%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP150^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 08:06:57 AM UTC 2026
% Result : Theorem 30.07s 7.42s
% Output : Refutation 29.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 285
% Syntax : Number of formulae : 572 ( 213 unt; 0 typ; 0 def)
% Number of atoms : 1625 ( 715 equ; 2 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 6727 ( 88 ~; 29 |; 332 &;5774 @)
% ( 0 <=>; 504 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 10 con; 0-6 aty)
% Number of variables : 1669 ( 66 ^;1581 !; 22 ?;1669 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(type_decl,type,
type:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(plus_decl,type,
plus:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[TA: $tType] : $o ).
thf(field_decl,type,
field:
!>[TA: $tType] : $o ).
thf(minus_decl,type,
minus:
!>[TA: $tType] : $o ).
thf(times_decl,type,
times:
!>[TA: $tType] : $o ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : $o ).
thf(uminus_decl,type,
uminus:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(comm_ring_1_decl,type,
comm_ring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(field_char_0_decl,type,
field_char_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_decl,type,
comm_semiring:
!>[TA: $tType] : $o ).
thf(semigroup_add_decl,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(semigroup_mult_decl,type,
semigroup_mult:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_decl,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(polyno1549699593char_0_decl,type,
polyno1549699593char_0:
!>[TA: $tType] : $o ).
thf(linord581940658strict_decl,type,
linord581940658strict:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(semiri1193490041visors_decl,type,
semiri1193490041visors:
!>[TA: $tType] : $o ).
thf(semiri1923998003cancel_decl,type,
semiri1923998003cancel:
!>[TA: $tType] : $o ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(compow_decl,type,
compow:
!>[TA: $tType] : ( nat > TA > TA ) ).
thf(funpow_decl,type,
funpow:
!>[TA: $tType] : ( nat > ( TA > TA ) > TA > TA ) ).
thf(polyno1341257465_Ipoly_decl,type,
polyno1341257465_Ipoly:
!>[TA: $tType] : ( ( list @ TA ) > ( polyno1783536151e_poly @ TA ) > TA ) ).
thf(polyno427297311behead_decl,type,
polyno427297311behead:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno498386536degree_decl,type,
polyno498386536degree:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > nat ) ).
thf(polyno367318022egreen_decl,type,
polyno367318022egreen:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > nat > nat ) ).
thf(polyno545456796e_head_decl,type,
polyno545456796e_head:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno646301383dconst_decl,type,
polyno646301383dconst:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > TA ) ).
thf(polyno47817938_headn_decl,type,
polyno47817938_headn:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > nat > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno2122670676snpoly_decl,type,
polyno2122670676snpoly:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > $o ) ).
thf(polyno86455060npolyh_decl,type,
polyno86455060npolyh:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > nat > $o ) ).
thf(polyno750620841le_Add_decl,type,
polyno750620841le_Add:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno649217638_Bound_decl,type,
polyno649217638_Bound:
!>[TA: $tType] : ( nat > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno333904939elle_C_decl,type,
polyno333904939elle_C:
!>[TA: $tType] : ( TA > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno1644367587lle_CN_decl,type,
polyno1644367587lle_CN:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > nat > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno850874092le_Mul_decl,type,
polyno850874092le_Mul:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno858086008le_Neg_decl,type,
polyno858086008le_Neg:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno1645220415lle_Pw_decl,type,
polyno1645220415lle_Pw:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > nat > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno900443112le_Sub_decl,type,
polyno900443112le_Sub:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno75289385y_cmul_decl,type,
polyno75289385y_cmul:
!>[TA: $tType] : ( TA > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno1008312662_deriv_decl,type,
polyno1008312662_deriv:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno1211105166iv_aux_decl,type,
polyno1211105166iv_aux:
!>[TA: $tType] : ( TA > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno210676577divide_decl,type,
polyno210676577divide:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) > ( product_prod @ nat @ ( polyno1783536151e_poly @ TA ) ) ) ).
thf(polyno430940995de_aux_decl,type,
polyno430940995de_aux:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > nat > ( polyno1783536151e_poly @ TA ) > nat > ( polyno1783536151e_poly @ TA ) > ( product_prod @ nat @ ( polyno1783536151e_poly @ TA ) ) ) ).
