%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP044^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:32 AM UTC 2026
% Result : Theorem 14.98s 4.55s
% Output : Refutation 16.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 314
% Syntax : Number of formulae : 630 ( 432 unt; 0 typ; 0 def)
% Number of atoms : 1446 ( 951 equ; 2 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 3903 ( 210 ~; 82 |; 78 &;3121 @)
% ( 0 <=>; 412 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 14 con; 0-2 aty)
% Number of variables : 1332 ( 18 ^;1304 !; 10 ?;1332 :)
% Comments :
%------------------------------------------------------------------------------
thf(poly_poly_a_type,type,
poly_poly_a: $tType ).
thf(list_poly_a_type,type,
list_poly_a: $tType ).
thf(list_list_a_type,type,
list_list_a: $tType ).
thf(poly_nat_type,type,
poly_nat: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(poly_a_type,type,
poly_a: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(descar226543321ms_nat_decl,type,
descar226543321ms_nat: list_nat > list_nat ).
thf(descar282223555poly_a_decl,type,
descar282223555poly_a: list_poly_a > list_poly_a ).
thf(descar1375166517sums_a_decl,type,
descar1375166517sums_a: list_a > list_a ).
thf(descar466059845root_a_decl,type,
descar466059845root_a: a > poly_a > poly_a ).
thf(descar357075861poly_a_decl,type,
descar357075861poly_a: list_poly_a > nat ).
thf(descar2095969287nges_a_decl,type,
descar2095969287nges_a: list_a > nat ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(one_one_poly_a_decl,type,
one_one_poly_a: poly_a ).
thf(one_one_a_decl,type,
one_one_a: a ).
thf(times_times_nat_decl,type,
times_times_nat: nat > nat > nat ).
thf(times_times_poly_a_decl,type,
times_times_poly_a: poly_a > poly_a > poly_a ).
thf(times_times_a_decl,type,
times_times_a: a > a > a ).
thf(uminus_uminus_poly_a_decl,type,
uminus_uminus_poly_a: poly_a > poly_a ).
thf(uminus_uminus_a_decl,type,
uminus_uminus_a: a > a ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(zero_zero_poly_a_decl,type,
zero_zero_poly_a: poly_a ).
thf(zero_zero_a_decl,type,
zero_zero_a: a ).
thf(append_nat_decl,type,
append_nat: list_nat > list_nat > list_nat ).
thf(append_a_decl,type,
append_a: list_a > list_a > list_a ).
thf(cons_list_a_decl,type,
cons_list_a: list_a > list_list_a > list_list_a ).
thf(cons_nat_decl,type,
cons_nat: nat > list_nat > list_nat ).
thf(cons_poly_a_decl,type,
cons_poly_a: poly_a > list_poly_a > list_poly_a ).
thf(cons_a_decl,type,
cons_a: a > list_a > list_a ).
thf(nil_list_a_decl,type,
nil_list_a: list_list_a ).
thf(nil_nat_decl,type,
nil_nat: list_nat ).
thf(nil_a_decl,type,
nil_a: list_a ).
thf(null_a_decl,type,
null_a: list_a > $o ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_poly_a_decl,type,
ord_less_poly_a: poly_a > poly_a > $o ).
thf(ord_less_a_decl,type,
ord_less_a: a > a > $o ).
thf(poly_nat2_decl,type,
poly_nat2: list_nat > poly_nat ).
thf(poly_a2_decl,type,
poly_a2: list_a > poly_a ).
thf(coeffs_a_decl,type,
coeffs_a: poly_a > list_a ).
thf(is_zero_a_decl,type,
is_zero_a: poly_a > $o ).
thf(pCons_a_decl,type,
pCons_a: a > poly_a > poly_a ).
thf(smult_nat_decl,type,
smult_nat: nat > poly_nat > poly_nat ).
thf(smult_a_decl,type,
smult_a: a > poly_a > poly_a ).
thf(g_decl,type,
g: poly_a ).
thf(v_decl,type,
v: poly_a > nat ).
thf(xs_decl,type,
xs: list_a ).
thf(ys_decl,type,
ys: list_a ).
thf(164,axiom,
! [A: a,B: poly_a,C: poly_a] :
( ( times_times_poly_a @ ( smult_a @ A @ B ) @ C )
= ( smult_a @ A @ ( times_times_poly_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_mult__smult__left) ).
thf(892,plain,
! [A: a,B: poly_a,C: poly_a] :
( ( times_times_poly_a @ ( smult_a @ A @ B ) @ C )
= ( smult_a @ A @ ( times_times_poly_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(144,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
=> ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_divisors__zero) ).
thf(809,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
=> ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(307,axiom,
( ( descar2095969287nges_a @ nil_a )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_sign__changes__Nil) ).
thf(1411,plain,
( ( descar2095969287nges_a @ nil_a )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(195,axiom,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
=> ( ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_divisors__zero) ).
thf(1024,plain,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
=> ( ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(247,axiom,
~ ( ord_less_a @ zero_zero_a @ zero_zero_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_less__numeral__extra_I3_J) ).
thf(1190,plain,
~ ( ord_less_a @ zero_zero_a @ zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(219,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ A @ zero_zero_poly_a )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
=> ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_mult__neg__pos) ).
thf(1105,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ A @ zero_zero_poly_a )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
=> ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(13,axiom,
! [A: poly_a] :
( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ A ) )
= ( ord_less_poly_a @ A @ zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_less__neg__neg) ).
thf(347,plain,
! [A: poly_a] :
( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ A ) )
= ( ord_less_poly_a @ A @ zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(212,axiom,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
=> ( ( ord_less_a @ zero_zero_a @ A )
=> ( ord_less_a @ zero_zero_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_zero__less__mult__pos) ).
thf(1083,plain,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
=> ( ( ord_less_a @ zero_zero_a @ A )
=> ( ord_less_a @ zero_zero_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(174,axiom,
! [A: a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( cons_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( cons_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_Cons__eq__appendI) ).
thf(941,plain,
! [A: a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( cons_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( cons_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_gr__implies__not__zero) ).
thf(555,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_mult__cancel2) ).
thf(481,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(67,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_mult__zero__right) ).
thf(523,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(209,axiom,
( is_zero_a
= ( ^ [A: poly_a] : ( A = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_is__zero__null) ).
thf(1073,plain,
( is_zero_a
= ( ^ [A: poly_a] : ( A = zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(232,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
= ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
& ( ord_less_poly_a @ zero_zero_poly_a @ B ) )
| ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
& ( ord_less_poly_a @ B @ zero_zero_poly_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_zero__less__mult__iff) ).
thf(1142,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
= ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
& ( ord_less_poly_a @ zero_zero_poly_a @ B ) )
| ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
& ( ord_less_poly_a @ B @ zero_zero_poly_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(63,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ ( uminus_uminus_poly_a @ B ) )
= ( ord_less_poly_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_neg__less__iff__less) ).
thf(511,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ ( uminus_uminus_poly_a @ B ) )
= ( ord_less_poly_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(111,axiom,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( cons_a @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_list__nonempty__induct) ).
thf(677,plain,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( cons_a @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(198,axiom,
! [A: poly_a] :
( ( smult_a @ one_one_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_smult__1__left) ).
thf(1041,plain,
! [A: poly_a] :
( ( smult_a @ one_one_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(31,axiom,
! [A: poly_a,B: poly_a] :
( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ ( uminus_uminus_poly_a @ B ) )
= ( times_times_poly_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_minus__mult__minus) ).
thf(408,plain,
! [A: poly_a,B: poly_a] :
( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ ( uminus_uminus_poly_a @ B ) )
= ( times_times_poly_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(181,axiom,
! [A: a] :
( ( times_times_a @ ( uminus_uminus_a @ one_one_a ) @ A )
= ( uminus_uminus_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_mult__minus1) ).
thf(977,plain,
! [A: a] :
( ( times_times_a @ ( uminus_uminus_a @ one_one_a ) @ A )
= ( uminus_uminus_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(25,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(384,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(280,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_strict__sorted_Oinduct) ).
thf(1310,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(50,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_neq0__conv) ).
thf(472,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(261,axiom,
! [A: a,B: poly_a] :
( ( smult_a @ ( uminus_uminus_a @ A ) @ B )
= ( uminus_uminus_poly_a @ ( smult_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_smult__minus__left) ).
thf(1233,plain,
! [A: a,B: poly_a] :
( ( smult_a @ ( uminus_uminus_a @ A ) @ B )
= ( uminus_uminus_poly_a @ ( smult_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(283,axiom,
( one_one_poly_a
= ( pCons_a @ one_one_a @ zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_one__poly__eq__simps_I1_J) ).
thf(1327,plain,
( one_one_poly_a
= ( pCons_a @ one_one_a @ zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(205,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_less__one) ).
thf(1063,plain,
! [A: nat] :
( ( ord_less_nat @ A @ one_one_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(257,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ one_one_poly_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_comm__monoid__mult__class_Omult__1) ).
thf(1222,plain,
! [A: poly_a] :
( ( times_times_poly_a @ one_one_poly_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(216,axiom,
! [A: a,B: list_a] :
( ( cons_a @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_not__Cons__self2) ).
thf(1095,plain,
! [A: a,B: list_a] :
( ( cons_a @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(249,axiom,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_append__Nil2) ).
thf(1196,plain,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(166,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= B )
= ( ( B = zero_zero_a )
| ( A = one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_mult__cancel__right2) ).
thf(898,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= B )
= ( ( B = zero_zero_a )
| ( A = one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(264,axiom,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ B @ A ) )
= ( B = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_self__append__conv2) ).
thf(1243,plain,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ B @ A ) )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(300,axiom,
! [A: poly_a] :
( ( ( coeffs_a @ A )
= nil_a )
= ( A = zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_coeffs__eq__Nil) ).
thf(1391,plain,
! [A: poly_a] :
( ( ( coeffs_a @ A )
= nil_a )
= ( A = zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(162,axiom,
! [A: a,B: a,C: a] :
( ( A != zero_zero_a )
=> ( ( ( times_times_a @ A @ B )
= ( times_times_a @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_mult__left__cancel) ).
thf(885,plain,
! [A: a,B: a,C: a] :
( ( A != zero_zero_a )
=> ( ( ( times_times_a @ A @ B )
= ( times_times_a @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(294,axiom,
( ys
= ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_ys__def) ).
thf(1359,plain,
( ys
= ( append_a @ ( coeffs_a @ g ) @ ( cons_a @ zero_zero_a @ nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(271,axiom,
! [A: a] :
( ( times_times_a @ A @ one_one_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_mult_Oright__neutral) ).
thf(1265,plain,
! [A: a] :
( ( times_times_a @ A @ one_one_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(259,axiom,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_append__Nil) ).
thf(1228,plain,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(79,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_mult_Ocomm__neutral) ).
