%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP193^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:08 AM UTC 2026
% Result : Theorem 22.55s 6.15s
% Output : Refutation 23.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 332
% Syntax : Number of formulae : 666 ( 195 unt; 0 typ; 0 def)
% Number of atoms : 2215 ( 487 equ; 12 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 5960 ( 284 ~; 86 |; 176 &;4258 @)
% ( 0 <=>;1156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 252 ( 252 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 13 con; 0-4 aty)
% Number of variables : 2115 ( 157 ^;1820 !; 138 ?;2115 :)
% Comments :
%------------------------------------------------------------------------------
thf(poly_poly_poly_real_type,type,
poly_poly_poly_real: $tType ).
thf(set_poly_poly_real_type,type,
set_poly_poly_real: $tType ).
thf(poly_poly_real_type,type,
poly_poly_real: $tType ).
thf(poly_poly_int_type,type,
poly_poly_int: $tType ).
thf(set_poly_real_type,type,
set_poly_real: $tType ).
thf(set_poly_int_type,type,
set_poly_int: $tType ).
thf(set_set_real_type,type,
set_set_real: $tType ).
thf(set_set_int_type,type,
set_set_int: $tType ).
thf(poly_real_type,type,
poly_real: $tType ).
thf(poly_int_type,type,
poly_int: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(set_int_type,type,
set_int: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(finite_finite_int_decl,type,
finite_finite_int: set_int > $o ).
thf(finite_finite_real_decl,type,
finite_finite_real: set_real > $o ).
thf(finite26677625et_int_decl,type,
finite26677625et_int: set_set_int > $o ).
thf(finite475462905t_real_decl,type,
finite475462905t_real: set_set_real > $o ).
thf(one_one_int_decl,type,
one_one_int: int ).
thf(one_one_poly_real_decl,type,
one_one_poly_real: poly_real ).
thf(zero_zero_int_decl,type,
zero_zero_int: int ).
thf(zero_zero_poly_int_decl,type,
zero_zero_poly_int: poly_int ).
thf(zero_zero_poly_real_decl,type,
zero_zero_poly_real: poly_real ).
thf(zero_zero_real_decl,type,
zero_zero_real: real ).
thf(groups2051521940al_int_decl,type,
groups2051521940al_int: ( real > int ) > set_real > int ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $o ).
thf(ord_less_poly_real_decl,type,
ord_less_poly_real: poly_real > poly_real > $o ).
thf(ord_less_real_decl,type,
ord_less_real: real > real > $o ).
thf(ord_less_set_int_decl,type,
ord_less_set_int: set_int > set_int > $o ).
thf(ord_less_set_real_decl,type,
ord_less_set_real: set_real > set_real > $o ).
thf(ord_less_eq_real_o_decl,type,
ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
thf(ord_less_eq_int_decl,type,
ord_less_eq_int: int > int > $o ).
thf(ord_le1180086932y_real_decl,type,
ord_le1180086932y_real: poly_real > poly_real > $o ).
thf(ord_less_eq_real_decl,type,
ord_less_eq_real: real > real > $o ).
thf(ord_less_eq_set_int_decl,type,
ord_less_eq_set_int: set_int > set_int > $o ).
thf(ord_less_eq_set_real_decl,type,
ord_less_eq_set_real: set_real > set_real > $o ).
thf(is_zero_real_decl,type,
is_zero_real: poly_real > $o ).
thf(poly_int2_decl,type,
poly_int2: poly_int > int > int ).
thf(poly_real2_decl,type,
poly_real2: poly_real > real > real ).
thf(poly_cutoff_real_decl,type,
poly_cutoff_real: nat > poly_real > poly_real ).
thf(collect_int_decl,type,
collect_int: ( int > $o ) > set_int ).
thf(collect_real_decl,type,
collect_real: ( real > $o ) > set_real ).
thf(collect_set_int_decl,type,
collect_set_int: ( set_int > $o ) > set_set_int ).
thf(collect_set_real_decl,type,
collect_set_real: ( set_real > $o ) > set_set_real ).
thf(sturm_308542325x_poly_decl,type,
sturm_308542325x_poly: real > real > poly_real > poly_real > int ).
thf(sturm_1953858694_cross_decl,type,
sturm_1953858694_cross: poly_real > real > real > int ).
thf(sturm_276991412p_poly_decl,type,
sturm_276991412p_poly: poly_real > poly_real > real > int ).
thf(member_int_decl,type,
member_int: int > set_int > $o ).
thf(member_real_decl,type,
member_real: real > set_real > $o ).
thf(a_decl,type,
a: real ).
thf(a2_decl,type,
a2: real ).
thf(b_decl,type,
b: real ).
thf(b2_decl,type,
b2: real ).
thf(p_decl,type,
p: poly_real ).
thf(249,axiom,
! [A: set_real,B: real] :
( ( finite_finite_real @ A )
=> ( ( member_real @ B @ A )
=> ? [C: real] :
( ( member_real @ C @ A )
& ( ord_less_eq_real @ C @ B )
& ! [D: real] :
( ( member_real @ D @ A )
=> ( ( ord_less_eq_real @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_finite__has__minimal2) ).
thf(1337,plain,
! [A: set_real,B: real] :
( ( finite_finite_real @ A )
=> ( ( member_real @ B @ A )
=> ? [C: real] :
( ( member_real @ C @ A )
& ( ord_less_eq_real @ C @ B )
& ! [D: real] :
( ( member_real @ D @ A )
=> ( ( ord_less_eq_real @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(289,axiom,
! [A: set_real,B: set_real] :
( ( finite_finite_real @ A )
=> ( ( ord_less_eq_set_real @ B @ A )
=> ( finite_finite_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_rev__finite__subset) ).
thf(1469,plain,
! [A: set_real,B: set_real] :
( ( finite_finite_real @ A )
=> ( ( ord_less_eq_set_real @ B @ A )
=> ( finite_finite_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(320,axiom,
! [A: int,B: real > int,C: real,D: real] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_order__le__less__subst1) ).
thf(1633,plain,
! [A: int,B: real > int,C: real,D: real] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(195,axiom,
! [A: poly_real] :
( ( ! [B: real] :
( ( poly_real2 @ A @ B )
= zero_zero_real ) )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_poly__all__0__iff__0) ).
thf(1105,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)],[195]) ).
thf(7,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_eq_int @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_pinf_I6_J) ).
thf(347,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_eq_int @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(153,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_order_Oorder__iff__strict) ).
thf(909,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(160,axiom,
! [A: int,B: int] :
( ( A = B )
| ~ ( ord_less_eq_int @ A @ B )
| ~ ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_verit__la__disequality) ).
thf(941,plain,
! [A: int,B: int] :
( ( A = B )
| ~ ( ord_less_eq_int @ A @ B )
| ~ ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(310,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/sandbox2/benchmark/theBenchmark.p',fact_145_ord__eq__less__subst) ).
thf(1586,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)],[310]) ).
thf(298,axiom,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_antisym__conv1) ).
thf(1501,plain,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(109,axiom,
( is_zero_real
= ( ^ [A: poly_real] : ( A = zero_zero_poly_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_is__zero__null) ).
thf(762,plain,
( is_zero_real
= ( ^ [A: poly_real] : ( A = zero_zero_poly_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(269,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_less__asym_H) ).
thf(1406,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(102,axiom,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_ord__eq__le__trans) ).
thf(730,plain,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(267,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_leD) ).
thf(1401,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(27,axiom,
! [A: int,B: int] :
( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( ord_less_int @ A @ C )
& ( ord_less_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_finite__interval__int4) ).
thf(449,plain,
! [A: int,B: int] :
( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( ord_less_int @ A @ C )
& ( ord_less_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(49,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_dual__order_Ostrict__implies__not__eq) ).
thf(511,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(75,axiom,
! [A: set_int,B: set_int] :
( ( ord_less_eq_set_int @ A @ B )
=> ( ( finite_finite_int @ B )
=> ( finite_finite_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_finite__subset) ).
thf(614,plain,
! [A: set_int,B: set_int] :
( ( ord_less_eq_set_int @ A @ B )
=> ( ( finite_finite_int @ B )
=> ( finite_finite_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(277,axiom,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_less__le) ).
thf(1426,plain,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(11,axiom,
! [A: int,B: real > int,C: real,D: real] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_order__subst1) ).
thf(384,plain,
! [A: int,B: real > int,C: real,D: real] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_order_Ostrict__trans1) ).
thf(472,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(222,axiom,
! [A: set_real,B: set_real,C: real > real > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_pigeonhole__infinite__rel) ).
thf(1222,plain,
! [A: set_real,B: set_real,C: real > real > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(215,axiom,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_le__numeral__extra_I3_J) ).
thf(1196,plain,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(148,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_order__refl) ).
thf(898,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(171,axiom,
! [A: int,B: int] :
( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( ord_less_eq_int @ A @ C )
& ( ord_less_eq_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_finite__interval__int1) ).
thf(1001,plain,
! [A: int,B: int] :
( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( ord_less_eq_int @ A @ C )
& ( ord_less_eq_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(200,axiom,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( finite_finite_real @ B )
=> ( finite_finite_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_finite__subset) ).
thf(1127,plain,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( finite_finite_real @ B )
=> ( finite_finite_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(133,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_not__less) ).
thf(841,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',fact_133_ord__eq__le__subst) ).
thf(973,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)],[166]) ).
thf(324,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ~ ( ord_less_real @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_antisym__conv2) ).
thf(1650,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ~ ( ord_less_real @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(12,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_order__trans) ).
thf(389,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(100,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_order_Onot__eq__order__implies__strict) ).
thf(724,plain,
! [A: int,B: int] :
( ( A != B )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(46,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_dual__order_Ostrict__trans2) ).
thf(504,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(246,axiom,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ( ~ ( ord_less_real @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_antisym__conv3) ).
thf(1330,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)],[246]) ).
thf(6,axiom,
! [A: poly_int] :
( ( ! [B: int] :
( ( poly_int2 @ A @ B )
= zero_zero_int ) )
= ( A = zero_zero_poly_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_poly__all__0__iff__0) ).
