TSTP Solution File: ITP193^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP193^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:23:54 EDT 2024
% Result : Theorem 38.64s 24.24s
% Output : Refutation 39.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 403
% Syntax : Number of formulae : 756 ( 210 unt; 52 typ; 0 def)
% Number of atoms : 2448 ( 435 equ; 8 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 7455 ( 208 ~; 53 |; 182 &;5866 @)
% ( 0 <=>;1146 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 267 ( 267 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 11 con; 0-4 aty)
% Number of variables : 2088 ( 171 ^1781 !; 94 ?;2088 :)
% ( 42 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(idom_type,type,
idom:
!>[TA: $tType] : $o ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(no_bot_type,type,
no_bot:
!>[TA: $tType] : $o ).
thf(no_top_type,type,
no_top:
!>[TA: $tType] : $o ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(comm_ring_1_type,type,
comm_ring_1:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : $o ).
thf(zero_less_one_type,type,
zero_less_one:
!>[TA: $tType] : $o ).
thf(dense_order_type,type,
dense_order:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_type,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(dense_linorder_type,type,
dense_linorder:
!>[TA: $tType] : $o ).
thf(ring_n68954251visors_type,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_type,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_type,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(ordere1818651114id_add_type,type,
ordere1818651114id_add:
!>[TA: $tType] : $o ).
thf(condit1656338222tinuum_type,type,
condit1656338222tinuum:
!>[TA: $tType] : $o ).
thf(condit1037483654norder_type,type,
condit1037483654norder:
!>[TA: $tType] : $o ).
thf(finite_finite2_type,type,
finite_finite2:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(groups1340683514dd_sum_type,type,
groups1340683514dd_sum:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > TA ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(is_zero_type,type,
is_zero:
!>[TA: $tType] : ( ( poly @ TA ) > $o ) ).
thf(poly2_type,type,
poly2:
!>[TA: $tType] : ( ( poly @ TA ) > TA > TA ) ).
thf(poly_cutoff_type,type,
poly_cutoff:
!>[TA: $tType] : ( nat > ( poly @ TA ) > ( poly @ TA ) ) ).
thf(reflect_poly_type,type,
reflect_poly:
!>[TA: $tType] : ( ( poly @ TA ) > ( poly @ TA ) ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(sturm_1539314049x_poly_type,type,
sturm_1539314049x_poly: real > real > ( poly @ real ) > ( poly @ real ) > int ).
thf(sturm_424270202_cross_type,type,
sturm_424270202_cross: ( poly @ real ) > real > real > int ).
thf(sturm_652470720p_poly_type,type,
sturm_652470720p_poly: ( poly @ real ) > ( poly @ real ) > real > int ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a_type,type,
a: real ).
thf(a2_type,type,
a2: real ).
thf(b_type,type,
b: real ).
thf(b2_type,type,
b2: real ).
thf(p_type,type,
p: poly @ real ).
thf(350,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_order_Ostrict__trans1) ).
thf(1322,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(61,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_14) ).
thf(479,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(208,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__has__maximal2) ).
thf(909,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(347,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_order_Ostrict__trans2) ).
thf(1315,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(218,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_le__less) ).
thf(941,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(175,axiom,
! [TA: $tType] :
( ( no_top @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_gt__ex) ).
thf(777,plain,
! [TA: $tType] :
( ( no_top @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(339,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_pinf_I7_J) ).
thf(1295,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(267,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_Collect__subset) ).
thf(1083,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(225,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_order_Ostrict__implies__order) ).
thf(962,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(311,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_gr__implies__not__zero) ).
thf(1200,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(233,axiom,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: set @ TB,B: TB > TA,C: TA,D: TB] :
( ( finite_finite2 @ TB @ A )
=> ( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( B @ E ) ) )
=> ( ( ( groups1340683514dd_sum @ TB @ TA @ B @ A )
= C )
=> ( ( member @ TB @ D @ A )
=> ( ord_less_eq @ TA @ ( B @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_sum__nonneg__leq__bound) ).
thf(977,plain,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: set @ TB,B: TB > TA,C: TA,D: TB] :
( ( finite_finite2 @ TB @ A )
=> ( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( B @ E ) ) )
=> ( ( ( groups1340683514dd_sum @ TB @ TA @ B @ A )
= C )
=> ( ( member @ TB @ D @ A )
=> ( ord_less_eq @ TA @ ( B @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(201,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_minf_I2_J) ).
thf(873,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(16,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_in__mono) ).
thf(379,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(121,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1_11) ).
thf(614,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(302,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_antisym__conv3) ).
thf(1173,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(78,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_predicate1I) ).
thf(523,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(298,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 ) ) )
=> ( ( poly2 @ real @ p @ A )
!= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_assms_I4_J) ).
thf(1158,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 ) ) )
=> ( ( poly2 @ real @ p @ A )
!= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(107,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_ord__eq__le__trans) ).
thf(582,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(161,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_dense__le__bounded) ).
thf(730,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(338,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB,B: TB > TA] :
( ! [C: TB] :
( ( member @ TB @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TA ) ) )
=> ( ( groups1340683514dd_sum @ TB @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_sum_Oneutral) ).
thf(1290,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB,B: TB > TA] :
( ! [C: TB] :
( ( member @ TB @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TA ) ) )
=> ( ( groups1340683514dd_sum @ TB @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(440,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(75,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_le__cases) ).
thf(511,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(20,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ozero_65) ).
thf(385,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(384,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(345,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_subset__iff__psubset__eq) ).
thf(1310,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(57,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oidom) ).
thf(472,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(322,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_dense__ge) ).
thf(1233,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(152,axiom,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ A ) )
=> ( ( ord_less @ real @ ( poly2 @ real @ C @ B ) @ ( zero_zero @ real ) )
=> ? [D: real] :
( ( ord_less @ real @ A @ D )
& ( ord_less @ real @ D @ B )
& ( ( poly2 @ real @ C @ D )
= ( zero_zero @ real ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_poly__IVT__neg) ).
thf(698,plain,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ A ) )
=> ( ( ord_less @ real @ ( poly2 @ real @ C @ B ) @ ( zero_zero @ real ) )
=> ? [D: real] :
( ( ord_less @ real @ A @ D )
& ( ord_less @ real @ D @ B )
& ( ( poly2 @ real @ C @ D )
= ( zero_zero @ real ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(220,axiom,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( B @ C ) ) )
=> ( ( ( groups1340683514dd_sum @ TA @ TB @ B @ A )
= ( zero_zero @ TB ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TB ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_sum__nonneg__eq__0__iff) ).
thf(945,plain,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( B @ C ) ) )
=> ( ( ( groups1340683514dd_sum @ TA @ TB @ B @ A )
= ( zero_zero @ TB ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TB ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType] :
( ( ordere1818651114id_add @ TB )
=> ! [A: set @ TA,B: TA > TB,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TB @ ( B @ D ) @ ( C @ D ) ) )
=> ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( ord_less @ TB @ ( B @ D ) @ ( C @ D ) ) )
=> ( ord_less @ TB @ ( groups1340683514dd_sum @ TA @ TB @ B @ A ) @ ( groups1340683514dd_sum @ TA @ TB @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_sum__strict__mono__ex1) ).
thf(930,plain,
! [TA: $tType,TB: $tType] :
( ( ordere1818651114id_add @ TB )
=> ! [A: set @ TA,B: TA > TB,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TB @ ( B @ D ) @ ( C @ D ) ) )
=> ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( ord_less @ TB @ ( B @ D ) @ ( C @ D ) ) )
=> ( ord_less @ TB @ ( groups1340683514dd_sum @ TA @ TB @ B @ A ) @ ( groups1340683514dd_sum @ TA @ TB @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(185,axiom,
! [A: poly @ real,B: real] :
( ( sturm_652470720p_poly @ A @ ( zero_zero @ ( poly @ real ) ) @ B )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_jump__poly0_I2_J) ).
thf(829,plain,
! [A: poly @ real,B: real] :
( ( sturm_652470720p_poly @ A @ ( zero_zero @ ( poly @ real ) ) @ B )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(239,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_le__numeral__extra_I3_J) ).
thf(1001,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(177,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rev__finite__subset) ).
thf(782,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(100,axiom,
ord @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oord_5) ).
thf(565,plain,
ord @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(330,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(1265,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(190,axiom,
dense_order @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Odense__order) ).
thf(841,plain,
dense_order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(36,axiom,
order @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oorder_4) ).
thf(417,plain,
order @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(231,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
& ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_less__fun__def) ).
thf(973,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
& ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(256,axiom,
comm_semiring_1 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__semiring__1_37) ).
thf(1046,plain,
comm_semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(260,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_less__trans) ).
thf(1055,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(341,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_le__neq__trans) ).
thf(1298,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(159,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_pinf_I1_J) ).
thf(719,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(346,axiom,
! [A: int,B: int] :
( finite_finite2 @ int
@ ( collect @ int
@ ^ [C: int] :
( ( ord_less_eq @ int @ A @ C )
& ( ord_less @ int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_finite__interval__int2) ).