thf(565,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(297,axiom,
! [A: a,B: a] :
( ( ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ B @ zero_zero_a ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ zero_zero_a @ B ) ) )
=> ( ( descar2095969287nges_a @ ( cons_a @ A @ ( cons_a @ B @ nil_a ) ) )
= one_one_nat ) )
& ( ~ ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ B @ zero_zero_a ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ zero_zero_a @ B ) ) )
=> ( ( descar2095969287nges_a @ ( cons_a @ A @ ( cons_a @ B @ nil_a ) ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_sign__changes__two) ).
thf(1366,plain,
! [A: a,B: a] :
( ( ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ B @ zero_zero_a ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ zero_zero_a @ B ) ) )
=> ( ( descar2095969287nges_a @ ( cons_a @ A @ ( cons_a @ B @ nil_a ) ) )
= one_one_nat ) )
& ( ~ ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ B @ zero_zero_a ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ zero_zero_a @ B ) ) )
=> ( ( descar2095969287nges_a @ ( cons_a @ A @ ( cons_a @ B @ nil_a ) ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(276,axiom,
! [A: nat,B: nat] :
( ( A
= ( times_times_nat @ A @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_mult__eq__self__implies__10) ).
thf(1298,plain,
! [A: nat,B: nat] :
( ( A
= ( times_times_nat @ A @ B ) )
=> ( ( B = one_one_nat )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(21,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_nat__mult__1__right) ).
thf(372,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_mult__less__mono1) ).
thf(344,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_less__not__refl2) ).
thf(357,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(204,axiom,
! [A: a,B: a] :
( ( A != zero_zero_a )
=> ( ( B != zero_zero_a )
=> ( ( times_times_a @ A @ B )
!= zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_no__zero__divisors) ).
thf(1059,plain,
! [A: a,B: a] :
( ( A != zero_zero_a )
=> ( ( B != zero_zero_a )
=> ( ( times_times_a @ A @ B )
!= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(176,axiom,
! [A: poly_a > $o,B: poly_a] :
( ( A @ zero_zero_poly_a )
=> ( ! [C: a,D: poly_a] :
( ( ( C != zero_zero_a )
| ( D != zero_zero_poly_a ) )
=> ( ( A @ D )
=> ( A @ ( pCons_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_pCons__induct) ).
thf(949,plain,
! [A: poly_a > $o,B: poly_a] :
( ( A @ zero_zero_poly_a )
=> ( ! [C: a,D: poly_a] :
( ( ( C != zero_zero_a )
| ( D != zero_zero_poly_a ) )
=> ( ( A @ D )
=> ( A @ ( pCons_a @ C @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_nat__0__less__mult__iff) ).
thf(559,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(302,axiom,
( ( (=) @ poly_a )
= ( ^ [A: poly_a,B: poly_a] :
( ( coeffs_a @ A )
= ( coeffs_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_coeffs__eq__iff) ).
thf(1398,plain,
( ( (=) @ poly_a )
= ( ^ [A: poly_a,B: poly_a] :
( ( coeffs_a @ A )
= ( coeffs_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(42,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_nat__mult__less__cancel__disj) ).
thf(448,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1,conjecture,
( ( descar2095969287nges_a @ ys )
= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( descar2095969287nges_a @ ys )
!= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(316,plain,
( ( descar2095969287nges_a @ ys )
!= ( descar2095969287nges_a @ ( coeffs_a @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,axiom,
! [A: a] :
( ( times_times_a @ one_one_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_comm__monoid__mult__class_Omult__1) ).
thf(638,plain,
! [A: a] :
( ( times_times_a @ one_one_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(155,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ ( times_times_poly_a @ A @ C ) )
= ( ord_less_poly_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_mult__less__cancel__left__pos) ).
thf(853,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ ( times_times_poly_a @ A @ C ) )
= ( ord_less_poly_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_mult__cancel__left) ).
thf(475,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(138,axiom,
! [A: a,B: a,C: a] :
( ( A != zero_zero_a )
=> ( ( ( times_times_a @ B @ A )
= ( times_times_a @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_mult__right__cancel) ).
thf(789,plain,
! [A: a,B: a,C: a] :
( ( A != zero_zero_a )
=> ( ( ( times_times_a @ B @ A )
= ( times_times_a @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(4,axiom,
! [A: list_poly_a] :
( ( descar357075861poly_a @ ( cons_poly_a @ zero_zero_poly_a @ A ) )
= ( descar357075861poly_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_sign__changes__0__Cons) ).
thf(321,plain,
! [A: list_poly_a] :
( ( descar357075861poly_a @ ( cons_poly_a @ zero_zero_poly_a @ A ) )
= ( descar357075861poly_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(101,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( ( times_times_poly_a @ B @ A )
= ( times_times_poly_a @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_mult__right__cancel) ).
thf(646,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( ( times_times_poly_a @ B @ A )
= ( times_times_poly_a @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(230,axiom,
! [A: a] :
( ( times_times_a @ zero_zero_a @ A )
= zero_zero_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_mult__zero__left) ).
thf(1136,plain,
! [A: a] :
( ( times_times_a @ zero_zero_a @ A )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(64,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_mult__0__right) ).
thf(514,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(143,axiom,
! [A: a,B: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_minus__less__iff) ).
thf(806,plain,
! [A: a,B: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(15,axiom,
! [A: poly_a,B: poly_a,C: list_poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
=> ( ( descar357075861poly_a @ ( cons_poly_a @ A @ ( cons_poly_a @ B @ C ) ) )
= ( descar357075861poly_a @ ( cons_poly_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_sign__changes__Cons__Cons__same) ).
thf(353,plain,
! [A: poly_a,B: poly_a,C: list_poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
=> ( ( descar357075861poly_a @ ( cons_poly_a @ A @ ( cons_poly_a @ B @ C ) ) )
= ( descar357075861poly_a @ ( cons_poly_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(148,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_append_Oassoc) ).
thf(821,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(91,axiom,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_less__numeral__extra_I4_J) ).
thf(602,plain,
~ ( ord_less_nat @ one_one_nat @ one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(112,axiom,
! [A: poly_a > $o,B: poly_a] :
( ! [C: a,D: poly_a] :
( ( ( D != zero_zero_poly_a )
=> ( A @ D ) )
=> ( A @ ( pCons_a @ C @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_pderiv_Oinduct) ).
thf(692,plain,
! [A: poly_a > $o,B: poly_a] :
( ! [C: a,D: poly_a] :
( ( ( D != zero_zero_poly_a )
=> ( A @ D ) )
=> ( A @ ( pCons_a @ C @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(224,axiom,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ A @ B ) )
= ( B = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_self__append__conv) ).
thf(1119,plain,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ A @ B ) )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(301,axiom,
! [A: a,B: poly_a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( descar2095969287nges_a @ ( coeffs_a @ ( descar466059845root_a @ A @ B ) ) )
= ( descar2095969287nges_a @ ( coeffs_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_coeff__sign__changes__reduce__root) ).
thf(1394,plain,
! [A: a,B: poly_a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( descar2095969287nges_a @ ( coeffs_a @ ( descar466059845root_a @ A @ B ) ) )
= ( descar2095969287nges_a @ ( coeffs_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(32,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_nat__less__induct) ).
thf(411,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(315,axiom,
( v
= ( ^ [A: poly_a] : ( descar2095969287nges_a @ ( coeffs_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_v__def) ).
thf(1433,plain,
( v
= ( ^ [A: poly_a] : ( descar2095969287nges_a @ ( coeffs_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(240,axiom,
! [A: a] :
( ( times_times_a @ A @ one_one_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_mult_Ocomm__neutral) ).
thf(1169,plain,
! [A: a] :
( ( times_times_a @ A @ one_one_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_nat__mult__eq__cancel__disj) ).
thf(397,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(208,axiom,
null_a @ nil_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_null__rec_I2_J) ).
thf(1072,plain,
null_a @ nil_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_nat__mult__eq__1__iff) ).
thf(453,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(252,axiom,
! [A: poly_a] :
~ ! [B: a,C: poly_a] :
( A
!= ( pCons_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_pderiv_Ocases) ).
thf(1206,plain,
! [A: poly_a] :
~ ! [B: a,C: poly_a] :
( A
!= ( pCons_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_less__not__refl3) ).
thf(380,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(39,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_mult_Oright__neutral) ).
thf(439,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(69,axiom,
! [A: poly_a] :
( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ zero_zero_poly_a )
= ( ord_less_poly_a @ zero_zero_poly_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_neg__less__0__iff__less) ).
thf(529,plain,
! [A: poly_a] :
( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ zero_zero_poly_a )
= ( ord_less_poly_a @ zero_zero_poly_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(139,axiom,
! [A: a] :
( ( times_times_a @ one_one_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_mult_Oleft__neutral) ).
thf(793,plain,
! [A: a] :
( ( times_times_a @ one_one_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(250,axiom,
! [A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ A )
= ( ord_less_a @ zero_zero_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_neg__less__pos) ).
thf(1199,plain,
! [A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ A )
= ( ord_less_a @ zero_zero_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(287,axiom,
~ ( ord_less_a @ one_one_a @ one_one_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_less__numeral__extra_I4_J) ).
thf(1338,plain,
~ ( ord_less_a @ one_one_a @ one_one_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(235,axiom,
! [A: poly_a] :
( ( zero_zero_poly_a = A )
= ( A = zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_zero__reorient) ).
thf(1153,plain,
! [A: poly_a] :
( ( zero_zero_poly_a = A )
= ( A = zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(130,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
=> ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_mult__strict__left__mono) ).
thf(761,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
=> ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(200,axiom,
zero_zero_a != one_one_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_zero__neq__one) ).
thf(1047,plain,
zero_zero_a != one_one_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(238,axiom,
! [A: a,B: a] :
( ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a )
= ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ B @ zero_zero_a ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ zero_zero_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_mult__less__0__iff) ).
thf(1163,plain,
! [A: a,B: a] :
( ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a )
= ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ B @ zero_zero_a ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ zero_zero_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(127,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( ord_less_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) )
= ( ord_less_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_mult__less__cancel__left__pos) ).
thf(746,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( ord_less_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) )
= ( ord_less_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(289,axiom,
! [A: a,B: a,C: a] :
( ( ( times_times_a @ A @ B )
= ( times_times_a @ C @ B ) )
= ( ( B = zero_zero_a )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_mult__cancel__right) ).
thf(1343,plain,
! [A: a,B: a,C: a] :
( ( ( times_times_a @ A @ B )
= ( times_times_a @ C @ B ) )
= ( ( B = zero_zero_a )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(194,axiom,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
= ( ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_mult__eq__0__iff) ).
thf(1021,plain,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= zero_zero_poly_a )
= ( ( A = zero_zero_poly_a )
| ( B = zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(268,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_psums_Ocases) ).
