TSTP Solution File: ITP194^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP194^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:43 EDT 2024
% Result : Theorem 11.48s 3.65s
% Output : Refutation 11.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 322
% Syntax : Number of formulae : 607 ( 235 unt; 39 typ; 0 def)
% Number of atoms : 1685 ( 485 equ; 12 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 4446 ( 257 ~; 49 |; 68 &;3236 @)
% ( 0 <=>; 836 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 163 ( 163 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 12 con; 0-6 aty)
% Number of variables : 1541 ( 80 ^1431 !; 30 ?;1541 :)
% Comments :
%------------------------------------------------------------------------------
thf(poly_poly_poly_real_type,type,
poly_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(poly_real_type,type,
poly_real: $tType ).
thf(poly_nat_type,type,
poly_nat: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(sgn_sgn_poly_real_type,type,
sgn_sgn_poly_real: poly_real > poly_real ).
thf(sgn_sgn_real_type,type,
sgn_sgn_real: real > real ).
thf(zero_zero_nat_type,type,
zero_zero_nat: nat ).
thf(zero_z1423781445y_real_type,type,
zero_z1423781445y_real: poly_poly_real ).
thf(zero_zero_poly_real_type,type,
zero_zero_poly_real: poly_real ).
thf(zero_zero_real_type,type,
zero_zero_real: real ).
thf(if_real_type,type,
if_real: $o > real > real > real ).
thf(ord_less_nat_type,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_poly_real_type,type,
ord_less_poly_real: poly_real > poly_real > $o ).
thf(ord_less_real_type,type,
ord_less_real: real > real > $o ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_le1180086932y_real_type,type,
ord_le1180086932y_real: poly_real > poly_real > $o ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: real > real > $o ).
thf(ord_min_real_type,type,
ord_min_real: real > real > real ).
thf(divide1561404011n_real_type,type,
divide1561404011n_real: real > poly_real > poly_real > poly_real > nat > nat > poly_real ).
thf(is_zero_real_type,type,
is_zero_real: poly_real > $o ).
thf(order_poly_real_type,type,
order_poly_real: poly_real > poly_poly_real > nat ).
thf(order_real_type,type,
order_real: real > poly_real > nat ).
thf(poly_poly_real2_type,type,
poly_poly_real2: poly_poly_real > poly_real > poly_real ).
thf(poly_real2_type,type,
poly_real2: poly_real > real > real ).
thf(poly_cutoff_real_type,type,
poly_cutoff_real: nat > poly_real > poly_real ).
thf(poly_shift_real_type,type,
poly_shift_real: nat > poly_real > poly_real ).
thf(reflect_poly_real_type,type,
reflect_poly_real: poly_real > poly_real ).
thf(sturm_1076696862f_real_type,type,
sturm_1076696862f_real: poly_real > real ).
thf(sturm_1308388506f_real_type,type,
sturm_1308388506f_real: poly_real > real ).
thf(member_real_type,type,
member_real: real > set_real > $o ).
thf(lb1_type,type,
lb1: real ).
thf(lb2_type,type,
lb2: real ).
thf(lb_type,type,
lb: real ).
thf(p_type,type,
p: poly_real ).
thf(thesis_type,type,
thesis: $o ).
thf(199,axiom,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_order__less__le__subst1) ).
thf(1024,plain,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(152,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_linorder__wlog) ).
thf(846,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(201,axiom,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_order__less__subst2) ).
thf(1031,plain,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(242,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ord_less_real @ C @ A )
& ( ord_less_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_field__lbound__gt__zero) ).
thf(1179,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ? [C: real] :
( ( ord_less_real @ zero_zero_real @ C )
& ( ord_less_real @ C @ A )
& ( ord_less_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(25,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_le__0__eq) ).
thf(352,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(119,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( ord_min_real @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_min_OcoboundedI2) ).
thf(683,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( ord_min_real @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(40,axiom,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_order__subst1) ).
thf(408,plain,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(190,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_bot__nat__0_Oextremum__uniqueI) ).
thf(977,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(75,axiom,
( ( reflect_poly_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_reflect__poly__0) ).
thf(523,plain,
( ( reflect_poly_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(134,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ A @ C )
=> ( ord_less_eq_real @ A @ ( ord_min_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_min_OboundedI) ).
thf(762,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ A @ C )
=> ( ord_less_eq_real @ A @ ( ord_min_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(161,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ C )
= ( ( ord_less_eq_real @ A @ C )
| ( ord_less_eq_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_min__le__iff__disj) ).
thf(873,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ C )
= ( ( ord_less_eq_real @ A @ C )
| ( ord_less_eq_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(249,axiom,
! [A: real,B: real,C: $o] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ B @ A )
=> C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_less__imp__triv) ).
thf(1205,plain,
! [A: real,B: real,C: $o] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(51,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_300_less__induct) ).
thf(449,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)],[51]) ).
thf(234,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_ord__eq__less__subst) ).
thf(1142,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(269,axiom,
! [A: real,B: real,C: poly_real] :
( ( ! [D: real] :
( ( ( ord_less_real @ A @ D )
& ( ord_less_eq_real @ D @ B ) )
=> ( ( poly_real2 @ C @ D )
!= zero_zero_real ) ) )
= ( ! [D: real] :
( ( ( ord_less_real @ A @ D )
& ( ord_less_eq_real @ D @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ D ) ) )
| ! [D: real] :
( ( ( ord_less_real @ A @ D )
& ( ord_less_eq_real @ D @ B ) )
=> ( ord_less_real @ ( poly_real2 @ C @ D ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_not__eq__pos__or__neg__iff__1) ).
thf(1269,plain,
! [A: real,B: real,C: poly_real] :
( ( ! [D: real] :
( ( ( ord_less_real @ A @ D )
& ( ord_less_eq_real @ D @ B ) )
=> ( ( poly_real2 @ C @ D )
!= zero_zero_real ) ) )
= ( ! [D: real] :
( ( ( ord_less_real @ A @ D )
& ( ord_less_eq_real @ D @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ D ) ) )
| ! [D: real] :
( ( ( ord_less_real @ A @ D )
& ( ord_less_eq_real @ D @ B ) )
=> ( ord_less_real @ ( poly_real2 @ C @ D ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(48,axiom,
! [A: real,B: real,C: real] :
( ( ord_min_real @ ( ord_min_real @ A @ B ) @ C )
= ( ord_min_real @ A @ ( ord_min_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_min_Oassoc) ).
thf(440,plain,
! [A: real,B: real,C: real] :
( ( ord_min_real @ ( ord_min_real @ A @ B ) @ C )
= ( ord_min_real @ A @ ( ord_min_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(113,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_gr__implies__not0) ).
thf(655,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(69,axiom,
( ord_min_real
= ( ^ [A: real,B: real] : ( ord_min_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_min_Ocommute) ).