thf(344,plain,
! [A: poly_int] :
( ( ! [B: int] :
( ( poly_int2 @ A @ B )
= zero_zero_int ) )
= ( A = zero_zero_poly_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(287,axiom,
! [A: int,B: real > int,C: real,D: real] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_order__less__subst1) ).
thf(1455,plain,
! [A: int,B: real > int,C: real,D: real] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(214,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_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_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_order__less__le__subst1) ).
thf(1191,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_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_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(70,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_minf_I2_J) ).
thf(587,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(244,axiom,
~ ( ord_less_real @ zero_zero_real @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__numeral__extra_I3_J) ).
thf(1323,plain,
~ ( ord_less_real @ zero_zero_real @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(156,axiom,
ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_le__numeral__extra_I3_J) ).
thf(917,plain,
ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(96,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_not__le) ).
thf(702,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(57,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_order_Ostrict__implies__order) ).
thf(542,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(32,axiom,
! [A: int,B: int] :
( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_le__cases) ).
thf(460,plain,
! [A: int,B: int] :
( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(189,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_pinf_I4_J) ).
thf(1087,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(141,axiom,
! [A: int,B: int] :
( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( ord_less_int @ A @ C )
& ( ord_less_eq_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_finite__interval__int3) ).
thf(870,plain,
! [A: int,B: int] :
( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( ord_less_int @ A @ C )
& ( ord_less_eq_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(314,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_order_Ostrict__trans2) ).
thf(1609,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(175,axiom,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ord_less_eq_int @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: int,E: int] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_linorder__wlog) ).
thf(1013,plain,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ord_less_eq_int @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: int,E: int] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(198,axiom,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_ord__less__eq__subst) ).
thf(1115,plain,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(308,axiom,
! [A: real > $o,B: real > $o,C: real > $o,D: real > $o] :
( ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_pinf_I1_J) ).
thf(1568,plain,
! [A: real > $o,B: real > $o,C: real > $o,D: real > $o] :
( ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(295,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_less__not__sym) ).
thf(1494,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(193,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_dual__order_Oorder__iff__strict) ).
thf(1100,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',fact_204_order_Ostrict__trans) ).
thf(1232,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)],[224]) ).
thf(80,axiom,
! [A: real,B: real,C: real] :
( ( A = B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_ord__eq__le__trans) ).
thf(638,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)],[80]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',fact_129_ord__le__eq__subst) ).
thf(853,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)],[137]) ).
thf(266,axiom,
! [A: real] :
~ ( ord_less_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_dual__order_Oirrefl) ).
thf(1398,plain,
! [A: real] :
~ ( ord_less_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(145,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_antisym) ).
thf(881,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)],[145]) ).
thf(19,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( ord_less_eq_int @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_minf_I6_J) ).
thf(416,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( ord_less_eq_int @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(36,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_dual__order_Oorder__iff__strict) ).
thf(475,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(326,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_less__imp__neq) ).
thf(1664,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(119,axiom,
! [A: int,B: int] :
( ( A != B )
= ( ( ord_less_int @ A @ B )
| ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_neq__iff) ).
thf(789,plain,
! [A: int,B: int] :
( ( A != B )
= ( ( ord_less_int @ A @ B )
| ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(82,axiom,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_le__less) ).
thf(646,plain,
( ord_less_eq_int
= ( ^ [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(329,axiom,
! [A: real] :
? [B: real] :
( ( ord_less_real @ A @ B )
| ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_ex__gt__or__lt) ).
thf(1677,plain,
! [A: real] :
? [B: real] :
( ( ord_less_real @ A @ B )
| ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(212,axiom,
! [A: real] :
( ( ( ( ord_less_real @ a @ A )
& ( ord_less_eq_real @ A @ a2 ) )
| ( ( ord_less_eq_real @ b2 @ A )
& ( ord_less_real @ A @ b ) ) )
=> ( ( poly_real2 @ p @ A )
!= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_assms_I4_J) ).
thf(1183,plain,
! [A: real] :
( ( ( ( ord_less_real @ a @ A )
& ( ord_less_eq_real @ A @ a2 ) )
| ( ( ord_less_eq_real @ b2 @ A )
& ( ord_less_real @ A @ b ) ) )
=> ( ( poly_real2 @ p @ A )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(176,axiom,
! [A: int > $o,B: int > $o] :
( ( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_int @ ( collect_int @ A ) )
& ( finite_finite_int @ ( collect_int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__Collect__disjI) ).
thf(1020,plain,
! [A: int > $o,B: int > $o] :
( ( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_int @ ( collect_int @ A ) )
& ( finite_finite_int @ ( collect_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(65,axiom,
( ( (=) @ int )
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ B @ A )
& ( ord_less_eq_int @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_dual__order_Oeq__iff) ).
thf(574,plain,
( ( (=) @ int )
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ B @ A )
& ( ord_less_eq_int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(181,axiom,
! [A: int] :
? [B: int] : ( ord_less_int @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_lt__ex) ).
thf(1051,plain,
! [A: int] :
? [B: int] : ( ord_less_int @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(125,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( A = B )
| ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_verit__la__generic) ).
thf(821,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( A = B )
| ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(151,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_le__less__linear) ).
thf(905,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(38,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_less__le) ).
thf(480,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(111,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_verit__comp__simplify1_I1_J) ).
thf(766,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(210,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ! [D: real] :
( ( ord_less_real @ A @ D )
=> ( ( ord_less_real @ D @ B )
=> ( ord_less_eq_real @ D @ C ) ) )
=> ( ord_less_eq_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_dense__le__bounded) ).
thf(1169,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ! [D: real] :
( ( ord_less_real @ A @ D )
=> ( ( ord_less_real @ D @ B )
=> ( ord_less_eq_real @ D @ C ) ) )
=> ( ord_less_eq_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(29,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_dual__order_Oantisym) ).
thf(453,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)],[29]) ).
thf(319,axiom,
! [A: real > $o,B: real > $o,C: real > $o,D: real > $o] :
( ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_pinf_I2_J) ).
thf(1622,plain,
! [A: real > $o,B: real > $o,C: real > $o,D: real > $o] :
( ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: real] :
! [F: real] :
( ( ord_less_real @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(170,axiom,
! [A: int,B: int,C: $o] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ A )
=> C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_less__imp__triv) ).
thf(998,plain,
! [A: int,B: int,C: $o] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(17,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_order__class_Oorder_Oeq__iff) ).
thf(411,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)],[17]) ).
thf(279,axiom,
ord_less_real @ b2 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I3_J) ).
thf(1433,plain,
ord_less_real @ b2 @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(47,axiom,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_le__cases) ).
thf(507,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)],[47]) ).
thf(312,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_order_Oasym) ).
thf(1604,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(89,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_le__numeral__extra_I3_J) ).
thf(678,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(52,axiom,
! [A: int,B: int] :
( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( ord_less_eq_int @ A @ C )
& ( ord_less_int @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_finite__interval__int2) ).
thf(529,plain,
! [A: int,B: int] :
( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( ord_less_eq_int @ A @ C )
& ( ord_less_int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(59,axiom,
! [A: set_int,B: set_int > $o] :
( ( finite_finite_int @ A )
=> ( ! [C: set_int] :
( ( finite_finite_int @ C )
=> ( ! [D: set_int] :
( ( ord_less_set_int @ D @ C )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_finite__psubset__induct) ).
thf(546,plain,
! [A: set_int,B: set_int > $o] :
( ( finite_finite_int @ A )
=> ( ! [C: set_int] :
( ( finite_finite_int @ C )
=> ( ! [D: set_int] :
( ( ord_less_set_int @ D @ C )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(217,axiom,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ! [D: real] :
( ( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B ) )
=> ( ( poly_real2 @ C @ D )
!= zero_zero_real ) )
=> ( ( sturm_1953858694_cross @ C @ A @ B )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_cross__no__root) ).
thf(1199,plain,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ! [D: real] :
( ( ( ord_less_real @ A @ D )
& ( ord_less_real @ D @ B ) )
=> ( ( poly_real2 @ C @ D )
!= zero_zero_real ) )
=> ( ( sturm_1953858694_cross @ C @ A @ B )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(204,axiom,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ C @ B )
=> ( ord_less_eq_real @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_minf_I6_J) ).
thf(1153,plain,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ C @ B )
=> ( ord_less_eq_real @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(123,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_eq__iff) ).
thf(810,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)],[123]) ).
thf(10,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_order_Ostrict__trans) ).
thf(381,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(54,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ( ord_less_int @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_not__less__iff__gr__or__eq) ).
thf(534,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_int @ A @ B ) )
= ( ( ord_less_int @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(185,axiom,
! [A: int,B: int,C: $o,D: $o] :
( ( A = B )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( C = D ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> C )
= ( ( ord_less_eq_int @ zero_zero_int @ B )
=> D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_imp__le__cong) ).
thf(1067,plain,
! [A: int,B: int,C: $o,D: $o] :
( ( A = B )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( C = D ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ A )
=> C )
= ( ( ord_less_eq_int @ zero_zero_int @ B )
=> D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(183,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_order__le__less__subst1) ).
thf(1057,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(208,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_le__less__trans) ).
thf(1163,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1,conjecture,
( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( ( poly_real2 @ p @ A )
= zero_zero_real )
& ( ord_less_real @ a @ A )
& ( ord_less_real @ A @ b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( ( poly_real2 @ p @ A )
= zero_zero_real )
& ( ord_less_real @ a @ A )
& ( ord_less_real @ A @ b ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(334,plain,
~ ( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( ( poly_real2 @ p @ A )
= zero_zero_real )
& ( ord_less_real @ a @ A )
& ( ord_less_real @ A @ b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(263,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_less__imp__not__less) ).
thf(1387,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(190,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_less__le__trans) ).
thf(1091,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(71,axiom,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_ord__eq__less__trans) ).
thf(598,plain,
! [A: int,B: int,C: int] :
( ( A = B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(21,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_less__imp__neq) ).