thf(1255,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(34,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_comm__monoid__mult__class_Omult__1) ).
thf(424,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(96,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_mult__zero__right) ).
thf(630,plain,
! [A: poly_a] :
( ( times_times_poly_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(146,axiom,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_append_Oleft__neutral) ).
thf(815,plain,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(122,axiom,
! [A: a] :
( ( times_times_a @ A @ ( uminus_uminus_a @ one_one_a ) )
= ( uminus_uminus_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_mult__minus1__right) ).
thf(729,plain,
! [A: a] :
( ( times_times_a @ A @ ( uminus_uminus_a @ one_one_a ) )
= ( uminus_uminus_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(54,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_mult__0) ).
thf(484,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(17,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_zero__less__iff__neq__zero) ).
thf(361,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_gr__implies__not0) ).
thf(435,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(275,axiom,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
=> ( ( ord_less_a @ zero_zero_a @ B )
=> ( ord_less_a @ zero_zero_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_zero__less__mult__pos2) ).
thf(1296,plain,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
=> ( ( ord_less_a @ zero_zero_a @ B )
=> ( ord_less_a @ zero_zero_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(85,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_less__irrefl__nat) ).
thf(583,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(163,axiom,
! [A: a,B: a] :
( ( ( uminus_uminus_a @ A )
= ( uminus_uminus_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_neg__equal__iff__equal) ).
thf(889,plain,
! [A: a,B: a] :
( ( ( uminus_uminus_a @ A )
= ( uminus_uminus_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(227,axiom,
( ( poly_a2 @ nil_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Poly_Osimps_I1_J) ).
thf(1128,plain,
( ( poly_a2 @ nil_a )
= zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(191,axiom,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= A )
= ( ( A = zero_zero_poly_a )
| ( B = one_one_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_mult__cancel__left2) ).
thf(1012,plain,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= A )
= ( ( A = zero_zero_poly_a )
| ( B = one_one_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(7,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_less__not__refl) ).
thf(329,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(243,axiom,
! [A: a,B: list_a] :
~ ( null_a @ ( cons_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_null__rec_I1_J) ).
thf(1178,plain,
! [A: a,B: list_a] :
~ ( null_a @ ( cons_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(57,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_mult__zero__left) ).
thf(493,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(253,axiom,
! [A: a,B: a] :
( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
= ( times_times_a @ A @ ( uminus_uminus_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_minus__mult__commute) ).
thf(1210,plain,
! [A: a,B: a] :
( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
= ( times_times_a @ A @ ( uminus_uminus_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(211,axiom,
! [A: poly_a,B: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( B != zero_zero_poly_a )
=> ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_no__zero__divisors) ).
thf(1079,plain,
! [A: poly_a,B: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( B != zero_zero_poly_a )
=> ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(196,axiom,
! [A: a,B: poly_a] :
( ( uminus_uminus_poly_a @ ( pCons_a @ A @ B ) )
= ( pCons_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_poly_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_minus__pCons) ).
thf(1027,plain,
! [A: a,B: poly_a] :
( ( uminus_uminus_poly_a @ ( pCons_a @ A @ B ) )
= ( pCons_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_poly_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(45,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_not__gr0) ).
thf(456,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(151,axiom,
! [A: list_a,B: list_a,C: list_a,D: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ? [E: list_a] :
( ( ( A
= ( append_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) )
| ( ( ( append_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_append__eq__append__conv2) ).
thf(842,plain,
! [A: list_a,B: list_a,C: list_a,D: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ? [E: list_a] :
( ( ( A
= ( append_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) )
| ( ( ( append_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_mult__less__mono2) ).
thf(324,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(180,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ ( times_times_poly_a @ C @ B ) )
= ( ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
& ( ord_less_poly_a @ A @ C ) )
| ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
& ( ord_less_poly_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_mult__less__cancel__right__disj) ).
thf(974,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ ( times_times_poly_a @ C @ B ) )
= ( ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
& ( ord_less_poly_a @ A @ C ) )
| ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
& ( ord_less_poly_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(304,axiom,
( ( coeffs_a @ one_one_poly_a )
= ( cons_a @ one_one_a @ nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_coeffs__1__eq) ).
thf(1402,plain,
( ( coeffs_a @ one_one_poly_a )
= ( cons_a @ one_one_a @ nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(214,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_one__reorient) ).
thf(1089,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(161,axiom,
! [A: poly_a > poly_a > $o,B: poly_a,C: poly_a] :
( ( A @ zero_zero_poly_a @ zero_zero_poly_a )
=> ( ! [D: a,E: poly_a,F: a,G: poly_a] :
( ( A @ E @ G )
=> ( A @ ( pCons_a @ D @ E ) @ ( pCons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_poly__induct2) ).
thf(874,plain,
! [A: poly_a > poly_a > $o,B: poly_a,C: poly_a] :
( ( A @ zero_zero_poly_a @ zero_zero_poly_a )
=> ( ! [D: a,E: poly_a,F: a,G: poly_a] :
( ( A @ E @ G )
=> ( A @ ( pCons_a @ D @ E ) @ ( pCons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(269,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ C @ zero_zero_a )
=> ( ord_less_a @ ( times_times_a @ C @ B ) @ ( times_times_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_mult__strict__left__mono__neg) ).
thf(1259,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ C @ zero_zero_a )
=> ( ord_less_a @ ( times_times_a @ C @ B ) @ ( times_times_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(102,axiom,
! [A: a,B: list_a,C: a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_list_Oinject) ).
thf(650,plain,
! [A: a,B: list_a,C: a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(221,axiom,
! [A: a] :
( ( smult_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_smult__0__right) ).
thf(1111,plain,
! [A: a] :
( ( smult_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(182,axiom,
! [A: a,B: poly_a] :
( ( ( pCons_a @ A @ B )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
& ( B = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_pCons__eq__0__iff) ).
thf(980,plain,
! [A: a,B: poly_a] :
( ( ( pCons_a @ A @ B )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
& ( B = zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(88,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_not__less__zero) ).
thf(593,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_linorder__neqE__nat) ).
thf(499,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(185,axiom,
! [A: a,B: poly_a,C: a] :
( ( ( smult_a @ A @ B )
= ( pCons_a @ C @ B ) )
=> ( B = zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_synthetic__div__unique__lemma) ).
thf(989,plain,
! [A: a,B: poly_a,C: a] :
( ( ( smult_a @ A @ B )
= ( pCons_a @ C @ B ) )
=> ( B = zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(156,axiom,
! [A: a,B: a] :
( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_less__minus__iff) ).
thf(857,plain,
! [A: a,B: a] :
( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(136,axiom,
! [A: list_a,B: a,C: list_a,D: a] :
( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
= ( append_a @ C @ ( cons_a @ D @ nil_a ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_append1__eq__conv) ).
thf(783,plain,
! [A: list_a,B: a,C: list_a,D: a] :
( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
= ( append_a @ C @ ( cons_a @ D @ nil_a ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(33,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_nat__mult__less__cancel1) ).
thf(420,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(284,axiom,
! [A: a,B: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_neg__less__iff__less) ).
thf(1329,plain,
! [A: a,B: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(237,axiom,
! [A: a,B: a] :
( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
= ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_mult__minus__left) ).
thf(1160,plain,
! [A: a,B: a] :
( ( times_times_a @ ( uminus_uminus_a @ A ) @ B )
= ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(295,axiom,
! [A: a] :
( ( descar2095969287nges_a @ ( cons_a @ A @ nil_a ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_sign__changes__singleton) ).
thf(1361,plain,
! [A: a] :
( ( descar2095969287nges_a @ ( cons_a @ A @ nil_a ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(172,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: a,E: list_a,F: list_a] :
( ( A @ F @ E )
=> ( A @ ( cons_a @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_splice_Oinduct) ).
thf(933,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: a,E: list_a,F: list_a] :
( ( A @ F @ E )
=> ( A @ ( cons_a @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(129,axiom,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a )
=> ( ( A != zero_zero_poly_a )
& ( B != zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_mult__not__zero) ).
thf(753,plain,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
!= zero_zero_poly_a )
=> ( ( A != zero_zero_poly_a )
& ( B != zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(72,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_gr0I) ).
thf(537,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(312,axiom,
! [A: poly_a] :
( ( poly_a2 @ ( coeffs_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Poly__coeffs) ).
thf(1424,plain,
! [A: poly_a] :
( ( poly_a2 @ ( coeffs_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(68,axiom,
! [A: poly_a,B: poly_a] :
( ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
= ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_mult__minus__right) ).
thf(526,plain,
! [A: poly_a,B: poly_a] :
( ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
= ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(87,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_mult__pos__pos) ).
thf(590,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(310,axiom,
( xs
= ( coeffs_a @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_xs__def) ).
thf(1419,plain,
( xs
= ( coeffs_a @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(167,axiom,
! [A: a,B: a] :
( ( A
= ( uminus_uminus_a @ B ) )
= ( B
= ( uminus_uminus_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_equation__minus__iff) ).
thf(901,plain,
! [A: a,B: a] :
( ( A
= ( uminus_uminus_a @ B ) )
= ( B
= ( uminus_uminus_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(210,axiom,
! [A: list_a,B: list_a] :
( ( A = B )
=> ( A
= ( append_a @ nil_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_eq__Nil__appendI) ).
thf(1075,plain,
! [A: list_a,B: list_a] :
( ( A = B )
=> ( A
= ( append_a @ nil_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(217,axiom,
! [A: a] :
( ( one_one_a = A )
= ( A = one_one_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_one__reorient) ).
thf(1099,plain,
! [A: a] :
( ( one_one_a = A )
= ( A = one_one_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(266,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
=> ( ord_less_poly_a @ ( times_times_poly_a @ C @ B ) @ ( times_times_poly_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_mult__strict__left__mono__neg) ).
thf(1249,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
=> ( ord_less_poly_a @ ( times_times_poly_a @ C @ B ) @ ( times_times_poly_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(125,axiom,
( ( pCons_a @ one_one_a @ zero_zero_poly_a )
= one_one_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_pCons__one) ).
thf(738,plain,
( ( pCons_a @ one_one_a @ zero_zero_poly_a )
= one_one_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(260,axiom,
( ( uminus_uminus_a @ zero_zero_a )
= zero_zero_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_add_Oinverse__neutral) ).
thf(1231,plain,
( ( uminus_uminus_a @ zero_zero_a )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(248,axiom,
! [A: poly_a] :
~ ! [B: a,C: poly_a] :
( A
!= ( pCons_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_pCons__cases) ).
thf(1192,plain,
! [A: poly_a] :
~ ! [B: a,C: poly_a] :
( A
!= ( pCons_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(201,axiom,
! [A: a] :
( ( A
= ( uminus_uminus_a @ A ) )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_equal__neg__zero) ).