thf(1313,plain,
! [A: int,B: int] :
( finite_finite2 @ int
@ ( collect @ int
@ ^ [C: int] :
( ( ord_less_eq @ int @ A @ C )
& ( ord_less @ int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(308,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_dense__le) ).
thf(1191,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(51,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__ring__1_61) ).
thf(460,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(125,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_order__class_Oorder_Oantisym) ).
thf(619,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(188,axiom,
ring_n68954251visors @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oring__no__zero__divisors_34) ).
thf(838,plain,
ring_n68954251visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(210,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_dense__ge__bounded) ).
thf(917,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(166,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
| ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__Collect__conjI) ).
thf(751,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
| ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(262,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_dual__order_Ostrict__implies__order) ).
thf(1059,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(291,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_dual__order_Ostrict__iff__order) ).
thf(1132,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_ord__eq__less__subst) ).
thf(817,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_le__funE) ).
thf(559,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(193,axiom,
! [A: int,B: int] :
( finite_finite2 @ int
@ ( collect @ int
@ ^ [C: int] :
( ( ord_less @ int @ A @ C )
& ( ord_less_eq @ int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_finite__interval__int3) ).
thf(853,plain,
! [A: int,B: int] :
( finite_finite2 @ int
@ ( collect @ int
@ ^ [C: int] :
( ( ord_less @ int @ A @ C )
& ( ord_less_eq @ int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(296,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 ) )
=> ( ( poly2 @ real @ C @ D )
!= ( zero_zero @ real ) ) )
=> ( ( sturm_424270202_cross @ C @ A @ B )
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_cross__no__root) ).
thf(1147,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 ) )
=> ( ( poly2 @ real @ C @ D )
!= ( zero_zero @ real ) ) )
=> ( ( sturm_424270202_cross @ C @ A @ B )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(200,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_order__le__less__subst2) ).
thf(870,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(35,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_26) ).
thf(416,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(283,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_less__irrefl) ).
thf(1115,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(244,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_dual__order_Oorder__iff__strict) ).
thf(1013,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(172,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_minf_I7_J) ).
thf(770,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(212,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_subset__psubset__trans) ).
thf(924,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(49,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_set__eq__subset) ).
thf(443,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_order__subst2) ).
thf(376,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(64,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_subset__iff) ).
thf(485,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(246,axiom,
dense_linorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Odense__linorder) ).
thf(1020,plain,
dense_linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1,conjecture,
( finite_finite2 @ real
@ ( collect @ real
@ ^ [A: real] :
( ( ( poly2 @ real @ p @ A )
= ( zero_zero @ real ) )
& ( ord_less @ real @ a @ A )
& ( ord_less @ real @ A @ b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( finite_finite2 @ real
@ ( collect @ real
@ ^ [A: real] :
( ( ( poly2 @ real @ p @ A )
= ( zero_zero @ real ) )
& ( ord_less @ real @ a @ A )
& ( ord_less @ real @ A @ b ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(353,plain,
~ ( finite_finite2 @ real
@ ( collect @ real
@ ^ [A: real] :
( ( ( poly2 @ real @ 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(304,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_dual__order_Ostrict__trans1) ).
thf(1183,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(62,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ A @ B )
| ( A = B )
| ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_verit__la__generic) ).
thf(480,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)],[62]) ).
thf(254,axiom,
! [A: real,B: real] :
( ( sturm_424270202_cross @ ( zero_zero @ ( poly @ real ) ) @ A @ B )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_cross__0) ).
thf(1040,plain,
! [A: real,B: real] :
( ( sturm_424270202_cross @ ( zero_zero @ ( poly @ real ) ) @ A @ B )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(281,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_psubset__subset__trans) ).
thf(1109,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType] :
( ( canoni770627133id_add @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( ( groups1340683514dd_sum @ TA @ TB @ B @ A )
= ( zero_zero @ TB ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TB ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_sum__eq__0__iff) ).
thf(692,plain,
! [TA: $tType,TB: $tType] :
( ( canoni770627133id_add @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( ( groups1340683514dd_sum @ TA @ TB @ B @ A )
= ( zero_zero @ TB ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TB ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(162,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_pinf_I8_J) ).
thf(734,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(223,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_dual__order_Oirrefl) ).
thf(956,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(285,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ B @ C )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_pinf_I11_J) ).
thf(1119,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(25,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( one @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oone_66) ).
thf(396,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( one @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(238,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_not__less) ).
thf(998,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(32,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(411,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(80,axiom,
comm_semiring_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__semiring__0) ).
thf(527,plain,
comm_semiring_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(146,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( reflect_poly @ TA @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_reflect__poly__0) ).
thf(678,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( reflect_poly @ TA @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(82,axiom,
ordere216010020id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_9) ).
thf(529,plain,
ordere216010020id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(169,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_minf_I3_J) ).
thf(761,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(17,axiom,
comm_ring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__ring__1) ).
thf(381,plain,
comm_ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
ordere1818651114id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_7) ).
thf(366,plain,
ordere1818651114id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > $o] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_pigeonhole__infinite__rel) ).
thf(714,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > $o] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(257,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_minf_I6_J) ).
thf(1047,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(261,axiom,
! [TA: $tType,A: TA > $o] :
( ~ ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ? [B: TA] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_not__finite__existsD) ).
thf(1057,plain,
! [TA: $tType,A: TA > $o] :
( ~ ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ? [B: TA] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(299,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TB )
=> ! [A: set @ TA,B: TA > TB,C: TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( groups1340683514dd_sum @ TA @ TB @ B
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) ) ) )
= ( groups1340683514dd_sum @ TA @ TB
@ ^ [D: TA] : ( if @ TB @ ( C @ D ) @ ( B @ D ) @ ( zero_zero @ TB ) )
@ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_sum_Ointer__filter) ).
thf(1163,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TB )
=> ! [A: set @ TA,B: TA > TB,C: TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ( groups1340683514dd_sum @ TA @ TB @ B
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) ) ) )
= ( groups1340683514dd_sum @ TA @ TB
@ ^ [D: TA] : ( if @ TB @ ( C @ D ) @ ( B @ D ) @ ( zero_zero @ TB ) )
@ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(318,axiom,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ( poly2 @ real @ C @ A )
!= ( zero_zero @ real ) )
=> ( ( ( poly2 @ real @ C @ B )
!= ( zero_zero @ real ) )
=> ( ( sturm_1539314049x_poly @ A @ B @ ( one_one @ ( poly @ real ) ) @ C )
= ( sturm_424270202_cross @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_cindex__poly__cross) ).
thf(1223,plain,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ( poly2 @ real @ C @ A )
!= ( zero_zero @ real ) )
=> ( ( ( poly2 @ real @ C @ B )
!= ( zero_zero @ real ) )
=> ( ( sturm_1539314049x_poly @ A @ B @ ( one_one @ ( poly @ real ) ) @ C )
= ( sturm_424270202_cross @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(271,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom_36) ).
thf(1091,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(183,axiom,
one @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oone_49) ).
thf(825,plain,
one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(247,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_less__numeral__extra_I1_J) ).
thf(1021,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(327,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_order__le__less__subst1) ).
thf(1255,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(197,axiom,
! [TA: $tType] :
( ( no_bot @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_lt__ex) ).
thf(862,plain,
! [TA: $tType] :
( ( no_bot @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(97,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add_10) ).
thf(561,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(129,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
& ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__Collect__disjI) ).
thf(630,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
& ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_le__funD) ).
thf(429,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(55,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Orderings_Oord_64) ).
thf(467,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(101,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_19) ).
thf(566,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(251,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_le__less__linear) ).
thf(1032,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(6,axiom,
no_top @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top_16) ).
thf(361,plain,
no_top @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(127,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_order_Ostrict__trans) ).
thf(625,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(435,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(141,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_verit__comp__simplify1_I1_J) ).
thf(665,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(67,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_57) ).
thf(493,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(156,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_not__less__zero) ).
thf(710,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',fact_189_conj__le__cong) ).
thf(842,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)],[191]) ).
thf(279,axiom,
ord_less @ real @ a2 @ b2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(1106,plain,
ord_less @ real @ a2 @ b2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(93,axiom,
preorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Opreorder_3) ).
thf(551,plain,
preorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(288,axiom,
linordered_field @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).
thf(1128,plain,
linordered_field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(122,axiom,
condit1037483654norder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder) ).
thf(615,plain,
condit1037483654norder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(264,axiom,
( finite_finite2 @ real
@ ( collect @ real
@ ^ [A: real] :
( ( poly2 @ real @ p @ A )
= ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062) ).
thf(1064,plain,
( finite_finite2 @ real
@ ( collect @ real
@ ^ [A: real] :
( ( poly2 @ real @ p @ A )
= ( zero_zero @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(30,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_equalityE) ).
thf(403,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(274,axiom,
comm_ring_1 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__ring__1_42) ).
thf(1096,plain,
comm_ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(241,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ C @ B )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_minf_I11_J) ).