thf(511,plain,
( ord_min_real
= ( ^ [A: real,B: real] : ( ord_min_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(215,axiom,
! [A: poly_real,B: real] :
( ( A != zero_zero_poly_real )
=> ~ ! [C: real] :
( ( ord_less_real @ C @ B )
=> ~ ! [D: real] :
( ( ( ord_less_eq_real @ C @ D )
& ( ord_less_real @ D @ B ) )
=> ( ( poly_real2 @ A @ D )
!= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_last__non__root__interval) ).
thf(1078,plain,
! [A: poly_real,B: real] :
( ( A != zero_zero_poly_real )
=> ~ ! [C: real] :
( ( ord_less_real @ C @ B )
=> ~ ! [D: real] :
( ( ( ord_less_eq_real @ C @ D )
& ( ord_less_real @ D @ B ) )
=> ( ( poly_real2 @ A @ D )
!= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(232,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_less__imp__not__less) ).
thf(1137,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(238,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_11_poly__IVT__pos) ).
thf(1164,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)],[238]) ).
thf(126,axiom,
! [A: real > real > $o,B: real,C: real] :
( ! [D: real,E: real] :
( ( ord_less_eq_real @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: real,E: real] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_linorder__wlog) ).
thf(715,plain,
! [A: real > real > $o,B: real,C: real] :
( ! [D: real,E: real] :
( ( ord_less_eq_real @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: real,E: real] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(283,axiom,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_leI) ).
thf(1327,plain,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(124,axiom,
! [A: real,B: real,C: real] :
( ( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_eq_real @ B @ C ) )
=> ( ( ( ord_less_eq_real @ B @ A )
=> ~ ( ord_less_eq_real @ A @ C ) )
=> ( ( ( ord_less_eq_real @ A @ C )
=> ~ ( ord_less_eq_real @ C @ B ) )
=> ( ( ( ord_less_eq_real @ C @ B )
=> ~ ( ord_less_eq_real @ B @ A ) )
=> ( ( ( ord_less_eq_real @ B @ C )
=> ~ ( ord_less_eq_real @ C @ A ) )
=> ~ ( ( ord_less_eq_real @ C @ A )
=> ~ ( ord_less_eq_real @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_le__cases3) ).
thf(698,plain,
! [A: real,B: real,C: real] :
( ( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_eq_real @ B @ C ) )
=> ( ( ( ord_less_eq_real @ B @ A )
=> ~ ( ord_less_eq_real @ A @ C ) )
=> ( ( ( ord_less_eq_real @ A @ C )
=> ~ ( ord_less_eq_real @ C @ B ) )
=> ( ( ( ord_less_eq_real @ C @ B )
=> ~ ( ord_less_eq_real @ B @ A ) )
=> ( ( ( ord_less_eq_real @ B @ C )
=> ~ ( ord_less_eq_real @ C @ A ) )
=> ~ ( ( ord_less_eq_real @ C @ A )
=> ~ ( ord_less_eq_real @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(183,axiom,
! [A: set_real] :
( ? [B: real] : ( member_real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
=> ? [B: real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
& ! [C: real] :
( ! [D: real] :
( ( member_real @ D @ A )
=> ( ord_less_eq_real @ D @ C ) )
=> ( ord_less_eq_real @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_complete__real) ).
thf(945,plain,
! [A: set_real] :
( ? [B: real] : ( member_real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
=> ? [B: real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
& ! [C: real] :
( ! [D: real] :
( ( member_real @ D @ A )
=> ( ord_less_eq_real @ D @ C ) )
=> ( ord_less_eq_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(80,axiom,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_ord__eq__le__subst) ).
thf(538,plain,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(221,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_order_Ostrict__trans) ).
thf(1095,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(140,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_ord__le__eq__subst) ).
thf(782,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(206,axiom,
( ( sgn_sgn_real @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_sgn__zero) ).
thf(1046,plain,
( ( sgn_sgn_real @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(7,axiom,
! [A: poly_real] :
( ( ord_less_poly_real @ zero_zero_poly_real @ ( sgn_sgn_poly_real @ A ) )
= ( ord_less_poly_real @ zero_zero_poly_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_sgn__greater) ).
thf(301,plain,
! [A: poly_real] :
( ( ord_less_poly_real @ zero_zero_poly_real @ ( sgn_sgn_poly_real @ A ) )
= ( ord_less_poly_real @ zero_zero_poly_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,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_178_nat__neq__iff) ).
thf(320,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)],[13]) ).
thf(264,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_less__asym_H) ).
thf(1254,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(273,axiom,
! [A: real] :
? [B: real] : ( ord_less_real @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_lt__ex) ).
thf(1287,plain,
! [A: real] :
? [B: real] : ( ord_less_real @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(90,axiom,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_ord__le__eq__subst) ).
thf(570,plain,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(31,axiom,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_le__cases) ).
thf(372,plain,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(268,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( B = C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_ord__less__eq__trans) ).
thf(1264,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( B = C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(131,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_eq__iff) ).
thf(751,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(22,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_less__le) ).
thf(344,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(282,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_order_Ostrict__implies__not__eq) ).
thf(1323,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(149,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_less__numeral__extra_I3_J) ).
thf(838,plain,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(179,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_leD) ).
thf(934,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(246,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_ord__less__eq__subst) ).
thf(1191,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(217,axiom,
( ( sgn_sgn_real @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_sgn__0) ).
thf(1087,plain,
( ( sgn_sgn_real @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(262,axiom,
p != zero_zero_poly_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms) ).
thf(1247,plain,
p != zero_zero_poly_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(281,axiom,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_order__less__subst2) ).
thf(1319,plain,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(99,axiom,
! [A: real] :
( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
= ( sgn_sgn_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_sgn__sgn) ).
thf(606,plain,
! [A: real] :
( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
= ( sgn_sgn_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(137,axiom,
ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_le__numeral__extra_I3_J) ).
thf(770,plain,
ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(42,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_ord__eq__le__subst) ).
thf(416,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(3,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_14_poly__all__0__iff__0) ).
thf(289,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)],[3]) ).
thf(49,axiom,
! [A: real] :
( ( ord_min_real @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_min_Oidem) ).
thf(443,plain,
! [A: real] :
( ( ord_min_real @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(208,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( ord_min_real @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_min_Ostrict__coboundedI2) ).
thf(1051,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( ord_min_real @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(98,axiom,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_order__less__le__subst1) ).
thf(602,plain,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(139,axiom,
! [A: nat,B: real > nat,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_ord__eq__le__subst) ).
thf(774,plain,
! [A: nat,B: real > nat,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(9,axiom,
! [A: poly_real] :
( ( ord_less_poly_real @ ( sgn_sgn_poly_real @ A ) @ zero_zero_poly_real )
= ( ord_less_poly_real @ A @ zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_sgn__less) ).