thf(429,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(258,axiom,
ord_less_real @ a2 @ b2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(1370,plain,
ord_less_real @ a2 @ b2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(226,axiom,
! [A: real > $o] :
( ~ ( finite_finite_real @ ( collect_real @ A ) )
=> ? [B: real] : ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_not__finite__existsD) ).
thf(1238,plain,
! [A: real > $o] :
( ~ ( finite_finite_real @ ( collect_real @ A ) )
=> ? [B: real] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(305,axiom,
! [A: real,B: real] :
( ( A != B )
= ( ( ord_less_real @ A @ B )
| ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_neq__iff) ).
thf(1560,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)],[305]) ).
thf(138,axiom,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_subsetD) ).
thf(862,plain,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(8,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ~ ( ord_less_eq_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_less__le__not__le) ).
thf(349,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ~ ( ord_less_eq_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_ord__le__eq__subst) ).
thf(392,plain,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ 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)],[13]) ).
thf(293,axiom,
! [A: real,B: int > real,C: int,D: int] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_order__less__subst1) ).
thf(1487,plain,
! [A: real,B: int > real,C: int,D: int] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(144,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_leD) ).
thf(879,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(136,axiom,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_less__eq__int__code_I1_J) ).
thf(852,plain,
ord_less_eq_int @ zero_zero_int @ zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',fact_20_poly__IVT__neg) ).
thf(1296,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)],[240]) ).
thf(128,axiom,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ A )
= ( ord_less_int @ zero_zero_int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_int__one__le__iff__zero__less) ).
thf(830,plain,
! [A: int] :
( ( ord_less_eq_int @ one_one_int @ A )
= ( ord_less_int @ zero_zero_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(206,axiom,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_leI) ).
thf(1159,plain,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(187,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_order__le__less__subst2) ).
thf(1079,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(30,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_minf_I8_J) ).
thf(456,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ~ ( ord_less_eq_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(135,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_order__less__le__subst2) ).
thf(847,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(40,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_int @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_pinf_I5_J) ).
thf(484,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ~ ( ord_less_int @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(105,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_less__numeral__extra_I3_J) ).
thf(742,plain,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(197,axiom,
! [A: real,B: real] :
( ! [C: real] :
( ( ord_less_real @ A @ C )
=> ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_dense__ge) ).
thf(1111,plain,
! [A: real,B: real] :
( ! [C: real] :
( ( ord_less_real @ A @ C )
=> ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(173,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_le__less__trans) ).
thf(1006,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(74,axiom,
! [A: int > $o,B: int > $o] :
( ! [C: int] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_int @ ( collect_int @ A ) @ ( collect_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_Collect__mono) ).
thf(610,plain,
! [A: int > $o,B: int > $o] :
( ! [C: int] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_int @ ( collect_int @ A ) @ ( collect_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(44,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ~ ( ord_less_int @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_antisym__conv2) ).
thf(499,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ~ ( ord_less_int @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(94,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_dual__order_Oasym) ).
thf(697,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(302,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( B = C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_ord__less__eq__trans) ).
thf(1541,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)],[302]) ).
thf(15,axiom,
! [A: poly_real] :
( ( zero_zero_poly_real = A )
= ( A = zero_zero_poly_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_zero__reorient) ).
thf(403,plain,
! [A: poly_real] :
( ( zero_zero_poly_real = A )
= ( A = zero_zero_poly_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(297,axiom,
! [A: real > $o,B: real > $o] :
( ( ord_less_eq_set_real @ ( collect_real @ A ) @ ( collect_real @ B ) )
= ( ! [C: real] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_Collect__mono__iff) ).
thf(1498,plain,
! [A: real > $o,B: real > $o] :
( ( ord_less_eq_set_real @ ( collect_real @ A ) @ ( collect_real @ B ) )
= ( ! [C: real] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(146,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_order_Otrans) ).
thf(884,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(255,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_order_Ostrict__trans1) ).
thf(1361,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(60,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_linear) ).
thf(554,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(55,axiom,
! [A: int > $o,B: int > $o] :
( ! [C: int] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_int @ A )
= ( collect_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Collect__cong) ).
thf(537,plain,
! [A: int > $o,B: int > $o] :
( ! [C: int] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_int @ A )
= ( collect_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(87,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__not__sym) ).
thf(669,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(276,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_order_Oorder__iff__strict) ).
thf(1424,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(284,axiom,
! [A: real,B: real] :
( ( ~ ( ord_less_real @ A @ B ) )
= ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_not__less) ).
thf(1446,plain,
! [A: real,B: real] :
( ( ~ ( ord_less_real @ A @ B ) )
= ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(205,axiom,
! [A: poly_real,B: real,C: poly_real] :
( ( ( poly_real2 @ A @ B )
!= zero_zero_real )
=> ( ( sturm_276991412p_poly @ C @ A @ B )
= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_jump__poly__not__root) ).
thf(1155,plain,
! [A: poly_real,B: real,C: poly_real] :
( ( ( poly_real2 @ A @ B )
!= zero_zero_real )
=> ( ( sturm_276991412p_poly @ C @ A @ B )
= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(315,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_dual__order_Ostrict__implies__order) ).
thf(1612,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(90,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_dual__order_Orefl) ).
thf(679,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(165,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_dual__order_Oantisym) ).
thf(970,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(131,axiom,
! [A: set_int,B: int > $o] :
( ord_less_eq_set_int
@ ( collect_int
@ ^ [C: int] :
( ( member_int @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_Collect__subset) ).
thf(837,plain,
! [A: set_int,B: int > $o] :
( ord_less_eq_set_int
@ ( collect_int
@ ^ [C: int] :
( ( member_int @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(232,axiom,
! [A: real,B: real] :
( ( A != B )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_order_Onot__eq__order__implies__strict) ).
thf(1263,plain,
! [A: real,B: real] :
( ( A != B )
=> ( ( ord_less_eq_real @ A @ B )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(168,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/sandbox2/benchmark/theBenchmark.p',fact_219_complete__real) ).
thf(985,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)],[168]) ).
thf(301,axiom,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_order_Ostrict__iff__order) ).
thf(1539,plain,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(233,axiom,
! [A: set_int,B: set_real,C: int > real > $o] :
( ~ ( finite_finite_int @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: int] :
( ( member_int @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite_finite_int
@ ( collect_int
@ ^ [E: int] :
( ( member_int @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_pigeonhole__infinite__rel) ).
thf(1266,plain,
! [A: set_int,B: set_real,C: int > real > $o] :
( ~ ( finite_finite_int @ A )
=> ( ( finite_finite_real @ B )
=> ( ! [D: int] :
( ( member_int @ D @ A )
=> ? [E: real] :
( ( member_real @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: real] :
( ( member_real @ D @ B )
& ~ ( finite_finite_int
@ ( collect_int
@ ^ [E: int] :
( ( member_int @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',fact_208_linorder__less__wlog) ).
thf(1131,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)],[202]) ).
thf(327,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_order_Ostrict__implies__order) ).
thf(1668,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(154,axiom,
! [A: real,B: real] :
( ( sturm_1953858694_cross @ zero_zero_poly_real @ A @ B )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_cross__0) ).
thf(911,plain,
! [A: real,B: real] :
( ( sturm_1953858694_cross @ zero_zero_poly_real @ A @ B )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(50,axiom,
! [A: int,B: real > int,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_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_ord__eq__le__subst) ).
thf(515,plain,
! [A: int,B: real > int,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_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(203,axiom,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__mem__eq) ).
thf(1150,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(247,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_le__less__linear) ).
thf(1333,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(280,axiom,
( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( poly_real2 @ p @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062) ).
thf(1434,plain,
( finite_finite_real
@ ( collect_real
@ ^ [A: real] :
( ( poly_real2 @ p @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(120,axiom,
! [A: int,B: int,C: $o,D: $o] :
( ( A = B )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( C = D ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ A )
& C )
= ( ( ord_less_eq_int @ zero_zero_int @ B )
& D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_conj__le__cong) ).
thf(792,plain,
! [A: int,B: int,C: $o,D: $o] :
( ( A = B )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ B )
=> ( C = D ) )
=> ( ( ( ord_less_eq_int @ zero_zero_int @ A )
& C )
= ( ( ord_less_eq_int @ zero_zero_int @ B )
& D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(237,axiom,
! [A: real] :
~ ( ord_less_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_verit__comp__simplify1_I1_J) ).
thf(1286,plain,
! [A: real] :
~ ( ord_less_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(62,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_ord__eq__le__subst) ).
thf(558,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(317,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/sandbox2/benchmark/theBenchmark.p',fact_171_dense) ).
thf(1616,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)],[317]) ).
thf(114,axiom,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_verit__comp__simplify1_I3_J) ).
thf(773,plain,
! [A: int,B: int] :
( ( ~ ( ord_less_eq_int @ A @ B ) )
= ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(159,axiom,
! [A: int,B: int,C: int] :
( ( ( ord_less_eq_int @ A @ B )
=> ~ ( ord_less_eq_int @ B @ C ) )
=> ( ( ( ord_less_eq_int @ B @ A )
=> ~ ( ord_less_eq_int @ A @ C ) )
=> ( ( ( ord_less_eq_int @ A @ C )
=> ~ ( ord_less_eq_int @ C @ B ) )
=> ( ( ( ord_less_eq_int @ C @ B )
=> ~ ( ord_less_eq_int @ B @ A ) )
=> ( ( ( ord_less_eq_int @ B @ C )
=> ~ ( ord_less_eq_int @ C @ A ) )
=> ~ ( ( ord_less_eq_int @ C @ A )
=> ~ ( ord_less_eq_int @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_le__cases3) ).
thf(926,plain,
! [A: int,B: int,C: int] :
( ( ( ord_less_eq_int @ A @ B )
=> ~ ( ord_less_eq_int @ B @ C ) )
=> ( ( ( ord_less_eq_int @ B @ A )
=> ~ ( ord_less_eq_int @ A @ C ) )
=> ( ( ( ord_less_eq_int @ A @ C )
=> ~ ( ord_less_eq_int @ C @ B ) )
=> ( ( ( ord_less_eq_int @ C @ B )
=> ~ ( ord_less_eq_int @ B @ A ) )
=> ( ( ( ord_less_eq_int @ B @ C )
=> ~ ( ord_less_eq_int @ C @ A ) )
=> ~ ( ( ord_less_eq_int @ C @ A )
=> ~ ( ord_less_eq_int @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(306,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_dual__order_Ostrict__trans2) ).