thf(1006,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TC )
=> ! [A: TB > TA > TC,B: set @ TA,C: set @ TB] :
( ( groups1340683514dd_sum @ TB @ TC
@ ^ [D: TB] : ( groups1340683514dd_sum @ TA @ TC @ ( A @ D ) @ B )
@ C )
= ( groups1340683514dd_sum @ TA @ TC
@ ^ [D: TA] :
( groups1340683514dd_sum @ TB @ TC
@ ^ [E: TB] : ( A @ E @ D )
@ C )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_sum_Oswap) ).
thf(388,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TC )
=> ! [A: TB > TA > TC,B: set @ TA,C: set @ TB] :
( ( groups1340683514dd_sum @ TB @ TC
@ ^ [D: TB] : ( groups1340683514dd_sum @ TA @ TC @ ( A @ D ) @ B )
@ C )
= ( groups1340683514dd_sum @ TA @ TC
@ ^ [D: TA] :
( groups1340683514dd_sum @ TB @ TC
@ ^ [E: TB] : ( A @ E @ D )
@ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(293,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( is_zero @ TA )
= ( ^ [A: poly @ TA] :
( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_is__zero__null) ).
thf(1138,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( is_zero @ TA )
= ( ^ [A: poly @ TA] :
( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(110,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_21) ).
thf(593,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(38,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( preorder @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Orderings_Opreorder_59) ).
thf(420,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( preorder @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(70,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero_less_one @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ozero__less__one_58) ).
thf(499,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero_less_one @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(195,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_le__imp__less__or__eq) ).
thf(857,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(165,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_minf_I1_J) ).
thf(742,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(578,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(282,axiom,
! [A: poly @ real,B: real,C: poly @ real] :
( ( ( poly2 @ real @ A @ B )
!= ( zero_zero @ real ) )
=> ( ( sturm_652470720p_poly @ C @ A @ B )
= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_jump__poly__not__root) ).
thf(1111,plain,
! [A: poly @ real,B: real,C: poly @ real] :
( ( ( poly2 @ real @ A @ B )
!= ( zero_zero @ real ) )
=> ( ( sturm_652470720p_poly @ C @ A @ B )
= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(319,axiom,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_less__int__code_I1_J) ).
thf(1227,plain,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(352,axiom,
ord_less @ real @ b2 @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I3_J) ).
thf(1329,plain,
ord_less @ real @ b2 @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(65,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(488,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(215,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_gr__zeroI) ).
thf(933,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_order__less__le__subst1) ).
thf(669,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(206,axiom,
! [TA: $tType,TB: $tType] :
( ( ordere1818651114id_add @ TB )
=> ! [A: TA > TB,B: set @ TA,C: TA > TB,D: TA] :
( ( ( groups1340683514dd_sum @ TA @ TB @ A @ B )
= ( groups1340683514dd_sum @ TA @ TB @ C @ B ) )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ord_less_eq @ TB @ ( A @ E ) @ ( C @ E ) ) )
=> ( ( member @ TA @ D @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( ( A @ D )
= ( C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_sum__mono__inv) ).
thf(901,plain,
! [TA: $tType,TB: $tType] :
( ( ordere1818651114id_add @ TB )
=> ! [A: TA > TB,B: set @ TA,C: TA > TB,D: TA] :
( ( ( groups1340683514dd_sum @ TA @ TB @ A @ B )
= ( groups1340683514dd_sum @ TA @ TB @ C @ B ) )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ord_less_eq @ TB @ ( A @ E ) @ ( C @ E ) ) )
=> ( ( member @ TA @ D @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( ( A @ D )
= ( C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(131,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_less__le__trans) ).
thf(642,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(79,axiom,
no_bot @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Ono__bot) ).
thf(526,plain,
no_bot @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(229,axiom,
idom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oidom_1) ).
thf(970,plain,
idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(250,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_less__imp__neq) ).
thf(1028,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(266,axiom,
zero_less_one @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ozero__less__one_39) ).
thf(1082,plain,
zero_less_one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(245,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_less__imp__not__eq2) ).
thf(1016,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(313,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_dual__order_Ostrict__trans) ).
thf(1207,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_le__fun__def) ).
thf(590,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(297,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_linorder__cases) ).
thf(1155,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(90,axiom,
comm_semiring_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__0_12) ).
thf(547,plain,
comm_semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(126,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_order_Ostrict__iff__order) ).
thf(622,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(351,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB,B: TB,C: TB > TA] :
( ( finite_finite2 @ TB @ A )
=> ( ( ( member @ TB @ B @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA
@ ^ [D: TB] : ( if @ TA @ ( B = D ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ A )
= ( C @ B ) ) )
& ( ~ ( member @ TB @ B @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA
@ ^ [D: TB] : ( if @ TA @ ( B = D ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ A )
= ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_sum_Odelta_H) ).
thf(1324,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB,B: TB,C: TB > TA] :
( ( finite_finite2 @ TB @ A )
=> ( ( ( member @ TB @ B @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA
@ ^ [D: TB] : ( if @ TA @ ( B = D ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ A )
= ( C @ B ) ) )
& ( ~ ( member @ TB @ B @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA
@ ^ [D: TB] : ( if @ TA @ ( B = D ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ A )
= ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(133,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0_46) ).
thf(647,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(340,axiom,
order @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_45) ).
thf(1297,plain,
order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(321,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_less__numeral__extra_I3_J) ).
thf(1231,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(137,axiom,
! [A: int,B: int] :
( finite_finite2 @ int
@ ( collect @ int
@ ^ [C: int] :
( ( ord_less_eq @ int @ A @ C )
& ( ord_less_eq @ int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_finite__interval__int1) ).
thf(654,plain,
! [A: int,B: int] :
( finite_finite2 @ 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)],[137]) ).
thf(234,axiom,
no_bot @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Ono__bot_44) ).
thf(984,plain,
no_bot @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(103,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_order__trans) ).
thf(569,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(176,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_order_Oorder__iff__strict) ).
thf(779,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(13,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_subset__antisym) ).
thf(371,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(72,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_order__class_Oorder_Oeq__iff) ).
thf(503,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(276,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_leI) ).
thf(1099,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(235,axiom,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: set @ TB,B: TB > TA,C: TB] :
( ( finite_finite2 @ TB @ A )
=> ( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( B @ D ) ) )
=> ( ( ( groups1340683514dd_sum @ TB @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( member @ TB @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_sum__nonneg__0) ).
thf(985,plain,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: set @ TB,B: TB > TA,C: TB] :
( ( finite_finite2 @ TB @ A )
=> ( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( B @ D ) ) )
=> ( ( ( groups1340683514dd_sum @ TB @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( member @ TB @ C @ A )
=> ( ( B @ C )
= ( zero_zero @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(324,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Collect__mono__iff) ).
thf(1241,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(74,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_antisym__conv) ).
thf(508,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(211,axiom,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_psubset__eq) ).
thf(921,plain,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(88,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_antisym) ).
thf(541,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(170,axiom,
! [A: real,B: real,C: poly @ real] :
( ( sturm_1539314049x_poly @ A @ B @ C @ ( zero_zero @ ( poly @ real ) ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_cindex__poly__0_I2_J) ).
thf(765,plain,
! [A: real,B: real,C: poly @ real] :
( ( sturm_1539314049x_poly @ A @ B @ C @ ( zero_zero @ ( poly @ real ) ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(26,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom) ).
thf(398,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(306,axiom,
linorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_41) ).
thf(1187,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(83,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_17) ).
thf(530,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(108,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_equalityD2) ).
thf(586,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(140,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_zero__less__iff__neq__zero) ).
thf(662,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(213,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_less__imp__not__eq) ).
thf(926,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(130,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_pinf_I2_J) ).
thf(633,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(5,axiom,
one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oone) ).
thf(360,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(222,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_order_Onot__eq__order__implies__strict) ).
thf(953,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(305,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite__subset) ).
thf(1185,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(207,axiom,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: set @ TB,B: TB > TA] :
( ! [C: TB] :
( ( member @ TB @ C @ A )
=> ( ord_less_eq @ TA @ ( B @ C ) @ ( zero_zero @ TA ) ) )
=> ( ord_less_eq @ TA @ ( groups1340683514dd_sum @ TB @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_sum__nonpos) ).
thf(906,plain,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: set @ TB,B: TB > TA] :
( ! [C: TB] :
( ( member @ TB @ C @ A )
=> ( ord_less_eq @ TA @ ( B @ C ) @ ( zero_zero @ TA ) ) )
=> ( ord_less_eq @ TA @ ( groups1340683514dd_sum @ TB @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(334,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_ord__eq__less__trans) ).
thf(1278,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(40,axiom,
condit1037483654norder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_6) ).
thf(425,plain,
condit1037483654norder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_order__subst1) ).