thf(307,plain,
! [A: poly_real] :
( ( ord_less_poly_real @ ( sgn_sgn_poly_real @ A ) @ zero_zero_poly_real )
= ( ord_less_poly_real @ A @ zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: poly_poly_real] :
( ( zero_z1423781445y_real = A )
= ( A = zero_z1423781445y_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_zero__reorient) ).
thf(292,plain,
! [A: poly_poly_real] :
( ( zero_z1423781445y_real = A )
= ( A = zero_z1423781445y_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_linorder__cases) ).
thf(678,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_le__neq__implies__less) ).
thf(546,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(176,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_dual__order_Ostrict__trans) ).
thf(925,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(247,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B )
| ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_less__linear) ).
thf(1199,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B )
| ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(236,axiom,
! [A: nat,B: real > nat,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_ord__eq__less__subst) ).
thf(1153,plain,
! [A: nat,B: real > nat,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(279,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_less__trans) ).
thf(1311,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(18,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_order_Otrans) ).
thf(334,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(219,axiom,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( A
= ( ord_min_real @ A @ B ) )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_min_Ostrict__order__iff) ).
thf(1091,plain,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( A
= ( ord_min_real @ A @ B ) )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(204,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_le__less) ).
thf(1042,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(87,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_antisym__conv3) ).
thf(561,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_leI) ).
thf(424,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_order_Otrans) ).
thf(429,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(185,axiom,
! [A: nat] :
? [B: nat] : ( ord_less_nat @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_gt__ex) ).
thf(957,plain,
! [A: nat] :
? [B: nat] : ( ord_less_nat @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(255,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ ( ord_min_real @ B @ C ) )
=> ~ ( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_min_Ostrict__boundedE) ).
thf(1223,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ ( ord_min_real @ B @ C ) )
=> ~ ( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(168,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_min_real @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_min_Oabsorb1) ).
thf(894,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_min_real @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_le__trans) ).
thf(862,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(24,axiom,
! [A: real,B: real] :
( ( ord_min_real @ ( ord_min_real @ A @ B ) @ B )
= ( ord_min_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_min_Oright__idem) ).
thf(349,plain,
! [A: real,B: real] :
( ( ord_min_real @ ( ord_min_real @ A @ B ) @ B )
= ( ord_min_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_dual__order_Ostrict__implies__not__eq) ).
thf(467,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(28,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_not__gr0) ).
thf(361,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(163,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_bot__nat__0_Oextremum__unique) ).
thf(879,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_less__imp__le__nat) ).
thf(852,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(166,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_le__less) ).
thf(889,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(251,axiom,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_linorder__cases) ).
thf(1210,plain,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(74,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_le__numeral__extra_I3_J) ).
thf(522,plain,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(146,axiom,
! [A: real,B: real] :
( ( ord_min_real @ A @ ( ord_min_real @ A @ B ) )
= ( ord_min_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_min_Oleft__idem) ).
thf(830,plain,
! [A: real,B: real] :
( ( ord_min_real @ A @ ( ord_min_real @ A @ B ) )
= ( ord_min_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1,conjecture,
! [A: real] :
( ( ( poly_real2 @ p @ A )
!= zero_zero_real )
| ( ord_less_real @ lb @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: real] :
( ( ( poly_real2 @ p @ A )
!= zero_zero_real )
| ( ord_less_real @ lb @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(285,plain,
~ ! [A: real] :
( ( ( poly_real2 @ p @ A )
!= zero_zero_real )
| ( ord_less_real @ lb @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(225,axiom,
! [A: real,B: real,C: real] :
( ( A = B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_ord__eq__less__trans) ).
thf(1106,plain,
! [A: real,B: real,C: real] :
( ( A = B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(218,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_less__eq__real__def) ).
thf(1089,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(102,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_min_real @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_min__absorb2) ).
thf(615,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_min_real @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(198,axiom,
! [A: real > real > $o,B: real,C: real] :
( ! [D: real,E: real] :
( ( ord_less_real @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: real] : ( A @ D @ D )
=> ( ! [D: real,E: real] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_linorder__less__wlog) ).
thf(1006,plain,
! [A: real > real > $o,B: real,C: real] :
( ! [D: real,E: real] :
( ( ord_less_real @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: real] : ( A @ D @ D )
=> ( ! [D: real,E: real] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(160,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_order__less__subst1) ).
thf(869,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(73,axiom,
! [A: nat] :
( ( poly_cutoff_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_poly__cutoff__0) ).
thf(519,plain,
! [A: nat] :
( ( poly_cutoff_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(91,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_ord__le__eq__subst) ).
thf(578,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(266,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_63_reflect__poly__at__0__eq__0__iff) ).
thf(1259,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)],[266]) ).
thf(12,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_min_real @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_min_Oabsorb2) ).
thf(317,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_min_real @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(226,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_72_order__root) ).
thf(1111,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)],[226]) ).
thf(257,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_less__imp__not__eq2) ).
thf(1227,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(191,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_eq__refl) ).
thf(980,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_less__not__sym) ).
thf(403,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(58,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_127_order__0I) ).
thf(471,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)],[58]) ).
thf(284,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_10_poly__IVT__neg) ).
thf(1329,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)],[284]) ).
thf(200,axiom,
! [A: real,B: real] :
( ( ~ ( ord_less_real @ A @ B ) )
= ( ( ord_less_real @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_not__less__iff__gr__or__eq) ).
thf(1028,plain,
! [A: real,B: real] :
( ( ~ ( ord_less_real @ A @ B ) )
= ( ( ord_less_real @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(20,axiom,
! [A: nat,B: nat,C: $o] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ A )
=> C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_less__imp__triv) ).
thf(339,plain,
! [A: nat,B: nat,C: $o] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(275,axiom,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_ord__eq__less__subst) ).
thf(1292,plain,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(62,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( A
= ( ord_min_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_min_Oorder__iff) ).
thf(489,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( A
= ( ord_min_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(94,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_less__imp__not__eq2) ).
thf(590,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(188,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_linear) ).
thf(970,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(84,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_min_Ocobounded1) ).
thf(554,plain,
! [A: real,B: real] : ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(132,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_ord__le__eq__trans) ).
thf(753,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(120,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_less__asym_H) ).
thf(686,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(214,axiom,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ( ~ ( ord_less_real @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_antisym__conv3) ).
thf(1075,plain,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ( ~ ( ord_less_real @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(227,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ A )
=> ( ord_less_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_dual__order_Ostrict__trans) ).
thf(1114,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ A )
=> ( ord_less_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_less__or__eq__imp__le) ).
thf(647,plain,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(258,axiom,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_order__le__less__subst1) ).
thf(1231,plain,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(53,axiom,
( ( '?' @ nat )
= ( ^ [A: nat > $o] :
? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_exists__least__iff) ).
thf(457,plain,
( ( '?' @ nat )
= ( ^ [A: nat > $o] :
? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(192,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_75_divide__poly__main__0) ).
thf(984,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)],[192]) ).
thf(127,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_ord__eq__less__trans) ).
thf(721,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(66,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_less__zeroE) ).