thf(1050,plain,
! [A: a] :
( ( A
= ( uminus_uminus_a @ A ) )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(189,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_minus__poly__rev__list_Oinduct) ).
thf(1002,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(314,axiom,
! [A: a,B: a,C: list_a] :
( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
=> ( ( descar2095969287nges_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
= ( descar2095969287nges_a @ ( cons_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_sign__changes__Cons__Cons__same) ).
thf(1429,plain,
! [A: a,B: a,C: list_a] :
( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
=> ( ( descar2095969287nges_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
= ( descar2095969287nges_a @ ( cons_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(265,axiom,
! [A: a] :
( ( ord_less_a @ A @ ( uminus_uminus_a @ A ) )
= ( ord_less_a @ A @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_less__neg__neg) ).
thf(1246,plain,
! [A: a] :
( ( ord_less_a @ A @ ( uminus_uminus_a @ A ) )
= ( ord_less_a @ A @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(282,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ C @ B ) )
= ( ( ( ord_less_a @ zero_zero_a @ B )
& ( ord_less_a @ A @ C ) )
| ( ( ord_less_a @ B @ zero_zero_a )
& ( ord_less_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_mult__less__cancel__right__disj) ).
thf(1324,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ C @ B ) )
= ( ( ( ord_less_a @ zero_zero_a @ B )
& ( ord_less_a @ A @ C ) )
| ( ( ord_less_a @ B @ zero_zero_a )
& ( ord_less_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(222,axiom,
! [A: list_a,B: list_a] :
( ( nil_a
= ( append_a @ A @ B ) )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_Nil__is__append__conv) ).
thf(1114,plain,
! [A: list_a,B: list_a] :
( ( nil_a
= ( append_a @ A @ B ) )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(251,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_list_Oexhaust) ).
thf(1202,plain,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(173,axiom,
! [A: list_nat] :
( ( descar226543321ms_nat @ ( cons_nat @ zero_zero_nat @ A ) )
= ( cons_nat @ zero_zero_nat @ ( descar226543321ms_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_psums__0__Cons) ).
thf(938,plain,
! [A: list_nat] :
( ( descar226543321ms_nat @ ( cons_nat @ zero_zero_nat @ A ) )
= ( cons_nat @ zero_zero_nat @ ( descar226543321ms_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(97,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= ( times_times_poly_a @ A @ C ) )
= ( ( A = zero_zero_poly_a )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_mult__cancel__left) ).
thf(633,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= ( times_times_poly_a @ A @ C ) )
= ( ( A = zero_zero_poly_a )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( one_one_nat
= ( times_times_nat @ A @ B ) )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_nat__1__eq__mult__iff) ).
thf(508,plain,
! [A: nat,B: nat] :
( ( one_one_nat
= ( times_times_nat @ A @ B ) )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_nat__mult__eq__cancel1) ).
thf(586,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(106,axiom,
( ( pCons_a @ zero_zero_a @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_pCons__0__0) ).
thf(662,plain,
( ( pCons_a @ zero_zero_a @ zero_zero_poly_a )
= zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(246,axiom,
! [A: a] :
( ( descar1375166517sums_a @ ( cons_a @ A @ nil_a ) )
= ( cons_a @ A @ nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_psums_Osimps_I2_J) ).
thf(1187,plain,
! [A: a] :
( ( descar1375166517sums_a @ ( cons_a @ A @ nil_a ) )
= ( cons_a @ A @ nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(110,axiom,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= A )
= ( B = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_append__self__conv) ).
thf(674,plain,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= A )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(169,axiom,
! [A: list_a > $o,B: list_a] :
( ! [C: a,D: list_a] :
( ! [E: a,F: list_a] :
( ( D
= ( cons_a @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( ( A @ nil_a )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_min__list_Oinduct) ).
thf(906,plain,
! [A: list_a > $o,B: list_a] :
( ! [C: a,D: list_a] :
( ! [E: a,F: list_a] :
( ( D
= ( cons_a @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( ( A @ nil_a )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(36,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_zero__less__mult__pos2) ).
thf(430,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(277,axiom,
! [A: a,B: a] :
( ( A
= ( times_times_a @ A @ B ) )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_mult__cancel__left1) ).
thf(1301,plain,
! [A: a,B: a] :
( ( A
= ( times_times_a @ A @ B ) )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(82,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_gr__zeroI) ).
thf(573,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(22,axiom,
~ ( ord_less_poly_a @ zero_zero_poly_a @ zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_less__numeral__extra_I3_J) ).
thf(375,plain,
~ ( ord_less_poly_a @ zero_zero_poly_a @ zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(177,axiom,
! [A: poly_a] :
( ( smult_a @ zero_zero_a @ A )
= zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_smult__0__left) ).
thf(965,plain,
! [A: poly_a] :
( ( smult_a @ zero_zero_a @ A )
= zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(128,axiom,
! [A: a,B: poly_a] :
( ( ( smult_a @ A @ B )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
| ( B = zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_smult__eq__0__iff) ).
thf(750,plain,
! [A: a,B: poly_a] :
( ( ( smult_a @ A @ B )
= zero_zero_poly_a )
= ( ( A = zero_zero_a )
| ( B = zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(256,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ~ ( ord_less_a @ A @ B )
=> ( ord_less_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_linorder__neqE__linordered__idom) ).
thf(1219,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ~ ( ord_less_a @ A @ B )
=> ( ord_less_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(149,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_append__assoc) ).
thf(824,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(190,axiom,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a] : ( A @ D @ ( cons_a @ E @ nil_a ) )
=> ( ! [D: a > a > $o,E: a,F: a,G: list_a] :
( ( A @ D @ ( cons_a @ F @ G ) )
=> ( A @ D @ ( cons_a @ E @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_successively_Oinduct) ).
thf(1007,plain,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a] : ( A @ D @ ( cons_a @ E @ nil_a ) )
=> ( ! [D: a > a > $o,E: a,F: a,G: list_a] :
( ( A @ D @ ( cons_a @ F @ G ) )
=> ( A @ D @ ( cons_a @ E @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(123,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_same__append__eq) ).
thf(732,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(226,axiom,
! [A: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_add_Oinverse__inverse) ).
thf(1125,plain,
! [A: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(133,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ C @ zero_zero_a )
=> ( ord_less_a @ ( times_times_a @ B @ C ) @ ( times_times_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_mult__strict__right__mono__neg) ).
thf(772,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ C @ zero_zero_a )
=> ( ord_less_a @ ( times_times_a @ B @ C ) @ ( times_times_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(299,axiom,
g != zero_zero_poly_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nz) ).
thf(1388,plain,
g != zero_zero_poly_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(116,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_zero__less__mult__pos) ).
thf(711,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(78,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_mult__cancel1) ).
thf(562,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(168,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
=> ( ord_less_poly_a @ zero_zero_poly_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_zero__less__mult__pos2) ).
thf(904,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
=> ( ord_less_poly_a @ zero_zero_poly_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(100,axiom,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a,F: list_a] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_a @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_sorted__wrt_Oinduct) ).
thf(641,plain,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a,F: list_a] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_a @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(445,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(117,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_remdups__adj_Ocases) ).
thf(713,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(263,axiom,
! [A: a,B: list_a] :
( nil_a
!= ( cons_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_list_Odistinct_I1_J) ).
thf(1239,plain,
! [A: a,B: list_a] :
( nil_a
!= ( cons_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(285,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a )
= ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
& ( ord_less_poly_a @ B @ zero_zero_poly_a ) )
| ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
& ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_mult__less__0__iff) ).
thf(1332,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a )
= ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
& ( ord_less_poly_a @ B @ zero_zero_poly_a ) )
| ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
& ( ord_less_poly_a @ zero_zero_poly_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_nat__neq__iff) ).
thf(335,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(170,axiom,
! [A: a,B: a] :
( ( ord_less_a @ A @ zero_zero_a )
=> ( ( ord_less_a @ zero_zero_a @ B )
=> ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_mult__neg__pos) ).
thf(919,plain,
! [A: a,B: a] :
( ( ord_less_a @ A @ zero_zero_a )
=> ( ( ord_less_a @ zero_zero_a @ B )
=> ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(293,axiom,
! [A: poly_a,B: poly_a] :
( ( A
= ( times_times_poly_a @ B @ A ) )
= ( ( A = zero_zero_poly_a )
| ( B = one_one_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_mult__cancel__right1) ).
thf(1356,plain,
! [A: poly_a,B: poly_a] :
( ( A
= ( times_times_poly_a @ B @ A ) )
= ( ( A = zero_zero_poly_a )
| ( B = one_one_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(14,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_mult__strict__right__mono) ).
thf(350,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_not__less0) ).
thf(540,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_mult__eq__0__iff) ).
thf(391,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(231,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
=> ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_mult__strict__right__mono) ).
thf(1139,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
=> ( ord_less_poly_a @ ( times_times_poly_a @ A @ C ) @ ( times_times_poly_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_mult__neg__pos) ).
thf(466,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(215,axiom,
! [A: poly_nat] :
( ( smult_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_smult__1__left) ).
thf(1092,plain,
! [A: poly_nat] :
( ( smult_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(306,axiom,
! [A: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( coeffs_a @ A )
!= nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_not__0__coeffs__not__Nil) ).
thf(1408,plain,
! [A: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( coeffs_a @ A )
!= nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(223,axiom,
( ( pCons_a @ one_one_a @ zero_zero_poly_a )
= one_one_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_one__poly__eq__simps_I2_J) ).
thf(1117,plain,
( ( pCons_a @ one_one_a @ zero_zero_poly_a )
= one_one_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(291,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ zero_zero_a )
=> ( ( ord_less_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) )
= ( ord_less_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_mult__less__cancel__left__neg) ).
thf(1349,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ zero_zero_a )
=> ( ( ord_less_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) )
= ( ord_less_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_zero__less__mult__pos) ).
thf(451,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(3,axiom,
! [A: poly_a,B: list_poly_a] :
( ( descar357075861poly_a @ ( cons_poly_a @ A @ ( cons_poly_a @ zero_zero_poly_a @ B ) ) )
= ( descar357075861poly_a @ ( cons_poly_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_sign__changes__Cons__Cons__0) ).
thf(318,plain,
! [A: poly_a,B: list_poly_a] :
( ( descar357075861poly_a @ ( cons_poly_a @ A @ ( cons_poly_a @ zero_zero_poly_a @ B ) ) )
= ( descar357075861poly_a @ ( cons_poly_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(225,axiom,
! [A: poly_a,B: a,C: poly_a] :
( ( times_times_poly_a @ A @ ( smult_a @ B @ C ) )
= ( smult_a @ B @ ( times_times_poly_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_mult__smult__right) ).