thf(513,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(278,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TC )
=> ! [A: set @ TB,B: set @ TA,C: TB > TA > TC,D: TB > TA > $o] :
( ( finite_finite2 @ TB @ A )
=> ( ( finite_finite2 @ TA @ B )
=> ( ( groups1340683514dd_sum @ TB @ TC
@ ^ [E: TB] :
( groups1340683514dd_sum @ TA @ TC @ ( C @ E )
@ ( collect @ TA
@ ^ [F: TA] :
( ( member @ TA @ F @ B )
& ( D @ E @ F ) ) ) )
@ A )
= ( groups1340683514dd_sum @ TA @ TC
@ ^ [E: TA] :
( groups1340683514dd_sum @ TB @ TC
@ ^ [F: TB] : ( C @ F @ E )
@ ( collect @ TB
@ ^ [F: TB] :
( ( member @ TB @ F @ A )
& ( D @ F @ E ) ) ) )
@ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_sum_Oswap__restrict) ).
thf(1103,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comm_monoid_add @ TC )
=> ! [A: set @ TB,B: set @ TA,C: TB > TA > TC,D: TB > TA > $o] :
( ( finite_finite2 @ TB @ A )
=> ( ( finite_finite2 @ TA @ B )
=> ( ( groups1340683514dd_sum @ TB @ TC
@ ^ [E: TB] :
( groups1340683514dd_sum @ TA @ TC @ ( C @ E )
@ ( collect @ TA
@ ^ [F: TA] :
( ( member @ TA @ F @ B )
& ( D @ E @ F ) ) ) )
@ A )
= ( groups1340683514dd_sum @ TA @ TC
@ ^ [E: TA] :
( groups1340683514dd_sum @ TB @ TC
@ ^ [F: TB] : ( C @ F @ E )
@ ( collect @ TB
@ ^ [F: TB] :
( ( member @ TB @ F @ A )
& ( D @ F @ E ) ) ) )
@ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(182,axiom,
preorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_40) ).
thf(824,plain,
preorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(342,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_not__one__less__zero) ).
thf(1301,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_subsetD) ).
thf(601,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(292,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_not__less__iff__gr__or__eq) ).
thf(1135,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(33,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_54) ).
thf(412,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(98,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA ) )
=> ( ring_char_0 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Nat_Oring__char__0_63) ).
thf(562,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA ) )
=> ( ring_char_0 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(242,axiom,
condit1037483654norder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_30) ).
thf(1007,plain,
condit1037483654norder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(29,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_29) ).
thf(402,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(173,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( poly2 @ TA @ ( one_one @ ( poly @ TA ) ) @ A )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_poly__1) ).
thf(772,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( poly2 @ TA @ ( one_one @ ( poly @ TA ) ) @ A )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( B @ C ) ) )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( groups1340683514dd_sum @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_sum__nonneg) ).
thf(826,plain,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TA,B: TA > TB] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( B @ C ) ) )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( groups1340683514dd_sum @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(224,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_minf_I4_J) ).
thf(958,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(23,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_one__reorient) ).
thf(391,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(216,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( poly2 @ TA @ ( zero_zero @ ( poly @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_poly__0) ).
thf(936,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( poly2 @ TA @ ( zero_zero @ ( poly @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(18,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_subset__refl) ).
thf(382,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(332,axiom,
ord_less @ real @ a @ a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
thf(1271,plain,
ord_less @ real @ a @ a2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(119,axiom,
linord1659791738miring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__nonzero__semiring) ).
thf(611,plain,
linord1659791738miring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(280,axiom,
( ( ord_less_eq @ real )
= ( ^ [A: real,B: real] :
( ( ord_less @ real @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__eq__real__def) ).
thf(1107,plain,
( ( ord_less_eq @ real )
= ( ^ [A: real,B: real] :
( ( ord_less @ real @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(272,axiom,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_ex__gt__or__lt) ).
thf(1092,plain,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(270,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_less__eq__int__code_I1_J) ).
thf(1090,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(144,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_le__zero__eq) ).
thf(672,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(328,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_dual__order_Ostrict__implies__not__eq) ).
thf(1258,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(153,axiom,
ordere1818651114id_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add_31) ).
thf(704,plain,
ordere1818651114id_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(117,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_ord__le__eq__trans) ).
thf(604,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(309,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_neq__iff) ).
thf(1194,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(314,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_pinf_I3_J) ).
thf(1209,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(205,axiom,
no_top @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Ono__top_43) ).
thf(900,plain,
no_top @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(147,axiom,
! [A: poly @ real,B: real] :
( ( sturm_652470720p_poly @ ( zero_zero @ ( poly @ real ) ) @ A @ B )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_jump__poly0_I1_J) ).
thf(681,plain,
! [A: poly @ real,B: real] :
( ( sturm_652470720p_poly @ ( zero_zero @ ( poly @ real ) ) @ A @ B )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(335,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_linorder__neqE__linordered__idom) ).
thf(1282,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(163,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB] :
( ( groups1340683514dd_sum @ TB @ TA
@ ^ [B: TB] : ( zero_zero @ TA )
@ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_sum_Oneutral__const) ).
thf(736,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB] :
( ( groups1340683514dd_sum @ TB @ TA
@ ^ [B: TB] : ( zero_zero @ TA )
@ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(236,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_less__asym) ).
thf(990,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(113,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(599,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(344,axiom,
! [TA: $tType] :
( ( ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA] :
( ( A
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [B: TA] :
( ( poly2 @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_poly__roots__finite) ).
thf(1307,plain,
! [TA: $tType] :
( ( ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA] :
( ( A
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [B: TA] :
( ( poly2 @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(178,axiom,
! [TA: $tType] :
( ( condit1037483654norder @ TA )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_complete__interval) ).
thf(784,plain,
! [TA: $tType] :
( ( condit1037483654norder @ TA )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(284,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_less__imp__not__less) ).
thf(1117,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(7,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( order @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Orderings_Oorder_62) ).
thf(362,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( order @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(102,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_n68954251visors @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oring__no__zero__divisors_53) ).
thf(567,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_n68954251visors @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(135,axiom,
! [A: real,B: real,C: poly @ real] :
( ( sturm_1539314049x_poly @ A @ B @ ( zero_zero @ ( poly @ real ) ) @ C )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_cindex__poly__0_I1_J) ).
thf(649,plain,
! [A: real,B: real,C: poly @ real] :
( ( sturm_1539314049x_poly @ A @ B @ ( zero_zero @ ( poly @ real ) ) @ C )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(255,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_order__less__subst1) ).
thf(1043,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(123,axiom,
no_top @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Ono__top) ).
thf(616,plain,
no_top @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(287,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 ) )
=> ( ( poly2 @ real @ A @ D )
!= ( zero_zero @ real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_last__non__root__interval) ).
thf(1122,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 ) )
=> ( ( poly2 @ real @ A @ D )
!= ( zero_zero @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(59,axiom,
ordere1818651114id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__cancel__comm__monoid__add) ).
thf(477,plain,
ordere1818651114id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(21,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder_15) ).
thf(387,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_semiring_0 @ TB )
=> ! [A: TA > ( poly @ TB ),B: set @ TA,C: TB] :
( ( poly2 @ TB @ ( groups1340683514dd_sum @ TA @ ( poly @ TB ) @ A @ B ) @ C )
= ( groups1340683514dd_sum @ TA @ TB
@ ^ [D: TA] : ( poly2 @ TB @ ( A @ D ) @ C )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_poly__sum) ).
thf(758,plain,
! [TA: $tType,TB: $tType] :
( ( comm_semiring_0 @ TB )
=> ! [A: TA > ( poly @ TB ),B: set @ TA,C: TB] :
( ( poly2 @ TB @ ( groups1340683514dd_sum @ TA @ ( poly @ TB ) @ A @ B ) @ C )
= ( groups1340683514dd_sum @ TA @ TB
@ ^ [D: TA] : ( poly2 @ TB @ ( A @ D ) @ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(85,axiom,
wellorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(535,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(63,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_subset__trans) ).
thf(483,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(226,axiom,
! [A: real,B: real,C: poly @ real] :
( ( ! [D: real] :
( ( ( ord_less_eq @ real @ A @ D )
& ( ord_less @ real @ D @ B ) )
=> ( ( poly2 @ real @ C @ D )
!= ( zero_zero @ real ) ) ) )
= ( ! [D: real] :
( ( ( ord_less_eq @ real @ A @ D )
& ( ord_less @ real @ D @ B ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ D ) ) )
| ! [D: real] :
( ( ( ord_less_eq @ real @ A @ D )
& ( ord_less @ real @ D @ B ) )
=> ( ord_less @ real @ ( poly2 @ real @ C @ D ) @ ( zero_zero @ real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_not__eq__pos__or__neg__iff__2) ).
thf(964,plain,
! [A: real,B: real,C: poly @ real] :
( ( ! [D: real] :
( ( ( ord_less_eq @ real @ A @ D )
& ( ord_less @ real @ D @ B ) )
=> ( ( poly2 @ real @ C @ D )
!= ( zero_zero @ real ) ) ) )
= ( ! [D: real] :
( ( ( ord_less_eq @ real @ A @ D )
& ( ord_less @ real @ D @ B ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ D ) ) )
| ! [D: real] :
( ( ( ord_less_eq @ real @ A @ D )
& ( ord_less @ real @ D @ B ) )
=> ( ord_less @ real @ ( poly2 @ real @ C @ D ) @ ( zero_zero @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(10,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Olinorder) ).
thf(367,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(94,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_eq__refl) ).