thf(503,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(71,axiom,
( ord_min_real
= ( ^ [A: real,B: real] : ( if_real @ ( ord_less_eq_real @ A @ B ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_min__def) ).
thf(515,plain,
( ord_min_real
= ( ^ [A: real,B: real] : ( if_real @ ( ord_less_eq_real @ A @ B ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(235,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ ( ord_min_real @ B @ C ) )
= ( ( ord_less_real @ A @ B )
& ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_min__less__iff__conj) ).
thf(1150,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ ( ord_min_real @ B @ C ) )
= ( ( ord_less_real @ A @ B )
& ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(260,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_271_neqE) ).
thf(1241,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)],[260]) ).
thf(68,axiom,
! [A: nat] :
( ( poly_shift_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_poly__shift__0) ).
thf(508,plain,
! [A: nat] :
( ( poly_shift_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(239,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_leD) ).
thf(1170,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(86,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_less__not__refl) ).
thf(558,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(92,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_order__refl) ).
thf(586,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(248,axiom,
! [A: real] :
( ( ( sgn_sgn_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_sgn__zero__iff) ).
thf(1202,plain,
! [A: real] :
( ( ( sgn_sgn_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(142,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_180_infinite__descent0) ).
thf(792,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)],[142]) ).
thf(135,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_zero__le) ).
thf(765,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(209,axiom,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_order__le__less__subst1) ).
thf(1054,plain,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(36,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_min_real @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_min_Oabsorb__iff2) ).
thf(398,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_min_real @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(202,axiom,
! [A: real] :
( ( ord_less_eq_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_sgn__le__0__iff) ).
thf(1035,plain,
! [A: real] :
( ( ord_less_eq_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(6,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_30_poly__eq__poly__eq__iff) ).
thf(298,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)],[6]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_less__not__refl2) ).
thf(412,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(103,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_gr0I) ).
thf(618,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(70,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_linear) ).
thf(513,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(224,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( ord_min_real @ A @ B ) @ C )
= ( ( ord_less_real @ A @ C )
| ( ord_less_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_min__less__iff__disj) ).
thf(1103,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( ord_min_real @ A @ B ) @ C )
= ( ( ord_less_real @ A @ C )
| ( ord_less_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(155,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_min_real @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_min_Oabsorb__iff1) ).
thf(856,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_min_real @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(171,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_ord__eq__less__subst) ).
thf(904,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(123,axiom,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_order__subst2) ).
thf(694,plain,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_antisym) ).
thf(843,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(265,axiom,
! [A: real] :
~ ( ord_less_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_less__irrefl) ).
thf(1256,plain,
! [A: real] :
~ ( ord_less_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(256,axiom,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_le__numeral__extra_I3_J) ).
thf(1226,plain,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(109,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_bot__nat__0_Oextremum) ).
thf(641,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(180,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_gr__implies__not__zero) ).
thf(936,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_less__not__refl3) ).
thf(313,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(65,axiom,
! [A: real,B: real,C: real] :
( ( A = B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_ord__eq__le__trans) ).
thf(498,plain,
! [A: real,B: real,C: real] :
( ( A = B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(210,axiom,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_poly__0) ).
thf(1058,plain,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(174,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_order__less__subst2) ).
thf(919,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(116,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_Nat_Oex__has__greatest__nat) ).
thf(672,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(34,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_dual__order_Otrans) ).
thf(391,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(233,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_273_neq__iff) ).
thf(1139,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)],[233]) ).
thf(170,axiom,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_order__subst2) ).
thf(900,plain,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(118,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_le__refl) ).
thf(681,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(228,axiom,
~ ! [A: real] :
~ ! [B: real] :
( ( ( poly_real2 @ p @ B )
= zero_zero_real )
=> ( ord_less_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb1_O_A_092_060forall_062x_O_Apoly_Ap_Ax_A_061_A0_A_092_060longrightarrow_062_Alb1_A_060_Ax_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(1117,plain,
~ ! [A: real] :
~ ! [B: real] :
( ( ( poly_real2 @ p @ B )
= zero_zero_real )
=> ( ord_less_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(207,axiom,
! [A: poly_real,B: poly_real] :
( ( ( poly_real2 @ A )
= ( poly_real2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_poly__eq__poly__eq__iff) ).
thf(1048,plain,
! [A: poly_real,B: poly_real] :
( ( ( poly_real2 @ A )
= ( poly_real2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(194,axiom,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_less__le) ).
thf(990,plain,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(89,axiom,
! [A: poly_real] :
( ( ( sgn_sgn_poly_real @ A )
= zero_zero_poly_real )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_sgn__eq__0__iff) ).
thf(567,plain,
! [A: poly_real] :
( ( ( sgn_sgn_poly_real @ A )
= zero_zero_poly_real )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(229,axiom,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_order__le__less__subst2) ).
thf(1122,plain,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(278,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_less__imp__neq) ).
thf(1307,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(33,axiom,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_order__subst1) ).
thf(387,plain,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(64,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_order__subst2) ).
thf(494,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(133,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_order__subst1) ).
thf(758,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(79,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zero__less__iff__neq__zero) ).
thf(535,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(145,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_le__cases3) ).
thf(816,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(100,axiom,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_eq__refl) ).
thf(609,plain,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(14,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_order__less__le__subst1) ).
thf(323,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(95,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_eq__iff) ).
thf(594,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(128,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat] : ( A @ D @ D )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_linorder__less__wlog) ).
thf(726,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat] : ( A @ D @ D )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(104,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ ( ord_min_real @ B @ C ) )
=> ~ ( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_min_OboundedE) ).
thf(621,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ ( ord_min_real @ B @ C ) )
=> ~ ( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_order__le__less__subst2) ).
thf(915,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(182,axiom,
( ( sgn_sgn_poly_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_sgn__0) ).
thf(943,plain,
( ( sgn_sgn_poly_real @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(16,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_order__class_Oorder_Oeq__iff) ).
thf(330,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(156,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_nat__less__le) ).
thf(858,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(30,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_ord__less__eq__trans) ).
thf(367,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(83,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_order__refl) ).
thf(552,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_less__imp__not__less) ).
thf(462,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(178,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_order__class_Oorder_Oeq__iff) ).
thf(932,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(211,axiom,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_order__less__subst1) ).
thf(1061,plain,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(172,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( ord_min_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_min_OcoboundedI1) ).
thf(912,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( ord_min_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(186,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_ord__eq__le__subst) ).
thf(959,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(252,axiom,
! [A: real] :
( ( ( sgn_sgn_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_sgn__eq__0__iff) ).
thf(1213,plain,
! [A: real] :
( ( ( sgn_sgn_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(241,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zero__reorient) ).
thf(1176,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(35,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_order__le__less__subst1) ).
thf(394,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(263,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_less__imp__not__eq) ).
thf(1250,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(107,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_le__antisym) ).
thf(636,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(205,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_less__asym) ).
