ( ord_less_real @ one_one_real @ zero_zero_real ) ),
inference(simp,[status(thm)],[2039]) ).
thf(2041,plain,
! [A: real] :
( ( ( sk12 @ A )
!= one_one_real )
| ( A != zero_zero_real ) ),
inference(simp,[status(thm)],[2040]) ).
thf(2042,plain,
( ( sk12 @ zero_zero_real )
!= one_one_real ),
inference(simp,[status(thm)],[2041]) ).
thf(87,axiom,
! [A: real] :
( ( synthetic_div_real @ zero_zero_poly_real @ A )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_synthetic__div__0) ).
thf(538,plain,
! [A: real] :
( ( synthetic_div_real @ zero_zero_poly_real @ A )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(53,axiom,
( cr_poly_real
= ( ^ [A: nat > real,B: poly_real] :
( A
= ( coeff_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_cr__poly__def) ).
thf(417,plain,
( cr_poly_real
= ( ^ [A: nat > real,B: poly_real] :
( A
= ( coeff_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(122,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_nat__induct) ).
thf(664,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(665,plain,
! [A: nat > $o] :
( ( A @ zero_zero_nat )
=> ( ! [B: nat] :
( ( A @ B )
=> ( A @ ( suc @ B ) ) )
=> ! [B: nat] : ( A @ B ) ) ),
inference(miniscope,[status(thm)],[664]) ).
thf(666,plain,
! [B: nat,A: nat > $o] :
( ( ~ ( A @ zero_zero_nat )
| ( A @ ( sk26 @ A ) )
| ( A @ B ) )
& ( ~ ( A @ zero_zero_nat )
| ~ ( A @ ( suc @ ( sk26 @ A ) ) )
| ( A @ B ) ) ),
inference(cnf,[status(esa)],[665]) ).
thf(667,plain,
! [B: nat,A: nat > $o] :
( ~ ( A @ zero_zero_nat )
| ( A @ ( sk26 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[666]) ).
thf(669,plain,
! [A: nat] :
( ( zero_zero_nat != zero_zero_nat )
| ( zero_zero_nat
= ( sk26 @ ( (=) @ nat @ zero_zero_nat ) ) )
| ( zero_zero_nat = A ) ),
inference(replace_leibeq,[status(thm)],[667:[bind(A,$thf( (=) @ nat @ zero_zero_nat ))]]) ).
thf(671,plain,
! [A: nat] :
( ( zero_zero_nat != zero_zero_nat )
| ( ( sk26 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat )
| ( zero_zero_nat = A ) ),
inference(lifteq,[status(thm)],[669]) ).
thf(672,plain,
! [A: nat] :
( ( ( sk26 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat )
| ( zero_zero_nat = A ) ),
inference(simp,[status(thm)],[671]) ).
thf(2080,plain,
! [B: nat,A: nat] :
( ( ( sk26 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat )
| ( zero_zero_nat != zero_zero_nat )
| ( A
!= ( suc @ B ) ) ),
inference(paramod_ordered,[status(thm)],[672,425]) ).
thf(2081,plain,
! [B: nat,A: nat] :
( ( ( sk26 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat )
| ( A
!= ( suc @ B ) ) ),
inference(simp,[status(thm)],[2080]) ).
thf(2082,plain,
( ( sk26 @ ( (=) @ nat @ zero_zero_nat ) )
= zero_zero_nat ),
inference(pattern_uni,[status(thm)],[2081:[bind(A,$thf( suc @ C )),bind(B,$thf( C ))]]) ).
thf(2393,plain,
! [B: nat,A: set_nat] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] : ( member_nat @ C @ A ) ) )
| ( A
!= ( collect_nat
@ ^ [C: nat] : ( ord_less_nat @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[629,797]) ).
thf(2394,plain,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] :
( member_nat @ B
@ ( collect_nat
@ ^ [C: nat] : ( ord_less_nat @ C @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2393:[bind(A,$thf( collect_nat @ ^ [C: nat] : ( ord_less_nat @ C @ B ) )),bind(B,$thf( B ))]]) ).
thf(2396,plain,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] :
( member_nat @ B
@ ( collect_nat
@ ^ [C: nat] : ( ord_less_nat @ C @ A ) ) ) ) ),
inference(simp,[status(thm)],[2394]) ).
thf(2400,plain,
! [B: nat,A: set_nat] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] : ( member_nat @ C @ A ) ) )
| ( A
!= ( collect_nat
@ ^ [C: nat] :
( member_nat @ C
@ ( collect_nat
@ ^ [D: nat] : ( ord_less_nat @ D @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[629,2396]) ).
thf(2401,plain,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] :
( member_nat @ B
@ ( collect_nat
@ ^ [C: nat] :
( member_nat @ C
@ ( collect_nat
@ ^ [D: nat] : ( ord_less_nat @ D @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2400:[bind(A,$thf( collect_nat @ ^ [C: nat] : ( member_nat @ C @ ( collect_nat @ ^ [D: nat] : ( ord_less_nat @ D @ B ) ) ) )),bind(B,$thf( B ))]]) ).
thf(2405,plain,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] :
( member_nat @ B
@ ( collect_nat
@ ^ [C: nat] :
( member_nat @ C
@ ( collect_nat
@ ^ [D: nat] : ( ord_less_nat @ D @ A ) ) ) ) ) ) ),
inference(simp,[status(thm)],[2401]) ).
thf(5,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_one__reorient) ).
thf(255,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(256,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(cnf,[status(esa)],[255]) ).
thf(257,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(lifteq,[status(thm)],[256]) ).
thf(234,axiom,
~ ! [A: poly_real] :
( ! [B: nat] : ( member_real @ ( coeff_real @ A @ B ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( poly_real2 @ A @ x )
!= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062) ).
thf(1088,plain,
~ ! [A: poly_real] :
( ! [B: nat] : ( member_real @ ( coeff_real @ A @ B ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( poly_real2 @ A @ x )
!= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1089,plain,
~ ! [A: poly_real] :
( ! [B: nat] : ( member_real @ ( coeff_real @ A @ B ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( poly_real2 @ A @ x )
!= zero_zero_real ) ) ),
inference(polarity_switch,[status(thm)],[1088]) ).
thf(1090,plain,
! [A: nat] :
( ( member_real @ ( coeff_real @ sk73 @ A ) @ ring_1_Ints_real )
& ( sk73 != zero_zero_poly_real )
& ( ( poly_real2 @ sk73 @ x )
= zero_zero_real ) ),
inference(cnf,[status(esa)],[1089]) ).
thf(1093,plain,
( ( poly_real2 @ sk73 @ x )
= zero_zero_real ),
inference(cnfConj,[status(thm)],[1090]) ).
thf(1095,plain,
( ( poly_real2 @ sk73 @ x )
= zero_zero_real ),
inference(lifteq,[status(thm)],[1093]) ).
thf(51,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_zero__induct) ).
thf(404,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_gcd__nat_Ostrict__implies__not__eq) ).
thf(320,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(96,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_diff__induct) ).
thf(565,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ one_one_nat )
=> ( dvd_dvd_nat @ A @ one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_dvd__unit__imp__unit) ).
thf(307,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ one_one_nat )
=> ( dvd_dvd_nat @ A @ one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(308,plain,
! [B: nat,A: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ~ ( dvd_dvd_nat @ B @ one_one_nat )
| ( dvd_dvd_nat @ A @ one_one_nat ) ),
inference(cnf,[status(esa)],[307]) ).
thf(14,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_nat__dvd__1__iff__1) ).
thf(279,plain,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(280,plain,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
inference(cnf,[status(esa)],[279]) ).
thf(281,plain,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
= ( A = one_one_nat ) ),
inference(lifteq,[status(thm)],[280]) ).
thf(2149,plain,
! [B: nat,A: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ( B != one_one_nat )
| ( A = one_one_nat ) ),
inference(rewrite,[status(thm)],[308,281]) ).
thf(2150,plain,
! [B: nat,A: nat] :
( ( B != one_one_nat )
| ( A = one_one_nat )
| ~ ( dvd_dvd_nat @ A @ B ) ),
inference(lifteq,[status(thm)],[2149]) ).
thf(139,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_zero__reorient) ).
thf(722,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(723,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(cnf,[status(esa)],[722]) ).
thf(724,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(lifteq,[status(thm)],[723]) ).
thf(3443,plain,
! [B: nat,A: nat] :
( ( ( A != one_one_nat )
= ( ? [C: nat] :
( B
= ( suc @ C ) ) ) )
| ( ( one_one_nat = A )
!= ( B = zero_zero_nat ) ) ),
inference(paramod_ordered,[status(thm)],[257,3434]) ).
thf(3444,plain,
( ( zero_zero_nat != one_one_nat )
= ( ? [A: nat] :
( one_one_nat
= ( suc @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[3443:[bind(A,$thf( zero_zero_nat )),bind(B,$thf( one_one_nat ))]]) ).
thf(3482,plain,
! [A: nat] :
( ( ( A != zero_zero_nat )
= ( ? [B: nat] :
( one_one_nat
= ( suc @ B ) ) ) )
| ( ( zero_zero_nat = A )
!= ( zero_zero_nat = one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[724,3444]) ).
thf(3483,plain,
( ( one_one_nat != zero_zero_nat )
= ( ? [A: nat] :
( one_one_nat
= ( suc @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[3482:[bind(A,$thf( one_one_nat ))]]) ).
thf(3551,plain,
( ~ ( ( one_one_nat != zero_zero_nat ) )
| ? [A: nat] :
( one_one_nat
= ( suc @ A ) ) ),
inference(bool_ext,[status(thm)],[3483]) ).
thf(3629,plain,
( ( one_one_nat = zero_zero_nat )
| ( one_one_nat
= ( suc @ sk80 ) ) ),
inference(cnf,[status(esa)],[3551]) ).
thf(3630,plain,
( ( zero_zero_nat = one_one_nat )
| ( ( suc @ sk80 )
= one_one_nat ) ),
inference(lifteq,[status(thm)],[3629]) ).
thf(277,plain,
zero_zero_nat != one_one_nat,
inference(polarity_switch,[status(thm)],[276]) ).
thf(278,plain,
zero_zero_nat != one_one_nat,
inference(lifteq,[status(thm)],[277]) ).
thf(3762,plain,
( ( suc @ sk80 )
= one_one_nat ),
inference(simplifyReflect,[status(thm)],[3630,278]) ).
thf(93,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_n__not__Suc__n) ).
thf(557,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(558,plain,
~ ? [A: nat] :
( A
= ( suc @ A ) ),
inference(miniscope,[status(thm)],[557]) ).
thf(559,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(cnf,[status(esa)],[558]) ).
thf(560,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(lifteq,[status(thm)],[559]) ).
thf(3788,plain,
! [A: nat] :
( ( one_one_nat != A )
| ( ( suc @ sk80 )
!= ( suc @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3762,560]) ).
thf(3789,plain,
sk80 != one_one_nat,
inference(pattern_uni,[status(thm)],[3788:[bind(A,$thf( sk80 ))]]) ).
thf(3796,plain,
! [B: nat,A: nat] :
( ( B != one_one_nat )
| ~ ( dvd_dvd_nat @ A @ B )
| ( one_one_nat != one_one_nat )
| ( A != sk80 ) ),
inference(paramod_ordered,[status(thm)],[2150,3789]) ).
thf(3797,plain,
! [B: nat,A: nat] :
( ( B != one_one_nat )
| ~ ( dvd_dvd_nat @ A @ B )
| ( A != sk80 ) ),
inference(simp,[status(thm)],[3796]) ).
thf(3798,plain,
! [A: nat] :
( ( A != one_one_nat )
| ~ ( dvd_dvd_nat @ sk80 @ A ) ),
inference(pattern_uni,[status(thm)],[3797:[bind(A,$thf( sk80 ))]]) ).
thf(3803,plain,
~ ( dvd_dvd_nat @ sk80 @ one_one_nat ),
inference(simp,[status(thm)],[3798]) ).
thf(3819,plain,
sk80 != one_one_nat,
inference(rewrite,[status(thm)],[3803,281]) ).
thf(3820,plain,
sk80 != one_one_nat,
inference(lifteq,[status(thm)],[3819]) ).
thf(97,axiom,
! [A: real,B: real] :
( ( A != B )
=> ( ~ ( ord_less_real @ A @ B )
=> ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_linorder__neqE__linordered__idom) ).
thf(570,plain,
! [A: real,B: real] :
( ( A != B )
=> ( ~ ( ord_less_real @ A @ B )
=> ( ord_less_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(138,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_not__gr__zero) ).
thf(719,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
= ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_gcd__nat_Ostrict__iff__order) ).
thf(372,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_Suc__lessD) ).
thf(587,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(187,axiom,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_poly__0) ).
thf(917,plain,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(190,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zero__reorient) ).
thf(934,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(225,axiom,
! [A: set_real,B: set_poly_real,C: real > poly_real > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite1810960971y_real @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: poly_real] :
( ( member_poly_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: poly_real] :
( ( member_poly_real @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_pigeonhole__infinite__rel) ).
thf(1055,plain,
! [A: set_real,B: set_poly_real,C: real > poly_real > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite1810960971y_real @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: poly_real] :
( ( member_poly_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: poly_real] :
( ( member_poly_real @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(163,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_dvd__pos__nat) ).
thf(802,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( ( dvd_dvd_nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_gcd__nat_Ostrict__trans1) ).
thf(344,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( ( dvd_dvd_nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(246,axiom,
member_real @ zero_zero_real @ field_1537545994s_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Rats__0) ).
thf(1130,plain,
member_real @ zero_zero_real @ field_1537545994s_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(48,axiom,
~ ( member_real @ x @ field_1537545994s_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_irrationsl) ).
thf(397,plain,
~ ( member_real @ x @ field_1537545994s_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(398,plain,
~ ( member_real @ x @ field_1537545994s_real ),
inference(polarity_switch,[status(thm)],[397]) ).