thf(552,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(52,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_dual__order_Orefl) ).
thf(462,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(263,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( poly_cutoff @ TA @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_poly__cutoff__0) ).
thf(1061,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( poly_cutoff @ TA @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(27,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_18) ).
thf(399,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(151,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_neqE) ).
thf(695,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linorder @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Orderings_Olinorder_60) ).
thf(394,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linorder @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(47,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_predicate1D) ).
thf(438,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(43,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_23) ).
thf(431,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(315,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB,B: TB,C: TB > TA] :
( ( finite_finite2 @ TB @ A )
=> ( ( ( member @ TB @ B @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA
@ ^ [D: TB] : ( if @ TA @ ( D = B ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ A )
= ( C @ B ) ) )
& ( ~ ( member @ TB @ B @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA
@ ^ [D: TB] : ( if @ TA @ ( D = B ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ A )
= ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_sum_Odelta) ).
thf(1213,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB,B: TB,C: TB > TA] :
( ( finite_finite2 @ TB @ A )
=> ( ( ( member @ TB @ B @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA
@ ^ [D: TB] : ( if @ TA @ ( D = B ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ A )
= ( C @ B ) ) )
& ( ~ ( member @ TB @ B @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA
@ ^ [D: TB] : ( if @ TA @ ( D = B ) @ ( C @ D ) @ ( zero_zero @ TA ) )
@ A )
= ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(171,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_le__less__trans) ).
thf(768,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(303,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ord__less__eq__subst) ).
thf(1176,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(118,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_dual__order_Oeq__iff) ).
thf(608,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(252,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ( ( '?' @ TA )
= ( ^ [A: TA > $o] :
? [B: TA] :
( ( A @ B )
& ! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_exists__least__iff) ).
thf(1034,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ( ( '?' @ TA )
= ( ^ [A: TA > $o] :
? [B: TA] :
( ( A @ B )
& ! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(145,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(675,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(91,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(548,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(14,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_24) ).
thf(374,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(134,axiom,
comm_semiring_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__semiring__0_38) ).
thf(648,plain,
comm_semiring_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(179,axiom,
linord1659791738miring @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_32) ).
thf(812,plain,
linord1659791738miring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(217,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_pinf_I6_J) ).
thf(939,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(295,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_minf_I8_J) ).
thf(1145,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(167,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_pinf_I4_J) ).
thf(754,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(228,axiom,
( sturm_1539314049x_poly
= ( ^ [A: real,B: real,C: poly @ real,D: poly @ real] :
( groups1340683514dd_sum @ real @ int @ ( sturm_652470720p_poly @ C @ D )
@ ( collect @ real
@ ^ [E: real] :
( ( ( poly2 @ real @ D @ E )
= ( zero_zero @ real ) )
& ( ord_less @ real @ A @ E )
& ( ord_less @ real @ E @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_cindex__poly__def) ).
thf(968,plain,
( sturm_1539314049x_poly
= ( ^ [A: real,B: real,C: poly @ real,D: poly @ real] :
( groups1340683514dd_sum @ real @ int @ ( sturm_652470720p_poly @ C @ D )
@ ( collect @ real
@ ^ [E: real] :
( ( ( poly2 @ real @ D @ E )
= ( zero_zero @ real ) )
& ( ord_less @ real @ A @ E )
& ( ord_less @ real @ E @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(258,axiom,
! [A: real,B: real,C: poly @ real] :
( ( ! [D: real] :
( ( ( ord_less @ real @ A @ D )
& ( ord_less_eq @ real @ D @ B ) )
=> ( ( poly2 @ real @ C @ D )
!= ( zero_zero @ real ) ) ) )
= ( ! [D: real] :
( ( ( ord_less @ real @ A @ D )
& ( ord_less_eq @ real @ D @ B ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ D ) ) )
| ! [D: real] :
( ( ( ord_less @ real @ A @ D )
& ( ord_less_eq @ real @ D @ B ) )
=> ( ord_less @ real @ ( poly2 @ real @ C @ D ) @ ( zero_zero @ real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_not__eq__pos__or__neg__iff__1) ).
thf(1049,plain,
! [A: real,B: real,C: poly @ real] :
( ( ! [D: real] :
( ( ( ord_less @ real @ A @ D )
& ( ord_less_eq @ real @ D @ B ) )
=> ( ( poly2 @ real @ C @ D )
!= ( zero_zero @ real ) ) ) )
= ( ! [D: real] :
( ( ( ord_less @ real @ A @ D )
& ( ord_less_eq @ real @ D @ B ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ D ) ) )
| ! [D: real] :
( ( ( ord_less @ real @ A @ D )
& ( ord_less_eq @ real @ D @ B ) )
=> ( ord_less @ real @ ( poly2 @ real @ C @ D ) @ ( zero_zero @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(41,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_less__eq__set__def) ).
thf(426,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(300,axiom,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( poly2 @ real @ C @ A ) @ ( zero_zero @ real ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ B ) )
=> ? [D: real] :
( ( ord_less @ real @ A @ D )
& ( ord_less @ real @ D @ B )
& ( ( poly2 @ real @ C @ D )
= ( zero_zero @ real ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_poly__IVT__pos) ).
thf(1166,plain,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( poly2 @ real @ C @ A ) @ ( zero_zero @ real ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ B ) )
=> ? [D: real] :
( ( ord_less @ real @ A @ D )
& ( ord_less @ real @ D @ B )
& ( ( poly2 @ real @ C @ D )
= ( zero_zero @ real ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(84,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_equalityD1) ).
thf(531,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(219,axiom,
zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_48) ).
thf(944,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(124,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_le__numeral__extra_I4_J) ).
thf(617,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ord__eq__le__subst) ).
thf(516,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(249,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_antisym__conv1) ).
thf(1025,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(154,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ~ ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_less__le__not__le) ).
thf(705,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ~ ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(326,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_not__le) ).
thf(1252,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(164,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA] :
( ( ! [B: TA] :
( ( poly2 @ TA @ A @ B )
= ( zero_zero @ TA ) ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_poly__all__0__iff__0) ).
thf(739,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA] :
( ( ! [B: TA] :
( ( poly2 @ TA @ A @ B )
= ( zero_zero @ TA ) ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(157,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_psubset__imp__subset) ).
thf(712,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(240,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(1003,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(106,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_dual__order_Otrans) ).
thf(580,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(194,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_infinite__super) ).
thf(855,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(34,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere1818651114id_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oordered__cancel__comm__monoid__add_50) ).
thf(414,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere1818651114id_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(230,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_order_Oasym) ).
thf(971,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(307,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_Collect__mono) ).
thf(1188,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(329,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ A @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_antisym__conv2) ).
thf(1262,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ A @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(348,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_order__less__subst2) ).
thf(1317,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(268,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_not__gr__zero) ).
thf(1085,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(4,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone_20) ).
thf(359,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(290,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_dual__order_Oasym) ).
thf(1130,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(89,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_dual__order_Oantisym) ).
thf(544,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(336,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zero__reorient) ).
thf(1285,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(316,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_order__less__le__subst2) ).
thf(1218,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(294,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_order_Ostrict__implies__not__eq) ).
thf(1141,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(317,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_less__not__sym) ).
thf(1221,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(114,axiom,
ordere216010020id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__comm__monoid__add) ).
thf(600,plain,
ordere216010020id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(259,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_less__le) ).
thf(1052,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(198,axiom,
( p
!= ( zero_zero @ ( poly @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_False) ).
thf(864,plain,
( p
!= ( zero_zero @ ( poly @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(273,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_less__asym_H) ).
thf(1094,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(243,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__has__minimal2) ).
thf(1008,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(111,axiom,
idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oidom_2) ).
thf(595,plain,
idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TA,B: TA,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( ord_less @ TB @ ( zero_zero @ TB ) @ ( C @ B ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( C @ D ) ) )
=> ( ord_less @ TB @ ( zero_zero @ TB ) @ ( groups1340683514dd_sum @ TA @ TB @ C @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_sum__pos2) ).
thf(656,plain,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TA,B: TA,C: TA > TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ( ( ord_less @ TB @ ( zero_zero @ TB ) @ ( C @ B ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( C @ D ) ) )
=> ( ord_less @ TB @ ( zero_zero @ TB ) @ ( groups1340683514dd_sum @ TA @ TB @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(248,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_zero__le) ).
thf(1023,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(50,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_le__cases3) ).
thf(446,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_ord__le__eq__subst) ).
thf(571,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(333,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 ) )
=> ( ( poly2 @ real @ A @ D )
!= ( zero_zero @ real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_next__non__root__interval) ).
thf(1272,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 ) )
=> ( ( poly2 @ real @ A @ D )
!= ( zero_zero @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(120,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_order__refl) ).
thf(612,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(54,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__idom_55) ).
thf(465,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(128,axiom,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_less__set__def) ).
thf(627,plain,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(95,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_subset__eq) ).
thf(556,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(539,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(68,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_25) ).
thf(495,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(203,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( poly_cutoff @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( poly_cutoff @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_poly__cutoff__1) ).