thf(1044,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(277,axiom,
! [A: real] :
( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_sgn__less) ).
thf(1304,plain,
! [A: real] :
( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(44,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_272_neqE) ).
thf(426,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)],[44]) ).
thf(250,axiom,
~ ( ord_less_real @ zero_zero_real @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_less__numeral__extra_I3_J) ).
thf(1208,plain,
~ ( ord_less_real @ zero_zero_real @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_eq__imp__le) ).
thf(531,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(32,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_ex__least__nat__le) ).
thf(374,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ zero_zero_nat )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(231,axiom,
! [A: real] :
( ( ( poly_real2 @ p @ A )
= zero_zero_real )
=> ( ord_less_real @ lb1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_lb1) ).
thf(1134,plain,
! [A: real] :
( ( ( poly_real2 @ p @ A )
= zero_zero_real )
=> ( ord_less_real @ lb1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_nat__le__linear) ).
thf(342,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [A: real,B: real,C: real] :
( ( ord_min_real @ A @ ( ord_min_real @ B @ C ) )
= ( ord_min_real @ B @ ( ord_min_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_min_Oleft__commute) ).
thf(355,plain,
! [A: real,B: real,C: real] :
( ( ord_min_real @ A @ ( ord_min_real @ B @ C ) )
= ( ord_min_real @ B @ ( ord_min_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(148,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_le__cases) ).
thf(836,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(76,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_less__nat__zero__code) ).
thf(525,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(5,axiom,
! [A: poly_real] :
( ( poly_poly_real2 @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_poly__0) ).
thf(295,plain,
! [A: poly_real] :
( ( poly_poly_real2 @ zero_z1423781445y_real @ A )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_dual__order_Oantisym) ).
thf(327,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(184,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_order__trans) ).
thf(954,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(125,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_not__less0) ).
thf(712,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(197,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_126_order__0I) ).
thf(1003,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)],[197]) ).
thf(222,axiom,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_zero__le__sgn__iff) ).
thf(1098,plain,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(10,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( A
= ( ord_min_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_min_OorderE) ).
thf(310,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( A
= ( ord_min_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(276,axiom,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_order__less__subst1) ).
thf(1300,plain,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(203,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_order__less__subst1) ).
thf(1038,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(150,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_gr__zeroI) ).
thf(840,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(143,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_ord__le__eq__trans) ).
thf(808,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(110,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_order__subst1) ).
thf(643,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(254,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_144_linorder__neqE__linordered__idom) ).
thf(1220,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)],[254]) ).
thf(245,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( ord_min_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_min_Ostrict__coboundedI1) ).
thf(1188,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( ord_min_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(244,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_less__not__sym) ).
thf(1186,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(267,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_dual__order_Oasym) ).
thf(1262,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(259,axiom,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ~ ! [B: real] :
( ! [C: real] :
( ( ( poly_real2 @ A @ C )
= zero_zero_real )
=> ( ord_less_real @ C @ B ) )
=> ~ ! [C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( sgn_sgn_real @ ( poly_real2 @ A @ C ) )
= ( sturm_1308388506f_real @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_root__ub) ).
thf(1235,plain,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ~ ! [B: real] :
( ! [C: real] :
( ( ( poly_real2 @ A @ C )
= zero_zero_real )
=> ( ord_less_real @ C @ B ) )
=> ~ ! [C: real] :
( ( ord_less_eq_real @ B @ C )
=> ( ( sgn_sgn_real @ ( poly_real2 @ A @ C ) )
= ( sturm_1308388506f_real @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(129,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_less__imp__neq) ).
thf(744,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(101,axiom,
~ ( ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_less__numeral__extra_I3_J) ).
thf(613,plain,
~ ( ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(272,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_13_poly__all__0__iff__0) ).
thf(1284,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)],[272]) ).
thf(97,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_dual__order_Orefl) ).
thf(600,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(50,axiom,
! [A: poly_real] :
( ( zero_zero_poly_real = A )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zero__reorient) ).
thf(446,plain,
! [A: poly_real] :
( ( zero_zero_poly_real = A )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(270,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_order__le__less__subst1) ).
thf(1272,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(162,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_dual__order_Oantisym) ).
thf(876,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(106,axiom,
! [A: nat,B: nat > $o,C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ A @ D )
=> ( B @ D ) )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ D @ A )
=> ( ! [E: nat] :
( ( ord_less_nat @ D @ E )
=> ( B @ E ) )
=> ( B @ D ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_nat__descend__induct) ).
thf(627,plain,
! [A: nat,B: nat > $o,C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ A @ D )
=> ( B @ D ) )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ D @ A )
=> ( ! [E: nat] :
( ( ord_less_nat @ D @ E )
=> ( B @ E ) )
=> ( B @ D ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(216,axiom,
! [A: real] :
( ( ( sgn_sgn_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_sgn__0__0) ).
thf(1084,plain,
! [A: real] :
( ( ( sgn_sgn_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(85,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ B @ A )
& ( ord_less_eq_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_dual__order_Oeq__iff) ).
thf(556,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ B @ A )
& ( ord_less_eq_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(60,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_order__subst2) ).
thf(482,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(121,axiom,
! [A: real,B: real] :
( ( A
= ( ord_min_real @ A @ B ) )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_min_OorderI) ).
thf(688,plain,
! [A: real,B: real] :
( ( A
= ( ord_min_real @ A @ B ) )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(230,axiom,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_ord__less__eq__subst) ).
thf(1126,plain,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(274,axiom,
! [A: real,B: real,C: poly_real] :
( ( ! [D: real] :
( ( ( ord_less_eq_real @ A @ D )
& ( ord_less_real @ D @ B ) )
=> ( ( poly_real2 @ C @ D )
!= zero_zero_real ) ) )
= ( ! [D: real] :
( ( ( ord_less_eq_real @ A @ D )
& ( ord_less_real @ D @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ D ) ) )
| ! [D: real] :
( ( ( ord_less_eq_real @ A @ D )
& ( ord_less_real @ D @ B ) )
=> ( ord_less_real @ ( poly_real2 @ C @ D ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_not__eq__pos__or__neg__iff__2) ).
thf(1289,plain,
! [A: real,B: real,C: poly_real] :
( ( ! [D: real] :
( ( ( ord_less_eq_real @ A @ D )
& ( ord_less_real @ D @ B ) )
=> ( ( poly_real2 @ C @ D )
!= zero_zero_real ) ) )
= ( ! [D: real] :
( ( ( ord_less_eq_real @ A @ D )
& ( ord_less_real @ D @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ C @ D ) ) )
| ! [D: real] :
( ( ( ord_less_eq_real @ A @ D )
& ( ord_less_real @ D @ B ) )
=> ( ord_less_real @ ( poly_real2 @ C @ D ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(138,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_dual__order_Otrans) ).
thf(771,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(253,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_order__le__less__subst2) ).
thf(1216,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ( ord_less_nat @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_not__less__iff__gr__or__eq) ).