thf(polyno452058812olymul_decl,type,
polyno452058812olymul:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno620195148lynate_decl,type,
polyno620195148lynate:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno476449744olypow_decl,type,
polyno476449744olypow:
!>[TA: $tType] : ( nat > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno501627832olysub_decl,type,
polyno501627832olysub:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno1789993463subst0_decl,type,
polyno1789993463subst0:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno222789899shift1_decl,type,
polyno222789899shift1:
!>[TA: $tType] : ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) ).
thf(polyno156741596_wf_bs_decl,type,
polyno156741596_wf_bs:
!>[TA: $tType] : ( ( list @ TA ) > ( polyno1783536151e_poly @ TA ) > $o ) ).
thf(n0_decl,type,
n0: nat ).
thf(n1_decl,type,
n1: nat ).
thf(p_decl,type,
p: polyno1783536151e_poly @ a ).
thf(q_decl,type,
q: polyno1783536151e_poly @ a ).
thf(137,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_mult__right__cancel) ).
thf(645,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(258,axiom,
polyno86455060npolyh @ a @ q @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_nq) ).
thf(1036,plain,
polyno86455060npolyh @ a @ q @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(179,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_no__zero__divisors) ).
thf(809,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_nat__mult__eq__1__iff) ).
thf(629,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)],[131]) ).
thf(192,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( polyno750620841le_Add @ TA @ A @ B )
!= ( polyno850874092le_Mul @ TA @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_poly_Odistinct_I29_J) ).
thf(846,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( polyno750620841le_Add @ TA @ A @ B )
!= ( polyno850874092le_Mul @ TA @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(208,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_comm__monoid__mult__class_Omult__1) ).
thf(893,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(93,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ring_1 @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Oring__1) ).
thf(518,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ring_1 @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(75,axiom,
! [TA: $tType,A: nat] :
( ( polyno47817938_headn @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( ^ [B: nat] : ( polyno649217638_Bound @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_headn_Osimps_I3_J) ).
thf(468,plain,
! [TA: $tType,A: nat] :
( ( polyno47817938_headn @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( ^ [B: nat] : ( polyno649217638_Bound @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(225,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( polyno427297311behead @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_behead_Osimps_I2_J) ).
thf(941,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( polyno427297311behead @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(145,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_nat__mult__1__right) ).
thf(666,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(282,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno1645220415lle_Pw @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_poly__cmul_Osimps_I8_J) ).
thf(1110,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno1645220415lle_Pw @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(214,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_poly__deriv__aux_Osimps_I4_J) ).
thf(909,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(24,axiom,
comm_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring) ).
thf(333,plain,
comm_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_add__mult__distrib) ).
thf(481,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(32,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno367318022egreen @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( ^ [C: nat] : ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_degreen_Osimps_I8_J) ).
thf(352,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno367318022egreen @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( ^ [C: nat] : ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(52,axiom,
times @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Otimes) ).
thf(408,plain,
times @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(95,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= A )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mult__cancel__left2) ).
thf(523,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= A )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(270,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno900443112le_Sub @ TA @ A @ B ) @ C )
= ( polyno850874092le_Mul @ TA @ ( polyno900443112le_Sub @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_polymul_Osimps_I7_J) ).
thf(1073,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno900443112le_Sub @ TA @ A @ B ) @ C )
= ( polyno850874092le_Mul @ TA @ ( polyno900443112le_Sub @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(201,axiom,
! [TA: $tType,A: nat,B: nat] :
( ( ( polyno649217638_Bound @ TA @ A )
= ( polyno649217638_Bound @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_poly_Oinject_I2_J) ).
thf(873,plain,
! [TA: $tType,A: nat,B: nat] :
( ( ( polyno649217638_Bound @ TA @ A )
= ( polyno649217638_Bound @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(42,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno498386536degree @ TA @ ( polyno1644367587lle_CN @ TA @ A @ ( zero_zero @ nat ) @ B ) )
= ( plus_plus @ nat @ ( one_one @ nat ) @ ( polyno498386536degree @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_degree_Osimps_I1_J) ).
thf(379,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno498386536degree @ TA @ ( polyno1644367587lle_CN @ TA @ A @ ( zero_zero @ nat ) @ B ) )
= ( plus_plus @ nat @ ( one_one @ nat ) @ ( polyno498386536degree @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(127,axiom,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( polyno1789993463subst0 @ TA @ B @ ( polyno1644367587lle_CN @ TA @ C @ A @ D ) )
= ( polyno750620841le_Add @ TA @ ( polyno1789993463subst0 @ TA @ B @ C ) @ ( polyno850874092le_Mul @ TA @ B @ ( polyno1789993463subst0 @ TA @ B @ D ) ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( polyno1789993463subst0 @ TA @ B @ ( polyno1644367587lle_CN @ TA @ C @ A @ D ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno1789993463subst0 @ TA @ B @ C ) @ A @ ( polyno1789993463subst0 @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_polysubst0_Osimps_I8_J) ).