thf(891,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( poly_cutoff @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( poly_cutoff @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(11,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Oring__char__0) ).
thf(368,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(232,axiom,
ordere216010020id_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_33) ).
thf(976,plain,
ordere216010020id_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(149,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_ord__less__eq__trans) ).
thf(688,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(180,axiom,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: set @ TA] :
( ( finite_finite2 @ TA @ C )
=> ( ! [D: set @ TA] :
( ( ord_less @ ( set @ TA ) @ D @ C )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__psubset__induct) ).
thf(813,plain,
! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: set @ TA] :
( ( finite_finite2 @ TA @ C )
=> ( ! [D: set @ TA] :
( ( ord_less @ ( set @ TA ) @ D @ C )
=> ( B @ D ) )
=> ( B @ C ) ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(277,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_minf_I5_J) ).
thf(1101,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(136,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_less__imp__triv) ).
thf(652,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(325,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/sandbox/benchmark/theBenchmark.p',fact_190_imp__le__cong) ).
thf(1244,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)],[325]) ).
thf(37,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord1659791738miring @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_51) ).
thf(418,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord1659791738miring @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(209,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__code) ).
thf(914,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(44,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_22) ).
thf(433,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(142,axiom,
! [A: int,B: int] :
( finite_finite2 @ int
@ ( collect @ int
@ ^ [C: int] :
( ( ord_less @ int @ A @ C )
& ( ord_less @ int @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_finite__interval__int4) ).
thf(667,plain,
! [A: int,B: int] :
( finite_finite2 @ int
@ ( collect @ int
@ ^ [C: int] :
( ( ord_less @ int @ A @ C )
& ( ord_less @ int @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(60,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_8) ).
thf(478,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(549,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(86,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_pred__subset__eq) ).
thf(536,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(186,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_psubsetE) ).
thf(832,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__set__choice) ).
thf(684,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(320,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_leD) ).
thf(1229,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(343,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
& ( ord_less @ TA @ C @ A )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_field__lbound__gt__zero) ).
thf(1303,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
& ( ord_less @ TA @ C @ A )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(39,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( reflect_poly @ TA @ ( one_one @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_reflect__poly__1) ).
thf(422,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( reflect_poly @ TA @ ( one_one @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(199,axiom,
! [TA: $tType,A: set @ TA,B: TA > nat] :
( ( finite_finite2 @ TA @ A )
=> ( ( ( groups1340683514dd_sum @ TA @ nat @ B @ A )
= ( one_one @ nat ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ( B @ C )
= ( one_one @ nat ) )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( B @ D )
= ( zero_zero @ nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_sum__eq__1__iff) ).
thf(867,plain,
! [TA: $tType,A: set @ TA,B: TA > nat] :
( ( finite_finite2 @ TA @ A )
=> ( ( ( groups1340683514dd_sum @ TA @ nat @ B @ A )
= ( one_one @ nat ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ( B @ C )
= ( one_one @ nat ) )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( B @ D )
= ( zero_zero @ nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(116,axiom,
zero_less_one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__less__one_13) ).
thf(603,plain,
zero_less_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(31,axiom,
zero_less_one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ozero__less__one) ).
thf(410,plain,
zero_less_one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(227,axiom,
comm_monoid_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocomm__monoid__add_35) ).
thf(967,plain,
comm_monoid_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(221,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( ( poly2 @ TA @ ( reflect_poly @ TA @ A ) @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_reflect__poly__at__0__eq__0__iff) ).
thf(950,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( ( poly2 @ TA @ ( reflect_poly @ TA @ A ) @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(275,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_psubsetD) ).
thf(1097,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB,B: TB > TA] :
( ~ ( finite_finite2 @ TB @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_sum_Oinfinite) ).
thf(835,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TB,B: TB > TA] :
( ~ ( finite_finite2 @ TB @ A )
=> ( ( groups1340683514dd_sum @ TB @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(99,axiom,
ring_n68954251visors @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oring__no__zero__divisors) ).
thf(564,plain,
ring_n68954251visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(73,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_rev__predicate1D) ).
thf(506,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(46,axiom,
finite_finite @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_27) ).
thf(437,plain,
finite_finite @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(265,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA] : ( A @ D @ D )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_linorder__less__wlog) ).
thf(1065,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA] : ( A @ D @ D )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(301,axiom,
ord @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_47) ).
thf(1172,plain,
ord @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(204,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( ( poly2 @ TA @ A )
= ( poly2 @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_poly__eq__poly__eq__iff) ).
thf(897,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( ( poly2 @ TA @ A )
= ( poly2 @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(58,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_verit__la__disequality) ).
thf(474,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(337,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_psubset__trans) ).
thf(1288,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ( ( ord_less @ ( set @ TA ) @ B @ C )
=> ( ord_less @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(28,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere216010020id_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oordered__comm__monoid__add_52) ).
thf(400,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere216010020id_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(310,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_less__linear) ).
thf(1197,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(189,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_less__imp__le) ).
thf(839,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(160,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ ( set @ TA )
@ ( collect @ ( set @ TA )
@ ^ [B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_finite__Collect__subsets) ).
thf(728,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ ( set @ TA )
@ ( collect @ ( set @ TA )
@ ^ [B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(323,axiom,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TB > TA,B: set @ TB] :
( ( ( groups1340683514dd_sum @ TB @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ~ ! [C: TB] :
( ( member @ TB @ C @ B )
=> ( ( A @ C )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_sum_Onot__neutral__contains__not__neutral) ).
thf(1236,plain,
! [TA: $tType,TB: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TB > TA,B: set @ TB] :
( ( ( groups1340683514dd_sum @ TB @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ~ ! [C: TB] :
( ( member @ TB @ C @ B )
=> ( ( A @ C )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(53,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_28) ).
thf(464,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(289,axiom,
condit1656338222tinuum @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum) ).
thf(1129,plain,
condit1656338222tinuum @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(331,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A != B )
=> ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_psubsetI) ).
thf(1268,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A != B )
=> ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(196,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_not__le__imp__less) ).
thf(860,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(112,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_eq__iff) ).
thf(596,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(81,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(528,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(132,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_less__induct) ).
thf(644,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(237,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TC,B: set @ TA,C: TA > TB,D: TA > TC,E: TC > TB] :
( ( finite_finite2 @ TC @ A )
=> ( ( finite_finite2 @ TA @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( C @ F ) ) )
=> ( ! [F: TC] :
( ( member @ TC @ F @ A )
=> ? [G: TA] :
( ( member @ TA @ G @ B )
& ( ( D @ G )
= F )
& ( ord_less_eq @ TB @ ( E @ F ) @ ( C @ G ) ) ) )
=> ( ord_less_eq @ TB @ ( groups1340683514dd_sum @ TC @ TB @ E @ A ) @ ( groups1340683514dd_sum @ TA @ TB @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_sum__le__included) ).
thf(992,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TC,B: set @ TA,C: TA > TB,D: TA > TC,E: TC > TB] :
( ( finite_finite2 @ TC @ A )
=> ( ( finite_finite2 @ TA @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ord_less_eq @ TB @ ( zero_zero @ TB ) @ ( C @ F ) ) )
=> ( ! [F: TC] :
( ( member @ TC @ F @ A )
=> ? [G: TA] :
( ( member @ TA @ G @ B )
& ( ( D @ G )
= F )
& ( ord_less_eq @ TB @ ( E @ F ) @ ( C @ G ) ) ) )
=> ( ord_less_eq @ TB @ ( groups1340683514dd_sum @ TC @ TB @ E @ A ) @ ( groups1340683514dd_sum @ TA @ TB @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(192,axiom,
! [TA: $tType] :
( ( dense_order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_dense) ).
thf(850,plain,
! [TA: $tType] :
( ( dense_order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(286,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_pinf_I5_J) ).
thf(1120,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_le__funI) ).
thf(501,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(12,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_56) ).
thf(369,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(349,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_dual__order_Ostrict__trans2) ).
thf(1320,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TB @ ( B @ D ) @ ( C @ D ) ) )
=> ( ord_less_eq @ TB @ ( groups1340683514dd_sum @ TA @ TB @ B @ A ) @ ( groups1340683514dd_sum @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_sum__mono) ).
thf(469,plain,
! [TA: $tType,TB: $tType] :
( ( ordere216010020id_add @ TB )
=> ! [A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TB @ ( B @ D ) @ ( C @ D ) ) )
=> ( ord_less_eq @ TB @ ( groups1340683514dd_sum @ TA @ TB @ B @ A ) @ ( groups1340683514dd_sum @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(3,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_linorder__wlog) ).
thf(354,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(139,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ A )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_int__one__le__iff__zero__less) ).
thf(659,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)],[139]) ).
thf(312,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_verit__comp__simplify1_I3_J) ).
thf(1204,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(69,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_subsetI) ).
thf(496,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(8,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_order_Otrans) ).
thf(364,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(155,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_less__numeral__extra_I4_J) ).