thf(1122,plain,
! [A: poly_a,B: a,C: poly_a] :
( ( times_times_poly_a @ A @ ( smult_a @ B @ C ) )
= ( smult_a @ B @ ( times_times_poly_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(90,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_bot__nat__0_Onot__eq__extremum) ).
thf(599,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(279,axiom,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_append_Oright__neutral) ).
thf(1307,plain,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(131,axiom,
! [A: list_a,B: a,C: list_a] :
( ( A
= ( cons_a @ B @ C ) )
=> ( A != nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_list_OdiscI) ).
thf(764,plain,
! [A: list_a,B: a,C: list_a] :
( ( A
= ( cons_a @ B @ C ) )
=> ( A != nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(92,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_infinite__descent0) ).
thf(604,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(23,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_less__nat__zero__code) ).
thf(377,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(187,axiom,
! [A: a,B: a] :
( ( times_times_a @ A @ ( uminus_uminus_a @ B ) )
= ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_mult__minus__right) ).
thf(996,plain,
! [A: a,B: a] :
( ( times_times_a @ A @ ( uminus_uminus_a @ B ) )
= ( uminus_uminus_a @ ( times_times_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(158,axiom,
! [A: a,B: poly_a] :
( ( A != zero_zero_a )
=> ( ( B != zero_zero_poly_a )
=> ( ( descar466059845root_a @ A @ B )
!= zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_reduce__root__nonzero) ).
thf(863,plain,
! [A: a,B: poly_a] :
( ( A != zero_zero_a )
=> ( ( B != zero_zero_poly_a )
=> ( ( descar466059845root_a @ A @ B )
!= zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(242,axiom,
! [A: a,B: a,C: a] :
( ( ( times_times_a @ A @ B )
= ( times_times_a @ A @ C ) )
= ( ( A = zero_zero_a )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_mult__cancel__left) ).
thf(1175,plain,
! [A: a,B: a,C: a] :
( ( ( times_times_a @ A @ B )
= ( times_times_a @ A @ C ) )
= ( ( A = zero_zero_a )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_no__zero__divisors) ).
thf(387,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(71,axiom,
~ ( ord_less_poly_a @ one_one_poly_a @ one_one_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_less__numeral__extra_I4_J) ).
thf(535,plain,
~ ( ord_less_poly_a @ one_one_poly_a @ one_one_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(93,axiom,
! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= A )
= ( A = zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_neg__equal__zero) ).
thf(621,plain,
! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= A )
= ( A = zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(165,axiom,
! [A: a,B: list_a,C: list_a] :
( ( append_a @ ( cons_a @ A @ B ) @ C )
= ( cons_a @ A @ ( append_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_append__Cons) ).
thf(895,plain,
! [A: a,B: list_a,C: list_a] :
( ( append_a @ ( cons_a @ A @ B ) @ C )
= ( cons_a @ A @ ( append_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(132,axiom,
! [A: a,B: poly_a,C: a,D: poly_a] :
( ( ( pCons_a @ A @ B )
= ( pCons_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_pCons__eq__iff) ).
thf(769,plain,
! [A: a,B: poly_a,C: a,D: poly_a] :
( ( ( pCons_a @ A @ B )
= ( pCons_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(274,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ A )
= ( times_times_a @ B @ B ) )
= ( ( A = B )
| ( A
= ( uminus_uminus_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_square__eq__iff) ).
thf(1293,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ A )
= ( times_times_a @ B @ B ) )
= ( ( A = B )
| ( A
= ( uminus_uminus_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(19,axiom,
( ( uminus_uminus_poly_a @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_add_Oinverse__neutral) ).
thf(367,plain,
( ( uminus_uminus_poly_a @ zero_zero_poly_a )
= zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(75,axiom,
! [A: poly_a,B: poly_a] :
( ( A != B )
=> ( ~ ( ord_less_poly_a @ A @ B )
=> ( ord_less_poly_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_linorder__neqE__linordered__idom) ).
thf(552,plain,
! [A: poly_a,B: poly_a] :
( ( A != B )
=> ( ~ ( ord_less_poly_a @ A @ B )
=> ( ord_less_poly_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(141,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ zero_zero_poly_a )
=> ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ ( times_times_poly_a @ A @ C ) )
= ( ord_less_poly_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_mult__less__cancel__left__neg) ).
thf(799,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ zero_zero_poly_a )
=> ( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ ( times_times_poly_a @ A @ C ) )
= ( ord_less_poly_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(121,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_zero__neq__one) ).
thf(726,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(153,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
=> ( ord_less_poly_a @ ( times_times_poly_a @ B @ A ) @ zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_mult__pos__neg2) ).
thf(848,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
=> ( ord_less_poly_a @ ( times_times_poly_a @ B @ A ) @ zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(113,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ one_one_poly_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_mult_Oleft__neutral) ).
thf(700,plain,
! [A: poly_a] :
( ( times_times_poly_a @ one_one_poly_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(66,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_mult_Oleft__neutral) ).
thf(520,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(183,axiom,
! [A: list_a] :
( ( A = nil_a )
= ( null_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_eq__Nil__null) ).
thf(983,plain,
! [A: list_a] :
( ( A = nil_a )
= ( null_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(206,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ ( uminus_uminus_poly_a @ one_one_poly_a ) @ A )
= ( uminus_uminus_poly_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_mult__minus1) ).
thf(1066,plain,
! [A: poly_a] :
( ( times_times_poly_a @ ( uminus_uminus_poly_a @ one_one_poly_a ) @ A )
= ( uminus_uminus_poly_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(135,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= A )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_mult__cancel__left2) ).
thf(780,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= A )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(192,axiom,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( ord_less_a @ B @ zero_zero_a )
=> ( ord_less_a @ ( times_times_a @ B @ A ) @ zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_mult__pos__neg2) ).
thf(1015,plain,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( ord_less_a @ B @ zero_zero_a )
=> ( ord_less_a @ ( times_times_a @ B @ A ) @ zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(296,axiom,
( ( descar2095969287nges_a @ xs )
= ( v @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062) ).
thf(1364,plain,
( ( descar2095969287nges_a @ xs )
= ( v @ ( times_times_poly_a @ ( pCons_a @ one_one_a @ ( pCons_a @ ( uminus_uminus_a @ one_one_a ) @ zero_zero_poly_a ) ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(61,axiom,
! [A: poly_a,B: poly_a] :
( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
= ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_minus__mult__commute) ).
thf(505,plain,
! [A: poly_a,B: poly_a] :
( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
= ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(103,axiom,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_zero__reorient) ).
thf(653,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(171,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_list_Oinducts) ).
thf(922,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(254,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ A )
= zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_mult__zero__left) ).
thf(1213,plain,
! [A: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ A )
= zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(150,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( A @ E )
=> ( ( A @ ( cons_a @ D @ E ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_induct__list012) ).
thf(827,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( A @ E )
=> ( ( A @ ( cons_a @ D @ E ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(98,axiom,
( times_times_poly_a
= ( ^ [A: poly_a,B: poly_a] : ( times_times_poly_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_mult_Ocommute) ).
thf(636,plain,
( times_times_poly_a
= ( ^ [A: poly_a,B: poly_a] : ( times_times_poly_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(199,axiom,
! [A: list_a] :
( ( A != nil_a )
= ( ? [B: a,C: list_a] :
( A
= ( cons_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_neq__Nil__conv) ).
thf(1044,plain,
! [A: list_a] :
( ( A != nil_a )
= ( ? [B: a,C: list_a] :
( A
= ( cons_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(28,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_not__gr__zero) ).
thf(394,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(184,axiom,
! [A: a,B: a] :
( ( A
= ( times_times_a @ B @ A ) )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_mult__cancel__right1) ).
thf(986,plain,
! [A: a,B: a] :
( ( A
= ( times_times_a @ B @ A ) )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(154,axiom,
( ( descar1375166517sums_a @ nil_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_psums_Osimps_I1_J) ).
thf(851,plain,
( ( descar1375166517sums_a @ nil_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(218,axiom,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= nil_a )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_append__is__Nil__conv) ).
thf(1102,plain,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= nil_a )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(308,axiom,
! [A: a,B: poly_a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( descar2095969287nges_a @ ( coeffs_a @ ( smult_a @ A @ B ) ) )
= ( descar2095969287nges_a @ ( coeffs_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_coeff__sign__changes__smult) ).
thf(1413,plain,
! [A: a,B: poly_a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( descar2095969287nges_a @ ( coeffs_a @ ( smult_a @ A @ B ) ) )
= ( descar2095969287nges_a @ ( coeffs_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(56,axiom,
! [A: poly_a] :
( ( A
= ( uminus_uminus_poly_a @ A ) )
= ( A = zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_equal__neg__zero) ).
thf(490,plain,
! [A: poly_a] :
( ( A
= ( uminus_uminus_poly_a @ A ) )
= ( A = zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(278,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) )
= ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ B @ C ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_mult__less__cancel__left__disj) ).
thf(1304,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) )
= ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ B @ C ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(239,axiom,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_neg__equal__0__iff__equal) ).
thf(1166,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(55,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
& ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_mult__less__cancel2) ).
thf(487,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
& ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(145,axiom,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( ord_less_a @ B @ zero_zero_a )
=> ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_mult__pos__neg) ).
thf(812,plain,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( ord_less_a @ B @ zero_zero_a )
=> ( ord_less_a @ ( times_times_a @ A @ B ) @ zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(288,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_append__same__eq) ).
thf(1340,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(233,axiom,
! [A: list_a] :
( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ A ) )
= ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_psums__0__Cons) ).
thf(1145,plain,
! [A: list_a] :
( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ A ) )
= ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(193,axiom,
! [A: list_a] :
( ( poly_a2 @ ( append_a @ A @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= ( poly_a2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Poly__snoc__zero) ).
thf(1018,plain,
! [A: list_a] :
( ( poly_a2 @ ( append_a @ A @ ( cons_a @ zero_zero_a @ nil_a ) ) )
= ( poly_a2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(178,axiom,
! [A: a,B: a,C: poly_a] :
( ( descar466059845root_a @ A @ ( pCons_a @ B @ C ) )
= ( pCons_a @ B @ ( smult_a @ A @ ( descar466059845root_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_reduce__root__pCons) ).
thf(968,plain,
! [A: a,B: a,C: poly_a] :
( ( descar466059845root_a @ A @ ( pCons_a @ B @ C ) )
= ( pCons_a @ B @ ( smult_a @ A @ ( descar466059845root_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(244,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ zero_zero_a @ C )
=> ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(1181,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ zero_zero_a @ C )
=> ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_mult__strict__left__mono) ).
thf(580,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(236,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_strict__sorted_Ocases) ).
thf(1156,plain,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(179,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ ( times_times_poly_a @ A @ C ) )
= ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
& ( ord_less_poly_a @ B @ C ) )
| ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
& ( ord_less_poly_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_mult__less__cancel__left__disj) ).