thf(1563,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(84,axiom,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_subset__iff) ).
thf(657,plain,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(163,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_less__imp__le) ).
thf(965,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',fact_229_order__le__less__subst1) ).
thf(1680,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)],[330]) ).
thf(126,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_linorder__cases) ).
thf(824,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(234,axiom,
! [A: int,B: real > int,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_ord__eq__less__subst) ).
thf(1273,plain,
! [A: int,B: real > int,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(311,axiom,
! [A: real,B: int > real,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_ord__eq__less__subst) ).
thf(1595,plain,
! [A: real,B: int > real,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(25,axiom,
! [A: int] :
? [B: int] : ( ord_less_int @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_gt__ex) ).
thf(444,plain,
! [A: int] :
? [B: int] : ( ord_less_int @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(69,axiom,
! [A: int,B: int > $o] :
( ( member_int @ A @ ( collect_int @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__Collect__eq) ).
thf(584,plain,
! [A: int,B: int > $o] :
( ( member_int @ A @ ( collect_int @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(264,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ! [D: real] :
( ( ord_less_real @ A @ D )
=> ( ( ord_less_real @ D @ B )
=> ( ord_less_eq_real @ C @ D ) ) )
=> ( ord_less_eq_real @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_dense__ge__bounded) ).
thf(1389,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ! [D: real] :
( ( ord_less_real @ A @ D )
=> ( ( ord_less_real @ D @ B )
=> ( ord_less_eq_real @ C @ D ) ) )
=> ( ord_less_eq_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(318,axiom,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_not__le__imp__less) ).
thf(1620,plain,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(67,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_dual__order_Ostrict__implies__order) ).
thf(579,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(268,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/sandbox2/benchmark/theBenchmark.p',fact_51_not__eq__pos__or__neg__iff__1) ).
thf(1403,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)],[268]) ).
thf(199,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ C @ A )
=> ( ord_less_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_dual__order_Ostrict__trans1) ).
thf(1124,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ C @ A )
=> ( ord_less_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(18,axiom,
! [A: real,B: real] :
( ( A = B )
| ~ ( ord_less_eq_real @ A @ B )
| ~ ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_verit__la__disequality) ).
thf(413,plain,
! [A: real,B: real] :
( ( A = B )
| ~ ( ord_less_eq_real @ A @ B )
| ~ ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(278,axiom,
! [A: real,B: real,C: real] :
( ( A = B )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_ord__eq__less__trans) ).
thf(1428,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)],[278]) ).
thf(64,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_less__asym) ).
thf(572,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(259,axiom,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_order__le__less__subst2) ).
thf(1371,plain,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(3,axiom,
! [A: poly_int,B: poly_int] :
( ( ( poly_int2 @ A )
= ( poly_int2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_poly__eq__poly__eq__iff) ).
thf(335,plain,
! [A: poly_int,B: poly_int] :
( ( ( poly_int2 @ A )
= ( poly_int2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(231,axiom,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_order__less__subst2) ).
thf(1258,plain,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(321,axiom,
! [A: real,B: real] :
( ! [C: real] :
( ( ord_less_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_dense__le) ).
thf(1638,plain,
! [A: real,B: real] :
( ! [C: real] :
( ( ord_less_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(254,axiom,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_order__less__le__subst2) ).
thf(1356,plain,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(56,axiom,
! [A: int > $o] :
( ~ ( finite_finite_int @ ( collect_int @ A ) )
=> ? [B: int] : ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_not__finite__existsD) ).
thf(540,plain,
! [A: int > $o] :
( ~ ( finite_finite_int @ ( collect_int @ A ) )
=> ? [B: int] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(110,axiom,
~ ( ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_less__numeral__extra_I3_J) ).
thf(764,plain,
~ ( ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(235,axiom,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ~ ( ord_less_eq_real @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_pinf_I6_J) ).
thf(1282,plain,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ~ ( ord_less_eq_real @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(117,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_leI) ).
thf(784,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(180,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_order__class_Oorder_Oantisym) ).
thf(1048,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)],[180]) ).
thf(294,axiom,
( sturm_308542325x_poly
= ( ^ [A: real,B: real,C: poly_real,D: poly_real] :
( groups2051521940al_int @ ( sturm_276991412p_poly @ C @ D )
@ ( collect_real
@ ^ [E: real] :
( ( ( poly_real2 @ D @ E )
= zero_zero_real )
& ( ord_less_real @ A @ E )
& ( ord_less_real @ E @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_cindex__poly__def) ).
thf(1492,plain,
( sturm_308542325x_poly
= ( ^ [A: real,B: real,C: poly_real,D: poly_real] :
( groups2051521940al_int @ ( sturm_276991412p_poly @ C @ D )
@ ( collect_real
@ ^ [E: real] :
( ( ( poly_real2 @ D @ E )
= zero_zero_real )
& ( ord_less_real @ A @ E )
& ( ord_less_real @ E @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(76,axiom,
! [A: real,B: int > real,C: int,D: int] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_order__subst1) ).
thf(616,plain,
! [A: real,B: int > real,C: int,D: int] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ 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)],[76]) ).
thf(211,axiom,
! [A: set_real,B: set_real > $o] :
( ( finite_finite_real @ A )
=> ( ! [C: set_real] :
( ( finite_finite_real @ C )
=> ( ! [D: set_real] :
( ( ord_less_set_real @ D @ C )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_finite__psubset__induct) ).
thf(1175,plain,
! [A: set_real,B: set_real > $o] :
( ( finite_finite_real @ A )
=> ( ! [C: set_real] :
( ( finite_finite_real @ C )
=> ( ! [D: set_real] :
( ( ord_less_set_real @ D @ C )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(149,axiom,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_in__mono) ).
thf(900,plain,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',fact_137_order__subst2) ).
thf(406,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)],[16]) ).
thf(91,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_ord__eq__less__subst) ).
thf(681,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(270,axiom,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ~ ( ord_less_real @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_pinf_I5_J) ).
thf(1408,plain,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ~ ( ord_less_real @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(28,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_dual__order_Ostrict__iff__order) ).
thf(451,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(63,axiom,
! [A: int,B: real > int,C: real,D: real] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_order__less__le__subst1) ).
thf(567,plain,
! [A: int,B: real > int,C: real,D: real] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(48,axiom,
( ( (=) @ int )
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( ord_less_eq_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_eq__iff) ).
thf(509,plain,
( ( (=) @ int )
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( ord_less_eq_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(179,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_ord__le__eq__trans) ).
thf(1043,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',fact_233_order__le__less__subst2) ).
thf(1376,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)],[260]) ).
thf(282,axiom,
p != zero_zero_poly_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_False) ).
thf(1439,plain,
p != zero_zero_poly_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(37,axiom,
! [A: poly_real,B: real] :
( ( sturm_276991412p_poly @ zero_zero_poly_real @ A @ B )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_jump__poly0_I1_J) ).
thf(477,plain,
! [A: poly_real,B: real] :
( ( sturm_276991412p_poly @ zero_zero_poly_real @ A @ B )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(108,axiom,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_eq__refl) ).
thf(758,plain,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(77,axiom,
! [A: set_int,B: set_int] :
( ( finite_finite_int @ A )
=> ( ( ord_less_eq_set_int @ B @ A )
=> ( finite_finite_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rev__finite__subset) ).
thf(621,plain,
! [A: set_int,B: set_int] :
( ( finite_finite_int @ A )
=> ( ( ord_less_eq_set_int @ B @ A )
=> ( finite_finite_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(245,axiom,
! [A: real,B: int > real,C: int,D: int] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_order__less__le__subst1) ).
thf(1325,plain,
! [A: real,B: int > real,C: int,D: int] :
( ( ord_less_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(250,axiom,
! [A: real] :
? [B: real] : ( ord_less_real @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_gt__ex) ).
thf(1344,plain,
! [A: real] :
? [B: real] : ( ord_less_real @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(239,axiom,
! [A: poly_real,B: poly_real] :
( ( ( poly_real2 @ A )
= ( poly_real2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_poly__eq__poly__eq__iff) ).
thf(1293,plain,
! [A: poly_real,B: poly_real] :
( ( ( poly_real2 @ A )
= ( poly_real2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(261,axiom,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_real @ A )
= ( collect_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Collect__cong) ).
thf(1381,plain,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_real @ A )
= ( collect_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(33,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_less__linear) ).
thf(462,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(332,axiom,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_order__less__le__subst2) ).
thf(1688,plain,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(112,axiom,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
( ord_less_eq_real_o
@ ^ [C: real] : ( member_real @ C @ A )
@ ^ [C: real] : ( member_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_less__eq__set__def) ).
thf(769,plain,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
( ord_less_eq_real_o
@ ^ [C: real] : ( member_real @ C @ A )
@ ^ [C: real] : ( member_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(288,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/sandbox2/benchmark/theBenchmark.p',fact_149_ord__less__eq__subst) ).
thf(1460,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)],[288]) ).
thf(93,axiom,
( ( (=) @ int )
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( ord_less_eq_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_order__class_Oorder_Oeq__iff) ).
thf(695,plain,
( ( (=) @ int )
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( ord_less_eq_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(281,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_less__imp__not__eq2) ).
thf(1435,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(256,axiom,
! [A: real,B: real,C: $o] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ B @ A )
=> C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_less__imp__triv) ).
thf(1364,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)],[256]) ).
thf(296,axiom,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_dual__order_Ostrict__iff__order) ).
thf(1496,plain,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(194,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_le__neq__trans) ).
thf(1102,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(23,axiom,
! [A: int > $o,B: int > $o] :
( ( ord_less_eq_set_int @ ( collect_int @ A ) @ ( collect_int @ B ) )
= ( ! [C: int] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_Collect__mono__iff) ).