thf(1244,plain,
( ~ $true
| ( ( member_real @ x @ field_1537545994s_real )
!= ( member_real @ zero_zero_real @ field_1537545994s_real ) ) ),
inference(paramod_ordered,[status(thm)],[1130,398]) ).
thf(1245,plain,
( ( member_real @ x @ field_1537545994s_real )
!= ( member_real @ zero_zero_real @ field_1537545994s_real ) ),
inference(simp,[status(thm)],[1244]) ).
thf(1246,plain,
( ( x != zero_zero_real )
| ( field_1537545994s_real != field_1537545994s_real ) ),
inference(simp,[status(thm)],[1245]) ).
thf(1247,plain,
x != zero_zero_real,
inference(simp,[status(thm)],[1246]) ).
thf(153,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_lessI) ).
thf(770,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(202,axiom,
! [A: real] :
( ( poly_real2 @ one_one_poly_real @ A )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_poly__1) ).
thf(983,plain,
! [A: real] :
( ( poly_real2 @ one_one_poly_real @ A )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(984,plain,
! [A: real] :
( ( poly_real2 @ one_one_poly_real @ A )
= one_one_real ),
inference(cnf,[status(esa)],[983]) ).
thf(985,plain,
! [A: real] :
( ( poly_real2 @ one_one_poly_real @ A )
= one_one_real ),
inference(lifteq,[status(thm)],[984]) ).
thf(1528,plain,
! [A: real] :
( ( zero_zero_real = one_one_real )
| ( ( poly_real2 @ one_one_poly_real @ A )
!= ( poly_real2 @ sk73 @ x ) ) ),
inference(paramod_ordered,[status(thm)],[985,1095]) ).
thf(1537,plain,
! [A: real] :
( ( zero_zero_real = one_one_real )
| ( sk73 != one_one_poly_real )
| ( A != x ) ),
inference(simp,[status(thm)],[1528]) ).
thf(1541,plain,
( ( zero_zero_real = one_one_real )
| ( sk73 != one_one_poly_real ) ),
inference(simp,[status(thm)],[1537]) ).
thf(1568,plain,
sk73 != one_one_poly_real,
inference(simplifyReflect,[status(thm)],[1541,1137]) ).
thf(16,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_gcd__nat_Ostrict__trans2) ).
thf(289,plain,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(64,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ one_one_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( B @ C )
=> ( B @ ( suc @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_nat__induct__non__zero) ).
thf(448,plain,
! [A: nat,B: nat > $o] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( B @ one_one_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ( B @ C )
=> ( B @ ( suc @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(54,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_less__one) ).
thf(419,plain,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(420,plain,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
inference(cnf,[status(esa)],[419]) ).
thf(421,plain,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
inference(lifteq,[status(thm)],[420]) ).
thf(176,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_All__less__Suc2) ).
thf(870,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(7,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_dvd__refl) ).
thf(261,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1111,plain,
( ( pderiv_real @ p )
!= zero_zero_poly_real ),
inference(polarity_switch,[status(thm)],[1110]) ).
thf(1112,plain,
( ( pderiv_real @ p )
!= zero_zero_poly_real ),
inference(lifteq,[status(thm)],[1111]) ).
thf(1229,plain,
( ( zero_zero_poly_real != zero_zero_poly_real )
| ( ( pderiv_real @ p )
!= ( pderiv_real @ one_one_poly_real ) ) ),
inference(paramod_ordered,[status(thm)],[1105,1112]) ).
thf(1230,plain,
( ( pderiv_real @ p )
!= ( pderiv_real @ one_one_poly_real ) ),
inference(simp,[status(thm)],[1229]) ).
thf(1232,plain,
p != one_one_poly_real,
inference(simp,[status(thm)],[1230]) ).
thf(217,axiom,
! [A: poly_real] :
( ( poly_real2 @ A @ zero_zero_real )
= ( coeff_real @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_poly__0__coeff__0) ).
thf(1028,plain,
! [A: poly_real] :
( ( poly_real2 @ A @ zero_zero_real )
= ( coeff_real @ A @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1029,plain,
! [A: poly_real] :
( ( poly_real2 @ A @ zero_zero_real )
= ( coeff_real @ A @ zero_zero_nat ) ),
inference(cnf,[status(esa)],[1028]) ).
thf(1030,plain,
! [A: poly_real] :
( ( coeff_real @ A @ zero_zero_nat )
= ( poly_real2 @ A @ zero_zero_real ) ),
inference(lifteq,[status(thm)],[1029]) ).
thf(239,axiom,
! [A: nat] : ( member_real @ ( coeff_real @ p @ A ) @ ring_1_Ints_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_p_I1_J) ).
thf(1106,plain,
! [A: nat] : ( member_real @ ( coeff_real @ p @ A ) @ ring_1_Ints_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1107,plain,
! [A: nat] : ( member_real @ ( coeff_real @ p @ A ) @ ring_1_Ints_real ),
inference(cnf,[status(esa)],[1106]) ).
thf(1765,plain,
! [A: nat] :
( ~ $true
| ( ( member_real @ ( coeff_real @ p @ A ) @ ring_1_Ints_real )
!= ( member_real @ x @ field_1537545994s_real ) ) ),
inference(paramod_ordered,[status(thm)],[1107,398]) ).
thf(1766,plain,
! [A: nat] :
( ( member_real @ ( coeff_real @ p @ A ) @ ring_1_Ints_real )
!= ( member_real @ x @ field_1537545994s_real ) ),
inference(simp,[status(thm)],[1765]) ).
thf(1769,plain,
! [A: nat] :
( ( ( coeff_real @ p @ A )
!= x )
| ( field_1537545994s_real != ring_1_Ints_real ) ),
inference(simp,[status(thm)],[1766]) ).
thf(3267,plain,
! [B: nat,A: poly_real] :
( ( ( poly_real2 @ A @ zero_zero_real )
!= x )
| ( field_1537545994s_real != ring_1_Ints_real )
| ( ( coeff_real @ A @ zero_zero_nat )
!= ( coeff_real @ p @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1030,1769]) ).
thf(3268,plain,
( ( ( poly_real2 @ p @ zero_zero_real )
!= x )
| ( field_1537545994s_real != ring_1_Ints_real ) ),
inference(pattern_uni,[status(thm)],[3267:[bind(A,$thf( p )),bind(B,$thf( zero_zero_nat ))]]) ).
thf(158,axiom,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( algebraic_int_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_int__imp__algebraic__int) ).
thf(789,plain,
! [A: real] :
( ( member_real @ A @ ring_1_Ints_real )
=> ( algebraic_int_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(103,axiom,
zero_zero_poly_real != one_one_poly_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_zero__neq__one) ).
thf(589,plain,
zero_zero_poly_real != one_one_poly_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(590,plain,
zero_zero_poly_real != one_one_poly_real,
inference(polarity_switch,[status(thm)],[589]) ).
thf(591,plain,
zero_zero_poly_real != one_one_poly_real,
inference(lifteq,[status(thm)],[590]) ).
thf(221,axiom,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ A ) )
=> ( ( ord_less_real @ ( poly_real2 @ C @ B ) @ zero_zero_real )
=> ? [D: real] :
( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B )
& ( ( poly_real2 @ C @ D )
= zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_poly__IVT__neg) ).
thf(1040,plain,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ A ) )
=> ( ( ord_less_real @ ( poly_real2 @ C @ B ) @ zero_zero_real )
=> ? [D: real] :
( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B )
& ( ( poly_real2 @ C @ D )
= zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(191,axiom,
! [A: set_real,B: set_nat,C: real > nat > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_pigeonhole__infinite__rel) ).
thf(937,plain,
! [A: set_real,B: set_nat,C: real > nat > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(198,axiom,
( pcr_poly_real_real @ ( (=) @ real )
@ ^ [A: nat] : zero_zero_real
@ zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_zero__poly_Otransfer) ).
thf(966,plain,
( pcr_poly_real_real @ ( (=) @ real )
@ ^ [A: nat] : zero_zero_real
@ zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(183,axiom,
! [A: poly_real,B: real] :
( ( ( poly_real2 @ A @ B )
!= zero_zero_real )
=> ( ( order_real @ B @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_order__0I) ).
thf(905,plain,
! [A: poly_real,B: real] :
( ( ( poly_real2 @ A @ B )
!= zero_zero_real )
=> ( ( order_real @ B @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_less__antisym) ).
thf(602,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(377,plain,
! [A: nat] :
( ( A = zero_zero_nat )
| ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) ),
inference(cnfConj,[status(thm)],[375]) ).
thf(380,plain,
! [A: nat] :
( ( A = zero_zero_nat )
| ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) ),
inference(lifteq,[status(thm)],[377]) ).
thf(381,plain,
! [A: nat] :
( ( A = zero_zero_nat )
| ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) ),
inference(simp,[status(thm)],[380]) ).
thf(181,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_267_infinite__descent0) ).
thf(886,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)],[181]) ).
thf(887,plain,
! [A: nat > $o] :
( ( A @ zero_zero_nat )
=> ( ! [B: nat] :
( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ~ ( A @ B )
=> ? [C: nat] :
( ( ord_less_nat @ C @ B )
& ~ ( A @ C ) ) ) )
=> ! [B: nat] : ( A @ B ) ) ),
inference(miniscope,[status(thm)],[886]) ).
thf(888,plain,
! [C: nat,B: nat,A: nat > $o] :
( ( ~ ( A @ zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( sk47 @ A ) )
| ( A @ C ) )
& ( ~ ( A @ zero_zero_nat )
| ~ ( A @ ( sk47 @ A ) )
| ( A @ C ) )
& ( ~ ( A @ zero_zero_nat )
| ~ ( ord_less_nat @ B @ ( sk47 @ A ) )
| ( A @ B )
| ( A @ C ) ) ),
inference(cnf,[status(esa)],[887]) ).
thf(889,plain,
! [B: nat,A: nat > $o] :
( ~ ( A @ zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( sk47 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[888]) ).
thf(892,plain,
! [A: nat] :
( ( zero_zero_nat != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) )
| ( zero_zero_nat = A ) ),
inference(replace_leibeq,[status(thm)],[889:[bind(A,$thf( (=) @ nat @ zero_zero_nat ))]]) ).
thf(899,plain,
! [A: nat] :
( ( zero_zero_nat != zero_zero_nat )
| ( zero_zero_nat = A )
| ( ord_less_nat @ zero_zero_nat @ ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) ) ),
inference(lifteq,[status(thm)],[892]) ).
thf(900,plain,
! [A: nat] :
( ( zero_zero_nat = A )
| ( ord_less_nat @ zero_zero_nat @ ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) ) ),
inference(simp,[status(thm)],[899]) ).
thf(2591,plain,
! [B: nat,A: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) )
| ( zero_zero_nat != zero_zero_nat )
| ( A
!= ( suc @ B ) ) ),
inference(paramod_ordered,[status(thm)],[900,425]) ).
thf(2592,plain,
! [B: nat,A: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) )
| ( A
!= ( suc @ B ) ) ),
inference(simp,[status(thm)],[2591]) ).
thf(2593,plain,
ord_less_nat @ zero_zero_nat @ ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ),
inference(pattern_uni,[status(thm)],[2592:[bind(A,$thf( suc @ C )),bind(B,$thf( C ))]]) ).
thf(386,plain,
~ ? [A: nat] : ( ord_less_nat @ A @ zero_zero_nat ),
inference(miniscope,[status(thm)],[385]) ).
thf(387,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(cnf,[status(esa)],[386]) ).
thf(2804,plain,
! [A: nat] :
( ~ $true
| ( ( ord_less_nat @ zero_zero_nat @ ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) )
!= ( ord_less_nat @ A @ zero_zero_nat ) ) ),
inference(paramod_ordered,[status(thm)],[2593,387]) ).
thf(2805,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) )
!= ( ord_less_nat @ A @ zero_zero_nat ) ),
inference(simp,[status(thm)],[2804]) ).
thf(2808,plain,
! [A: nat] :
( ( zero_zero_nat != A )
| ( ( sk47 @ ( (=) @ nat @ zero_zero_nat ) )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2805]) ).
thf(2815,plain,
( ( sk47 @ ( (=) @ nat @ zero_zero_nat ) )
!= zero_zero_nat ),
inference(simp,[status(thm)],[2808]) ).
thf(3984,plain,
! [A: nat] :
( ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real )
| ( zero_zero_nat != zero_zero_nat )
| ( A
!= ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[381,2815]) ).
thf(3985,plain,
! [A: nat] :
( ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real )
| ( A
!= ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) ) ),
inference(simp,[status(thm)],[3984]) ).
thf(3986,plain,
( ( poly_shift_real @ ( sk47 @ ( (=) @ nat @ zero_zero_nat ) ) @ one_one_poly_real )
= zero_zero_poly_real ),
inference(pattern_uni,[status(thm)],[3985:[bind(A,$thf( sk47 @ ( (=) @ nat @ zero_zero_nat ) ))]]) ).
thf(178,axiom,
! [A: poly_real] :
( ( dvd_dvd_poly_real @ zero_zero_poly_real @ A )
=> ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_dvd__0__left) ).
thf(877,plain,
! [A: poly_real] :
( ( dvd_dvd_poly_real @ zero_zero_poly_real @ A )
=> ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_not__less__eq) ).
thf(734,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(196,axiom,
! [A: poly_real] :
( ( ( coeff_real @ A @ zero_zero_nat )
!= zero_zero_real )
=> ( ( degree_real @ ( reflect_poly_real @ A ) )
= ( degree_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_degree__reflect__poly__eq) ).
thf(956,plain,
! [A: poly_real] :
( ( ( coeff_real @ A @ zero_zero_nat )
!= zero_zero_real )
=> ( ( degree_real @ ( reflect_poly_real @ A ) )
= ( degree_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(230,axiom,
! [A: set_poly_real,B: set_real,C: poly_real > real > $o] :
( ~ ( finite1810960971y_real @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: poly_real] :
( ( member_poly_real @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [E: poly_real] :
( ( member_poly_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_pigeonhole__infinite__rel) ).