thf(891,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ( ord_less_nat @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(271,axiom,
! [A: real] :
( ! [B: real] :
( ( ( poly_real2 @ p @ B )
= zero_zero_real )
=> ( ord_less_real @ A @ B ) )
=> ( ! [B: real] :
( ( ord_less_eq_real @ B @ A )
=> ( ( sgn_sgn_real @ ( poly_real2 @ p @ B ) )
= ( sturm_1076696862f_real @ p ) ) )
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_that) ).
thf(1276,plain,
! [A: real] :
( ! [B: real] :
( ( ( poly_real2 @ p @ B )
= zero_zero_real )
=> ( ord_less_real @ A @ B ) )
=> ( ! [B: real] :
( ( ord_less_eq_real @ B @ A )
=> ( ( sgn_sgn_real @ ( poly_real2 @ p @ B ) )
= ( sturm_1076696862f_real @ p ) ) )
=> thesis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(93,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_min_Ocobounded2) ).
thf(588,plain,
! [A: real,B: real] : ( ord_less_eq_real @ ( ord_min_real @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(144,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_274_neq__iff) ).
thf(813,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)],[144]) ).
thf(72,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_le0) ).
thf(517,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_order__class_Oorder_Oantisym) ).
thf(748,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(8,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_73_order__root) ).
thf(304,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)],[8]) ).
thf(223,axiom,
( lb
= ( ord_min_real @ lb1 @ lb2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_lb__def) ).
thf(1101,plain,
( lb
= ( ord_min_real @ lb1 @ lb2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(112,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_bot__nat__0_Onot__eq__extremum) ).
thf(652,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(261,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ? [C: real] :
( ( ord_less_real @ A @ C )
& ( ord_less_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_dense) ).
thf(1244,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ? [C: real] :
( ( ord_less_real @ A @ C )
& ( ord_less_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(196,axiom,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_ord__less__eq__subst) ).
thf(995,plain,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(115,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_172_infinite__descent) ).
thf(667,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)],[115]) ).
thf(23,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_zero__reorient) ).
thf(346,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(82,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_min_real @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_min__absorb1) ).
thf(549,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_min_real @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(237,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_sgn__greater) ).
thf(1161,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(46,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_ord__eq__le__trans) ).
thf(432,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B )
| ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_less__linear) ).
thf(405,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B )
| ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_less__asym) ).
thf(854,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_dual__order_Oasym) ).
thf(790,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(159,axiom,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_order__le__less__subst2) ).
thf(865,plain,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(147,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_dual__order_Oirrefl) ).
thf(833,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(187,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_171_linorder__neqE__nat) ).
thf(967,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)],[187]) ).
thf(88,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_bot__nat__0_Oextremum__strict) ).
thf(564,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(280,axiom,
~ ! [A: real] :
~ ! [B: real] :
( ( ord_less_eq_real @ B @ A )
=> ( ( sgn_sgn_real @ ( poly_real2 @ p @ B ) )
= ( sturm_1076696862f_real @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb2_O_A_092_060forall_062x_092_060le_062lb2_O_Asgn_A_Ipoly_Ap_Ax_J_A_061_Asgn__neg__inf_Ap_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(1314,plain,
~ ! [A: real] :
~ ! [B: real] :
( ( ord_less_eq_real @ B @ A )
=> ( ( sgn_sgn_real @ ( poly_real2 @ p @ B ) )
= ( sturm_1076696862f_real @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(67,axiom,
( is_zero_real
= ( ^ [A: poly_real] : ( A = zero_zero_poly_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_is__zero__null) ).
thf(506,plain,
( is_zero_real
= ( ^ [A: poly_real] : ( A = zero_zero_poly_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(27,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_le__zero__eq) ).
thf(358,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(47,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_antisym) ).
thf(437,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(37,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_less__irrefl__nat) ).
thf(400,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(212,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_dual__order_Ostrict__implies__not__eq) ).
thf(1065,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(240,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_order__less__subst2) ).
thf(1172,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(169,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_less__trans) ).
thf(897,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(59,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_ord__less__eq__subst) ).
thf(474,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(136,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ ( ord_min_real @ B @ C ) )
= ( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_min_Obounded__iff) ).
thf(767,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ ( ord_min_real @ B @ C ) )
= ( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(165,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_less__irrefl) ).
thf(886,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(177,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_order_Ostrict__implies__not__eq) ).
thf(928,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(193,axiom,
! [A: real] :
( ( ord_less_eq_real @ A @ lb2 )
=> ( ( sgn_sgn_real @ ( poly_real2 @ p @ A ) )
= ( sturm_1076696862f_real @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_lb2) ).
thf(987,plain,
! [A: real] :
( ( ord_less_eq_real @ A @ lb2 )
=> ( ( sgn_sgn_real @ ( poly_real2 @ p @ A ) )
= ( sturm_1076696862f_real @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(56,axiom,
! [A: poly_real] :
( ( ( sgn_sgn_poly_real @ A )
= zero_zero_poly_real )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_sgn__0__0) ).
thf(464,plain,
! [A: poly_real] :
( ( ( sgn_sgn_poly_real @ A )
= zero_zero_poly_real )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(17,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_less__eq__nat_Osimps_I1_J) ).
thf(332,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(157,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_le__eq__less__or__eq) ).
thf(860,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(96,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_less__mono__imp__le__mono) ).
thf(596,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(77,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( ord_min_real @ A @ C ) @ ( ord_min_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_min_Omono) ).
thf(528,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( ord_min_real @ A @ C ) @ ( ord_min_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(54,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_order__trans) ).
thf(459,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(195,axiom,
! [A: real] :
~ ( ord_less_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_dual__order_Oirrefl) ).
thf(992,plain,
! [A: real] :
~ ( ord_less_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_order_Ostrict__trans) ).
thf(691,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(220,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_order_Oasym) ).
thf(1093,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(105,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_not__gr__zero) ).
thf(624,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(61,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_neq0__conv) ).
thf(486,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(19,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_dual__order_Orefl) ).
thf(337,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(181,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_not__less__zero) ).
thf(940,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(175,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_dual__order_Oeq__iff) ).
thf(923,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(243,axiom,
! [A: real] :
? [B: real] : ( ord_less_real @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_gt__ex) ).
thf(1184,plain,
! [A: real] :
? [B: real] : ( ord_less_real @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(114,axiom,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_ord__le__eq__subst) ).
thf(659,plain,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_order_Oasym) ).
thf(639,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_antisym__conv) ).
thf(491,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(29,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_order__class_Oorder_Oantisym) ).
thf(364,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_less__imp__not__eq) ).
thf(882,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(189,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_173_nat__less__induct) ).
thf(972,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)],[189]) ).
thf(52,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_antisym__conv) ).