thf(438,plain,
! [A: int > $o,B: int > $o] :
( ( ord_less_eq_set_int @ ( collect_int @ A ) @ ( collect_int @ B ) )
= ( ! [C: int] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(219,axiom,
! [A: real,B: real] :
( ( A != B )
=> ( ~ ( ord_less_real @ A @ B )
=> ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_neqE) ).
thf(1213,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)],[219]) ).
thf(127,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_dual__order_Ostrict__trans) ).
thf(827,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',fact_141_order__subst1) ).
thf(490,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)],[42]) ).
thf(209,axiom,
! [A: real > $o,B: real > $o] :
( ( finite_finite_real
@ ( collect_real
@ ^ [C: real] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_real @ ( collect_real @ A ) )
& ( finite_finite_real @ ( collect_real @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__Collect__disjI) ).
thf(1166,plain,
! [A: real > $o,B: real > $o] :
( ( finite_finite_real
@ ( collect_real
@ ^ [C: real] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_real @ ( collect_real @ A ) )
& ( finite_finite_real @ ( collect_real @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',fact_157_order__less__subst2) ).
thf(1208,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)],[218]) ).
thf(83,axiom,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_ord__le__eq__subst) ).
thf(648,plain,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(107,axiom,
! [A: real,B: int > real,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_ord__eq__le__subst) ).
thf(749,plain,
! [A: real,B: int > real,C: int,D: int] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ 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)],[107]) ).
thf(290,axiom,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_ord__less__eq__subst) ).
thf(1472,plain,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_real @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(31,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ B @ A )
& ( ord_less_eq_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_dual__order_Oeq__iff) ).
thf(458,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)],[31]) ).
thf(273,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B )
| ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_less__linear) ).
thf(1413,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)],[273]) ).
thf(186,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_antisym) ).
thf(1076,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(53,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_le__imp__less__or__eq) ).
thf(531,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(161,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_order__refl) ).
thf(944,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(124,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_ord__le__eq__subst) ).
thf(812,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(300,axiom,
! [A: real,B: real,C: real > $o] :
( ( ord_less_real @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: real] :
( ( ord_less_eq_real @ A @ D )
& ( ord_less_eq_real @ D @ B )
& ! [E: real] :
( ( ( ord_less_eq_real @ A @ E )
& ( ord_less_real @ E @ D ) )
=> ( C @ E ) )
& ! [E: real] :
( ! [F: real] :
( ( ( ord_less_eq_real @ A @ F )
& ( ord_less_real @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq_real @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_complete__interval) ).
thf(1509,plain,
! [A: real,B: real,C: real > $o] :
( ( ord_less_real @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: real] :
( ( ord_less_eq_real @ A @ D )
& ( ord_less_eq_real @ D @ B )
& ! [E: real] :
( ( ( ord_less_eq_real @ A @ E )
& ( ord_less_real @ E @ D ) )
=> ( C @ E ) )
& ! [E: real] :
( ! [F: real] :
( ( ( ord_less_eq_real @ A @ F )
& ( ord_less_real @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq_real @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(115,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_order__subst2) ).
thf(776,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(172,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_dual__order_Oirrefl) ).
thf(1003,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(92,axiom,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_order__subst2) ).
thf(690,plain,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ 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)],[92]) ).
thf(142,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_minf_I3_J) ).
thf(872,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ C @ B )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(97,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_order_Ostrict__trans2) ).
thf(705,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(147,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_minf_I1_J) ).
thf(887,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(307,axiom,
! [A: set_real] :
( ( finite_finite_real @ A )
=> ( finite475462905t_real
@ ( collect_set_real
@ ^ [B: set_real] : ( ord_less_eq_set_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_finite__Collect__subsets) ).
thf(1566,plain,
! [A: set_real] :
( ( finite_finite_real @ A )
=> ( finite475462905t_real
@ ( collect_set_real
@ ^ [B: set_real] : ( ord_less_eq_set_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(323,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_zero__reorient) ).
thf(1647,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',fact_220_field__lbound__gt__zero) ).
thf(1252,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)],[230]) ).
thf(104,axiom,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_neqE) ).
thf(739,plain,
! [A: int,B: int] :
( ( A != B )
=> ( ~ ( ord_less_int @ A @ B )
=> ( ord_less_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(292,axiom,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_poly__0) ).
thf(1484,plain,
! [A: real] :
( ( poly_real2 @ zero_zero_poly_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(192,axiom,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_pinf_I8_J) ).
thf(1098,plain,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(182,axiom,
! [A: int > $o,B: int > $o] :
( ( ( finite_finite_int @ ( collect_int @ A ) )
| ( finite_finite_int @ ( collect_int @ B ) ) )
=> ( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__Collect__conjI) ).
thf(1053,plain,
! [A: int > $o,B: int > $o] :
( ( ( finite_finite_int @ ( collect_int @ A ) )
| ( finite_finite_int @ ( collect_int @ B ) ) )
=> ( finite_finite_int
@ ( collect_int
@ ^ [C: int] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(286,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_less__le__trans) ).
thf(1452,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(24,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_antisym__conv) ).
thf(441,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)],[24]) ).
thf(178,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_order__less__subst1) ).
thf(1038,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(99,axiom,
! [A: set_int,B: int] :
( ( finite_finite_int @ A )
=> ( ( member_int @ B @ A )
=> ? [C: int] :
( ( member_int @ C @ A )
& ( ord_less_eq_int @ B @ C )
& ! [D: int] :
( ( member_int @ D @ A )
=> ( ( ord_less_eq_int @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_finite__has__maximal2) ).
thf(717,plain,
! [A: set_int,B: int] :
( ( finite_finite_int @ A )
=> ( ( member_int @ B @ A )
=> ? [C: int] :
( ( member_int @ C @ A )
& ( ord_less_eq_int @ B @ C )
& ! [D: int] :
( ( member_int @ D @ A )
=> ( ( ord_less_eq_int @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(45,axiom,
! [A: int] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_dual__order_Orefl) ).
thf(502,plain,
! [A: int] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(225,axiom,
! [A: real,B: real] :
( ( ~ ( ord_less_eq_real @ A @ B ) )
= ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_verit__comp__simplify1_I3_J) ).
thf(1235,plain,
! [A: real,B: real] :
( ( ~ ( ord_less_eq_real @ A @ B ) )
= ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(4,axiom,
! [A: poly_int] :
( ( zero_zero_poly_int = A )
= ( A = zero_zero_poly_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_zero__reorient) ).
thf(338,plain,
! [A: poly_int] :
( ( zero_zero_poly_int = A )
= ( A = zero_zero_poly_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(66,axiom,
! [A: real,B: real,C: poly_real] :
( ( sturm_308542325x_poly @ A @ B @ C @ zero_zero_poly_real )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_cindex__poly__0_I2_J) ).
thf(576,plain,
! [A: real,B: real,C: poly_real] :
( ( sturm_308542325x_poly @ A @ B @ C @ zero_zero_poly_real )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(309,axiom,
! [A: set_real,B: real] :
( ( finite_finite_real @ A )
=> ( ( member_real @ B @ A )
=> ? [C: real] :
( ( member_real @ C @ A )
& ( ord_less_eq_real @ B @ C )
& ! [D: real] :
( ( member_real @ D @ A )
=> ( ( ord_less_eq_real @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite__has__maximal2) ).
thf(1579,plain,
! [A: set_real,B: real] :
( ( finite_finite_real @ A )
=> ( ( member_real @ B @ A )
=> ? [C: real] :
( ( member_real @ C @ A )
& ( ord_less_eq_real @ B @ C )
& ! [D: real] :
( ( member_real @ D @ A )
=> ( ( ord_less_eq_real @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(221,axiom,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_real @ ( collect_real @ A ) @ ( collect_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_Collect__mono) ).
thf(1218,plain,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_real @ ( collect_real @ A ) @ ( collect_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(81,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ~ ( ord_less_int @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_antisym__conv3) ).
thf(643,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ~ ( ord_less_int @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(58,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_linear) ).
thf(544,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)],[58]) ).
thf(152,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_less__imp__not__less) ).
thf(907,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(106,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_ord__le__eq__trans) ).
thf(744,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)],[106]) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',fact_115_le__cases3) ).
thf(1023,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)],[177]) ).
thf(236,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_dual__order_Oasym) ).
thf(1284,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(191,axiom,
! [A: int,B: int] :
( ( A = B )
=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_eq__refl) ).
thf(1094,plain,
! [A: int,B: int] :
( ( A = B )
=> ( ord_less_eq_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(328,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/sandbox2/benchmark/theBenchmark.p',fact_43_next__non__root__interval) ).
thf(1670,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)],[328]) ).
thf(26,axiom,
! [A: set_int] :
( ( collect_int
@ ^ [B: int] : ( member_int @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Collect__mem__eq) ).
thf(446,plain,
! [A: set_int] :
( ( collect_int
@ ^ [B: int] : ( member_int @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(143,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_antisym__conv) ).
thf(876,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(227,axiom,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_pinf_I3_J) ).
thf(1240,plain,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(299,axiom,
! [A: real,B: int > real,C: int,D: int] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_order__le__less__subst1) ).
thf(1504,plain,
! [A: real,B: int > real,C: int,D: int] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(101,axiom,
! [A: int] :
~ ( ord_less_int @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_less__irrefl) ).
thf(727,plain,
! [A: int] :
~ ( ord_less_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(61,axiom,
! [A: int,B: int] :
( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_not__le__imp__less) ).
thf(556,plain,
! [A: int,B: int] :
( ~ ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(331,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_le__imp__less__or__eq) ).
thf(1685,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_real @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(304,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/sandbox2/benchmark/theBenchmark.p',fact_44_last__non__root__interval) ).
thf(1553,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)],[304]) ).
thf(39,axiom,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_subset__eq) ).
thf(482,plain,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(88,axiom,
! [A: set_int,B: set_int,C: int > int > $o] :
( ~ ( finite_finite_int @ A )
=> ( ( finite_finite_int @ B )
=> ( ! [D: int] :
( ( member_int @ D @ A )
=> ? [E: int] :
( ( member_int @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: int] :
( ( member_int @ D @ B )
& ~ ( finite_finite_int
@ ( collect_int
@ ^ [E: int] :
( ( member_int @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_pigeonhole__infinite__rel) ).