thf(614,plain,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( polyno1789993463subst0 @ TA @ B @ ( polyno1644367587lle_CN @ TA @ C @ A @ D ) )
= ( polyno750620841le_Add @ TA @ ( polyno1789993463subst0 @ TA @ B @ C ) @ ( polyno850874092le_Mul @ TA @ B @ ( polyno1789993463subst0 @ TA @ B @ D ) ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( polyno1789993463subst0 @ TA @ B @ ( polyno1644367587lle_CN @ TA @ C @ A @ D ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno1789993463subst0 @ TA @ B @ C ) @ A @ ( polyno1789993463subst0 @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(197,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ( ( polyno210676577divide @ TA )
= ( ^ [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] : ( polyno430940995de_aux @ TA @ ( polyno545456796e_head @ TA @ B ) @ ( polyno498386536degree @ TA @ B ) @ B @ ( zero_zero @ nat ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_polydivide__def) ).
thf(861,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ( ( polyno210676577divide @ TA )
= ( ^ [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] : ( polyno430940995de_aux @ TA @ ( polyno545456796e_head @ TA @ B ) @ ( polyno498386536degree @ TA @ B ) @ B @ ( zero_zero @ nat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(64,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno367318022egreen @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( ^ [C: nat] : ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_degreen_Osimps_I4_J) ).
thf(440,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno367318022egreen @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( ^ [C: nat] : ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(141,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_poly__deriv__aux_Osimps_I6_J) ).
thf(655,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(44,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno367318022egreen @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( ^ [C: nat] : ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_degreen_Osimps_I6_J) ).
thf(384,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno367318022egreen @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( ^ [C: nat] : ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(163,axiom,
! [TA: $tType] :
( ( funpow @ TA )
= ( compow @ ( TA > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_funpow__code__def) ).
thf(715,plain,
! [TA: $tType] :
( ( funpow @ TA )
= ( compow @ ( TA > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(27,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1789993463subst0 @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1789993463subst0 @ TA @ A @ B ) @ ( polyno1789993463subst0 @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_polysubst0_Osimps_I6_J) ).
thf(340,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1789993463subst0 @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1789993463subst0 @ TA @ A @ B ) @ ( polyno1789993463subst0 @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(170,axiom,
! [TA: $tType] :
( ( ( minus @ TA )
& ( plus @ TA )
& ( uminus @ TA )
& ( zero @ TA )
& ( power @ TA ) )
=> ! [A: list @ TA,B: TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Ipoly_Osimps_I1_J) ).
thf(782,plain,
! [TA: $tType] :
( ( ( minus @ TA )
& ( plus @ TA )
& ( uminus @ TA )
& ( zero @ TA )
& ( power @ TA ) )
=> ! [A: list @ TA,B: TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(161,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_zero__reorient) ).
thf(709,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(190,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ab_semigroup_add @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Oab__semigroup__add) ).
thf(841,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ab_semigroup_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(9,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno2122670676snpoly @ TA @ A )
=> ( ( polyno2122670676snpoly @ TA @ B )
=> ( polyno2122670676snpoly @ TA @ ( polyno501627832olysub @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_polysub__norm) ).
thf(301,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno2122670676snpoly @ TA @ A )
=> ( ( polyno2122670676snpoly @ TA @ B )
=> ( polyno2122670676snpoly @ TA @ ( polyno501627832olysub @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(139,axiom,
uminus @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_2) ).
thf(651,plain,
uminus @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(237,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ ( times_times @ TA @ A @ A ) @ ( times_times @ TA @ B @ B ) )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_sum__squares__eq__zero__iff) ).
thf(973,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ ( times_times @ TA @ A @ A ) @ ( times_times @ TA @ B @ B ) )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(205,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( comm_semiring @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Ocomm__semiring) ).
thf(885,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( comm_semiring @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(17,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno367318022egreen @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) )
= ( ^ [D: nat] : ( if @ nat @ ( B = D ) @ ( plus_plus @ nat @ ( one_one @ nat ) @ ( polyno367318022egreen @ TA @ C @ B ) ) @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_degreen_Osimps_I1_J) ).