thf(971,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ ( times_times_poly_a @ A @ C ) )
= ( ( ( ord_less_poly_a @ zero_zero_poly_a @ A )
& ( ord_less_poly_a @ B @ C ) )
| ( ( ord_less_poly_a @ A @ zero_zero_poly_a )
& ( ord_less_poly_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(6,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_less__numeral__extra_I3_J) ).
thf(327,plain,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(267,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
=> ( ord_less_poly_a @ ( times_times_poly_a @ B @ C ) @ ( times_times_poly_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_mult__strict__right__mono__neg) ).
thf(1252,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ C @ zero_zero_poly_a )
=> ( ord_less_poly_a @ ( times_times_poly_a @ B @ C ) @ ( times_times_poly_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(186,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ zero_zero_a @ C )
=> ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_mult__strict__left__mono) ).
thf(993,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ zero_zero_a @ C )
=> ( ord_less_a @ ( times_times_a @ C @ A ) @ ( times_times_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(258,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_mult__eq__0__iff) ).
thf(1225,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(303,axiom,
( is_zero_a
= ( ^ [A: poly_a] : ( null_a @ ( coeffs_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_is__zero__def) ).
thf(1400,plain,
( is_zero_a
= ( ^ [A: poly_a] : ( null_a @ ( coeffs_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(202,axiom,
! [A: a] :
( ( smult_a @ A @ one_one_poly_a )
= ( pCons_a @ A @ zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_smult__one) ).
thf(1053,plain,
! [A: a] :
( ( smult_a @ A @ one_one_poly_a )
= ( pCons_a @ A @ zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(118,axiom,
! [A: a,B: a] :
( ( times_times_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
= ( times_times_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_minus__mult__minus) ).
thf(717,plain,
! [A: a,B: a] :
( ( times_times_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
= ( times_times_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(60,axiom,
! [A: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( uminus_uminus_poly_a @ A ) )
= ( ord_less_poly_a @ A @ zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_neg__0__less__iff__less) ).
thf(502,plain,
! [A: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ ( uminus_uminus_poly_a @ A ) )
= ( ord_less_poly_a @ A @ zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(270,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_mult__poly__0__right) ).
thf(1262,plain,
! [A: poly_a] :
( ( times_times_poly_a @ A @ zero_zero_poly_a )
= zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(47,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_bot__nat__0_Oextremum__strict) ).
thf(463,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(10,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
= ( ord_less_poly_a @ ( uminus_uminus_poly_a @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_minus__less__iff) ).
thf(338,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
= ( ord_less_poly_a @ ( uminus_uminus_poly_a @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(228,axiom,
! [A: list_poly_a] :
( ( descar282223555poly_a @ ( cons_poly_a @ zero_zero_poly_a @ A ) )
= ( cons_poly_a @ zero_zero_poly_a @ ( descar282223555poly_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_psums__0__Cons) ).
thf(1130,plain,
! [A: list_poly_a] :
( ( descar282223555poly_a @ ( cons_poly_a @ zero_zero_poly_a @ A ) )
= ( cons_poly_a @ zero_zero_poly_a @ ( descar282223555poly_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(273,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
!= zero_zero_a )
=> ( ( A != zero_zero_a )
& ( B != zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_mult__not__zero) ).
thf(1285,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
!= zero_zero_a )
=> ( ( A != zero_zero_a )
& ( B != zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(213,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ! [B: list_list_a] :
( A
!= ( cons_list_a @ nil_a @ B ) )
=> ~ ! [B: a,C: list_a,D: list_list_a] :
( A
!= ( cons_list_a @ ( cons_a @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_transpose_Ocases) ).
thf(1085,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ! [B: list_list_a] :
( A
!= ( cons_list_a @ nil_a @ B ) )
=> ~ ! [B: a,C: list_a,D: list_list_a] :
( A
!= ( cons_list_a @ ( cons_a @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_mult__left__cancel) ).
thf(576,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(305,axiom,
! [A: list_a,B: poly_a] :
( ( ( poly_a2 @ A )
= B )
=> ( ( descar2095969287nges_a @ A )
= ( descar2095969287nges_a @ ( coeffs_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_sign__changes__coeff__sign__changes) ).
thf(1404,plain,
! [A: list_a,B: poly_a] :
( ( ( poly_a2 @ A )
= B )
=> ( ( descar2095969287nges_a @ A )
= ( descar2095969287nges_a @ ( coeffs_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(114,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_plus__coeffs_Oinduct) ).
thf(703,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(104,axiom,
( one_one_a
!= ( uminus_uminus_a @ one_one_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_one__neq__neg__one) ).
thf(656,plain,
( one_one_a
!= ( uminus_uminus_a @ one_one_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(292,axiom,
! [A: a,B: a] :
( ( ( uminus_uminus_a @ A )
= B )
= ( ( uminus_uminus_a @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_minus__equation__iff) ).
thf(1353,plain,
! [A: a,B: a] :
( ( ( uminus_uminus_a @ A )
= B )
= ( ( uminus_uminus_a @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(313,axiom,
( ( coeffs_a @ zero_zero_poly_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_coeffs__0__eq__Nil) ).
thf(1427,plain,
( ( coeffs_a @ zero_zero_poly_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(81,axiom,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_mult_Ocommute) ).
thf(571,plain,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(152,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ zero_zero_a @ C )
=> ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_mult__strict__right__mono) ).
thf(845,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ zero_zero_a @ C )
=> ( ord_less_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(311,axiom,
! [A: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ zero_zero_a @ A ) )
= ( descar2095969287nges_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_sign__changes__0__Cons) ).
thf(1421,plain,
! [A: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ zero_zero_a @ A ) )
= ( descar2095969287nges_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(95,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
= ( ord_less_poly_a @ B @ ( uminus_uminus_poly_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_less__minus__iff) ).
thf(627,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ A @ ( uminus_uminus_poly_a @ B ) )
= ( ord_less_poly_a @ B @ ( uminus_uminus_poly_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(109,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
=> ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(671,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ord_less_poly_a @ A @ B )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ C )
=> ( ord_less_poly_a @ ( times_times_poly_a @ C @ A ) @ ( times_times_poly_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(281,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
= ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_mult_Oassoc) ).
thf(1321,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
= ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(255,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) )
= ( times_times_poly_a @ B @ ( times_times_poly_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_mult_Oleft__commute) ).
thf(1216,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) )
= ( times_times_poly_a @ B @ ( times_times_poly_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(220,axiom,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= A )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_neg__equal__zero) ).
thf(1108,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= A )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(298,axiom,
! [A: a,B: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ A @ ( cons_a @ zero_zero_a @ B ) ) )
= ( descar2095969287nges_a @ ( cons_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_sign__changes__Cons__Cons__0) ).
thf(1385,plain,
! [A: a,B: list_a] :
( ( descar2095969287nges_a @ ( cons_a @ A @ ( cons_a @ zero_zero_a @ B ) ) )
= ( descar2095969287nges_a @ ( cons_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(65,axiom,
! [A: poly_a] :
( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ A ) )
= ( zero_zero_poly_a = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_neg__0__equal__iff__equal) ).
thf(517,plain,
! [A: poly_a] :
( ( zero_zero_poly_a
= ( uminus_uminus_poly_a @ A ) )
= ( zero_zero_poly_a = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(175,axiom,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( ord_less_a @ zero_zero_a @ B )
=> ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_mult__pos__pos) ).
thf(946,plain,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ A )
=> ( ( ord_less_a @ zero_zero_a @ B )
=> ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(137,axiom,
! [A: a] :
( ( zero_zero_a
= ( uminus_uminus_a @ A ) )
= ( zero_zero_a = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_neg__0__equal__iff__equal) ).
thf(786,plain,
! [A: a] :
( ( zero_zero_a
= ( uminus_uminus_a @ A ) )
= ( zero_zero_a = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(197,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ( A @ nil_a @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_list__induct2_H) ).
thf(1030,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ( A @ nil_a @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_mult_Oleft__commute) ).
thf(568,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(108,axiom,
! [A: list_a] :
( ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) )
=> ( A = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_min__list_Ocases) ).
thf(667,plain,
! [A: list_a] :
( ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) )
=> ( A = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(52,axiom,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ A )
= ( times_times_poly_a @ B @ B ) )
= ( ( A = B )
| ( A
= ( uminus_uminus_poly_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_square__eq__iff) ).
thf(478,plain,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ A )
= ( times_times_poly_a @ B @ B ) )
= ( ( A = B )
| ( A
= ( uminus_uminus_poly_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(229,axiom,
! [A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_a @ zero_zero_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_neg__less__0__iff__less) ).
thf(1133,plain,
! [A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_a @ zero_zero_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(188,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
=> ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_mult__pos__pos) ).
thf(999,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ( ord_less_poly_a @ zero_zero_poly_a @ B )
=> ( ord_less_poly_a @ zero_zero_poly_a @ ( times_times_poly_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_divisors__zero) ).
thf(432,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(147,axiom,
! [A: a] :
( ( times_times_a @ A @ zero_zero_a )
= zero_zero_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_mult__zero__right) ).
thf(818,plain,
! [A: a] :
( ( times_times_a @ A @ zero_zero_a )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(234,axiom,
! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( append_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( append_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_append__eq__appendI) ).
thf(1148,plain,
! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( append_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( append_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(159,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( ( times_times_poly_a @ A @ B )
= ( times_times_poly_a @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_mult__left__cancel) ).
thf(867,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( A != zero_zero_poly_a )
=> ( ( ( times_times_poly_a @ A @ B )
= ( times_times_poly_a @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(124,axiom,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= B )
= ( A = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_append__self__conv2) ).
thf(735,plain,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= B )
= ( A = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_mult__pos__neg) ).
thf(341,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(286,axiom,
! [A: a,B: list_a] :
( ( poly_a2 @ ( cons_a @ A @ B ) )
= ( pCons_a @ A @ ( poly_a2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Poly_Osimps_I2_J) ).
thf(1335,plain,
! [A: a,B: list_a] :
( ( poly_a2 @ ( cons_a @ A @ B ) )
= ( pCons_a @ A @ ( poly_a2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(241,axiom,
zero_zero_poly_a != one_one_poly_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_zero__neq__one) ).
thf(1172,plain,
zero_zero_poly_a != one_one_poly_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_mult__not__zero) ).
thf(400,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(70,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_nat__mult__1) ).
thf(532,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(119,axiom,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
= ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ zero_zero_a @ B ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ B @ zero_zero_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_zero__less__mult__iff) ).