thf(454,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(213,axiom,
! [A: poly_real,B: real] :
( ( A != zero_zero_poly_real )
=> ~ ! [C: real] :
( ( ord_less_real @ B @ C )
=> ~ ! [D: real] :
( ( ( ord_less_real @ B @ D )
& ( ord_less_eq_real @ D @ C ) )
=> ( ( poly_real2 @ A @ D )
!= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_next__non__root__interval) ).
thf(1069,plain,
! [A: poly_real,B: real] :
( ( A != zero_zero_poly_real )
=> ~ ! [C: real] :
( ( ord_less_real @ B @ C )
=> ~ ! [D: real] :
( ( ( ord_less_real @ B @ D )
& ( ord_less_eq_real @ D @ C ) )
=> ( ( poly_real2 @ A @ D )
!= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1337,plain,
$false,
inference(e,[status(thm)],[1024,846,1031,1179,352,683,408,977,523,762,873,1205,449,1142,1269,440,655,511,1078,1137,1164,715,1327,698,945,538,1095,782,1046,301,320,1254,1287,570,372,1264,751,344,1323,838,934,1191,1087,1247,1319,606,770,416,289,443,1051,602,774,307,292,678,546,925,1199,1153,1311,334,1091,1042,561,424,429,957,1223,894,862,349,467,361,879,852,889,1210,522,830,285,1106,1089,615,1006,869,519,578,1259,317,1111,1227,980,403,471,1329,1028,339,1292,489,590,970,554,753,686,1075,1114,647,1231,457,984,721,503,515,1150,1241,508,1170,558,586,1202,792,765,1054,398,1035,298,412,618,513,1103,856,904,694,843,1256,1226,641,936,313,498,1058,919,672,391,1139,900,681,1117,1048,990,567,1122,1307,387,494,758,535,816,609,323,594,726,621,915,943,330,858,367,552,462,932,1061,912,959,1213,1176,394,1250,636,1044,1304,426,1208,531,374,1134,342,355,836,525,295,327,954,712,1003,1098,310,1300,1038,840,808,643,1220,1188,1186,1262,1235,744,613,1284,600,446,1272,876,627,1084,556,482,688,1126,1289,771,1216,891,1276,588,813,517,748,304,1101,652,1244,995,667,346,549,1161,432,405,854,790,865,833,967,564,1314,506,358,437,400,1065,1172,897,474,767,886,928,987,464,332,860,596,528,459,992,691,1093,624,486,337,940,923,1184,659,639,491,364,882,972,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP194^1 : TPTP v8.1.2. Released v7.5.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 14:24:24 EDT 2024
% 0.16/0.36 % CPUTime :
% 1.02/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.15 % [INFO] Parsing done (259ms).
% 1.61/1.16 % [INFO] Running in sequential loop mode.
% 2.42/1.37 % [INFO] eprover registered as external prover.
% 2.42/1.37 % [INFO] cvc4 registered as external prover.
% 2.42/1.37 % [INFO] Scanning for conjecture ...
% 2.60/1.46 % [INFO] Found a conjecture and 350 axioms. Running axiom selection ...
% 3.02/1.54 % [INFO] Axiom selection finished. Selected 282 axioms (removed 68 axioms).
% 3.58/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 3.58/1.71 % [INFO] Type checking passed.
% 3.58/1.71 % [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 ...
% 11.48/3.64 % External prover 'e' found a proof!
% 11.48/3.64 % [INFO] Killing All external provers ...
% 11.48/3.64 % Time passed: 3125ms (effective reasoning time: 2480ms)
% 11.48/3.64 % 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)>
% 11.48/3.65 % Axioms used in derivation (282): fact_311_order_Ostrict__trans, fact_52_min_Oleft__commute, fact_199_nat__descend__induct, fact_96_min_Omono, fact_129_not__eq__pos__or__neg__iff__2, fact_320_not__less__iff__gr__or__eq, fact_160_le__trans, fact_226_le__cases, fact_35_min_Oleft__idem, fact_258_ord__less__eq__subst, fact_223_le__cases3, fact_244_order__subst2, fact_181_gr__implies__not0, fact_94_le__numeral__extra_I3_J, fact_183_not__less0, fact_13_poly__all__0__iff__0, fact_323_order_Ostrict__implies__not__eq, fact_270_gt__ex, fact_283_less__asym_H, fact_174_less__irrefl__nat, fact_203_dual__order_Oeq__iff, fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb1_O_A_092_060forall_062x_O_Apoly_Ap_Ax_A_061_A0_A_092_060longrightarrow_062_Alb1_A_060_Ax_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_10_poly__IVT__neg, fact_45_min_Ostrict__boundedE, fact_268_lt__ex, fact_72_order__root, fact_214_ord__le__eq__trans, fact_296_less__imp__not__eq, fact_9_not__gr__zero, fact_1_lb__def, fact_191_order__refl, fact_221_antisym__conv, fact_98_min_OorderE, fact_3_assms, fact_19_field__lbound__gt__zero, fact_234_eq__iff, fact_224_order_Otrans, fact_116_min_Oabsorb__iff1, fact_229_eq__refl, fact_165_less__mono__imp__le__mono, fact_288_less__irrefl, fact_225_order_Otrans, fact_31_min__less__iff__conj, fact_186_less__eq__nat_Osimps_I1_J, fact_300_less__induct, fact_259_ord__less__eq__subst, fact_168_le__eq__less__or__eq, fact_188_ex__least__nat__le, fact_29_poly__eq__poly__eq__iff, fact_304_less__imp__not__eq2, fact_313_less__imp__not__less, fact_281_less__asym, fact_172_infinite__descent, fact_205_dual__order_Otrans, fact_278_less__imp__neq, fact_15_less__numeral__extra_I3_J, fact_200_dual__order_Oantisym, fact_243_ord__eq__le__subst, fact_280_less__asym, fact_202_dual__order_Oeq__iff, fact_47_min__less__iff__disj, fact_286_less__linear, fact_159_le__refl, fact_69_poly__shift__0, fact_331_le__less, fact_134_sgn__greater, fact_106_min_OboundedE, fact_264_order__less__subst2, fact_63_reflect__poly__at__0__eq__0__iff, fact_124_min__le__iff__disj, fact_265_order__less__subst2, fact_322_order_Ostrict__implies__not__eq, fact_303_less__imp__not__eq2, fact_95_less__eq__real__def, fact_23_zero__less__iff__neq__zero, fact_321_not__less__iff__gr__or__eq, fact_213_order__class_Oorder_Oantisym, fact_201_dual__order_Oantisym, fact_62_next__non__root__interval, fact_17_less__numeral__extra_I3_J, fact_30_poly__eq__poly__eq__iff, fact_169_less__imp__le__nat, fact_58_poly__cutoff__0, fact_114_min_Ocobounded2, fact_251_order__subst1, fact_173_nat__less__induct, fact_137_