thf(320,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno367318022egreen @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) )
= ( ^ [D: nat] : ( if @ nat @ ( B = D ) @ ( plus_plus @ nat @ ( one_one @ nat ) @ ( polyno367318022egreen @ TA @ C @ B ) ) @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(110,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno86455060npolyh @ TA @ C @ D )
=> ( ( ( polyno501627832olysub @ TA @ A @ C )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( A = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_polysub__0) ).
thf(565,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno86455060npolyh @ TA @ C @ D )
=> ( ( ( polyno501627832olysub @ TA @ A @ C )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(264,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno858086008le_Neg @ TA @ B ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno858086008le_Neg @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_poly__cmul_Osimps_I7_J) ).
thf(1055,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno858086008le_Neg @ TA @ B ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno858086008le_Neg @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(171,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno850874092le_Mul @ TA @ A @ B )
!= ( polyno1645220415lle_Pw @ TA @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_poly_Odistinct_I47_J) ).
thf(785,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno850874092le_Mul @ TA @ A @ B )
!= ( polyno1645220415lle_Pw @ TA @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(88,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( field @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Fields_Ofield) ).
thf(504,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( field @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(189,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_mult__left__cancel) ).
thf(838,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(228,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat,B: ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ),C: polyno1783536151e_poly @ TA,D: nat] :
( ! [E: polyno1783536151e_poly @ TA] :
( ( polyno86455060npolyh @ TA @ E @ A )
=> ( polyno86455060npolyh @ TA @ ( B @ E ) @ A ) )
=> ( ( polyno86455060npolyh @ TA @ C @ A )
=> ( polyno86455060npolyh @ TA @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_funpow__isnpolyh) ).
thf(949,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat,B: ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ),C: polyno1783536151e_poly @ TA,D: nat] :
( ! [E: polyno1783536151e_poly @ TA] :
( ( polyno86455060npolyh @ TA @ E @ A )
=> ( polyno86455060npolyh @ TA @ ( B @ E ) @ A ) )
=> ( ( polyno86455060npolyh @ TA @ C @ A )
=> ( polyno86455060npolyh @ TA @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ D @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(102,axiom,
! [TA: $tType] :
( ( semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_mult_Oassoc) ).
thf(542,plain,
! [TA: $tType] :
( ( semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(211,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( one @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Oone) ).
thf(902,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( one @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(274,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_polymul_Osimps_I26_J) ).
thf(1087,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(200,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( ( polyno1645220415lle_Pw @ TA @ A @ B )
= ( polyno1645220415lle_Pw @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_poly_Oinject_I7_J) ).
thf(870,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( ( polyno1645220415lle_Pw @ TA @ A @ B )
= ( polyno1645220415lle_Pw @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(124,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno156741596_wf_bs @ TA @ A @ B )
=> ( ( polyno156741596_wf_bs @ TA @ A @ C )
=> ( polyno156741596_wf_bs @ TA @ A @ ( polyno501627832olysub @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_wf__bs__polysub) ).
thf(606,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno156741596_wf_bs @ TA @ A @ B )
=> ( ( polyno156741596_wf_bs @ TA @ A @ C )
=> ( polyno156741596_wf_bs @ TA @ A @ ( polyno501627832olysub @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(54,axiom,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ D ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_combine__common__factor) ).
thf(416,plain,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ D ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(3,axiom,
semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring) ).
thf(289,plain,
semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(65,axiom,
semigroup_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult) ).
thf(443,plain,
semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(260,axiom,
( ( ! [A: list @ a] :
( ( polyno1341257465_Ipoly @ a @ A @ ( polyno452058812olymul @ a @ p @ q ) )
= ( polyno1341257465_Ipoly @ a @ A @ ( polyno452058812olymul @ a @ q @ p ) ) ) )
= ( ( polyno452058812olymul @ a @ p @ q )
= ( polyno452058812olymul @ a @ q @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062) ).
thf(1040,plain,
( ( ! [A: list @ a] :
( ( polyno1341257465_Ipoly @ a @ A @ ( polyno452058812olymul @ a @ p @ q ) )
= ( polyno1341257465_Ipoly @ a @ A @ ( polyno452058812olymul @ a @ q @ p ) ) ) )
= ( ( polyno452058812olymul @ a @ p @ q )
= ( polyno452058812olymul @ a @ q @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(41,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_add_Oassoc) ).