thf(708,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(202,axiom,
! [A: set @ real] :
( ? [B: real] : ( member @ real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member @ real @ C @ A )
=> ( ord_less_eq @ real @ C @ B ) )
=> ? [B: real] :
( ! [C: real] :
( ( member @ real @ C @ A )
=> ( ord_less_eq @ real @ C @ B ) )
& ! [C: real] :
( ! [D: real] :
( ( member @ real @ D @ A )
=> ( ord_less_eq @ real @ D @ C ) )
=> ( ord_less_eq @ real @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_complete__real) ).
thf(882,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)],[202]) ).
thf(253,axiom,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_subset__not__subset__eq) ).
thf(1037,plain,
! [TA: $tType] :
( ( ord_less @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(174,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finite) ).
thf(775,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(66,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_linear) ).
thf(491,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(269,axiom,
! [TA: $tType] :
( ( zero_less_one @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_zero__less__one) ).
thf(1088,plain,
! [TA: $tType] :
( ( zero_less_one @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1330,plain,
$false,
inference(e,[status(thm)],[1322,479,909,1315,941,777,1295,1083,962,1200,977,873,379,614,1173,523,1158,582,730,1290,440,511,385,384,1310,472,1233,698,945,930,829,1001,782,565,1265,841,417,973,1046,1055,1298,719,1313,1191,460,619,838,917,751,1059,1132,817,559,853,1147,870,416,1115,1013,770,924,443,376,485,1020,353,1183,480,1040,1109,692,734,956,1119,396,998,411,527,678,529,761,381,366,714,1047,1057,1163,1223,1091,825,1021,1255,862,561,630,429,467,566,1032,361,625,435,665,493,710,842,1106,551,1128,615,1064,403,1096,1006,388,1138,593,420,499,857,742,578,1111,1227,1329,488,933,669,901,642,526,970,1028,1082,1016,1207,590,1155,547,622,1324,647,1297,1231,654,984,569,779,371,503,1099,985,1241,508,921,541,765,398,1187,530,586,662,926,633,360,953,1185,906,1278,425,513,1103,824,1301,601,1135,412,562,1007,402,772,826,958,391,936,382,1271,611,1107,1092,1090,672,1258,704,604,1194,1209,900,681,1282,736,990,599,1307,784,1117,362,567,649,1043,616,1122,477,387,758,535,483,964,367,552,462,1061,399,695,394,438,431,1213,768,1176,608,1034,675,548,374,648,812,939,1145,754,968,1049,426,1166,531,944,617,516,1025,705,1252,739,712,1003,580,855,414,971,1188,1262,1317,1085,359,1130,544,1285,1218,1141,1221,600,1052,864,1094,1008,595,656,1023,446,571,1272,612,465,627,556,539,495,891,368,976,688,813,1101,652,1244,418,914,433,667,478,549,536,832,684,1229,1303,422,867,603,410,967,950,1097,835,564,506,437,1065,1172,897,474,1288,400,1197,839,728,1236,464,1129,1268,860,596,528,644,992,850,1120,501,369,1320,469,354,659,1204,496,364,708,882,1037,775,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP193^2 : TPTP v8.2.0. Released v7.5.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 16:42:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.86/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.11 % [INFO] Parsing done (250ms).
% 1.82/1.12 % [INFO] Running in sequential loop mode.
% 2.69/1.34 % [INFO] eprover registered as external prover.
% 2.69/1.34 % [INFO] cvc4 registered as external prover.
% 2.69/1.34 % [INFO] Scanning for conjecture ...
% 2.85/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 351 axioms. Running axiom selection ...
% 3.03/1.53 % [INFO] Axiom selection finished. Selected 350 axioms (removed 1 axioms).
% 3.70/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 3.70/1.72 % [INFO] Type checking passed.
% 3.70/1.73 % [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 ...
% 38.64/24.24 % External prover 'e' found a proof!
% 38.64/24.24 % [INFO] Killing All external provers ...
% 38.64/24.24 % Time passed: 23718ms (effective reasoning time: 23116ms)
% 38.64/24.24 % 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)>
% 38.64/24.24 % Axioms used in derivation (350): tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_57, fact_81_ord__eq__less__subst, tcon_Real_Oreal___Rings_Ocomm__semiring__0_38, fact_75_order__subst2, tcon_Set_Oset___Orderings_Oorder_23, fact_215_less__eq__int__code_I1_J, tcon_Real_Oreal___Orderings_Olinorder_41, tcon_Nat_Onat___Groups_Oone_20, tcon_Nat_Onat___Orderings_Oord_18, fact_27_not__eq__pos__or__neg__iff__2, fact_66_le__cases3, fact_41_dual__order_Ostrict__implies__order, fact_168_set__eq__subset, fact_107_dual__order_Oirrefl, tcon_Real_Oreal___Orderings_Oord_47, fact_188_minf_I11_J, fact_100_less__imp__not__eq, tcon_Real_Oreal___Groups_Oordered__comm__monoid__add_33, fact_25_finite, tcon_Nat_Onat___Rings_Ocomm__semiring__1_11, fact_231_sum_Oneutral__const, fact_181_pinf_I11_J, tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_30, fact_207_verit__la__generic, tcon_fun___Finite__Set_Ofinite, fact_148_psubsetI, fact_61_order__class_Oorder_Oantisym, fact_220_cindex__poly__def, tcon_Polynomial_Opoly___Orderings_Oord_64, fact_62_ord__le__eq__trans, fact_171_Collect__mono__iff, fact_166_Collect__mono, fact_239_sum__mono, fact_146_dual__order_Ostrict__trans2, tcon_Int_Oint___Groups_Ozero, fact_125_order__less__le__subst1, fact_36_order__refl, tcon_Real_Oreal___Rings_Ocomm__semiring__1_37, fact_9_finite__Collect__disjI, fact_28_not__eq__pos__or__neg__iff__1, fact_172_less__fun__def, tcon_Real_Oreal___Orderings_Oorder_45, fact_8_finite__Collect__conjI, fact_251_not__one__less__zero, fact_238_sum_Oneutral, fact_140_not__le__imp__less, tcon_Nat_Onat___Orderings_Olinorder_15, tcon_Int_Oint___Nat_Oring__char__0, fact_108_order_Ostrict__trans, fact_185_minf_I4_J, fact_189_conj__le__cong, fact_119_leD, fact_216_pred__subset__eq, tcon_fun___Orderings_Oord, fact_29_poly__eq__poly__eq__iff, fact_39_complete__interval, fact_86_gt__ex, fact_242_sum__nonneg, fact_139_less__le__not__le, fact_163_equalityD2, tcon_Polynomial_Opoly___Rings_Oidom, fact_116_ex__gt__or__lt, fact_15_less__numeral__extra_I3_J, fact_49_dense__le__bounded, tcon_Polynomial_Opoly___Rings_Ocomm__ring__1_61, fact_138_le__imp__less__or__eq, fact_194_psubset__subset__trans, fact_19_finite__psubset__induct, fact_7_assms_I4_J, fact_137_le__less__linear, tcon_Real_Oreal___Orderings_Ono__bot_44, fact_247_sum__strict__mono__ex1, fact_196_psubset__trans, fact_206_jump__poly0_I1_J, fact_213_finite__interval__int3, fact_155_poly__cutoff__0, fact_158_in__mono, tcon_Int_Oint___Groups_Oordered__comm__monoid__add, fact_117_complete__real, fact_123_order__le__less__subst1, fact_58_linorder__wlog, fact_245_sum__le__included, fact_59_dual__order_Orefl, fact_89_order_Oasym, fact_153_verit__comp__simplify1_I3_J, fact_94_less__trans, fact_55_dual__order_Oantisym, fact_85_lt__ex, fact_64_order__class_Oorder_Oeq__iff, fact_37_cross__no__root, fact_144_order_Ostrict__iff__order, fact_53_infinite__super, fact_240_sum_Oswap__restrict, fact_221_reflect__poly__1, tcon_Polynomial_Opoly___Groups_Oordered__comm__monoid__add_52, fact_115_dual__order_Ostrict__implies__not__eq, fact_68_le__cases, fact_241_sum__nonpos, fact_32_zero__less__iff__neq__zero, fact_2_assms_I3_J, tcon_Nat_Onat___Orderings_Oorder_17, fact_77_le__fun__def, tcon_Int_Oint___Rings_Ocomm__ring__1, tcon_Real_Oreal___Rings_Oidom_1, fact_205_reflect__poly__0, fact_227_less__numeral__extra_I1_J, fact_236_sum_Oswap, fact_208_predicate1D, tcon_Real_Oreal___Orderings_Opreorder_40, fact_200_less__set__def, fact_219_cindex__poly__cross, fact_246_sum__nonneg__eq__0__iff, fact_157_subset__antisym, fact_218_cindex__poly__0_I1_J, fact_170_less__eq__set__def, fact_82_ord__less__eq__subst, fact_63_ord__eq__le__