thf(1072,plain,
! [A: set_poly_real,B: set_real,C: poly_real > real > $o] :
( ~ ( finite1810960971y_real @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: poly_real] :
( ( member_poly_real @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [E: poly_real] :
( ( member_poly_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(244,axiom,
! [A: real] :
( ( algebraic_real @ A )
=> ~ ! [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
=> ( ( B != zero_zero_poly_real )
=> ( ( poly_real2 @ B @ A )
!= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_algebraicE) ).
thf(1119,plain,
! [A: real] :
( ( algebraic_real @ A )
=> ~ ! [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
=> ( ( B != zero_zero_poly_real )
=> ( ( poly_real2 @ B @ A )
!= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(207,axiom,
! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_dvd__0__right) ).
thf(998,plain,
! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(543,plain,
! [A: real] : ( member_real @ ( sk12 @ A ) @ field_1537545994s_real ),
inference(cnfConj,[status(thm)],[542]) ).
thf(1402,plain,
! [A: real] :
( ~ $true
| ( ( member_real @ ( sk12 @ A ) @ field_1537545994s_real )
!= ( member_real @ x @ field_1537545994s_real ) ) ),
inference(paramod_ordered,[status(thm)],[543,398]) ).
thf(1403,plain,
! [A: real] :
( ( member_real @ ( sk12 @ A ) @ field_1537545994s_real )
!= ( member_real @ x @ field_1537545994s_real ) ),
inference(simp,[status(thm)],[1402]) ).
thf(1404,plain,
! [A: real] :
( ( ( sk12 @ A )
!= x )
| ( field_1537545994s_real != field_1537545994s_real ) ),
inference(simp,[status(thm)],[1403]) ).
thf(1405,plain,
! [A: real] :
( ( sk12 @ A )
!= x ),
inference(simp,[status(thm)],[1404]) ).
thf(9,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_dvd__0__left) ).
thf(265,plain,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(82,axiom,
! [A: real] :
( ( algebraic_int_real @ A )
=> ( algebraic_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_algebraic__int__imp__algebraic) ).
thf(527,plain,
! [A: real] :
( ( algebraic_int_real @ A )
=> ( algebraic_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(23,axiom,
~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_not__is__unit__0) ).
thf(312,plain,
~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(188,axiom,
! [A: real,B: real > $o] :
( ( algebraic_int_real @ A )
=> ( ! [C: poly_real,D: real] :
( ( ( coeff_real @ C @ ( degree_real @ C ) )
= one_one_real )
=> ( ! [E: nat] : ( member_real @ ( coeff_real @ C @ E ) @ ring_1_Ints_real )
=> ( ( ( poly_real2 @ C @ D )
= zero_zero_real )
=> ( B @ D ) ) ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_algebraic__int_Oinducts) ).
thf(920,plain,
! [A: real,B: real > $o] :
( ( algebraic_int_real @ A )
=> ( ! [C: poly_real,D: real] :
( ( ( coeff_real @ C @ ( degree_real @ C ) )
= one_one_real )
=> ( ! [E: nat] : ( member_real @ ( coeff_real @ C @ E ) @ ring_1_Ints_real )
=> ( ( ( poly_real2 @ C @ D )
= zero_zero_real )
=> ( B @ D ) ) ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_nat_OdiscI) ).
thf(546,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(166,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_not__less__less__Suc__eq) ).
thf(810,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(38,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ( dvd_dvd_nat @ A @ zero_zero_nat )
& ( A != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_gcd__nat_Onot__eq__extremum) ).
thf(366,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ( dvd_dvd_nat @ A @ zero_zero_nat )
& ( A != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(85,axiom,
~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_not__one__less__zero) ).
thf(534,plain,
~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(10,axiom,
! [A: poly_real] :
( ( poly_poly_real2 @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_poly__0) ).
thf(268,plain,
! [A: poly_real] :
( ( poly_poly_real2 @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(269,plain,
! [A: poly_real] :
( ( poly_poly_real2 @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
inference(cnf,[status(esa)],[268]) ).
thf(270,plain,
! [A: poly_real] :
( ( poly_poly_real2 @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
inference(lifteq,[status(thm)],[269]) ).
thf(83,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_gr0I) ).
thf(529,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(222,axiom,
! [A: poly_real,B: poly_real] :
( ( ( poly_real2 @ A )
= ( poly_real2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_poly__eq__poly__eq__iff) ).
thf(1047,plain,
! [A: poly_real,B: poly_real] :
( ( ( poly_real2 @ A )
= ( poly_real2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(162,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Zero__not__Suc) ).
thf(798,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(1091,plain,
! [A: nat] : ( member_real @ ( coeff_real @ sk73 @ A ) @ ring_1_Ints_real ),
inference(cnfConj,[status(thm)],[1090]) ).
thf(18,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_dvd__0__left__iff) ).
thf(300,plain,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(301,plain,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
= ( A = zero_zero_nat ) ),
inference(cnf,[status(esa)],[300]) ).
thf(302,plain,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
= ( A = zero_zero_nat ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_gcd__nat_Otrans) ).
thf(258,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(259,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ! [C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ A @ C ) ) ),
inference(miniscope,[status(thm)],[258]) ).
thf(260,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ~ ( dvd_dvd_nat @ B @ C )
| ( dvd_dvd_nat @ A @ C ) ),
inference(cnf,[status(esa)],[259]) ).
thf(106,axiom,
! [A: poly_real] :
( ( zero_zero_poly_real = A )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_zero__reorient) ).
thf(596,plain,
! [A: poly_real] :
( ( zero_zero_poly_real = A )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(597,plain,
! [A: poly_real] :
( ( zero_zero_poly_real = A )
= ( A = zero_zero_poly_real ) ),
inference(cnf,[status(esa)],[596]) ).
thf(598,plain,
! [A: poly_real] :
( ( zero_zero_poly_real = A )
= ( A = zero_zero_poly_real ) ),
inference(lifteq,[status(thm)],[597]) ).
thf(169,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat @ ( collect_nat @ A ) )
& ( finite_finite_nat @ ( collect_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__Collect__disjI) ).
thf(820,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat @ ( collect_nat @ A ) )
& ( finite_finite_nat @ ( collect_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(94,axiom,
! [A: poly_real,B: poly_real > $o] :
( ( member_poly_real @ A @ ( collect_poly_real @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_mem__Collect__eq) ).
thf(561,plain,
! [A: poly_real,B: poly_real > $o] :
( ( member_poly_real @ A @ ( collect_poly_real @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_gcd__nat_Oantisym) ).
thf(297,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(182,axiom,
( ( poly_real2 @ p @ x )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_p_I3_J) ).
thf(903,plain,
( ( poly_real2 @ p @ x )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(904,plain,
( ( poly_real2 @ p @ x )
= zero_zero_real ),
inference(lifteq,[status(thm)],[903]) ).
thf(2450,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( member_real @ ( sk77 @ A ) @ A )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
= zero_zero_real ) ),
inference(bool_ext,[status(thm)],[2448]) ).
thf(2460,plain,
! [A: set_real] :
( ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
= zero_zero_real )
| ~ ( finite_finite_real @ A )
| ( member_real @ ( sk77 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[2450]) ).
thf(2716,plain,
! [B: set_real,A: real] :
( ( zero_zero_real = one_one_real )
| ~ ( finite_finite_real @ B )
| ( member_real @ ( sk77 @ B ) @ B )
| ( ( poly_real2 @ one_one_poly_real @ A )
!= ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[985,2460]) ).
thf(2730,plain,
! [B: set_real,A: real] :
( ( zero_zero_real = one_one_real )
| ( member_real @ ( sk77 @ B ) @ B )
| ~ ( finite_finite_real @ B )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ( A
!= ( sk77 @ B ) ) ),
inference(simp,[status(thm)],[2716]) ).
thf(2734,plain,
! [A: set_real] :
( ( zero_zero_real = one_one_real )
| ( member_real @ ( sk77 @ A ) @ A )
| ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real ) ),
inference(simp,[status(thm)],[2730]) ).
thf(2839,plain,
! [A: set_real] :
( ( member_real @ ( sk77 @ A ) @ A )
| ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real ) ),
inference(simplifyReflect,[status(thm)],[2734,1137]) ).
thf(2842,plain,
! [B: set_real,A: set_real] :
( ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ B ) )
!= zero_zero_real )
| ~ ( finite_finite_real @ B )
| ( ( member_real @ ( sk77 @ A ) @ A )
!= ( member_real @ ( sk77 @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2839,2448]) ).
thf(2843,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= zero_zero_real )
| ~ ( finite_finite_real @ A ) ),
inference(pattern_uni,[status(thm)],[2842:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(2846,plain,
! [A: set_real] :
( ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= zero_zero_real )
| ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ~ ( finite_finite_real @ A ) ),
inference(lifteq,[status(thm)],[2843]) ).
thf(2851,plain,
! [A: set_real] :
( ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= zero_zero_real )
| ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real ) ),
inference(simp,[status(thm)],[2846]) ).
thf(2963,plain,
! [A: set_real] :
( ( zero_zero_real != zero_zero_real )
| ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= ( poly_real2 @ p @ x ) ) ),
inference(paramod_ordered,[status(thm)],[904,2851]) ).
thf(2964,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= ( poly_real2 @ p @ x ) ) ),
inference(simp,[status(thm)],[2963]) ).
thf(2969,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ( ( pderiv_real @ p )
!= p )
| ( ( sk77 @ A )
!= x ) ),
inference(simp,[status(thm)],[2964]) ).
thf(57,axiom,
( ( reflect_poly_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_reflect__poly__0) ).
thf(429,plain,
( ( reflect_poly_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(130,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_less__not__refl) ).
thf(693,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(114,axiom,
! [A: set_poly_real,B: set_poly_real,C: poly_real > poly_real > $o] :
( ~ ( finite1810960971y_real @ A )
=> ( ( finite1810960971y_real @ B )
=> ( ! [D: poly_real] :
( ( member_poly_real @ D @ A )
=> ? [E: poly_real] :
( ( member_poly_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: poly_real] :
( ( member_poly_real @ D @ B )
& ~ ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [E: poly_real] :
( ( member_poly_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_pigeonhole__infinite__rel) ).
thf(630,plain,
! [A: set_poly_real,B: set_poly_real,C: poly_real > poly_real > $o] :
( ~ ( finite1810960971y_real @ A )
=> ( ( finite1810960971y_real @ B )
=> ( ! [D: poly_real] :
( ( member_poly_real @ D @ A )
=> ? [E: poly_real] :
( ( member_poly_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: poly_real] :
( ( member_poly_real @ D @ B )
& ~ ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [E: poly_real] :
( ( member_poly_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(12,axiom,
( rsquar1555552848y_real
= ( ^ [A: poly_poly_real] :
( ( A != zero_z1423781445y_real )
& ! [B: poly_real] :
( ( ( order_poly_real @ B @ A )
= zero_zero_nat )
| ( ( order_poly_real @ B @ A )
= one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_rsquarefree__def) ).
thf(274,plain,
( rsquar1555552848y_real
= ( ^ [A: poly_poly_real] :
( ( A != zero_z1423781445y_real )
& ! [B: poly_real] :
( ( ( order_poly_real @ B @ A )
= zero_zero_nat )
| ( ( order_poly_real @ B @ A )
= one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(275,plain,
( ( ^ [A: poly_poly_real] :
( ( A != zero_z1423781445y_real )
& ! [B: poly_real] :
( ( ( order_poly_real @ B @ A )
= zero_zero_nat )
| ( ( order_poly_real @ B @ A )
= one_one_nat ) ) ) )
= rsquar1555552848y_real ),
inference(lifteq,[status(thm)],[274]) ).
thf(4,axiom,
! [A: poly_poly_real,B: poly_real] :
( ( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real )
= ( ( A = zero_z1423781445y_real )
| ( ( order_poly_real @ B @ A )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_order__root) ).
thf(252,plain,
! [A: poly_poly_real,B: poly_real] :
( ( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real )
= ( ( A = zero_z1423781445y_real )
| ( ( order_poly_real @ B @ A )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,axiom,
( dvd_dvd_nat
= ( ^ [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_gcd__nat_Oorder__iff__strict) ).
thf(361,plain,
( dvd_dvd_nat
= ( ^ [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(112,axiom,
( is_zero_real
= ( ^ [A: poly_real] : ( A = zero_zero_poly_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_is__zero__null) ).
thf(625,plain,
( is_zero_real
= ( ^ [A: poly_real] : ( A = zero_zero_poly_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_gr__implies__not0) ).
thf(682,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ B )
=> ~ ( dvd_dvd_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_nat__dvd__not__less) ).
thf(551,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ A @ B )
=> ~ ( dvd_dvd_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(135,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_Ex__less__Suc) ).
thf(710,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(186,axiom,
p != zero_zero_poly_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_p_I2_J) ).
thf(914,plain,
p != zero_zero_poly_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(915,plain,
p != zero_zero_poly_real,
inference(polarity_switch,[status(thm)],[914]) ).
thf(916,plain,
p != zero_zero_poly_real,
inference(lifteq,[status(thm)],[915]) ).
thf(66,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_Ex__less__Suc2) ).
thf(467,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(171,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_strict__inc__induct) ).
thf(830,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(231,axiom,
( algebraic_real
= ( ^ [A: real] :
? [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ field_1537545994s_real )
& ( B != zero_zero_poly_real )
& ( ( poly_real2 @ B @ A )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_algebraic__altdef) ).
thf(1079,plain,
( algebraic_real
= ( ^ [A: real] :
? [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ field_1537545994s_real )
& ( B != zero_zero_poly_real )
& ( ( poly_real2 @ B @ A )
= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(216,axiom,
ord_less_real @ zero_zero_real @ one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_zero__less__one) ).
thf(1027,plain,
ord_less_real @ zero_zero_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_gcd__nat_Oasym) ).
thf(324,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ~ ( ( dvd_dvd_nat @ B @ A )
& ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(200,axiom,
( rsquarefree_real
= ( ^ [A: poly_real] :
! [B: real] :
~ ( ( ( poly_real2 @ A @ B )
= zero_zero_real )
& ( ( poly_real2 @ ( pderiv_real @ A ) @ B )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rsquarefree__roots) ).