thf(671,plain,
! [A: set_int,B: set_int,C: int > int > $o] :
( ~ ( finite_finite_int @ A )
=> ( ( finite_finite_int @ B )
=> ( ! [D: int] :
( ( member_int @ D @ A )
=> ? [E: int] :
( ( member_int @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: int] :
( ( member_int @ D @ B )
& ~ ( finite_finite_int
@ ( collect_int
@ ^ [E: int] :
( ( member_int @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(150,axiom,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_less__int__code_I1_J) ).
thf(903,plain,
~ ( ord_less_int @ zero_zero_int @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(220,axiom,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ~ ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_less__le__not__le) ).
thf(1216,plain,
( ord_less_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)],[220]) ).
thf(213,axiom,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ C @ B )
=> ~ ( ord_less_eq_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_minf_I8_J) ).
thf(1189,plain,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ C @ B )
=> ~ ( ord_less_eq_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(113,axiom,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_order_Ostrict__iff__order) ).
thf(771,plain,
( ord_less_int
= ( ^ [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(196,axiom,
! [A: real,B: real] :
( ( ~ ( ord_less_real @ A @ B ) )
= ( ( ord_less_real @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_not__less__iff__gr__or__eq) ).
thf(1108,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)],[196]) ).
thf(275,axiom,
! [A: real] :
~ ( ord_less_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_less__irrefl) ).
thf(1421,plain,
! [A: real] :
~ ( ord_less_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_99_linorder__wlog) ).
thf(465,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)],[34]) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',fact_21_poly__IVT__pos) ).
thf(1316,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)],[243]) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',fact_97_dual__order_Otrans) ).
thf(1084,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)],[188]) ).
thf(51,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_order__subst1) ).
thf(524,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_eq_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(68,axiom,
! [A: int] :
( ( zero_zero_int = A )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zero__reorient) ).
thf(581,plain,
! [A: int] :
( ( zero_zero_int = A )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(43,axiom,
! [A: set_real,B: set_real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) )
=> ( ord_less_eq_set_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_subsetI) ).
thf(495,plain,
! [A: set_real,B: set_real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) )
=> ( ord_less_eq_set_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(272,axiom,
ord_less_real @ a @ a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
thf(1412,plain,
ord_less_real @ a @ a2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(238,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_dual__order_Ostrict__implies__not__eq) ).
thf(1289,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(134,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_dual__order_Otrans) ).
thf(844,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(95,axiom,
! [A: poly_real,B: real] :
( ( sturm_276991412p_poly @ A @ zero_zero_poly_real @ B )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_jump__poly0_I2_J) ).
thf(699,plain,
! [A: poly_real,B: real] :
( ( sturm_276991412p_poly @ A @ zero_zero_poly_real @ B )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(184,axiom,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_order__subst2) ).
thf(1062,plain,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_int @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',fact_178_less__trans) ).
thf(1481,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)],[291]) ).
thf(162,axiom,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ord_less_int @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: int] : ( A @ D @ D )
=> ( ! [D: int,E: int] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_linorder__less__wlog) ).
thf(946,plain,
! [A: int > int > $o,B: int,C: int] :
( ! [D: int,E: int] :
( ( ord_less_int @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: int] : ( A @ D @ D )
=> ( ! [D: int,E: int] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(9,axiom,
! [A: int,B: int,C: int > $o] :
( ( ord_less_int @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: int] :
( ( ord_less_eq_int @ A @ D )
& ( ord_less_eq_int @ D @ B )
& ! [E: int] :
( ( ( ord_less_eq_int @ A @ E )
& ( ord_less_int @ E @ D ) )
=> ( C @ E ) )
& ! [E: int] :
( ! [F: int] :
( ( ( ord_less_eq_int @ A @ F )
& ( ord_less_int @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq_int @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_complete__interval) ).
thf(351,plain,
! [A: int,B: int,C: int > $o] :
( ( ord_less_int @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: int] :
( ( ord_less_eq_int @ A @ D )
& ( ord_less_eq_int @ D @ B )
& ! [E: int] :
( ( ( ord_less_eq_int @ A @ E )
& ( ord_less_int @ E @ D ) )
=> ( C @ E ) )
& ! [E: int] :
( ! [F: int] :
( ( ( ord_less_eq_int @ A @ F )
& ( ord_less_int @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq_int @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_pinf_I8_J) ).
thf(401,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_eq_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(228,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_less__imp__not__eq) ).
thf(1244,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(116,axiom,
! [A: real,B: real,C: poly_real] :
( ( sturm_308542325x_poly @ A @ B @ zero_zero_poly_real @ C )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_cindex__poly__0_I1_J) ).
thf(781,plain,
! [A: real,B: real,C: poly_real] :
( ( sturm_308542325x_poly @ A @ B @ zero_zero_poly_real @ C )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(169,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_le__neq__trans) ).
thf(995,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( A != B )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(20,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_pinf_I1_J) ).
thf(418,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(118,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_dual__order_Ostrict__trans1) ).
thf(786,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_int @ C @ A )
=> ( ord_less_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(155,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_less__trans) ).
thf(914,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(22,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_ord__less__eq__trans) ).
thf(433,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ A @ B )
=> ( ( B = C )
=> ( ord_less_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(283,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_order_Ostrict__implies__not__eq) ).
thf(1442,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(207,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_less__imp__le) ).
thf(1161,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(316,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__eq__real__def) ).
thf(1614,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(252,axiom,
! [A: real > $o,B: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ A ) )
| ( finite_finite_real @ ( collect_real @ B ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [C: real] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__Collect__conjI) ).
thf(1348,plain,
! [A: real > $o,B: real > $o] :
( ( ( finite_finite_real @ ( collect_real @ A ) )
| ( finite_finite_real @ ( collect_real @ B ) ) )
=> ( finite_finite_real
@ ( collect_real
@ ^ [C: real] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(322,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/sandbox2/benchmark/theBenchmark.p',fact_153_order__less__subst1) ).
thf(1642,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)],[322]) ).
thf(130,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_order_Oasym) ).
thf(835,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',fact_210_dual__order_Ostrict__trans) ).
thf(1229,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)],[223]) ).
thf(303,axiom,
! [A: set_real,B: set_int,C: real > int > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite_finite_int @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: int] :
( ( member_int @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: int] :
( ( member_int @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_pigeonhole__infinite__rel) ).
thf(1546,plain,
! [A: set_real,B: set_int,C: real > int > $o] :
( ~ ( finite_finite_real @ A )
=> ( ( finite_finite_int @ B )
=> ( ! [D: real] :
( ( member_real @ D @ A )
=> ? [E: int] :
( ( member_int @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: int] :
( ( member_int @ D @ B )
& ~ ( finite_finite_real
@ ( collect_real
@ ^ [E: real] :
( ( member_real @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(265,axiom,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( finite_finite_real
@ ( collect_real
@ ^ [B: real] :
( ( poly_real2 @ A @ B )
= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_poly__roots__finite) ).
thf(1395,plain,
! [A: poly_real] :
( ( A != zero_zero_poly_real )
=> ( finite_finite_real
@ ( collect_real
@ ^ [B: real] :
( ( poly_real2 @ A @ B )
= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(241,axiom,
! [A: real > $o,B: real > $o,C: real > $o,D: real > $o] :
( ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_minf_I1_J) ).
thf(1303,plain,
! [A: real > $o,B: real > $o,C: real > $o,D: real > $o] :
( ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(229,axiom,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ( poly_real2 @ C @ A )
!= zero_zero_real )
=> ( ( ( poly_real2 @ C @ B )
!= zero_zero_real )
=> ( ( sturm_308542325x_poly @ A @ B @ one_one_poly_real @ C )
= ( sturm_1953858694_cross @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_cindex__poly__cross) ).
thf(1248,plain,
! [A: real,B: real,C: poly_real] :
( ( ord_less_real @ A @ B )
=> ( ( ( poly_real2 @ C @ A )
!= zero_zero_real )
=> ( ( ( poly_real2 @ C @ B )
!= zero_zero_real )
=> ( ( sturm_308542325x_poly @ A @ B @ one_one_poly_real @ C )
= ( sturm_1953858694_cross @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(140,axiom,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_antisym__conv1) ).
thf(867,plain,
! [A: int,B: int] :
( ~ ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(139,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_pinf_I7_J) ).
thf(865,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(72,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_less__imp__not__eq2) ).
thf(603,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(103,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_less__imp__not__eq) ).
thf(735,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(129,axiom,
! [A: set_int,B: set_int] :
( ( ord_less_eq_set_int @ A @ B )
=> ( ~ ( finite_finite_int @ A )
=> ~ ( finite_finite_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_infinite__super) ).
thf(833,plain,
! [A: set_int,B: set_int] :
( ( ord_less_eq_set_int @ A @ B )
=> ( ~ ( finite_finite_int @ A )
=> ~ ( finite_finite_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',fact_117_order_Otrans) ).
thf(967,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)],[164]) ).
thf(242,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_le__less) ).
thf(1314,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_less_real @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(5,axiom,
! [A: int] :
( ( poly_int2 @ zero_zero_poly_int @ A )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_poly__0) ).
thf(341,plain,
! [A: int] :
( ( poly_int2 @ zero_zero_poly_int @ A )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(271,axiom,
! [A: real] :
? [B: real] : ( ord_less_real @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_lt__ex) ).
thf(1410,plain,
! [A: real] :
? [B: real] : ( ord_less_real @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(86,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_order__less__subst2) ).
thf(664,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(216,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_less__asym) ).
thf(1197,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ~ ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(79,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_order__class_Oorder_Oantisym) ).
thf(635,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(251,axiom,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_pinf_I7_J) ).
thf(1346,plain,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ( ord_less_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(157,axiom,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_order__less__le__subst1) ).