sgn__less, fact_219_order__class_Oorder_Oeq__iff, fact_110_min_Oorder__iff, fact_104_min_Oabsorb2, fact_227_le__cases, fact_206_linorder__wlog, fact_241_ord__eq__le__subst, fact_290_ord__eq__less__trans, fact_277_dense, fact_269_gt__ex, fact_329_leI, fact_231_linear, fact_145_sgn__eq__0__iff, fact_73_order__root, fact_146_sgn__eq__0__iff, fact_275_order_Oasym, fact_218_order__class_Oorder_Oeq__iff, fact_256_ord__less__eq__subst, fact_209_dual__order_Orefl, fact_24_zero__reorient, fact_252_ord__eq__less__subst, fact_343_order__less__le__subst1, fact_328_leI, fact_261_order__less__subst1, fact_262_order__less__subst1, fact_217_ord__eq__le__trans, fact_338_order__le__less__subst2, fact_80_le__zero__eq, fact_192_order__refl, fact_237_ord__le__eq__subst, fact_176_less__not__refl2, fact_49_is__zero__null, fact_318_dual__order_Ostrict__trans, fact_215_ord__le__eq__trans, fact_235_eq__iff, fact_43_min_Ostrict__order__iff, fact_56_min_Oassoc, fact_327_leD, fact_167_less__or__eq__imp__le, fact_333_less__le, fact_162_le__antisym, fact_335_order__le__less__subst1, fact_289_less__irrefl, fact_228_eq__refl, fact_175_less__not__refl3, fact_236_ord__le__eq__subst, fact_233_antisym, fact_319_dual__order_Ostrict__trans, fact_245_order__subst2, fact_185_gr0I, fact_246_order__subst2, fact_195_min__absorb2, fact_120_min_OcoboundedI1, fact_139_sgn__0, fact_127_order__0I, fact_28_zero__reorient, fact_301_antisym__conv3, fact_179_bot__nat__0_Oextremum__strict, fact_240_ord__eq__le__subst, fact_337_order__le__less__subst1, fact_184_not__gr0, fact_276_order_Oasym, fact_142_sgn__zero, fact_267_order__less__subst2, fact_344_order__less__le__subst1, fact_190_bot__nat__0_Oextremum__uniqueI, fact_324_dual__order_Ostrict__implies__not__eq, fact_131_sgn__le__0__iff, fact_25_zero__reorient, fact_163_nat__le__linear, fact_291_ord__eq__less__trans, fact_154_neq0__conv, fact_292_ord__less__eq__trans, fact_247_order__subst2, fact_79__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb2_O_A_092_060forall_062x_092_060le_062lb2_O_Asgn_A_Ipoly_Ap_Ax_J_A_061_Asgn__neg__inf_Ap_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_0_lb1, fact_156_bot__nat__0_Onot__eq__extremum, fact_68_lb2, fact_33_min_Oidem, fact_315_exists__least__iff, fact_309_dual__order_Oirrefl, fact_255_ord__eq__less__subst, fact_171_linorder__neqE__nat, fact_216_ord__eq__le__trans, fact_238_ord__le__eq__subst, fact_308_linorder__cases, fact_295_dual__order_Oasym, fact_317_linorder__less__wlog, fact_193_min__absorb1, fact_210_order__trans, fact_100_min_OorderI, fact_39_min_Ostrict__coboundedI2, fact_342_order__less__le__subst1, fact_75_divide__poly__main__0, fact_88_that, fact_285_less__trans, fact_310_dual__order_Oirrefl, fact_11_poly__IVT__pos, fact_293_ord__less__eq__trans, fact_170_nat__less__le, fact_279_less__imp__neq, fact_102_min_Oabsorb1, fact_204_dual__order_Otrans, fact_263_order__less__subst1, fact_112_min_Ocobounded1, fact_126_order__0I, fact_287_less__linear, fact_180_infinite__descent0, fact_41_min_Ostrict__coboundedI1, fact_81_min_Obounded__iff, fact_197_min__def, fact_118_min_Oabsorb__iff2, fact_341_order__le__less__subst2, fact_260_order__less__subst1, fact_242_ord__eq__le__subst, fact_220_antisym__conv, fact_178_nat__neq__iff, fact_153_bot__nat__0_Oextremum, fact_207_linorder__wlog, fact_254_ord__eq__less__subst, fact_130_zero__le__sgn__iff, fact_274_neq__iff, fact_18_less__numeral__extra_I3_J, fact_138_root__ub, fact_89_complete__real, fact_284_less__trans, fact_108_min_OboundedI, fact_20_gr__zeroI, fact_257_ord__less__eq__subst, fact_189_bot__nat__0_Oextremum__unique, fact_135_sgn__less, fact_305_less__imp__triv, fact_208_dual__order_Orefl, fact_273_neq__iff, fact_271_neqE, fact_161_eq__imp__le, fact_336_order__le__less__subst1, fact_14_poly__all__0__iff__0, fact_249_order__subst1, fact_140_sgn__0, fact_307_linorder__cases, fact_332_less__le, fact_91_le__numeral__extra_I3_J, fact_21_not__less__zero, fact_272_neqE, fact_90_zero__le, fact_166_le__neq__implies__less, fact_143_sgn__sgn, fact_144_linorder__neqE__linordered__idom, fact_339_order__le__less__subst2, fact_334_order__le__less__subst1, fact_340_order__le__less__subst2, fact_212_order__class_Oorder_Oantisym, fact_316_linorder__less__wlog, fact_306_less__imp__triv, fact_232_antisym, fact_211_order__trans, fact_22_gr__implies__not__zero, fact_298_less__not__sym, fact_148_sgn__0__0, fact_151_sgn__zero__iff, fact_326_leD, fact_177_less__not__refl, fact_230_linear, fact_302_antisym__conv3, fact_325_dual__order_Ostrict__implies__not__eq, fact_239_ord__le__eq__subst, fact_132_sgn__greater, fact_266_order__less__subst2, fact_297_less__imp__not__eq, fact_314_less__imp__not__less, fact_330_le__less, fact_253_ord__eq__less__subst, fact_83_reflect__poly__0, fact_222_le__cases3, fact_182_less__zeroE, fact_26_zero__reorient, fact_8_poly__0, fact_54_min_Ocommute, fact_299_less__not__sym, fact_37_min_Oright__idem, fact_294_dual__order_Oasym, fact_250_order__subst1, fact_155_less__nat__zero__code, fact_187_le__0__eq, fact_78_not__eq__pos__or__neg__iff__1, fact_312_order_Ostrict__trans, fact_122_min_OcoboundedI2, fact_164_Nat_Oex__has__greatest__nat, fact_93_le__numeral__extra_I3_J, fact_61_last__non__root__interval, fact_152_le0, fact_248_order__subst1, fact_149_sgn__0__0, fact_282_less__asym_H, fact_6_poly__0
% 11.48/3.65 % No. of inferences in proof: 568
% 11.48/3.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3125 ms resp. 2480 ms w/o parsing
% 11.89/3.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.89/3.78 % [INFO] Killing All external provers ...
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