thf(974,plain,
( rsquarefree_real
= ( ^ [A: poly_real] :
! [B: real] :
~ ( ( ( poly_real2 @ A @ B )
= zero_zero_real )
& ( ( poly_real2 @ ( pderiv_real @ A ) @ B )
= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
=> ( dvd_dvd_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_unit__imp__dvd) ).
thf(317,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
=> ( dvd_dvd_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(212,axiom,
( ( pderiv_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_pderiv__0) ).
thf(1016,plain,
( ( pderiv_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1017,plain,
( ( pderiv_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(lifteq,[status(thm)],[1016]) ).
thf(2955,plain,
! [A: set_real] :
( ( zero_zero_real != zero_zero_real )
| ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= ( poly_real2 @ sk73 @ x ) ) ),
inference(paramod_ordered,[status(thm)],[1095,2851]) ).
thf(2956,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= ( poly_real2 @ sk73 @ x ) ) ),
inference(simp,[status(thm)],[2955]) ).
thf(2973,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( ( pderiv_real @ p )
!= one_one_poly_real )
| ( ( pderiv_real @ p )
!= sk73 )
| ( ( sk77 @ A )
!= x ) ),
inference(simp,[status(thm)],[2956]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_Suc__inject) ).
thf(725,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(50,axiom,
! [A: poly_real] :
( ( dvd_dvd_poly_real @ zero_zero_poly_real @ A )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_dvd__0__left__iff) ).
thf(401,plain,
! [A: poly_real] :
( ( dvd_dvd_poly_real @ zero_zero_poly_real @ A )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(402,plain,
! [A: poly_real] :
( ( dvd_dvd_poly_real @ zero_zero_poly_real @ A )
= ( A = zero_zero_poly_real ) ),
inference(cnf,[status(esa)],[401]) ).
thf(403,plain,
! [A: poly_real] :
( ( dvd_dvd_poly_real @ zero_zero_poly_real @ A )
= ( A = zero_zero_poly_real ) ),
inference(lifteq,[status(thm)],[402]) ).
thf(235,axiom,
( algebraic_int_real
= ( ^ [A: real] :
? [B: poly_real,C: real] :
( ( A = C )
& ( ( coeff_real @ B @ ( degree_real @ B ) )
= one_one_real )
& ! [D: nat] : ( member_real @ ( coeff_real @ B @ D ) @ ring_1_Ints_real )
& ( ( poly_real2 @ B @ C )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_algebraic__int_Osimps) ).
thf(1096,plain,
( algebraic_int_real
= ( ^ [A: real] :
? [B: poly_real,C: real] :
( ( A = C )
& ( ( coeff_real @ B @ ( degree_real @ B ) )
= one_one_real )
& ! [D: nat] : ( member_real @ ( coeff_real @ B @ D ) @ ring_1_Ints_real )
& ( ( poly_real2 @ B @ C )
= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(45,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_mem__Collect__eq) ).
thf(388,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(34,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_gcd__nat_Oextremum) ).
thf(356,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(105,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_not__less0) ).
thf(593,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(73,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_lift__Suc__mono__less__iff) ).
thf(499,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(204,axiom,
! [A: poly_real,B: real] :
( ( ( pderiv_real @ A )
!= zero_zero_poly_real )
=> ( ( ( order_real @ B @ A )
!= zero_zero_nat )
=> ( ( order_real @ B @ A )
= ( suc @ ( order_real @ B @ ( pderiv_real @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_order__pderiv) ).
thf(989,plain,
! [A: poly_real,B: real] :
( ( ( pderiv_real @ A )
!= zero_zero_poly_real )
=> ( ( ( order_real @ B @ A )
!= zero_zero_nat )
=> ( ( order_real @ B @ A )
= ( suc @ ( order_real @ B @ ( pderiv_real @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(79,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_gr0__implies__Suc) ).
thf(519,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(146,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ? [C: real] :
( ( member_real @ C @ field_1537545994s_real )
& ( ord_less_real @ A @ C )
& ( ord_less_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_Rats__dense__in__real) ).
thf(742,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ? [C: real] :
( ( member_real @ C @ field_1537545994s_real )
& ( ord_less_real @ A @ C )
& ( ord_less_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(99,axiom,
! [A: nat] :
( ( poly_cutoff_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_poly__cutoff__0) ).
thf(578,plain,
! [A: nat] :
( ( poly_cutoff_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(28,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_dvd__trans) ).
thf(328,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ C )
=> ( dvd_dvd_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(71,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_less__Suc__induct) ).
thf(488,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_dvd__antisym) ).
thf(339,plain,
! [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(92,axiom,
! [A: poly_poly_real,B: poly_real] :
( ( ( poly_poly_real2 @ A @ B )
!= zero_zero_poly_real )
=> ( ( order_poly_real @ B @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_order__0I) ).
thf(554,plain,
! [A: poly_poly_real,B: poly_real] :
( ( ( poly_poly_real2 @ A @ B )
!= zero_zero_poly_real )
=> ( ( order_poly_real @ B @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(86,axiom,
~ ( ord_less_poly_real @ one_one_poly_real @ zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_not__one__less__zero) ).
thf(536,plain,
~ ( ord_less_poly_real @ one_one_poly_real @ zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(537,plain,
~ ( ord_less_poly_real @ one_one_poly_real @ zero_zero_poly_real ),
inference(polarity_switch,[status(thm)],[536]) ).
thf(115,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_old_Onat_Oexhaust) ).
thf(637,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(134,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_gr__implies__not__zero) ).
thf(706,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(127,axiom,
! [A: nat > $o] :
( ~ ( finite_finite_nat @ ( collect_nat @ A ) )
=> ? [B: nat] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_not__finite__existsD) ).
thf(686,plain,
! [A: nat > $o] :
( ~ ( finite_finite_nat @ ( collect_nat @ A ) )
=> ? [B: nat] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(69,axiom,
! [A: nat > $o] :
( ~ ( A @ zero_zero_nat )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_exists__least__lemma) ).
thf(476,plain,
! [A: nat > $o] :
( ~ ( A @ zero_zero_nat )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(726,plain,
! [B: nat,A: nat] :
( ( ( suc @ A )
!= ( suc @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[725]) ).
thf(727,plain,
! [B: nat,A: nat] :
( ( ( suc @ A )
!= ( suc @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[726]) ).
thf(728,plain,
? [A: nat > nat] :
! [B: nat] :
( ( A @ ( suc @ B ) )
= B ),
inference(detectInverse,[status(thm)],[727]) ).
thf(729,plain,
! [A: nat] :
( ( sk30 @ ( suc @ A ) )
= A ),
inference(cnf,[status(esa)],[728]) ).
thf(2472,plain,
! [A: nat] :
( ( sk30 @ ( suc @ A ) )
= A ),
inference(lifteq,[status(thm)],[729]) ).
thf(220,axiom,
! [A: real] :
( ( dvd_dvd_real @ zero_zero_real @ A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_dvd__0__left__iff) ).
thf(1037,plain,
! [A: real] :
( ( dvd_dvd_real @ zero_zero_real @ A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1038,plain,
! [A: real] :
( ( dvd_dvd_real @ zero_zero_real @ A )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[1037]) ).
thf(1039,plain,
! [A: real] :
( ( dvd_dvd_real @ zero_zero_real @ A )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[1038]) ).
thf(206,axiom,
~ ( finite_finite_real @ field_1537545994s_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Rats__infinite) ).
thf(996,plain,
~ ( finite_finite_real @ field_1537545994s_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(997,plain,
~ ( finite_finite_real @ field_1537545994s_real ),
inference(polarity_switch,[status(thm)],[996]) ).
thf(144,axiom,
( ( degree_real @ zero_zero_poly_real )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_degree__0) ).
thf(737,plain,
( ( degree_real @ zero_zero_poly_real )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(738,plain,
( ( degree_real @ zero_zero_poly_real )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[737]) ).
thf(247,axiom,
! [A: poly_real] :
( ( ord_less_real @ zero_zero_real @ ( coeff_real @ A @ ( degree_real @ A ) ) )
=> ? [B: real] :
! [C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( coeff_real @ A @ ( degree_real @ A ) ) @ ( poly_real2 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_poly__pinfty__gt__lc) ).
thf(1131,plain,
! [A: poly_real] :
( ( ord_less_real @ zero_zero_real @ ( coeff_real @ A @ ( degree_real @ A ) ) )
=> ? [B: real] :
! [C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( coeff_real @ A @ ( degree_real @ A ) ) @ ( poly_real2 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(223,axiom,
! [A: real] :
( ( dvd_dvd_real @ zero_zero_real @ A )
=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_dvd__0__left) ).
thf(1050,plain,
! [A: real] :
( ( dvd_dvd_real @ zero_zero_real @ A )
=> ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(185,axiom,
! [A: poly_real] :
( ( ( pderiv_real @ A )
= zero_zero_poly_real )
= ( ( degree_real @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_pderiv__eq__0__iff) ).
thf(911,plain,
! [A: poly_real] :
( ( ( pderiv_real @ A )
= zero_zero_poly_real )
= ( ( degree_real @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(74,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_bot__nat__0_Oextremum__strict) ).
thf(503,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(109,axiom,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( poly_cutoff_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) )
& ( ( A != zero_zero_nat )
=> ( ( poly_cutoff_real @ A @ one_one_poly_real )
= one_one_poly_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_poly__cutoff__1) ).
thf(605,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( poly_cutoff_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) )
& ( ( A != zero_zero_nat )
=> ( ( poly_cutoff_real @ A @ one_one_poly_real )
= one_one_poly_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(31,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_dvd__0__right) ).
thf(342,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(343,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ),
inference(cnf,[status(esa)],[342]) ).
thf(35,axiom,
! [A: poly_poly_real] :
( ( ! [B: poly_real] :
( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real ) )
= ( A = zero_z1423781445y_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_poly__all__0__iff__0) ).
thf(358,plain,
! [A: poly_poly_real] :
( ( ! [B: poly_real] :
( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real ) )
= ( A = zero_z1423781445y_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(359,plain,
! [A: poly_poly_real] :
( ( ! [B: poly_real] :
( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real ) )
= ( A = zero_z1423781445y_real ) ),
inference(cnf,[status(esa)],[358]) ).
thf(360,plain,
! [A: poly_poly_real] :
( ( ! [B: poly_real] :
( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real ) )
= ( A = zero_z1423781445y_real ) ),
inference(lifteq,[status(thm)],[359]) ).
thf(164,axiom,
! [A: poly_real,B: poly_real] :
( ( ( coeff_real @ A )
= ( coeff_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_coeff__inject) ).
thf(805,plain,
! [A: poly_real,B: poly_real] :
( ( ( coeff_real @ A )
= ( coeff_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(22,axiom,
! [A: poly_poly_real,B: poly_poly_real] :
( ( ( poly_poly_real2 @ A )
= ( poly_poly_real2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_poly__eq__poly__eq__iff) ).
thf(309,plain,
! [A: poly_poly_real,B: poly_poly_real] :
( ( ( poly_poly_real2 @ A )
= ( poly_poly_real2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(310,plain,
! [B: poly_poly_real,A: poly_poly_real] :
( ( ( poly_poly_real2 @ A )
= ( poly_poly_real2 @ B ) )
= ( A = B ) ),
inference(cnf,[status(esa)],[309]) ).
thf(311,plain,
! [B: poly_poly_real,A: poly_poly_real] :
( ( ( poly_poly_real2 @ A )
= ( poly_poly_real2 @ B ) )
= ( A = B ) ),
inference(lifteq,[status(thm)],[310]) ).
thf(1559,plain,
! [A: nat] :
( ~ $true
| ( ( member_real @ ( coeff_real @ sk73 @ A ) @ ring_1_Ints_real )
!= ( member_real @ x @ field_1537545994s_real ) ) ),
inference(paramod_ordered,[status(thm)],[1091,398]) ).
thf(1560,plain,
! [A: nat] :
( ( member_real @ ( coeff_real @ sk73 @ A ) @ ring_1_Ints_real )
!= ( member_real @ x @ field_1537545994s_real ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1563,plain,
! [A: nat] :
( ( ( coeff_real @ sk73 @ A )
!= x )
| ( field_1537545994s_real != ring_1_Ints_real ) ),
inference(simp,[status(thm)],[1560]) ).
thf(195,axiom,
! [A: poly_real] :
( ( ( coeff_real @ ( reflect_poly_real @ A ) @ zero_zero_nat )
= zero_zero_real )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_coeff__0__reflect__poly__0__iff) ).
thf(953,plain,
! [A: poly_real] :
( ( ( coeff_real @ ( reflect_poly_real @ A ) @ zero_zero_nat )
= zero_zero_real )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(151,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_less__irrefl__nat) ).
thf(765,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(224,axiom,
( n
= ( degree_real @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_n__def) ).
thf(1053,plain,
( n
= ( degree_real @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1054,plain,
( ( degree_real @ p )
= n ),
inference(lifteq,[status(thm)],[1053]) ).
thf(160,axiom,
~ ( dvd_dvd_poly_real @ zero_zero_poly_real @ one_one_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_not__is__unit__0) ).
thf(794,plain,
~ ( dvd_dvd_poly_real @ zero_zero_poly_real @ one_one_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(3967,plain,
! [A: nat] :
( ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real )
| ( A != one_one_nat )
| ( zero_zero_nat != zero_zero_nat ) ),
inference(paramod_ordered,[status(thm)],[381,278]) ).
thf(3968,plain,
! [A: nat] :
( ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real )
| ( A != one_one_nat ) ),
inference(pattern_uni,[status(thm)],[3967:[]]) ).
thf(4004,plain,
( ( poly_shift_real @ one_one_nat @ one_one_poly_real )
= zero_zero_poly_real ),
inference(simp,[status(thm)],[3968]) ).
thf(148,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_292_nat__less__induct) ).
thf(750,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)],[148]) ).
thf(8,axiom,
! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_one__dvd) ).