thf(918,plain,
! [A: int,B: int > int,C: int,D: int] :
( ( ord_less_int @ A @ ( B @ C ) )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_eq_int @ E @ F )
=> ( ord_less_eq_int @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_int @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(121,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_less__asym_H) ).
thf(801,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ~ ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(248,axiom,
! [A: set_real,B: real > $o] :
( ord_less_eq_set_real
@ ( collect_real
@ ^ [C: real] :
( ( member_real @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_Collect__subset) ).
thf(1335,plain,
! [A: set_real,B: real > $o] :
( ord_less_eq_set_real
@ ( collect_real
@ ^ [C: real] :
( ( member_real @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(333,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_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/sandbox2/benchmark/theBenchmark.p',fact_241_order__less__le__subst2) ).
thf(1693,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_eq_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)],[333]) ).
thf(253,axiom,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_pinf_I4_J) ).
thf(1352,plain,
! [A: real] :
? [B: real] :
! [C: real] :
( ( ord_less_real @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(201,axiom,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ~ ( finite_finite_real @ A )
=> ~ ( finite_finite_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_infinite__super) ).
thf(1129,plain,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ~ ( finite_finite_real @ A )
=> ~ ( finite_finite_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(262,axiom,
! [A: real,B: real] :
( ~ ( ord_less_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_linorder__cases) ).
thf(1384,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)],[262]) ).
thf(167,axiom,
! [A: nat] :
( ( poly_cutoff_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_poly__cutoff__0) ).
thf(982,plain,
! [A: nat] :
( ( poly_cutoff_real @ A @ zero_zero_poly_real )
= zero_zero_poly_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',fact_103_order__trans) ).
thf(607,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)],[73]) ).
thf(78,axiom,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_pinf_I2_J) ).
thf(624,plain,
! [A: int > $o,B: int > $o,C: int > $o,D: int > $o] :
( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: int] :
! [F: int] :
( ( ord_less_int @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(132,axiom,
! [A: set_int] :
( ( finite_finite_int @ A )
=> ( finite26677625et_int
@ ( collect_set_int
@ ^ [B: set_int] : ( ord_less_eq_set_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_finite__Collect__subsets) ).
thf(839,plain,
! [A: set_int] :
( ( finite_finite_int @ A )
=> ( finite26677625et_int
@ ( collect_set_int
@ ^ [B: set_int] : ( ord_less_eq_set_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(313,axiom,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__Collect__eq) ).
thf(1606,plain,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(41,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_order_Ostrict__implies__not__eq) ).
thf(486,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(122,axiom,
! [A: set_int,B: int] :
( ( finite_finite_int @ A )
=> ( ( member_int @ B @ A )
=> ? [C: int] :
( ( member_int @ C @ A )
& ( ord_less_eq_int @ C @ B )
& ! [D: int] :
( ( member_int @ D @ A )
=> ( ( ord_less_eq_int @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_finite__has__minimal2) ).
thf(803,plain,
! [A: set_int,B: int] :
( ( finite_finite_int @ A )
=> ( ( member_int @ B @ A )
=> ? [C: int] :
( ( member_int @ C @ A )
& ( ord_less_eq_int @ C @ B )
& ! [D: int] :
( ( member_int @ D @ A )
=> ( ( ord_less_eq_int @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(174,axiom,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_pinf_I3_J) ).
thf(1009,plain,
! [A: int] :
? [B: int] :
! [C: int] :
( ( ord_less_int @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(158,axiom,
! [A: poly_int] :
( ( A != zero_zero_poly_int )
=> ( finite_finite_int
@ ( collect_int
@ ^ [B: int] :
( ( poly_int2 @ A @ B )
= zero_zero_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_poly__roots__finite) ).
thf(923,plain,
! [A: poly_int] :
( ( A != zero_zero_poly_int )
=> ( finite_finite_int
@ ( collect_int
@ ^ [B: int] :
( ( poly_int2 @ A @ B )
= zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(85,axiom,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_order__le__less__subst2) ).
thf(659,plain,
! [A: real,B: real,C: real > int,D: int] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_int @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(274,axiom,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_order__less__subst2) ).
thf(1416,plain,
! [A: int,B: int,C: int > real,D: real] :
( ( ord_less_int @ A @ B )
=> ( ( ord_less_real @ ( C @ B ) @ D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(285,axiom,
! [A: real,B: real] :
( ( ~ ( ord_less_eq_real @ A @ B ) )
= ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_not__le) ).
thf(1449,plain,
! [A: real,B: real] :
( ( ~ ( ord_less_eq_real @ A @ B ) )
= ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(98,axiom,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_ord__less__eq__subst) ).
thf(708,plain,
! [A: int,B: int,C: int > int,D: int] :
( ( ord_less_int @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: int,F: int] :
( ( ord_less_int @ E @ F )
=> ( ord_less_int @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_int @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(325,axiom,
! [A: real > $o,B: real > $o,C: real > $o,D: real > $o] :
( ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_minf_I2_J) ).
thf(1653,plain,
! [A: real > $o,B: real > $o,C: real > $o,D: real > $o] :
( ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: real] :
! [F: real] :
( ( ord_less_real @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',fact_50_not__eq__pos__or__neg__iff__2) ).
thf(1367,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)],[257]) ).
thf(1829,plain,
$false,
inference(e,[status(thm)],[1337,1469,1633,1105,347,909,941,1586,1501,762,1406,730,1401,449,511,614,1426,384,472,1222,1196,898,1001,1127,841,973,1650,389,724,504,1330,344,1455,1191,587,1323,917,702,542,460,1087,870,1609,1013,1115,1568,1494,1100,1232,638,853,1398,881,416,475,1664,789,646,1677,1183,1020,574,1051,821,905,480,766,1169,453,1622,998,411,1433,507,1604,678,529,546,1199,1153,810,381,534,1067,1057,1163,334,1387,1091,598,429,1370,1238,1560,862,349,392,1487,879,852,1296,830,1159,1079,456,847,484,742,1111,1006,610,499,697,1541,403,1498,884,1361,554,537,669,1424,1446,1155,1612,679,970,837,1263,985,1539,1266,1131,1668,911,515,1150,1333,1434,792,1286,558,1616,773,926,1563,657,965,1680,824,1273,1595,444,584,1389,1620,579,1403,1124,413,1428,572,1371,335,1258,1638,1356,540,764,1282,784,1048,1492,616,1175,900,406,681,1408,451,567,509,1043,1376,1439,477,758,621,1325,1344,1293,1381,462,1688,769,1460,695,1435,1364,1496,1102,438,1213,827,490,1166,1208,648,749,1472,458,1413,1076,531,944,812,1509,776,1003,690,872,705,887,1566,1647,1252,739,1484,1098,1053,1452,441,1038,717,502,1235,338,576,1579,1218,643,544,907,744,1023,1284,1094,1670,446,876,1240,1504,727,556,1685,1553,482,671,903,1216,1189,771,1108,1421,465,1316,1084,524,581,495,1412,1289,844,699,1062,1481,946,351,401,1244,781,995,418,786,914,433,1442,1161,1614,1348,1642,835,1229,1546,1395,1303,1248,867,865,603,735,833,967,1314,341,1410,664,1197,635,1346,918,801,1335,1693,1352,1129,1384,982,607,624,839,1606,486,803,1009,923,659,1416,1449,708,1653,1367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP193^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.08/0.21 % Computer : n010.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 20:10:18 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.45/1.23 % [INFO] Parsing done (436ms).
% 2.45/1.24 % [INFO] Running in sequential loop mode.
% 3.73/1.67 % [INFO] eprover registered as external prover.
% 3.73/1.68 % [INFO] Scanning for conjecture ...
% 4.18/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 350 axioms. Running axiom selection ...
% 4.38/1.97 % [INFO] Axiom selection finished. Selected 331 axioms (removed 19 axioms).
% 5.26/2.28 % [INFO] Problem is higher-order (TPTP THF).
% 5.62/2.32 % [INFO] Type checking passed.
% 5.62/2.32 % [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 ...
% 22.55/6.14 % External prover 'e' found a proof!
% 22.55/6.14 % [INFO] Killing All external provers ...