thf(376,plain,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(129,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno501627832olysub @ TA @ A @ A )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_polysub__same__0) ).
thf(623,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno501627832olysub @ TA @ A @ A )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(178,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_mult_Ocommute) ).
thf(806,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(234,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( polyno86455060npolyh @ TA @ ( polyno427297311behead @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_behead__isnpolyh) ).
thf(966,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( polyno86455060npolyh @ TA @ ( polyno427297311behead @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(183,axiom,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno649217638_Bound @ TA @ A )
!= ( polyno750620841le_Add @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_poly_Odistinct_I15_J) ).
thf(821,plain,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno649217638_Bound @ TA @ A )
!= ( polyno750620841le_Add @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(252,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( polyno850874092le_Mul @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_polymul_Osimps_I20_J) ).
thf(1020,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( polyno850874092le_Mul @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(113,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ D )
=> ( ( polyno367318022egreen @ TA @ A @ B )
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_degreen__npolyhCN) ).
thf(574,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ D )
=> ( ( polyno367318022egreen @ TA @ A @ B )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(240,axiom,
! [TA: $tType] :
( ( ( minus @ TA )
& ( plus @ TA )
& ( uminus @ TA )
& ( zero @ TA )
& ( power @ TA ) )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( times_times @ TA @ ( polyno1341257465_Ipoly @ TA @ A @ B ) @ ( polyno1341257465_Ipoly @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Ipoly_Osimps_I6_J) ).
thf(981,plain,
! [TA: $tType] :
( ( ( minus @ TA )
& ( plus @ TA )
& ( uminus @ TA )
& ( zero @ TA )
& ( power @ TA ) )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( times_times @ TA @ ( polyno1341257465_Ipoly @ TA @ A @ B ) @ ( polyno1341257465_Ipoly @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(133,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( polyno222789899shift1 @ TA )
= ( polyno1644367587lle_CN @ TA @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_shift1__def) ).
thf(634,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( polyno222789899shift1 @ TA )
= ( polyno1644367587lle_CN @ TA @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(285,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA,E: nat] :
( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno1645220415lle_Pw @ TA @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno1645220415lle_Pw @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_polymul_Osimps_I16_J) ).
thf(1119,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA,E: nat] :
( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno1645220415lle_Pw @ TA @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno1645220415lle_Pw @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(48,axiom,
! [TA: $tType,A: TA > TA > $o] :
( ( compow @ ( TA > TA > $o ) @ ( zero_zero @ nat ) @ A )
= ( (=) @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_relpowp_Osimps_I1_J) ).
thf(396,plain,
! [TA: $tType,A: TA > TA > $o] :
( ( compow @ ( TA > TA > $o ) @ ( zero_zero @ nat ) @ A )
= ( (=) @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(13,axiom,
! [TA: $tType] :
( ( comm_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_comm__semiring__class_Odistrib) ).
thf(312,plain,
! [TA: $tType] :
( ( comm_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno545456796e_head @ TA @ ( polyno1644367587lle_CN @ TA @ A @ ( zero_zero @ nat ) @ B ) )
= ( polyno545456796e_head @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_head_Osimps_I1_J) ).
thf(293,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno545456796e_head @ TA @ ( polyno1644367587lle_CN @ TA @ A @ ( zero_zero @ nat ) @ B ) )
= ( polyno545456796e_head @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(230,axiom,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( polyno649217638_Bound @ TA @ A )
!= ( polyno1644367587lle_CN @ TA @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_poly_Odistinct_I25_J) ).
thf(956,plain,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( polyno649217638_Bound @ TA @ A )
!= ( polyno1644367587lle_CN @ TA @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(280,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_polymul_Osimps_I24_J) ).
thf(1104,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(193,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mult_Oright__neutral) ).
thf(849,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(70,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semiri1923998003cancel @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Osemiring__no__zero__divisors__cancel) ).
thf(452,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semiri1923998003cancel @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(91,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_poly__deriv__aux_Osimps_I8_J) ).
thf(512,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',fact_92_mult__cancel1) ).
thf(678,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)],[149]) ).
thf(97,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] : ( polyno86455060npolyh @ TA @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zero__normh) ).
thf(529,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] : ( polyno86455060npolyh @ TA @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(143,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno646301383dconst @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) )
= ( polyno646301383dconst @ TA @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_headconst_Osimps_I1_J) ).