thf(720,plain,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ ( times_times_a @ A @ B ) )
= ( ( ( ord_less_a @ zero_zero_a @ A )
& ( ord_less_a @ zero_zero_a @ B ) )
| ( ( ord_less_a @ A @ zero_zero_a )
& ( ord_less_a @ B @ zero_zero_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(290,axiom,
! [A: a] :
( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_a @ A @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_neg__0__less__iff__less) ).
thf(1346,plain,
! [A: a] :
( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_a @ A @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(140,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ A )
= zero_zero_poly_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_mult__poly__0__left) ).
thf(796,plain,
! [A: poly_a] :
( ( times_times_poly_a @ zero_zero_poly_a @ A )
= zero_zero_poly_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(203,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
= ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(1056,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( times_times_poly_a @ ( times_times_poly_a @ A @ B ) @ C )
= ( times_times_poly_a @ A @ ( times_times_poly_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(107,axiom,
! [A: poly_a,B: poly_a] :
( ( A
= ( times_times_poly_a @ A @ B ) )
= ( ( A = zero_zero_poly_a )
| ( B = one_one_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_mult__cancel__left1) ).
thf(664,plain,
! [A: poly_a,B: poly_a] :
( ( A
= ( times_times_poly_a @ A @ B ) )
= ( ( A = zero_zero_poly_a )
| ( B = one_one_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(94,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_mult__is__0) ).
thf(624,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(126,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ ( cons_a @ F @ G ) )
=> ( ( A @ ( cons_a @ D @ E ) @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_shuffles_Oinduct) ).
thf(740,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ ( cons_a @ F @ G ) )
=> ( ( A @ ( cons_a @ D @ E ) @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(262,axiom,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= B )
= ( ( B = zero_zero_poly_a )
| ( A = one_one_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_mult__cancel__right2) ).
thf(1236,plain,
! [A: poly_a,B: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= B )
= ( ( B = zero_zero_poly_a )
| ( A = one_one_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_mult__pos__neg2) ).
thf(332,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(272,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( ( C = D )
=> ( A @ ( cons_a @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_a @ D @ E ) ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_remdups__adj_Oinduct) ).
thf(1268,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( ( C = D )
=> ( A @ ( cons_a @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_a @ D @ E ) ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(35,axiom,
! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= zero_zero_poly_a )
= ( A = zero_zero_poly_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_neg__equal__0__iff__equal) ).
thf(427,plain,
! [A: poly_a] :
( ( ( uminus_uminus_poly_a @ A )
= zero_zero_poly_a )
= ( A = zero_zero_poly_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(157,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_zero__reorient) ).
thf(860,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_mult__cancel__right) ).
thf(596,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(46,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_mult__right__cancel) ).
thf(459,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(120,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ A @ one_one_poly_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_mult_Ocomm__neutral) ).
thf(723,plain,
! [A: poly_a] :
( ( times_times_poly_a @ A @ one_one_poly_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(40,axiom,
! [A: poly_a] :
( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ A )
= ( ord_less_poly_a @ zero_zero_poly_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_neg__less__pos) ).
thf(442,plain,
! [A: poly_a] :
( ( ord_less_poly_a @ ( uminus_uminus_poly_a @ A ) @ A )
= ( ord_less_poly_a @ zero_zero_poly_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(160,axiom,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
=> ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_mult__pos__neg) ).
thf(871,plain,
! [A: poly_a,B: poly_a] :
( ( ord_less_poly_a @ zero_zero_poly_a @ A )
=> ( ( ord_less_poly_a @ B @ zero_zero_poly_a )
=> ( ord_less_poly_a @ ( times_times_poly_a @ A @ B ) @ zero_zero_poly_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(20,axiom,
! [A: poly_a,B: poly_a] :
( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
= ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_mult__minus__left) ).
thf(369,plain,
! [A: poly_a,B: poly_a] :
( ( times_times_poly_a @ ( uminus_uminus_poly_a @ A ) @ B )
= ( uminus_uminus_poly_a @ ( times_times_poly_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(142,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ one_one_poly_a ) )
= ( uminus_uminus_poly_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_mult__minus1__right) ).
thf(803,plain,
! [A: poly_a] :
( ( times_times_poly_a @ A @ ( uminus_uminus_poly_a @ one_one_poly_a ) )
= ( uminus_uminus_poly_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(49,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_less__zeroE) ).
thf(469,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(245,axiom,
! [A: poly_a] :
( ( times_times_poly_a @ A @ one_one_poly_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_mult_Oright__neutral) ).
thf(1184,plain,
! [A: poly_a] :
( ( times_times_poly_a @ A @ one_one_poly_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(105,axiom,
! [A: a,B: a,C: poly_a] :
( ( smult_a @ A @ ( pCons_a @ B @ C ) )
= ( pCons_a @ ( times_times_a @ A @ B ) @ ( smult_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_smult__pCons) ).
thf(659,plain,
! [A: a,B: a,C: poly_a] :
( ( smult_a @ A @ ( pCons_a @ B @ C ) )
= ( pCons_a @ ( times_times_a @ A @ B ) @ ( smult_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(74,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_infinite__descent) ).
thf(543,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(134,axiom,
! [A: ( a > a ) > list_a > list_a > $o,B: a > a,C: list_a,D: list_a] :
( ! [E: a > a,F: list_a] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > a,F: a,G: list_a,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_map__tailrec__rev_Oinduct) ).
thf(775,plain,
! [A: ( a > a ) > list_a > list_a > $o,B: a > a,C: list_a,D: list_a] :
( ! [E: a > a,F: list_a] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > a,F: a,G: list_a,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(18,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_mult_Oassoc) ).
thf(364,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(115,axiom,
! [A: list_nat] :
( ( poly_nat2 @ ( append_nat @ A @ ( cons_nat @ zero_zero_nat @ nil_nat ) ) )
= ( poly_nat2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Poly__snoc__zero) ).
thf(708,plain,
! [A: list_nat] :
( ( poly_nat2 @ ( append_nat @ A @ ( cons_nat @ zero_zero_nat @ nil_nat ) ) )
= ( poly_nat2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(309,axiom,
( ys
= ( descar1375166517sums_a @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ys) ).
thf(1417,plain,
( ys
= ( descar1375166517sums_a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(58,axiom,
! [A: nat,B: nat,C: poly_nat] :
( ( smult_nat @ A @ ( smult_nat @ B @ C ) )
= ( smult_nat @ ( times_times_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_smult__smult) ).
thf(496,plain,
! [A: nat,B: nat,C: poly_nat] :
( ( smult_nat @ A @ ( smult_nat @ B @ C ) )
= ( smult_nat @ ( times_times_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(207,axiom,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= ( times_times_poly_a @ C @ B ) )
= ( ( B = zero_zero_poly_a )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_mult__cancel__right) ).
thf(1069,plain,
! [A: poly_a,B: poly_a,C: poly_a] :
( ( ( times_times_poly_a @ A @ B )
= ( times_times_poly_a @ C @ B ) )
= ( ( B = zero_zero_poly_a )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1440,plain,
$false,
inference(e,[status(thm)],[892,809,1411,1024,1190,1105,347,1083,941,555,481,523,1073,1142,511,677,1041,408,977,384,1310,472,1233,1327,1063,1222,1095,1196,898,1243,1391,885,1359,1265,1228,565,1366,1298,372,344,357,1059,949,559,1398,448,316,638,853,475,789,321,646,1136,514,806,353,821,602,692,1119,1394,411,1433,1169,397,1072,453,1206,380,439,529,793,1199,1338,1153,761,1047,1163,746,1343,1021,1255,424,630,815,729,484,361,435,1296,583,889,1128,1012,329,1178,493,1210,1079,1027,456,842,324,974,1402,1089,874,1259,650,1111,980,593,499,989,857,783,420,1329,1160,1361,933,753,537,1424,526,590,1419,901,1075,1099,1249,738,1231,1192,1050,1002,1429,1246,1324,1114,1202,938,633,508,586,662,1187,674,906,430,1301,573,375,965,750,1219,824,1007,732,1125,772,1388,711,562,904,641,445,713,1239,1332,335,919,1356,350,540,391,1139,466,1092,1408,1117,1349,451,318,1122,599,1307,764,604,377,996,863,1175,387,535,621,895,769,1293,367,552,799,726,848,700,520,983,1066,780,1015,1364,505,653,922,1213,827,636,1044,394,986,851,1102,1413,490,1304,1166,487,812,1340,1145,1018,968,1181,580,1156,971,327,1252,993,1225,1400,1053,717,502,1262,463,338,1130,1285,1085,576,1404,703,656,1353,1427,571,845,1421,627,671,1321,1216,1108,1385,517,946,786,1030,568,667,478,1133,999,432,818,1148,867,735,341,1335,1172,400,532,720,1346,796,1056,664,624,740,1236,332,1268,427,860,596,459,723,442,871,369,803,469,1184,659,543,775,364,708,1417,496,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP044^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n013.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:40:06 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.06/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.31/1.25 % [INFO] Parsing done (446ms).
% 2.31/1.27 % [INFO] Running in sequential loop mode.
% 3.57/1.66 % [INFO] eprover registered as external prover.
% 3.57/1.66 % [INFO] Scanning for conjecture ...
% 4.01/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 346 axioms. Running axiom selection ...
% 4.28/1.96 % [INFO] Axiom selection finished. Selected 313 axioms (removed 33 axioms).
% 5.26/2.22 % [INFO] Problem is higher-order (TPTP THF).
% 5.26/2.25 % [INFO] Type checking passed.
% 5.26/2.25 % [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 ...
% 14.98/4.54 % External prover 'e' found a proof!
% 14.98/4.54 % [INFO] Killing All external provers ...