thf(263,plain,
! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(264,plain,
! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ),
inference(cnf,[status(esa)],[263]) ).
thf(173,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_less__not__refl3) ).
thf(856,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_Suc__lessE) ).
thf(573,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(290,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ! [C: nat] :
( ( dvd_dvd_nat @ B @ C )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ),
inference(miniscope,[status(thm)],[289]) ).
thf(291,plain,
! [C: nat,B: nat,A: nat] :
( ( ~ ( dvd_dvd_nat @ A @ B )
| ( A = B )
| ~ ( dvd_dvd_nat @ B @ C )
| ( dvd_dvd_nat @ A @ C ) )
& ( ~ ( dvd_dvd_nat @ A @ B )
| ( A = B )
| ~ ( dvd_dvd_nat @ B @ C )
| ( A != C ) ) ),
inference(cnf,[status(esa)],[290]) ).
thf(293,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( dvd_dvd_nat @ A @ B )
| ( A = B )
| ~ ( dvd_dvd_nat @ B @ C )
| ( A != C ) ),
inference(cnfConj,[status(thm)],[291]) ).
thf(295,plain,
! [C: nat,B: nat,A: nat] :
( ( A = B )
| ( A != C )
| ~ ( dvd_dvd_nat @ A @ B )
| ~ ( dvd_dvd_nat @ B @ C ) ),
inference(lifteq,[status(thm)],[293]) ).
thf(296,plain,
! [B: nat,A: nat] :
( ( B = A )
| ~ ( dvd_dvd_nat @ B @ A )
| ~ ( dvd_dvd_nat @ A @ B ) ),
inference(simp,[status(thm)],[295]) ).
thf(3915,plain,
! [B: nat,A: nat] :
( ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real )
| ( zero_zero_nat != zero_zero_nat )
| ( A
!= ( suc @ B ) ) ),
inference(paramod_ordered,[status(thm)],[381,425]) ).
thf(3916,plain,
! [B: nat,A: nat] :
( ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real )
| ( A
!= ( suc @ B ) ) ),
inference(simp,[status(thm)],[3915]) ).
thf(3917,plain,
! [A: nat] :
( ( poly_shift_real @ ( suc @ A ) @ one_one_poly_real )
= zero_zero_poly_real ),
inference(pattern_uni,[status(thm)],[3916:[bind(A,$thf( suc @ C )),bind(B,$thf( C ))]]) ).
thf(4017,plain,
! [A: nat] :
( ( poly_shift_real @ ( suc @ A ) @ one_one_poly_real )
= zero_zero_poly_real ),
inference(simp,[status(thm)],[3917]) ).
thf(62,axiom,
! [A: set_poly_real] :
( ( collect_poly_real
@ ^ [B: poly_real] : ( member_poly_real @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Collect__mem__eq) ).
thf(442,plain,
! [A: set_poly_real] :
( ( collect_poly_real
@ ^ [B: poly_real] : ( member_poly_real @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(443,plain,
! [A: set_poly_real] :
( ( collect_poly_real
@ ^ [B: poly_real] : ( member_poly_real @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[442]) ).
thf(444,plain,
! [A: set_poly_real] :
( ( collect_poly_real
@ ^ [B: poly_real] : ( member_poly_real @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[443]) ).
thf(107,axiom,
! [A: nat] :
( ( poly_shift_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_poly__shift__0) ).
thf(599,plain,
! [A: nat] :
( ( poly_shift_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(600,plain,
! [A: nat] :
( ( poly_shift_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(cnf,[status(esa)],[599]) ).
thf(601,plain,
! [A: nat] :
( ( poly_shift_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(lifteq,[status(thm)],[600]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_less__not__refl2) ).
thf(513,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(430,plain,
( ( reflect_poly_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(lifteq,[status(thm)],[429]) ).
thf(101,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_not__less__zero) ).
thf(584,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_Suc__less__eq2) ).
thf(772,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(3265,plain,
! [B: nat,A: poly_real] :
( ( member_real @ ( poly_real2 @ A @ zero_zero_real ) @ ring_1_Ints_real )
| ( ( coeff_real @ A @ zero_zero_nat )
!= ( coeff_real @ p @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1030,1107]) ).
thf(3266,plain,
member_real @ ( poly_real2 @ p @ zero_zero_real ) @ ring_1_Ints_real,
inference(pattern_uni,[status(thm)],[3265:[bind(A,$thf( p )),bind(B,$thf( zero_zero_nat ))]]) ).
thf(89,axiom,
member_real @ one_one_real @ field_1537545994s_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_Rats__1) ).
thf(545,plain,
member_real @ one_one_real @ field_1537545994s_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(975,plain,
( rsquarefree_real
= ( ^ [A: poly_real] :
! [B: real] :
~ ( ( ( poly_real2 @ A @ B )
= zero_zero_real )
& ( ( poly_real2 @ ( pderiv_real @ A ) @ B )
= zero_zero_real ) ) ) ),
inference(lifteq,[status(thm)],[974]) ).
thf(116,axiom,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_zero__less__Suc) ).
thf(641,plain,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_nat__neq__iff) ).
thf(391,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(42,axiom,
algebraic_real @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_assms_I2_J) ).
thf(382,plain,
algebraic_real @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(3913,plain,
! [A: nat] :
( ( ( poly_shift_real @ A @ one_one_poly_real )
= zero_zero_poly_real )
| ( n = zero_zero_nat )
| ( A
!= ( degree_real @ p ) ) ),
inference(paramod_ordered,[status(thm)],[381,1054]) ).
thf(3914,plain,
( ( ( poly_shift_real @ ( degree_real @ p ) @ one_one_poly_real )
= zero_zero_poly_real )
| ( n = zero_zero_nat ) ),
inference(pattern_uni,[status(thm)],[3913:[bind(A,$thf( degree_real @ p ))]]) ).
thf(4837,plain,
( ( ( poly_shift_real @ n @ one_one_poly_real )
= zero_zero_poly_real )
| ( n = zero_zero_nat ) ),
inference(rewrite,[status(thm)],[3914,1054]) ).
thf(318,plain,
! [A: nat] :
( ( dvd_dvd_nat @ A @ one_one_nat )
=> ! [B: nat] : ( dvd_dvd_nat @ A @ B ) ),
inference(miniscope,[status(thm)],[317]) ).
thf(319,plain,
! [B: nat,A: nat] :
( ~ ( dvd_dvd_nat @ A @ one_one_nat )
| ( dvd_dvd_nat @ A @ B ) ),
inference(cnf,[status(esa)],[318]) ).
thf(2737,plain,
! [B: nat,A: nat] :
( ( A != one_one_nat )
| ( dvd_dvd_nat @ A @ B ) ),
inference(rewrite,[status(thm)],[319,281]) ).
thf(2738,plain,
! [B: nat,A: nat] :
( ( A != one_one_nat )
| ( dvd_dvd_nat @ A @ B ) ),
inference(lifteq,[status(thm)],[2737]) ).
thf(918,plain,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(cnf,[status(esa)],[917]) ).
thf(919,plain,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(lifteq,[status(thm)],[918]) ).
thf(539,plain,
! [A: real] :
( ( synthetic_div_real @ zero_zero_poly_real @ A )
= zero_zero_poly_real ),
inference(cnf,[status(esa)],[538]) ).
thf(540,plain,
! [A: real] :
( ( synthetic_div_real @ zero_zero_poly_real @ A )
= zero_zero_poly_real ),
inference(lifteq,[status(thm)],[539]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_less__Suc__eq__0__disj) ).
thf(445,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(935,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[934]) ).
thf(936,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[935]) ).
thf(606,plain,
( ! [A: nat] :
( ( A = zero_zero_nat )
=> ( ( poly_cutoff_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) )
& ! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( poly_cutoff_real @ A @ one_one_poly_real )
= one_one_poly_real ) ) ),
inference(miniscope,[status(thm)],[605]) ).
thf(607,plain,
! [B: nat,A: nat] :
( ( ( A != zero_zero_nat )
| ( ( poly_cutoff_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) )
& ( ( B = zero_zero_nat )
| ( ( poly_cutoff_real @ B @ one_one_poly_real )
= one_one_poly_real ) ) ),
inference(cnf,[status(esa)],[606]) ).
thf(608,plain,
! [A: nat] :
( ( A != zero_zero_nat )
| ( ( poly_cutoff_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) ),
inference(cnfConj,[status(thm)],[607]) ).
thf(610,plain,
! [A: nat] :
( ( A != zero_zero_nat )
| ( ( poly_cutoff_real @ A @ one_one_poly_real )
= zero_zero_poly_real ) ),
inference(lifteq,[status(thm)],[608]) ).
thf(611,plain,
( ( poly_cutoff_real @ zero_zero_nat @ one_one_poly_real )
= zero_zero_poly_real ),
inference(simp,[status(thm)],[610]) ).
thf(157,axiom,
! [A: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_dvd__1__left) ).
thf(787,plain,
! [A: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(136,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_less__zeroE) ).
thf(713,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(4202,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( member_real @ ( sk77 @ A ) @ A )
| ( zero_zero_real != zero_zero_real )
| ~ ( finite_finite_real @ ring_1_Ints_real )
| ( ( sk77 @ ring_1_Ints_real )
!= one_one_real )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ ring_1_Ints_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[2460,4183]) ).
thf(4203,plain,
! [A: set_real] :
( ~ ( finite_finite_real @ A )
| ( member_real @ ( sk77 @ A ) @ A )
| ~ ( finite_finite_real @ ring_1_Ints_real )
| ( ( sk77 @ ring_1_Ints_real )
!= one_one_real )
| ( ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ A ) )
!= ( poly_real2 @ ( pderiv_real @ p ) @ ( sk77 @ ring_1_Ints_real ) ) ) ),
inference(simp,[status(thm)],[4202]) ).
thf(4204,plain,
( ~ ( finite_finite_real @ ring_1_Ints_real )
| ( member_real @ ( sk77 @ ring_1_Ints_real ) @ ring_1_Ints_real )
| ~ ( finite_finite_real @ ring_1_Ints_real )
| ( ( sk77 @ ring_1_Ints_real )
!= one_one_real ) ),
inference(pattern_uni,[status(thm)],[4203:[bind(A,$thf( ring_1_Ints_real ))]]) ).
thf(4218,plain,
( ~ ( finite_finite_real @ ring_1_Ints_real )
| ( member_real @ ( sk77 @ ring_1_Ints_real ) @ ring_1_Ints_real )
| ( ( sk77 @ ring_1_Ints_real )
!= one_one_real ) ),
inference(simp,[status(thm)],[4204]) ).
thf(2473,plain,
! [A: nat] :
( ( ( sk30 @ one_one_nat )
= A )
| ( ( suc @ zero_zero_nat )
!= ( suc @ A ) ) ),
inference(paramod_ordered,[status(thm)],[533,2472]) ).
thf(2474,plain,
( ( sk30 @ one_one_nat )
= zero_zero_nat ),
inference(pattern_uni,[status(thm)],[2473:[bind(A,$thf( zero_zero_nat ))]]) ).
thf(193,axiom,
! [A: poly_real,B: real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ A @ C ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( ( poly_real2 @ A @ B )
= zero_zero_real )
=> ( algebraic_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_algebraicI) ).
thf(947,plain,
! [A: poly_real,B: real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ A @ C ) @ ring_1_Ints_real )
=> ( ( A != zero_zero_poly_real )
=> ( ( ( poly_real2 @ A @ B )
= zero_zero_real )
=> ( algebraic_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(125,axiom,
( ( degree_real @ one_one_poly_real )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_degree__1) ).
thf(680,plain,
( ( degree_real @ one_one_poly_real )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(681,plain,
( ( degree_real @ one_one_poly_real )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[680]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_old_Onat_Oinject) ).
thf(784,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(362,plain,
( ( ^ [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
| ( A = B ) ) )
= dvd_dvd_nat ),
inference(lifteq,[status(thm)],[361]) ).
thf(19,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_gcd__nat_Oeq__iff) ).
thf(303,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_gcd__nat_Oextremum__uniqueI) ).
thf(271,plain,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(210,axiom,
! [A: poly_real] :
( ( dvd_dvd_poly_real @ A @ ( pderiv_real @ A ) )
= ( ( degree_real @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_dvd__pderiv__iff) ).
thf(1011,plain,
! [A: poly_real] :
( ( dvd_dvd_poly_real @ A @ ( pderiv_real @ A ) )
= ( ( degree_real @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(179,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_not__gr0) ).
thf(880,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(120,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Suc__neq__Zero) ).
thf(649,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_nat_Oinject) ).
thf(434,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(3480,plain,
( ~ ( ( zero_zero_nat != one_one_nat ) )
| ? [A: nat] :
( one_one_nat
= ( suc @ A ) ) ),
inference(bool_ext,[status(thm)],[3444]) ).
thf(3546,plain,
( ( zero_zero_nat = one_one_nat )
| ( one_one_nat
= ( suc @ sk79 ) ) ),
inference(cnf,[status(esa)],[3480]) ).
thf(3547,plain,
( ( zero_zero_nat = one_one_nat )
| ( ( suc @ sk79 )
= one_one_nat ) ),
inference(lifteq,[status(thm)],[3546]) ).
thf(3632,plain,
( ( suc @ sk79 )
= one_one_nat ),
inference(simplifyReflect,[status(thm)],[3547,278]) ).
thf(3658,plain,
! [A: nat] :
( ( one_one_nat != A )
| ( ( suc @ sk79 )
!= ( suc @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3632,560]) ).
thf(3659,plain,
sk79 != one_one_nat,
inference(pattern_uni,[status(thm)],[3658:[bind(A,$thf( sk79 ))]]) ).
thf(3723,plain,
! [B: nat,A: nat] :
( ( B != one_one_nat )
| ~ ( dvd_dvd_nat @ A @ B )
| ( one_one_nat != one_one_nat )
| ( A != sk79 ) ),
inference(paramod_ordered,[status(thm)],[2150,3659]) ).