% 22.55/6.14 % Time passed: 5794ms (effective reasoning time: 4893ms)
% 22.55/6.14 % 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)>
% 22.55/6.15 % Axioms used in derivation (331): fact_17_poly__roots__finite, fact_126_antisym, fact_201_linorder__cases, fact_247_not__less, fact_185_ord__eq__less__trans, fact_262_dense__le, fact_156_order__less__subst1, fact_323_pinf_I4_J, fact_281_dual__order_Ostrict__trans2, fact_102_dual__order_Orefl, fact_153_order__less__subst1, fact_61_order__refl, fact_175_less__asym, fact_84_finite__Collect__subsets, fact_329_minf_I1_J, fact_197_less__imp__not__eq2, fact_250_le__neq__trans, fact_206_less__imp__not__less, fact_158_order__less__subst2, fact_40_finite__has__minimal2, fact_14_finite__Collect__disjI, fact_312_verit__la__disequality, fact_115_le__cases3, fact_30_less__numeral__extra_I3_J, fact_182_less__irrefl, fact_107_ord__le__eq__trans, fact_144_order__subst1, fact_213_not__less__iff__gr__or__eq, fact_335_jump__poly__not__root, fact_167_neq__iff, fact_330_minf_I2_J, fact_106_order__class_Oorder_Oantisym, fact_305_Collect__mono, fact_331_minf_I2_J, fact_225_le__less, fact_122_eq__refl, fact_254_antisym__conv2, fact_215_order_Ostrict__implies__not__eq, fact_191_less__imp__not__eq, fact_24_poly__all__0__iff__0, fact_221_leD, fact_345_cindex__poly__0_I2_J, fact_300_subsetI, fact_41_finite__has__maximal2, fact_192_less__not__sym, fact_57_pigeonhole__infinite__rel, fact_332_minf_I3_J, fact_12_finite__Collect__conjI, fact_170_order_Oasym, fact_268_less__le__not__le, fact_259_less__le__trans, fact_226_le__less, fact_131_ord__le__eq__subst, fact_304_subset__iff, fact_88_finite__subset, fact_13_finite__Collect__disjI, fact_95_dual__order_Oeq__iff, fact_238_order__less__le__subst1, fact_265_le__imp__less__or__eq, fact_150_ord__less__eq__subst, fact_99_linorder__wlog, fact_275_order_Oorder__iff__strict, fact_311_Collect__mono__iff, fact_133_ord__eq__le__subst, fact_348_cindex__poly__def, fact_10_assms_I4_J, fact_337_jump__poly0_I1_J, fact_114_antisym__conv, fact_241_order__less__le__subst2, fact_123_linear, fact_210_dual__order_Ostrict__trans, fact_51_not__eq__pos__or__neg__iff__1, fact_75_mem__Collect__eq, fact_58_pigeonhole__infinite__rel, fact_291_pinf_I6_J, fact_160_order__less__subst2, fact_267_less__le__not__le, fact_180_less__linear, fact_285_minf_I8_J, fact_290_pinf_I6_J, fact_74_dual__order_Oorder__iff__strict, fact_204_order_Ostrict__trans, fact_203_dual__order_Oirrefl, fact_11_finite__Collect__conjI, fact_108_ord__le__eq__trans, fact_164_gt__ex, fact_263_le__less__linear, fact_255_less__imp__le, fact_105_order__class_Oorder_Oantisym, fact_110_ord__eq__le__trans, fact_314_verit__comp__simplify1_I1_J, fact_308_Collect__subset, fact_294_is__zero__null, fact_230_order__le__less__subst1, fact_198_less__imp__triv, fact_139_order__subst2, fact_21_poly__IVT__pos, fact_190_less__imp__not__eq, fact_181_less__linear, fact_130_ord__le__eq__subst, fact_104_order__trans, fact_145_ord__eq__less__subst, fact_240_order__less__le__subst1, fact_327_pinf_I7_J, fact_80_Collect__cong, fact_244_order__less__le__subst2, fact_69_dual__order_Ostrict__implies__order, fact_224_leI, fact_81_order_Ostrict__implies__order, fact_237_order__less__le__subst1, fact_228_less__le, fact_274_order_Ostrict__trans2, fact_219_complete__real, fact_154_order__less__subst1, fact_280_dual__order_Ostrict__trans1, fact_47_zero__reorient, fact_292_verit__comp__simplify1_I3_J, fact_141_order__subst1, fact_242_order__less__le__subst2, fact_214_order_Ostrict__implies__not__eq, fact_2_assms_I3_J, fact_71_dual__order_Ostrict__iff__order, fact_216_dual__order_Ostrict__implies__not__eq, fact_306_Collect__mono, fact_89_infinite__super, fact_287_minf_I6_J, fact_269_not__le__imp__less, fact_315_verit__comp__simplify1_I1_J, fact_149_ord__less__eq__subst, fact_118_order_Otrans, fact_186_ord__less__eq__trans, fact_162_lt__ex, fact_218_ex__gt__or__lt, fact_37_finite__psubset__induct, fact_98_dual__order_Otrans, fact_97_dual__order_Otrans, fact_32_le__numeral__extra_I3_J, fact_135_ord__eq__le__subst, fact_62_order__refl, fact_341_finite__interval__int4, fact_128_eq__iff, fact_256_less__imp__le, fact_46_zero__reorient, fact_320_pinf_I3_J, fact_271_order_Ostrict__trans1, fact_223_leI, fact_93_dual__order_Oantisym, fact_246_not__le, fact_18_poly__roots__finite, fact_309_less__eq__set__def, fact_264_le__less__linear, fact_171_dense, fact_282_dual__order_Ostrict__trans2, fact_227_less__le, fact_232_order__le__less__subst1, fact_236_order__le__less__subst2, fact_90_infinite__super, fact_72_dual__order_Ostrict__iff__order, fact_113_antisym__conv, fact_65_complete__interval, fact_208_linorder__less__wlog, fact_322_pinf_I4_J, fact_63_cross__no__root, fact_117_order_Otrans, fact_187_ord__less__eq__trans, fact_279_dual__order_Ostrict__trans1, fact_70_dual__order_Ostrict__implies__order, fact_101_dual__order_Orefl, fact_151_ord__less__eq__subst, fact_184_ord__eq__less__trans, fact_212_not__less__iff__gr__or__eq, fact_342_finite__interval__int3, fact_177_less__asym_H, fact_220_field__lbound__gt__zero, fact_119_le__cases, fact_45_zero__reorient, fact_132_ord__le__eq__subst, fact_155_order__less__subst1, fact_336_jump__poly0_I2_J, fact_59_not__finite__existsD, fact_94_dual__order_Oantisym, fact_127_eq__iff, fact_121_eq__refl, fact_9_poly__0, fact_92_rev__finite__subset, fact_334_imp__le__cong, fact_310_Collect__mono__iff, fact_55_pigeonhole__infinite__rel, fact_243_order__less__le__subst2, fact_253_antisym__conv2, fact_56_pigeonhole__infinite__rel, fact_195_antisym__conv3, fact_194_antisym__conv3, fact_297_poly__cutoff__0, fact_35_le__numeral__extra_I3_J, fact_83_dense__le__bounded, fact_303_subset__eq, fact_205_order_Ostrict__trans, fact_179_less__trans, fact_222_leD, fact_278_order_Ostrict__iff__order, fact_321_pinf_I3_J, fact_86_cross__0, fact_82_order_Ostrict__implies__order, fact_260_less__le__trans, fact_1_assms_I2_J, fact_288_pinf_I8_J, fact_302_subsetD, fact_349_int__one__le__iff__zero__less, fact_199_less__imp__triv, fact_137_order__subst2, fact_39_finite__has__minimal2, fact_172_less__imp__neq, fact_257_le__less__trans, fact_163_gt__ex, fact_53_poly__eq__poly__eq__iff, fact_188_dual__order_Oasym, fact_78_Collect__mem__eq, fact_136_ord__eq__le__subst, fact_152_ord__less__eq__subst, fact_193_less__not__sym, fact_286_minf_I6_J, fact_248_not__less, fact_289_pinf_I8_J, fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062, fact_326_pinf_I7_J, fact_239_order__less__le__subst1, fact_270_not__le__imp__less, fact_111_order__class_Oorder_Oeq__iff, fact_42_finite__has__maximal2, fact_176_less__asym_H, fact_85_finite__Collect__subsets, fact_140_order__subst2, fact_266_le__imp__less__or__eq, fact_313_verit__la__disequality, fact_38_finite__psubset__induct, fact_249_le__neq__trans, fact_207_less__imp__not__less, fact_211_dual__order_Ostrict__trans, fact_44_last__non__root__interval, fact_165_neqE, fact_339_finite__interval__int1, fact_96_dual__order_Oeq__iff, fact_87_finite__subset, fact_233_order__le__less__subst2, fact_73_dual__order_Oorder__iff__strict, fact_147_ord__eq__less__subst, fact_340_finite__interval__int2, fact_328_minf_I1_J, fact_91_rev__finite__subset, fact_258_le__less__trans, fact_284_minf_I8_J, fact_76_mem__Collect__eq, fact_166_neqE, fact_245_not__le, fact_68_order_Onot__eq__order__implies__strict, fact_27_less__numeral__extra_I3_J, fact_189_dual__order_Oasym, fact_317_pinf_I1_J, fact_100_linorder__wlog, fact_3_assms_I1_J, fact_161_lt__ex, fact_325_pinf_I5_J, fact_202_dual__order_Oirrefl, fact_178_less__trans, fact_333_conj__le__cong, fact_252_antisym__conv1, fact_142_order__subst1, fact_52_poly__eq__poly__eq__iff, fact_324_pinf_I5_J, fact_134_ord__eq__le__subst, fact_234_order__le__less__subst2, fact_338_verit__la__generic, fact_173_less__imp__neq, fact_79_Collect__cong, fact_183_less__irrefl, fact_50_not__eq__pos__or__neg__iff__2, fact_67_order_Onot__eq__order__implies__strict, fact_168_neq__iff, fact_109_ord__eq__le__trans, fact_48_zero__reorient, fact_66_complete__interval, fact_272_order_Ostrict__trans1, fact_301_in__mono, fact_277_order_Ostrict__iff__order, fact_43_next__non__root__interval, fact_344_less__eq__int__code_I1_J, fact_273_order_Ostrict__trans2, fact_276_order_Oorder__iff__strict, fact_347_cindex__poly__cross, fact_20_poly__IVT__neg, fact_307_Collect__subset, fact_112_order__class_Oorder_Oeq__iff, fact_4_False, fact_251_antisym__conv1, fact_22_poly__all__0__iff__0, fact_209_linorder__less__wlog, fact_283_dense__ge__bounded, fact_217_dual__order_Ostrict__implies__not__eq, fact_261_dense__ge, fact_148_ord__eq__less__subst, fact_343_less__int__code_I1_J, fact_64_less__eq__real__def, fact_157_order__less__subst2, fact_318_pinf_I2_J, fact_77_Collect__mem__eq, fact_196_less__imp__not__eq2, fact_174_less__asym, fact_129_ord__le__eq__subst, fact_31_less__numeral__extra_I3_J, fact_169_order_Oasym, fact_143_order__subst1, fact_231_order__le__less__subst1, fact_293_verit__comp__simplify1_I3_J, fact_103_order__trans, fact_229_order__le__less__subst1, fact_346_cindex__poly__0_I1_J, fact_36_le__numeral__extra_I3_J, fact_8_poly__0, fact_200_linorder__cases, fact_146_ord__eq__less__subst, fact_120_le__cases, fact_316_pinf_I1_J, fact_124_linear, fact_319_pinf_I2_J, fact_60_not__finite__existsD, fact_235_order__le__less__subst2, fact_125_antisym, fact_116_le__cases3, fact_159_order__less__subst2, fact_138_order__subst2
% 22.55/6.15 % No. of inferences in proof: 666
% 22.55/6.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5794 ms resp. 4893 ms w/o parsing
% 23.86/6.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.86/6.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------