% 14.98/4.54 % Time passed: 4186ms (effective reasoning time: 3268ms)
% 14.98/4.54 % 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)>
% 14.98/4.55 % Axioms used in derivation (313): fact_236_square__eq__iff, fact_272_mult__strict__right__mono, fact_249_min__list_Ocases, fact_211_divisors__zero, fact_100_mult__minus1__right, fact_289_zero__less__mult__pos2, fact_230_minus__less__iff, fact_187_one__reorient, fact_135_mult__zero__right, fact_119_list_Oinject, fact_188_minus__equation__iff, fact_197_not__less__zero, fact_214_mult__not__zero, fact_338_bot__nat__0_Oextremum__strict, fact_266_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_231_less__minus__iff, fact_160_minus__mult__minus, fact_128_mult__cancel__left, fact_134_mult__zero__right, fact_210_no__zero__divisors, fact_276_mult__less__cancel__left__disj, fact_271_mult__strict__right__mono, fact_308_mult__less__0__iff, fact_213_divisors__zero, fact_344_nat__mult__eq__cancel__disj, fact_316_mult__is__0, fact_186_one__reorient, fact_290_zero__less__mult__pos, fact_172_smult__one, fact_195_zero__less__iff__neq__zero, fact_336_gr__implies__not0, fact_89_psums_Ocases, fact_15_sign__changes__Nil, fact_82_mult__poly__0__left, fact_101_less__neg__neg, fact_178_mult_Oleft__commute, fact_16_xs__def, fact_44_smult__0__left, fact_38_pCons__eq__0__iff, fact_1_nz, fact_190_not__Cons__self2, fact_117_neg__equal__iff__equal, fact_291_zero__less__mult__pos, fact_162_mult__minus__left, fact_102_less__neg__neg, fact_136_mult__zero__right, fact_255_list_Oexhaust, fact_182_mult_Oassoc, fact_131_mult__eq__0__iff, fact_99_mult__minus1__right, fact_294_zero__less__mult__iff, fact_83_mult__poly__0__right, fact_260_append_Oleft__neutral, fact_164_append_Oright__neutral, fact_19_sign__changes__0__Cons, fact_118_add_Oinverse__inverse, fact_314_less__nat__zero__code, fact_311_mult__less__cancel2, fact_113_mult__cancel__right1, fact_279_mult__strict__left__mono, fact_138_mult__zero__left, fact_321_less__one, fact_143_equal__neg__zero, fact_324_linorder__neqE__nat, fact_286_mult__less__cancel__left__neg, fact_125_mult__cancel__right, fact_301_mult__pos__neg, fact_198_gr__zeroI, fact_185_ab__semigroup__mult__class_Omult__ac_I1_J, fact_144_neg__equal__0__iff__equal, fact_153_mult_Oleft__neutral, fact_313_neq0__conv, fact_310_nat__0__less__mult__iff, fact_66_Poly__snoc__zero, fact_169_self__append__conv, fact_115_mult__cancel__right2, fact_90_reduce__root__pCons, fact_191_append__eq__append__conv2, fact_343_nat__mult__less__cancel1, fact_299_mult__pos__pos, fact_137_mult__zero__left, fact_242_successively_Oinduct, fact_0_v__def, fact_239_strict__sorted_Ocases, fact_123_append_Oassoc, fact_206_mult__left__cancel, fact_251_splice_Oinduct, fact_235_square__eq__iff, fact_133_mult__eq__0__iff, fact_60_coeffs__1__eq, fact_68_Poly_Osimps_I2_J, fact_140_neg__equal__zero, fact_40_one__poly__eq__simps_I2_J, fact_273_mult__strict__right__mono, fact_84_plus__coeffs_Oinduct, fact_218_zero__neq__one, fact_345_mult__eq__self__implies__10, fact_241_list__nonempty__induct, fact_209_no__zero__divisors, fact_26_smult__smult, fact_227_comm__monoid__mult__class_Omult__1, fact_116_mult__cancel__right2, fact_62_sign__changes__singleton, fact_253_neq__Nil__conv, fact_154_mult_Oleft__neutral, fact_212_divisors__zero, fact_58_psums__0__Cons, fact_223_mult_Ocomm__neutral, fact_226_comm__monoid__mult__class_Omult__1, fact_305_mult__neg__pos, fact_120_same__append__eq, fact_296_mult__pos__neg2, fact_246_transpose_Ocases, fact_109_mult__cancel__left1, fact_220_less__numeral__extra_I4_J, fact_340_mult__less__mono2, fact_250_induct__list012, fact_293_zero__less__mult__iff, fact_342_nat__mult__eq__cancel1, fact_189_equation__minus__iff, fact_24_minus__pCons, fact_158_mult__minus__right, fact_157_neg__less__iff__less, fact_70_psums_Osimps_I2_J, fact_127_mult__cancel__right, fact_282_mult__strict__left__mono__neg, fact_274_mult__strict__right__mono__neg, fact_114_mult__cancel__right1, fact_121_append__same__eq, fact_183_mult_Oassoc, fact_20_sign__changes__0__Cons, fact_295_mult__pos__neg2, fact_150_mult_Oright__neutral, fact_284_mult__less__cancel__left__pos, fact_184_ab__semigroup__mult__class_Omult__ac_I1_J, fact_175_zero__reorient, fact_257_list_Odistinct_I1_J, fact_146_neg__0__equal__iff__equal, fact_67_Poly__snoc__zero, fact_252_list__induct2_H, fact_339_mult__less__mono1, fact_192_append__eq__appendI, fact_278_mult__strict__left__mono, fact_23_pCons__eq__iff, fact_285_mult__less__cancel__left__neg, fact_7_ys__def, fact_329_less__not__refl2, fact_27_smult__1__left, fact_244_sorted__wrt_Oinduct, fact_171_append__Nil2, fact_268_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_275_mult__strict__right__mono__neg, fact_196_gr__implies__not__zero, fact_205_mult__left__cancel, fact_270_mult__less__cancel__right__disj, fact_309_nat__mult__less__cancel__disj, fact_108_neg__less__0__iff__less, fact_323_nat__mult__1__right, fact_203_mult__right__cancel, fact_149_add_Oinverse__neutral, fact_31_mult__smult__left, fact_221_less__numeral__extra_I4_J, fact_328_less__not__refl3, fact_74_pCons__cases, fact_269_mult__less__cancel__right__disj, fact_287_zero__less__mult__pos2, fact_124_not__gr__zero, fact_215_mult__not__zero, fact_267_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_64__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062, fact_238_strict__sorted_Oinduct, fact_96_append1__eq__conv, fact_80_poly__induct2, fact_166_Nil__is__append__conv, fact_232_less__minus__iff, fact_48_smult__eq__0__iff, fact_303_mult__pos__neg, fact_208_no__zero__divisors, fact_298_mult__pos__pos, fact_245_remdups__adj_Ocases, fact_281_mult__strict__left__mono__neg, fact_170_append__self__conv, fact_142_equal__neg__zero, fact_132_mult__eq__0__iff, fact_92_reduce__root__nonzero, fact_177_linorder__neqE__linordered__idom, fact_265_null__rec_I2_J, fact_73_pCons__one, fact_180_mult_Ocommute, fact_300_mult__pos__pos, fact_103_neg__less__pos, fact_57_psums__0__Cons, fact_4_ys, fact_207_mult__left__cancel, fact_174_zero__reorient, fact_240_map__tailrec__rev_Oinduct, fact_111_mult__cancel__left2, fact_264_eq__Nil__null, fact_176_linorder__neqE__linordered__idom, fact_71_psums_Osimps_I1_J, fact_122_append__assoc, fact_315_bot__nat__0_Onot__eq__extremum, fact_318_mult__cancel1, fact_79_pderiv_Ocases, fact_56_psums__0__Cons, fact_317_mult__0__right, fact_151_mult_Oright__neutral, fact_216_mult__not__zero, fact_130_mult__cancel__left, fact_217_zero__neq__one, fact_341_mult__0, fact_330_less__not__refl, fact_53_coeffs__eq__Nil, fact_17_coeff__sign__changes__smult, fact_75_is__zero__null, fact_320_nat__mult__eq__1__iff, fact_55_coeffs__0__eq__Nil, fact_49_smult__pCons, fact_155_mult_Oleft__neutral, fact_98_mult__minus1, fact_3_coeffs__eq__iff, fact_248_min__list_Oinduct, fact_139_mult__zero__left, fact_337_infinite__descent0, fact_104_neg__less__pos, fact_319_nat__1__eq__mult__iff, fact_193_sign__changes__two, fact_147_neg__0__equal__iff__equal, fact_335_less__zeroE, fact_42_one__poly__eq__simps_I1_J, fact_165_append__is__Nil__conv, fact_30_smult__0__right, fact_129_mult__cancel__left, fact_228_comm__monoid__mult__class_Omult__1, fact_280_mult__strict__left__mono, fact_302_mult__pos__neg, fact_156_neg__less__iff__less, fact_148_add_Oinverse__neutral, fact_333_not__gr0, fact_107_neg__less__0__iff__less, fact_161_minus__mult__minus, fact_288_zero__less__mult__pos2, fact_327_less__irrefl__nat, fact_97_mult__minus1, fact_163_mult__minus__left, fact_202_mult__right__cancel, fact_32_mult__smult__right, fact_200_less__numeral__extra_I3_J, fact_6_sign__changes__coeff__sign__changes, fact_256_list_OdiscI, fact_29_smult__minus__left, fact_234_minus__mult__commute, fact_261_append__Nil, fact_225_mult_Ocomm__neutral, fact_332_gr0I, fact_277_mult__less__cancel__left__disj, fact_258_append__Cons, fact_233_minus__mult__commute, fact_13_Poly__coeffs, fact_159_mult__minus__right, fact_322_nat__mult__1, fact_307_mult__less__0__iff, fact_167_self__append__conv2, fact_259_Cons__eq__appendI, fact_243_remdups__adj_Oinduct, fact_145_neg__equal__0__iff__equal, fact_224_mult_Ocomm__neutral, fact_306_mult__neg__pos, fact_297_mult__pos__neg2, fact_9_coeff__sign__changes__reduce__root, fact_152_mult_Oright__neutral, fact_28_smult__1__left, fact_247_shuffles_Oinduct, fact_201_less__numeral__extra_I3_J, fact_181_mult_Ocommute, fact_292_zero__less__mult__pos, fact_263_null__rec_I1_J, fact_34_pCons__0__0, fact_94_sign__changes__Cons__Cons__same, fact_204_mult__right__cancel, fact_262_eq__Nil__appendI, fact_88_synthetic__div__unique__lemma, fact_106_neg__0__less__iff__less, fact_22_sign__changes__Cons__Cons__0, fact_11_is__zero__def, fact_219_zero__neq__one, fact_312_mult__cancel2, fact_21_sign__changes__Cons__Cons__0, fact_254_list_Oinducts, fact_105_neg__0__less__iff__less, fact_331_nat__neq__iff, fact_78_pCons__induct, fact_86_not__0__coeffs__not__Nil, fact_237_one__neq__neg__one, fact_199_less__numeral__extra_I3_J, fact_326_nat__less__induct, fact_179_mult_Oleft__commute, fact_229_minus__less__iff, fact_126_mult__cancel__right, fact_222_less__numeral__extra_I4_J, fact_81_pderiv_Oinduct, fact_141_neg__equal__zero, fact_95_sign__changes__Cons__Cons__same, fact_110_mult__cancel__left1, fact_87_minus__poly__rev__list_Oinduct, fact_304_mult__neg__pos, fact_69_Poly_Osimps_I1_J, fact_325_infinite__descent, fact_112_mult__cancel__left2, fact_283_mult__less__cancel__left__pos, fact_173_zero__reorient, fact_168_append__self__conv2, fact_334_not__less0
% 14.98/4.55 % No. of inferences in proof: 630
% 14.98/4.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4186 ms resp. 3268 ms w/o parsing
% 16.16/4.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.16/4.78 % [INFO] Killing All external provers ...
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