thf(3724,plain,
! [B: nat,A: nat] :
( ( B != one_one_nat )
| ~ ( dvd_dvd_nat @ A @ B )
| ( A != sk79 ) ),
inference(simp,[status(thm)],[3723]) ).
thf(3725,plain,
! [A: nat] :
( ( A != one_one_nat )
| ~ ( dvd_dvd_nat @ sk79 @ A ) ),
inference(pattern_uni,[status(thm)],[3724:[bind(A,$thf( sk79 ))]]) ).
thf(3731,plain,
~ ( dvd_dvd_nat @ sk79 @ one_one_nat ),
inference(simp,[status(thm)],[3725]) ).
thf(3746,plain,
sk79 != one_one_nat,
inference(rewrite,[status(thm)],[3731,281]) ).
thf(3747,plain,
sk79 != one_one_nat,
inference(lifteq,[status(thm)],[3746]) ).
thf(168,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_nat_Odistinct_I1_J) ).
thf(816,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(111,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ ( collect_nat @ A ) )
| ( finite_finite_nat @ ( collect_nat @ B ) ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__Collect__conjI) ).
thf(621,plain,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ ( collect_nat @ A ) )
| ( finite_finite_nat @ ( collect_nat @ B ) ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(3,axiom,
! [A: nat] :
~ ( ( dvd_dvd_nat @ A @ A )
& ( A != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_gcd__nat_Oirrefl) ).
thf(251,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1951,plain,
! [B: nat,A: nat] :
( ( ( A = zero_zero_nat )
= ( B = one_one_nat ) )
| ( ( dvd_dvd_nat @ zero_zero_nat @ A )
!= ( dvd_dvd_nat @ B @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[302,281]) ).
thf(1952,plain,
( ( one_one_nat = zero_zero_nat )
= ( zero_zero_nat = one_one_nat ) ),
inference(pattern_uni,[status(thm)],[1951:[bind(A,$thf( one_one_nat )),bind(B,$thf( zero_zero_nat ))]]) ).
thf(49,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Suc__mono) ).
thf(399,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(197,axiom,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ ( poly_real2 @ C @ A ) @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ B ) )
=> ? [D: real] :
( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B )
& ( ( poly_real2 @ C @ D )
= zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_poly__IVT__pos) ).
thf(959,plain,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ ( poly_real2 @ C @ A ) @ zero_zero_real )
=> ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ B ) )
=> ? [D: real] :
( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B )
& ( ( poly_real2 @ C @ D )
= zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(152,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( dvd_dvd_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_finite__divisors__nat) ).
thf(768,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( dvd_dvd_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(242,axiom,
! [A: poly_real] :
( ( ( degree_real @ A )
!= zero_zero_nat )
=> ~ ( dvd_dvd_poly_real @ A @ ( pderiv_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_not__dvd__pderiv) ).
thf(1113,plain,
! [A: poly_real] :
( ( ( degree_real @ A )
!= zero_zero_nat )
=> ~ ( dvd_dvd_poly_real @ A @ ( pderiv_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(208,axiom,
! [A: real > $o,B: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ A ) )
| ( finite_finite_real @ ( collect_real @ B ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [C: real] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__Collect__conjI) ).
thf(1000,plain,
! [A: real > $o,B: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ A ) )
| ( finite_finite_real @ ( collect_real @ B ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [C: real] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(58,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_All__less__Suc) ).
thf(431,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(180,axiom,
! [A: poly_real] :
( ( coeff_real @ ( reflect_poly_real @ A ) @ zero_zero_nat )
= ( coeff_real @ A @ ( degree_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_coeff__0__reflect__poly) ).
thf(883,plain,
! [A: poly_real] :
( ( coeff_real @ ( reflect_poly_real @ A ) @ zero_zero_nat )
= ( coeff_real @ A @ ( degree_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(3772,plain,
! [A: nat] :
( ( ( sk30 @ one_one_nat )
= A )
| ( ( suc @ sk80 )
!= ( suc @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3762,2472]) ).
thf(3773,plain,
( ( sk30 @ one_one_nat )
= sk80 ),
inference(pattern_uni,[status(thm)],[3772:[bind(A,$thf( sk80 ))]]) ).
thf(3806,plain,
sk80 = zero_zero_nat,
inference(rewrite,[status(thm)],[3773,2474]) ).
thf(47,axiom,
! [A: poly_real,B: poly_real] :
( ! [C: nat] :
( ( coeff_real @ A @ C )
= ( coeff_real @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_poly__eqI) ).
thf(394,plain,
! [A: poly_real,B: poly_real] :
( ! [C: nat] :
( ( coeff_real @ A @ C )
= ( coeff_real @ B @ C ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(203,axiom,
! [A: poly_real] :
( ( ( poly_real2 @ ( reflect_poly_real @ A ) @ zero_zero_real )
= zero_zero_real )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_reflect__poly__at__0__eq__0__iff) ).
thf(986,plain,
! [A: poly_real] :
( ( ( poly_real2 @ ( reflect_poly_real @ A ) @ zero_zero_real )
= zero_zero_real )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(68,axiom,
! [A: poly_real,B: real] :
( ( ( synthetic_div_real @ A @ B )
= zero_zero_poly_real )
= ( ( degree_real @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_synthetic__div__eq__0__iff) ).
thf(473,plain,
! [A: poly_real,B: real] :
( ( ( synthetic_div_real @ A @ B )
= zero_zero_poly_real )
= ( ( degree_real @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(123,axiom,
( ( coeff_real @ one_one_poly_real @ ( degree_real @ one_one_poly_real ) )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_lead__coeff__1) ).
thf(675,plain,
( ( coeff_real @ one_one_poly_real @ ( degree_real @ one_one_poly_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(192,axiom,
! [A: poly_real] :
( ( ( coeff_real @ A @ zero_zero_nat )
!= zero_zero_real )
=> ( ( reflect_poly_real @ ( reflect_poly_real @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_reflect__poly__reflect__poly) ).
thf(944,plain,
! [A: poly_real] :
( ( ( coeff_real @ A @ zero_zero_nat )
!= zero_zero_real )
=> ( ( reflect_poly_real @ ( reflect_poly_real @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(119,axiom,
member_poly_real @ zero_zero_poly_real @ ring_1690226883y_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Ints__0) ).
thf(648,plain,
member_poly_real @ zero_zero_poly_real @ ring_1690226883y_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(232,axiom,
! [A: poly_real,B: real] :
( ( ( poly_real2 @ A @ B )
= zero_zero_real )
=> ( ! [C: nat] : ( member_real @ ( coeff_real @ A @ C ) @ ring_1_Ints_real )
=> ( ( ( coeff_real @ A @ zero_zero_nat )
= one_one_real )
=> ( algebraic_int_real @ ( inverse_inverse_real @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_algebraic__int__inverse) ).
thf(1081,plain,
! [A: poly_real,B: real] :
( ( ( poly_real2 @ A @ B )
= zero_zero_real )
=> ( ! [C: nat] : ( member_real @ ( coeff_real @ A @ C ) @ ring_1_Ints_real )
=> ( ( ( coeff_real @ A @ zero_zero_nat )
= one_one_real )
=> ( algebraic_int_real @ ( inverse_inverse_real @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(514,plain,
! [B: nat,A: nat] :
( ~ ( ord_less_nat @ A @ B )
| ( B != A ) ),
inference(cnf,[status(esa)],[513]) ).
thf(515,plain,
! [B: nat,A: nat] :
( ( B != A )
| ~ ( ord_less_nat @ A @ B ) ),
inference(lifteq,[status(thm)],[514]) ).
thf(516,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(simp,[status(thm)],[515]) ).
thf(219,axiom,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( finite_finite_real
@ ( collect_real
@ ^ [B: real] :
( ( poly_real2 @ A @ B )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_poly__roots__finite) ).
thf(1034,plain,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( finite_finite_real
@ ( collect_real
@ ^ [B: real] :
( ( poly_real2 @ A @ B )
= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(2263,plain,
! [C: nat,B: nat,A: nat] :
( ( B != one_one_nat )
| ~ ( dvd_dvd_nat @ A @ B )
| ( one_one_nat != C )
| ( A
!= ( suc @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2150,560]) ).
thf(2264,plain,
! [B: nat,A: nat] :
( ( A != one_one_nat )
| ~ ( dvd_dvd_nat @ ( suc @ B ) @ A )
| ( one_one_nat != B ) ),
inference(pattern_uni,[status(thm)],[2263:[bind(A,$thf( suc @ D )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(2284,plain,
~ ( dvd_dvd_nat @ ( suc @ one_one_nat ) @ one_one_nat ),
inference(simp,[status(thm)],[2264]) ).
thf(2332,plain,
( ( suc @ one_one_nat )
!= one_one_nat ),
inference(rewrite,[status(thm)],[2284,281]) ).
thf(2333,plain,
( ( suc @ one_one_nat )
!= one_one_nat ),
inference(lifteq,[status(thm)],[2332]) ).
thf(213,axiom,
algebraic_int_real @ zero_zero_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_algebraic__int__0) ).
thf(1018,plain,
algebraic_int_real @ zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(626,plain,
( is_zero_real
= ( ^ [A: poly_real] : ( A = zero_zero_poly_real ) ) ),
inference(lifteq,[status(thm)],[625]) ).
thf(1181,plain,
! [A: poly_real] :
( ( is_zero_real @ A )
= ( A = zero_zero_poly_real ) ),
inference(func_ext,[status(esa)],[626]) ).
thf(170,axiom,
! [A: set_nat,B: set_nat,C: nat > nat > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_pigeonhole__infinite__rel) ).
thf(823,plain,
! [A: set_nat,B: set_nat,C: nat > nat > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(579,plain,
! [A: nat] :
( ( poly_cutoff_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(cnf,[status(esa)],[578]) ).
thf(580,plain,
! [A: nat] :
( ( poly_cutoff_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(lifteq,[status(thm)],[579]) ).
thf(129,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A
= ( suc @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_dvd__1__iff__1) ).
thf(690,plain,
! [A: nat] :
( ( dvd_dvd_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A
= ( suc @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_gcd__nat_Onot__eq__order__implies__strict) ).
thf(282,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( dvd_dvd_nat @ A @ B )
=> ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3259,plain,
! [B: nat,A: poly_real] :
( ( ( poly_real2 @ A @ zero_zero_real )
!= x )
| ( field_1537545994s_real != ring_1_Ints_real )
| ( ( coeff_real @ A @ zero_zero_nat )
!= ( coeff_real @ sk73 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1030,1563]) ).
thf(3260,plain,
( ( ( poly_real2 @ sk73 @ zero_zero_real )
!= x )
| ( field_1537545994s_real != ring_1_Ints_real ) ),
inference(pattern_uni,[status(thm)],[3259:[bind(A,$thf( sk73 )),bind(B,$thf( zero_zero_nat ))]]) ).
thf(145,axiom,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_real @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_lift__Suc__mono__less) ).
thf(739,plain,
! [A: nat > real,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_real @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_real @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(205,axiom,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_real @ A )
= ( collect_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Collect__cong) ).
thf(993,plain,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_real @ A )
= ( collect_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(159,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_neq0__conv) ).
thf(791,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( ( ( dvd_dvd_nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_gcd__nat_Ostrict__trans) ).
thf(331,plain,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( ( ( dvd_dvd_nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd_nat @ A @ C )
& ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(65,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_old_Onat_Odistinct_I2_J) ).
thf(463,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(67,axiom,
! [A: poly_poly_real] :
( ( A != zero_z1423781445y_real )
=> ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [B: poly_real] :
( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_poly__roots__finite) ).
thf(470,plain,
! [A: poly_poly_real] :
( ( A != zero_z1423781445y_real )
=> ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [B: poly_real] :
( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(117,axiom,
! [A: poly_real] : ( dvd_dvd_poly_real @ A @ zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_dvd__0__right) ).
thf(643,plain,
! [A: poly_real] : ( dvd_dvd_poly_real @ A @ zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(194,axiom,
( ( coeff_real @ zero_zero_poly_real )
= ( ^ [A: nat] : zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_zero__poly_Orep__eq) ).
thf(951,plain,
( ( coeff_real @ zero_zero_poly_real )
= ( ^ [A: nat] : zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(133,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_gr__zeroI) ).
thf(703,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(1092,plain,
sk73 != zero_zero_poly_real,
inference(cnfConj,[status(thm)],[1090]) ).
thf(1094,plain,
sk73 != zero_zero_poly_real,
inference(lifteq,[status(thm)],[1092]) ).
thf(4261,plain,
( ~ ( finite_finite_real @ ring_1_Ints_real )
| ( ( sk77 @ ring_1_Ints_real )
!= one_one_real )
| ~ $true
| ( ( member_real @ ( sk77 @ ring_1_Ints_real ) @ ring_1_Ints_real )
!= ( member_real @ x @ field_1537545994s_real ) ) ),
inference(paramod_ordered,[status(thm)],[4218,398]) ).
thf(4262,plain,
( ~ ( finite_finite_real @ ring_1_Ints_real )
| ( ( sk77 @ ring_1_Ints_real )
!= one_one_real )
| ( ( member_real @ ( sk77 @ ring_1_Ints_real ) @ ring_1_Ints_real )
!= ( member_real @ x @ field_1537545994s_real ) ) ),
inference(simp,[status(thm)],[4261]) ).
thf(4267,plain,
( ~ ( finite_finite_real @ ring_1_Ints_real )
| ( ( sk77 @ ring_1_Ints_real )
!= one_one_real )
| ( ( sk77 @ ring_1_Ints_real )
!= x )
| ( field_1537545994s_real != ring_1_Ints_real ) ),
inference(simp,[status(thm)],[4262]) ).
thf(24,axiom,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_gcd__nat_Oextremum__unique) ).
thf(314,plain,
! [A: nat] :
( ( dvd_dvd_nat @ zero_zero_nat @ A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3255,plain,
! [B: nat,A: poly_real] :
( ( member_real @ ( poly_real2 @ A @ zero_zero_real ) @ ring_1_Ints_real )
| ( ( coeff_real @ A @ zero_zero_nat )
!= ( coeff_real @ sk73 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1030,1091]) ).