trans, fact_179_pinf_I5_J, fact_52_finite__subset, fact_98_ord__less__eq__trans, fact_21_finite__has__maximal2, tcon_Real_Oreal___Nat_Oring__char__0_46, fact_133_le__less__trans, tcon_Real_Oreal___Rings_Oring__no__zero__divisors_34, fact_248_sum__nonneg__0, tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, help_If_1_1_T, fact_83_order__less__subst1, fact_95_less__linear, fact_80_le__funD, tcon_Set_Oset___Finite__Set_Ofinite_22, tcon_Polynomial_Opoly___Orderings_Oorder_62, fact_76_order__subst1, fact_175_pinf_I1_J, fact_204_predicate1I, fact_198_psubsetE, fact_149_minf_I8_J, fact_12_poly__IVT__pos, fact_24_zero__reorient, fact_124_order__le__less__subst2, fact_159_subsetD, fact_16_le__zero__eq, tcon_HOL_Obool___Orderings_Oorder_28, tcon_Polynomial_Opoly___Nat_Oring__char__0_63, fact_224_le__numeral__extra_I4_J, fact_127_not__le, tcon_HOL_Obool___Finite__Set_Ofinite_27, tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_6, fact_191_subset__iff__psubset__eq, tcon_Nat_Onat___Orderings_Ono__top_16, fact_109_less__imp__not__less, tcon_Int_Oint___Rings_Olinordered__idom, tcon_Int_Oint___Orderings_Olinorder, fact_57_dual__order_Otrans, tcon_Int_Oint___Rings_Ocomm__semiring__1, fact_250_sum__pos2, fact_35_gr__zeroI, tcon_Int_Oint___Orderings_Oorder_4, tcon_Int_Oint___Rings_Ozero__less__one, fact_20_finite__has__minimal2, fact_190_imp__le__cong, tcon_Real_Oreal___Groups_Oone_49, fact_132_less__imp__le, fact_217_cindex__poly__0_I2_J, fact_101_less__not__sym, tcon_Nat_Onat___Orderings_Owellorder, fact_210_finite__interval__int1, fact_38_less__eq__real__def, fact_136_dense__le, fact_161_subset__eq, fact_165_subset__refl, tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_56, tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_9, fact_180_pinf_I7_J, fact_244_sum_Ointer__filter, fact_84_order__less__subst2, fact_79_le__funE, tcon_Polynomial_Opoly___Rings_Oring__no__zero__divisors_53, fact_253_linorder__neqE__linordered__idom, fact_96_less__irrefl, fact_197_psubset__eq, tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum, fact_103_antisym__conv3, fact_122_less__le, tcon_Polynomial_Opoly___Groups_Oone_66, fact_56_dual__order_Oeq__iff, tcon_Int_Oint___Groups_Ocomm__monoid__add, tcon_Real_Oreal___Orderings_Ono__top_43, fact_6_not__gr__zero, fact_72_eq__iff, fact_1_assms_I2_J, fact_131_antisym__conv2, tcon_Polynomial_Opoly___Orderings_Opreorder_59, tcon_Real_Oreal___Orderings_Odense__order, fact_88_neq__iff, fact_150_minf_I6_J, fact_126_order__less__le__subst2, tcon_Real_Oreal___Orderings_Odense__linorder, fact_169_Collect__subset, fact_243_sum__mono__inv, tcon_Int_Oint___Rings_Oidom_2, fact_201_reflect__poly__at__0__eq__0__iff, fact_87_neqE, fact_167_subset__trans, fact_176_pinf_I2_J, tcon_Real_Oreal___Rings_Olinordered__idom_36, tcon_Set_Oset___Orderings_Oord_24, fact_73_ord__le__eq__subst, fact_183_minf_I2_J, fact_178_pinf_I4_J, fact_33_gr__implies__not__zero, fact_91_less__imp__neq, fact_234_sum__eq__1__iff, fact_214_less__int__code_I1_J, tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_51, fact_78_le__funI, fact_11_poly__IVT__neg, help_If_3_1_T, fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062, fact_92_less__asym, help_If_2_1_T, tcon_Int_Oint___Orderings_Oord_5, fact_228_less__numeral__extra_I4_J, fact_71_antisym, fact_232_sum_Oinfinite, fact_118_field__lbound__gt__zero, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_8, fact_230_sum_Odelta, fact_110_exists__least__iff, fact_17_zero__le, fact_104_less__imp__not__eq2, fact_74_ord__eq__le__subst, fact_93_less__asym_H, fact_249_sum__nonneg__leq__bound, tcon_Nat_Onat___Rings_Ozero__less__one_13, tcon_Polynomial_Opoly___Orderings_Olinorder_60, tcon_Real_Oreal___Rings_Ocomm__ring__1_42, fact_102_less__induct, tcon_Polynomial_Opoly___Groups_Oordered__cancel__comm__monoid__add_50, tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_54, fact_40_order_Onot__eq__order__implies__strict, fact_199_psubsetD, fact_193_subset__not__subset__eq, fact_112_dual__order_Ostrict__trans, tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_32, fact_252_zero__less__one, fact_18_le__numeral__extra_I3_J, fact_151_pinf_I8_J, fact_235_int__one__le__iff__zero__less, tcon_Int_Oint___Rings_Oring__no__zero__divisors, fact_113_not__less__iff__gr__or__eq, fact_99_dual__order_Oasym, fact_237_sum_Onot__neutral__contains__not__neutral, tcon_fun___Orderings_Opreorder, tcon_Int_Oint___Rings_Ocomm__semiring__0, fact_3_assms_I1_J, fact_186_minf_I5_J, tcon_Real_Oreal___Fields_Olinordered__field, fact_142_order_Ostrict__trans2, fact_226_one__reorient, fact_45_Collect__mem__eq, tcon_Real_Oreal___Groups_Ozero_48, fact_120_leI, tcon_HOL_Obool___Orderings_Opreorder_25, fact_90_dense, fact_187_minf_I7_J, fact_195_psubset__imp__subset, fact_135_dense__ge, fact_50_finite__Collect__subsets, fact_22_next__non__root__interval, fact_143_order_Oorder__iff__strict, fact_233_sum__eq__0__iff, tcon_HOL_Obool___Orderings_Olinorder_26, fact_111_linorder__less__wlog, fact_48_order_Ostrict__implies__order, fact_222_poly__1, fact_23_last__non__root__interval, fact_14_poly__all__0__iff__0, tcon_Polynomial_Opoly___Groups_Ozero_65, fact_130_antisym__conv1, fact_69_eq__refl, tcon_Int_Oint___Orderings_Ono__bot, fact_192_subset__psubset__trans, tcon_fun___Orderings_Oorder, fact_212_finite__interval__int4, tcon_Int_Oint___Orderings_Opreorder_3, fact_156_subsetI, fact_70_linear, fact_145_dual__order_Ostrict__trans1, fact_42_dual__order_Ostrict__iff__order, fact_4_False, fact_154_is__zero__null, fact_67_order_Otrans, fact_10_poly__roots__finite, tcon_Polynomial_Opoly___Rings_Olinordered__idom_55, tcon_Int_Oint___Orderings_Ono__top, fact_60_order__trans, fact_13_finite__code, fact_160_equalityE, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_229_sum_Odelta_H, fact_106_linorder__cases, fact_128_not__less, fact_174_verit__comp__simplify1_I1_J, fact_43_dual__order_Oorder__iff__strict, fact_54_rev__finite__subset, tcon_Set_Oset___Orderings_Opreorder_21, tcon_Int_Oint___Groups_Oordered__cancel__comm__monoid__add, fact_203_jump__poly0_I2_J, fact_211_finite__interval__int2, fact_34_not__less__zero, fact_162_equalityD1, fact_129_le__neq__trans, fact_141_order_Ostrict__trans1, fact_182_minf_I1_J, fact_184_minf_I3_J, fact_152_pinf_I6_J, fact_105_less__imp__triv, tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, fact_177_pinf_I3_J, tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add_31, tcon_Int_Oint___Groups_Oone, fact_147_dense__ge__bounded, fact_114_order_Ostrict__implies__not__eq, tcon_Real_Oreal___Groups_Ocomm__monoid__add_35, fact_223_poly__cutoff__1, fact_65_antisym__conv, tcon_Nat_Onat___Rings_Ocomm__semiring__0_12, fact_5_poly__0, tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_7, tcon_Nat_Onat___Groups_Ocomm__monoid__add_10, fact_134_less__le__trans, fact_46_Collect__cong, fact_209_rev__predicate1D, tcon_Nat_Onat___Orderings_Opreorder_14, tcon_Nat_Onat___Groups_Ozero_19, fact_26_finite__set__choice, fact_97_ord__eq__less__trans, fact_31_not__finite__existsD, fact_121_le__less, tcon_Polynomial_Opoly___Rings_Ozero__less__one_58, fact_51_cross__0, fact_173_verit__la__disequality, tcon_Real_Oreal___Rings_Ozero__less__one_39, fact_225_poly__sum, fact_202_jump__poly__not__root, fact_30_pigeonhole__infinite__rel, fact_44_mem__Collect__eq, tcon_HOL_Obool___Orderings_Oord_29, fact_164_subset__iff
% 38.64/24.24 % No. of inferences in proof: 704
% 38.64/24.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23718 ms resp. 23116 ms w/o parsing
% 39.21/24.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 39.21/24.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------