thf(3256,plain,
member_real @ ( poly_real2 @ sk73 @ zero_zero_real ) @ ring_1_Ints_real,
inference(pattern_uni,[status(thm)],[3255:[bind(A,$thf( sk73 )),bind(B,$thf( zero_zero_nat ))]]) ).
thf(233,axiom,
! [A: poly_real,B: real] :
( ( ( coeff_real @ A @ ( degree_real @ A ) )
= one_one_real )
=> ( ! [C: nat] : ( member_real @ ( coeff_real @ A @ C ) @ ring_1_Ints_real )
=> ( ( ( poly_real2 @ A @ B )
= zero_zero_real )
=> ( algebraic_int_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_algebraic__int_Ointros) ).
thf(1084,plain,
! [A: poly_real,B: real] :
( ( ( coeff_real @ A @ ( degree_real @ A ) )
= one_one_real )
=> ( ! [C: nat] : ( member_real @ ( coeff_real @ A @ C ) @ ring_1_Ints_real )
=> ( ( ( poly_real2 @ A @ B )
= zero_zero_real )
=> ( algebraic_int_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(189,axiom,
! [A: poly_real] :
( ( ! [B: real] :
( ( poly_real2 @ A @ B )
= zero_zero_real ) )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_poly__all__0__iff__0) ).
thf(931,plain,
! [A: poly_real] :
( ( ! [B: real] :
( ( poly_real2 @ A @ B )
= zero_zero_real ) )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1154,plain,
( ~ $true
| ( ( member_real @ x @ field_1537545994s_real )
!= ( member_real @ one_one_real @ field_1537545994s_real ) ) ),
inference(paramod_ordered,[status(thm)],[545,398]) ).
thf(1155,plain,
( ( member_real @ x @ field_1537545994s_real )
!= ( member_real @ one_one_real @ field_1537545994s_real ) ),
inference(simp,[status(thm)],[1154]) ).
thf(1156,plain,
( ( x != one_one_real )
| ( field_1537545994s_real != field_1537545994s_real ) ),
inference(simp,[status(thm)],[1155]) ).
thf(1157,plain,
x != one_one_real,
inference(simp,[status(thm)],[1156]) ).
thf(149,axiom,
! [A: poly_real > $o,B: poly_real > $o] :
( ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [C: poly_real] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1810960971y_real @ ( collect_poly_real @ A ) )
& ( finite1810960971y_real @ ( collect_poly_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__Collect__disjI) ).
thf(759,plain,
! [A: poly_real > $o,B: poly_real > $o] :
( ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [C: poly_real] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1810960971y_real @ ( collect_poly_real @ A ) )
& ( finite1810960971y_real @ ( collect_poly_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(245,axiom,
! [A: poly_real,B: real,C: nat] :
( ( ( pderiv_real @ A )
!= zero_zero_poly_real )
=> ( ( ( order_real @ B @ A )
!= zero_zero_nat )
=> ( ( ( order_real @ B @ ( pderiv_real @ A ) )
= C )
= ( ( order_real @ B @ A )
= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_order__pderiv2) ).
thf(1126,plain,
! [A: poly_real,B: real,C: nat] :
( ( ( pderiv_real @ A )
!= zero_zero_poly_real )
=> ( ( ( order_real @ B @ A )
!= zero_zero_nat )
=> ( ( ( order_real @ B @ ( pderiv_real @ A ) )
= C )
= ( ( order_real @ B @ A )
= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(771,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(cnf,[status(esa)],[770]) ).
thf(240,axiom,
! [A: real > $o] :
( ~ ( finite_finite_real @ ( collect_real @ A ) )
=> ? [B: real] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_not__finite__existsD) ).
thf(1108,plain,
! [A: real > $o] :
( ~ ( finite_finite_real @ ( collect_real @ A ) )
=> ? [B: real] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(201,axiom,
! [A: set_nat,B: set_real,C: nat > real > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_pigeonhole__infinite__rel) ).
thf(976,plain,
! [A: set_nat,B: set_real,C: nat > real > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(128,axiom,
! [A: real] :
( ( member_real @ A @ field_1537545994s_real )
=> ( member_real @ ( inverse_inverse_real @ A ) @ field_1537545994s_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_Rats__inverse) ).
thf(688,plain,
! [A: real] :
( ( member_real @ A @ field_1537545994s_real )
=> ( member_real @ ( inverse_inverse_real @ A ) @ field_1537545994s_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Suc__less__eq) ).
thf(581,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(132,axiom,
! [A: poly_real > $o,B: poly_real > $o] :
( ( ( finite1810960971y_real @ ( collect_poly_real @ A ) )
| ( finite1810960971y_real @ ( collect_poly_real @ B ) ) )
=> ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [C: poly_real] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__Collect__conjI) ).
thf(699,plain,
! [A: poly_real > $o,B: poly_real > $o] :
( ( ( finite1810960971y_real @ ( collect_poly_real @ A ) )
| ( finite1810960971y_real @ ( collect_poly_real @ B ) ) )
=> ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [C: poly_real] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(167,axiom,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( ( dvd_dvd_poly_real @ A @ one_one_poly_real )
= ( ( degree_real @ A )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_is__unit__iff__degree) ).
thf(813,plain,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( ( dvd_dvd_poly_real @ A @ one_one_poly_real )
= ( ( degree_real @ A )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_Suc__less__SucD) ).
thf(517,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(304,plain,
( ( ^ [A: nat,B: nat] :
( ( dvd_dvd_nat @ A @ B )
& ( dvd_dvd_nat @ B @ A ) ) )
= ( (=) @ nat ) ),
inference(lifteq,[status(thm)],[303]) ).
thf(226,axiom,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_mem__Collect__eq) ).
thf(1062,plain,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(389,plain,
! [B: nat > $o,A: nat] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
inference(cnf,[status(esa)],[388]) ).
thf(390,plain,
! [B: nat > $o,A: nat] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
inference(lifteq,[status(thm)],[389]) ).
thf(237,axiom,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( ( coeff_real @ A @ ( degree_real @ A ) )
!= zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_leading__coeff__neq__0) ).
thf(1101,plain,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( ( coeff_real @ A @ ( degree_real @ A ) )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(142,axiom,
! [A: poly_real > $o,B: poly_real > $o] :
( ! [C: poly_real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_poly_real @ A )
= ( collect_poly_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_Collect__cong) ).
thf(731,plain,
! [A: poly_real > $o,B: poly_real > $o] :
( ! [C: poly_real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_poly_real @ A )
= ( collect_poly_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(418,plain,
( cr_poly_real
= ( ^ [A: nat > real,B: poly_real] :
( A
= ( coeff_real @ B ) ) ) ),
inference(lifteq,[status(thm)],[417]) ).
thf(76,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_zero__less__iff__neq__zero) ).
thf(510,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(137,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_lift__Suc__mono__less) ).
thf(716,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(243,axiom,
! [A: poly_real] :
( ( poly_real2 @ ( reflect_poly_real @ A ) @ zero_zero_real )
= ( coeff_real @ A @ ( degree_real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_poly__reflect__poly__0) ).
thf(1116,plain,
! [A: poly_real] :
( ( poly_real2 @ ( reflect_poly_real @ A ) @ zero_zero_real )
= ( coeff_real @ A @ ( degree_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(248,axiom,
( algebraic_real
= ( ^ [A: real] :
? [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
& ( B != zero_zero_poly_real )
& ( ( poly_real2 @ B @ A )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_algebraic__def) ).
thf(1133,plain,
( algebraic_real
= ( ^ [A: real] :
? [B: poly_real] :
( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
& ( B != zero_zero_poly_real )
& ( ( poly_real2 @ B @ A )
= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(999,plain,
! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ),
inference(cnf,[status(esa)],[998]) ).
thf(199,axiom,
! [A: set_real,B: set_real,C: real > real > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_pigeonhole__infinite__rel) ).
thf(967,plain,
! [A: set_real,B: set_real,C: real > real > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(175,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_not0__implies__Suc) ).
thf(867,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(3642,plain,
! [A: nat] :
( ( ( sk30 @ one_one_nat )
= A )
| ( ( suc @ sk79 )
!= ( suc @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3632,2472]) ).
thf(3643,plain,
( ( sk30 @ one_one_nat )
= sk79 ),
inference(pattern_uni,[status(thm)],[3642:[bind(A,$thf( sk79 ))]]) ).
thf(3733,plain,
sk79 = zero_zero_nat,
inference(rewrite,[status(thm)],[3643,2474]) ).
thf(262,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
inference(cnf,[status(esa)],[261]) ).
thf(4396,plain,
! [B: nat > $o,A: nat] :
( ( member_nat @ A @ ( collect_nat @ B ) )
| ( ( B @ A )
!= ( algebraic_int_real @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[390,1018]) ).
thf(4484,plain,
! [A: nat] :
( member_nat @ A
@ ( collect_nat
@ ^ [B: nat] : ( algebraic_int_real @ zero_zero_real ) ) ),
inference(pre_uni,[status(thm)],[4396:[bind(A,$thf( A )),bind(B,$thf( ^ [C: nat] : ( algebraic_int_real @ zero_zero_real ) ))]]) ).
thf(4811,plain,
! [A: nat] :
( member_nat @ A
@ ( collect_nat
@ ^ [B: nat] : $true ) ),
inference(rewrite,[status(thm)],[4484,1018]) ).
thf(95,axiom,
ord_less_poly_real @ zero_zero_poly_real @ one_one_poly_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_zero__less__one) ).
thf(564,plain,
ord_less_poly_real @ zero_zero_poly_real @ one_one_poly_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(20,axiom,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_gcd__nat_Orefl) ).
thf(305,plain,
! [A: nat] : ( dvd_dvd_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,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_294_linorder__neqE__nat) ).
thf(437,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)],[60]) ).
thf(131,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Collect__cong) ).
thf(696,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(75,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_old_Onat_Odistinct_I1_J) ).
thf(506,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(227,axiom,
member_real @ zero_zero_real @ ring_1_Ints_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Ints__0) ).
thf(1065,plain,
member_real @ zero_zero_real @ ring_1_Ints_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(52,axiom,
! [A: poly_real > $o] :
( ~ ( finite1810960971y_real @ ( collect_poly_real @ A ) )
=> ? [B: poly_real] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_not__finite__existsD) ).
thf(415,plain,
! [A: poly_real > $o] :
( ~ ( finite1810960971y_real @ ( collect_poly_real @ A ) )
=> ? [B: poly_real] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1152,plain,
! [A: nat > real] :
( ( cr_poly_real @ A )
= ( ^ [B: poly_real] :
( A
= ( coeff_real @ B ) ) ) ),
inference(func_ext,[status(esa)],[418]) ).
thf(174,axiom,
! [A: set_poly_real,B: set_nat,C: poly_real > nat > $o] :
( ~ ( finite1810960971y_real @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: poly_real] :
( ( member_poly_real @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [E: poly_real] :
( ( member_poly_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_pigeonhole__infinite__rel) ).
thf(860,plain,
! [A: set_poly_real,B: set_nat,C: poly_real > nat > $o] :
( ~ ( finite1810960971y_real @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: poly_real] :
( ( member_poly_real @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite1810960971y_real
@ ( collect_poly_real
@ ^ [E: poly_real] :
( ( member_poly_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(214,axiom,
! [A: real,B: poly_real,C: real] :
( ( algebraic_int_real @ A )
=> ( ( ( poly_real2 @ B @ C )
= A )
=> ( ! [D: nat] : ( member_real @ ( coeff_real @ B @ D ) @ ring_1_Ints_real )
=> ( ( ( coeff_real @ B @ ( degree_real @ B ) )
= one_one_real )
=> ( ( ord_less_nat @ zero_zero_nat @ ( degree_real @ B ) )
=> ( algebraic_int_real @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_algebraic__int__root) ).
thf(1019,plain,
! [A: real,B: poly_real,C: real] :
( ( algebraic_int_real @ A )
=> ( ( ( poly_real2 @ B @ C )
= A )
=> ( ! [D: nat] : ( member_real @ ( coeff_real @ B @ D ) @ ring_1_Ints_real )
=> ( ( ( coeff_real @ B @ ( degree_real @ B ) )
= one_one_real )
=> ( ( ord_less_nat @ zero_zero_nat @ ( degree_real @ B ) )
=> ( algebraic_int_real @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(644,plain,
! [A: poly_real] : ( dvd_dvd_poly_real @ A @ zero_zero_poly_real ),
inference(cnf,[status(esa)],[643]) ).
thf(184,axiom,
! [A: real > $o,B: real > $o] :
( ( finite_finite_real
@ ( collect_real
@ ^ [C: real] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_real @ ( collect_real @ A ) )
& ( finite_finite_real @ ( collect_real @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__Collect__disjI) ).
thf(908,plain,
! [A: real > $o,B: real > $o] :
( ( finite_finite_real
@ ( collect_real
@ ^ [C: real] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_real @ ( collect_real @ A ) )
& ( finite_finite_real @ ( collect_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_Nat_OlessE) ).
thf(850,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(209,axiom,
! [A: real] :
( ( algebraic_int_real @ A )
=> ~ ! [B: poly_real] :
( ( ( coeff_real @ B @ ( degree_real @ B ) )
= one_one_real )
=> ( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
=> ( ( poly_real2 @ B @ A )
!= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_algebraic__int_Ocases) ).
thf(1004,plain,
! [A: real] :
( ( algebraic_int_real @ A )
=> ~ ! [B: poly_real] :
( ( ( coeff_real @ B @ ( degree_real @ B ) )
= one_one_real )
=> ( ! [C: nat] : ( member_real @ ( coeff_real @ B @ C ) @ ring_1_Ints_real )
=> ( ( poly_real2 @ B @ A )
!= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( dvd_dvd_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_gcd__nat_Ostrict__implies__order) ).
thf(369,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd_nat @ A @ B )
& ( A != B ) )
=> ( dvd_dvd_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(253,plain,
! [B: poly_real,A: poly_poly_real] :
( ( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real )
= ( ( A = zero_z1423781445y_real )
| ( ( order_poly_real @ B @ A )
!= zero_zero_nat ) ) ),
inference(cnf,[status(esa)],[252]) ).
thf(254,plain,
! [B: poly_real,A: poly_poly_real] :
( ( ( poly_poly_real2 @ A @ B )
= zero_zero_poly_real )
= ( ( A = zero_z1423781445y_real )
| ( ( order_poly_real @ B @ A )
!= zero_zero_nat ) ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(70,axiom,
! [A: real] :
( ( algebraic_int_real @ A )
=> ( ( member_real @ A @ field_1537545994s_real )
=> ( member_real @ A @ ring_1_Ints_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_rational__algebraic__int__is__int) ).
thf(486,plain,
! [A: real] :
( ( algebraic_int_real @ A )
=> ( ( member_real @ A @ field_1537545994s_real )
=> ( member_real @ A @ ring_1_Ints_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(155,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_293_infinite__descent) ).
thf(775,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)],[155]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_Suc__lessI) ).
thf(496,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(229,axiom,
! [A: poly_real,B: poly_real,C: nat,D: nat] :
( ( divide1561404011n_real @ zero_zero_real @ zero_zero_poly_real @ A @ B @ C @ D )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_divide__poly__main__0) ).
thf(1069,plain,
! [A: poly_real,B: poly_real,C: nat,D: nat] :
( ( divide1561404011n_real @ zero_zero_real @ zero_zero_poly_real @ A @ B @ C @ D )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(5117,plain,
$false,
inference(e,[status(thm)],[645,809,629,1024,1105,3434,1110,352,365,1823,4183,1031,1068,873,379,440,523,762,730,276,614,677,385,384,1137,533,797,2448,747,2042,538,417,2082,2405,257,1095,404,320,565,3820,570,719,372,587,917,934,1055,724,802,344,1247,770,1568,289,448,421,870,1100,261,1232,3268,789,591,1040,937,966,905,602,3986,397,877,734,956,1072,1119,998,1405,428,1104,265,527,312,307,920,546,810,381,366,534,270,529,1047,798,1091,302,260,598,820,561,297,2969,429,2396,693,630,275,2150,252,361,625,682,551,710,1106,916,467,522,830,1079,1027,324,974,317,1017,2973,725,403,1096,388,356,593,499,989,519,742,578,328,2460,1028,488,339,554,537,637,1016,706,686,476,2472,1039,997,985,738,1131,2851,1050,911,503,605,343,360,805,311,541,1563,398,953,765,1054,794,4004,1135,750,425,264,856,279,573,296,4017,444,601,513,430,584,772,3266,281,545,904,975,641,391,382,4837,2738,1107,919,540,445,936,611,787,713,4218,2474,947,681,274,784,996,362,2839,737,303,271,599,1011,419,880,649,434,387,3747,816,621,251,3483,1952,1112,983,2439,399,959,768,1015,1113,1000,431,653,1066,278,883,3806,394,986,473,722,675,426,589,944,680,255,648,1081,516,342,3444,1034,2333,1018,1181,823,557,580,690,282,3260,739,993,263,1098,1053,791,331,463,470,1130,643,544,951,808,703,1094,4267,314,3256,250,627,1084,363,931,1157,759,1126,771,1108,976,688,903,524,581,699,813,517,304,1062,390,401,1101,258,731,418,1030,914,510,2462,383,536,716,1116,1133,300,999,967,2815,422,867,373,3733,262,4811,564,305,358,437,664,696,796,506,268,532,1065,886,415,1152,860,596,1019,644,908,850,1004,442,369,254,486,309,543,1769,1088,592,1014,1037,775,560,496,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP094^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % 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
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % 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 19:54:56 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
% 1.01/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.00/1.19 % [INFO] Parsing done (390ms).
% 2.32/1.21 % [INFO] Running in sequential loop mode.
% 3.36/1.61 % [INFO] eprover registered as external prover.
% 3.36/1.62 % [INFO] Scanning for conjecture ...
% 3.54/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 344 axioms. Running axiom selection ...
% 3.97/1.94 % [INFO] Axiom selection finished. Selected 247 axioms (removed 97 axioms).
% 4.71/2.15 % [INFO] Problem is higher-order (TPTP THF).
% 4.71/2.18 % [INFO] Type checking passed.
% 4.71/2.18 % [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 ...
% 69.26/29.06 % External prover 'e' found a proof!
% 69.26/29.06 % [INFO] Killing All external provers ...
% 69.26/29.06 % Time passed: 28715ms (effective reasoning time: 27848ms)
% 69.26/29.06 % 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)>
% 69.26/29.07 % Axioms used in derivation (247): fact_325_gcd__nat_Oorder__iff__strict, fact_259_gr__implies__not__zero, fact_323_gcd__nat_Ostrict__implies__order, fact_114_poly__reflect__poly__0, fact_314_Ex__less__Suc2, fact_296_lift__Suc__mono__less__iff, fact_342_Rats__no__bot__less, fact_55_poly__cutoff__0, fact_330_gcd__nat_Oirrefl, fact_218_unit__imp__dvd, fact_71_order__root, fact_202_dvd__1__left, fact_167_degree__1, fact_78_divide__poly__main__0, fact_300_dvd__pos__nat, fact_242_rational__algebraic__int__is__int, fact_25_pigeonhole__infinite__rel, fact_270_strict__inc__induct, fact_313_gr0__conv__Suc, fact_33_poly__eq__poly__eq__iff, fact_21_not__finite__existsD, fact_289_less__not__refl2, fact_306_zero__less__one, fact_332_gcd__nat_Otrans, fact_186_dvd__0__left__iff, fact_23_not__finite__existsD, fact_195_not__is__unit__0, fact_338_poly__IVT__pos, fact_282_Suc__lessI, fact_337_gcd__nat_Oextremum__unique, fact_277_not__less__eq, fact_302_not__one__less__zero, fact_14_finite__Collect__disjI, fact_179_is__unit__iff__degree, fact_204_dvd__refl, fact_297_lift__Suc__mono__less__iff, fact_220_not0__implies__Suc, fact_244_algebraic__int__root, fact_119_mem__Collect__eq, fact_125_Collect__cong, fact_305_not__one__less__zero, fact_160_poly__cutoff__1, fact_236_algebraic__int_Ocases, fact_212_dvd__0__left, fact_176_one__reorient, fact_50_zero__reorient, fact_133_algebraic__def, fact_334_gcd__nat_Oasym, fact_281_less__SucE, fact_226_zero__induct, fact_333_gcd__nat_Orefl, fact_315_nat__dvd__not__less, fact_137_zero__poly_Orep__eq, fact_86_p_I1_J, fact_123_Collect__mem__eq, fact_328_gcd__nat_Ostrict__trans, fact_34_poly__eq__poly__eq__iff, fact_285_Nat_OlessE, fact_12_finite__Collect__conjI, fact_201_dvd__1__iff__1, fact_291_less__irrefl__nat, fact_326_gcd__nat_Ostrict__trans2, fact_284_Suc__lessD, fact_298_lift__Suc__mono__less, fact_29_pigeonhole__infinite__rel, fact_41_pderiv__0, fact_154_Rats__0, fact_231_old_Onat_Odistinct_I2_J, fact_64_synthetic__div__eq__0__iff, fact_232_nat_Odistinct_I1_J, fact_245_gcd__nat_Oextremum__uniqueI, fact_178_Rats__1, fact_52_is__zero__null, fact_196_not__is__unit__0, fact_269_not__less__less__Suc__eq, fact_276_All__less__Suc, fact_11_finite__Collect__conjI, fact_185_dvd__0__left__iff, fact_339_poly__IVT__neg, fact_278_less__Suc__eq, fact_38_degree__0, fact_228_nat__induct, fact_251_neq0__conv, fact_189_dvd__0__right, fact_127_Collect__cong, fact_301_finite__divisors__nat, fact_158_rsquarefree__def, fact_331_gcd__nat_Oeq__iff, fact_250_less__nat__zero__code, fact_31_pigeonhole__infinite__rel, fact_140_poly__0__coeff__0, fact_264_not__less0, fact_238_algebraic__int__0, fact_10_poly__0, fact_18_poly__all__0__iff__0, fact_181_poly__shift__1, fact_295_linorder__neqE__linordered__idom, fact_121_mem__Collect__eq, fact_335_gcd__nat_Oextremum, fact_47_zero__reorient, fact_247_finite__Collect__less__nat, fact_230_old_Onat_Odistinct_I1_J, fact_194_One__nat__def, fact_246_gcd__nat_Onot__eq__extremum, fact_225_Suc__neq__Zero, fact_191_dvd__0__right, fact_223_Zero__not__Suc, fact_207_zero__neq__one, fact_3_p_I2_J, fact_63__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062, fact_130_coeff__inject, fact_286_Rats__inverse, fact_336_gcd__nat_Oextremum__strict, fact_321_gcd__nat_Onot__eq__order__implies__strict, fact_221_old_Onat_Oinducts, fact_227_diff__induct, fact_283_Suc__lessE, fact_32_pigeonhole__infinite__rel, fact_126_Collect__cong, fact_199_old_Onat_Oinject, fact_87_reflect__poly__0, fact_248_not__gr__zero, fact_198_nat_Oinject, fact_131_algebraicE, fact_293_infinite__descent, fact_90_synthetic__div__0, fact_341_Rats__dense__in__real, fact_304_not__one__less__zero, fact_164_order__pderiv, fact_312_All__less__Suc2, fact_219_one__dvd, fact_324_gcd__nat_Ostrict__iff__order, fact_175_lead__coeff__1, fact_49_zero__reorient, fact_104_coeff__0__reflect__poly__0__iff, fact_263_not__gr0, fact_209_zero__neq__one, fact_15_finite__Collect__disjI, fact_132_algebraicI, fact_98_reflect__poly__reflect__poly, fact_265_less__zeroE, fact_240_int__imp__algebraic__int, fact_26_pigeonhole__infinite__rel, fact_168_poly__1, fact_272_less__trans__Suc, fact_120_mem__Collect__eq, fact_153_Rats__infinite, fact_290_less__not__refl3, fact_309_zero__less__one, fact_275_Suc__less__eq2, fact_177_Ints__1, fact_253_Suc__mono, fact_1_poly__roots__finite, fact_146_order__0I, fact_274_less__antisym, fact_258_zero__less__iff__neq__zero, fact_190_dvd__0__right, fact_260_not__less__zero, fact_203_dvd__trans, fact_311_gr0__implies__Suc, fact_310_less__Suc__eq__0__disj, fact_316_nat__induct__non__zero, fact_208_zero__neq__one, fact_13_finite__Collect__conjI, fact_134_algebraic__altdef, fact_27_pigeonhole__infinite__rel, fact_214_dvd__0__left, fact_280_less__SucI, fact_44_pderiv__eq__0__iff, fact_217_dvd__unit__imp__unit, fact_159_rsquarefree__def, fact_206_Suc__inject, fact_184_dvd__0__left__iff, fact_180_not__dvd__pderiv, fact_268_bot__nat__0_Oextremum__strict, fact_237_exists__least__lemma, fact_243_algebraic__int__inverse, fact_200_nat__dvd__1__iff__1, fact_145_order__0I, fact_308_zero__less__one, fact_156_Ints__0, fact_241_algebraic__int__imp__algebraic, fact_340_finite__M__bounded__by__nat, fact_239_dvd__antisym, fact_28_pigeonhole__infinite__rel, fact_37_irrationsl, fact_2_poly__roots__finite, fact_222_old_Onat_Oexhaust, fact_254_Suc__less__eq, fact_255_zero__less__Suc, fact_279_Ex__less__Suc, fact_124_Collect__mem__eq, fact_16_finite__Collect__disjI, fact_19_poly__all__0__iff__0, fact_36_assms_I2_J, fact_129_poly__eq__iff, fact_73_leading__coeff__0__iff, fact_109_degree__reflect__poly__eq, fact_48_zero__reorient, fact_128_poly__eqI, fact_271_less__Suc__induct, fact_155_Ints__0, fact_292_nat__less__induct, fact_95_coeff__0, fact_287_nat__neq__iff, fact_150_leading__coeff__neq__0, fact_233_algebraic__int_Oinducts, fact_122_Collect__mem__eq, fact_327_gcd__nat_Ostrict__trans1, fact_103_coeff__0__reflect__poly, fact_257_less__one, fact_288_less__not__refl, fact_299_lift__Suc__mono__less, fact_329_gcd__nat_Oantisym, fact_229_nat_OdiscI, fact_163_order__pderiv2, fact_4__092_060open_062pderiv_Ap_A_092_060noteq_062_A0_092_060close_062, fact_262_gr0I, fact_166_dvd__pderiv__iff, fact_266_gr__implies__not0, fact_58_reflect__poly__at__0__eq__0__iff, fact_70_order__root, fact_165_cr__poly__def, fact_234_algebraic__int_Ointros, fact_22_not__finite__existsD, fact_67_poly__shift__0, fact_24_pigeonhole__infinite__rel, fact_224_Zero__neq__Suc, fact_171_pderiv__1, fact_81_zero__poly_Otransfer, fact_252_lessI, fact_294_linorder__neqE__nat, fact_322_gcd__nat_Ostrict__implies__not__eq, fact_8_poly__0, fact_235_algebraic__int_Osimps, fact_249_bot__nat__0_Onot__eq__extremum, fact_256_less__Suc0, fact_205_n__not__Suc__n, fact_273_Suc__less__SucD, fact_5_p_I3_J, fact_20_rsquarefree__roots, fact_261_gr__zeroI, fact_35_n__def, fact_30_pigeonhole__infinite__rel, fact_343_poly__pinfty__gt__lc, fact_267_infinite__descent0, fact_213_dvd__0__left
% 69.26/29.07 % No. of inferences in proof: 812
% 69.26/29.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 28715 ms resp. 27848 ms w/o parsing
% 70.54/29.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 70.54/29.31 % [INFO] Killing All external provers ...
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