thf(661,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno646301383dconst @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) )
= ( polyno646301383dconst @ TA @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(174,axiom,
! [TA: $tType,A: nat,B: nat,C: TA > TA] :
( ( compow @ ( TA > TA ) @ A @ ( compow @ ( TA > TA ) @ B @ C ) )
= ( compow @ ( TA > TA ) @ ( times_times @ nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_funpow__mult) ).
thf(793,plain,
! [TA: $tType,A: nat,B: nat,C: TA > TA] :
( ( compow @ ( TA > TA ) @ A @ ( compow @ ( TA > TA ) @ B @ C ) )
= ( compow @ ( TA > TA ) @ ( times_times @ nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(37,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno498386536degree @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_degree_Osimps_I8_J) ).
thf(366,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno498386536degree @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_poly__deriv_Osimps_I4_J) ).
thf(534,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(268,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) @ C )
= ( polyno850874092le_Mul @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_polymul_Osimps_I10_J) ).
thf(1067,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) @ C )
= ( polyno850874092le_Mul @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(176,axiom,
! [TA: $tType] :
( ( polyno1549699593char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ! [C: list @ TA] :
( ( polyno156741596_wf_bs @ TA @ C @ A )
=> ( ( polyno1341257465_Ipoly @ TA @ C @ A )
= ( zero_zero @ TA ) ) )
=> ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_isnpolyh__zero__iff) ).
thf(798,plain,
! [TA: $tType] :
( ( polyno1549699593char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ! [C: list @ TA] :
( ( polyno156741596_wf_bs @ TA @ C @ A )
=> ( ( polyno1341257465_Ipoly @ TA @ C @ A )
= ( zero_zero @ TA ) ) )
=> ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(25,axiom,
! [TA: $tType] :
( ( polyno545456796e_head @ TA )
= ( ^ [A: polyno1783536151e_poly @ TA] : ( polyno47817938_headn @ TA @ A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_head__eq__headn0) ).
thf(334,plain,
! [TA: $tType] :
( ( polyno545456796e_head @ TA )
= ( ^ [A: polyno1783536151e_poly @ TA] : ( polyno47817938_headn @ TA @ A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(261,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno750620841le_Add @ TA @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno750620841le_Add @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_polymul_Osimps_I12_J) ).
thf(1042,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno750620841le_Add @ TA @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno750620841le_Add @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(31,axiom,
! [TA: $tType,A: nat] :
( ( polyno545456796e_head @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno649217638_Bound @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_head_Osimps_I3_J) ).
thf(349,plain,
! [TA: $tType,A: nat] :
( ( polyno545456796e_head @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno649217638_Bound @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(121,axiom,
! [TA: $tType,A: TA] :
( ( polyno646301383dconst @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_headconst_Osimps_I2_J) ).
thf(598,plain,
! [TA: $tType,A: TA] :
( ( polyno646301383dconst @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(7,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(297,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(59,axiom,
minus @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ominus_1) ).
thf(429,plain,
minus @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(172,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( polyno1549699593char_0 @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Polynomial__List_Oidom__char__0) ).
thf(788,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( polyno1549699593char_0 @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(181,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno1644367587lle_CN @ TA @ B @ ( zero_zero @ nat ) @ C ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno75289385y_cmul @ TA @ A @ B ) @ ( zero_zero @ nat ) @ ( polyno1211105166iv_aux @ TA @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_poly__deriv__aux_Osimps_I1_J) ).
thf(815,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno1644367587lle_CN @ TA @ B @ ( zero_zero @ nat ) @ C ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno75289385y_cmul @ TA @ A @ B ) @ ( zero_zero @ nat ) @ ( polyno1211105166iv_aux @ TA @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(81,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno545456796e_head @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( polyno850874092le_Mul @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_head_Osimps_I6_J) ).
thf(484,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno545456796e_head @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( polyno850874092le_Mul @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(203,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno649217638_Bound @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_poly_Odistinct_I1_J) ).
thf(879,plain,
! [TA: $tType,A: TA,B: nat] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno649217638_Bound @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(194,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_one__reorient) ).
thf(852,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(84,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( ( polyno850874092le_Mul @ TA @ A @ B )
= ( polyno850874092le_Mul @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_poly_Oinject_I5_J) ).
thf(493,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( ( polyno850874092le_Mul @ TA @ A @ B )
= ( polyno850874092le_Mul @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(105,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_divisors__zero) ).
thf(551,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(249,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: nat,B: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno649217638_Bound @ TA @ A ) @ B )
= ( polyno850874092le_Mul @ TA @ ( polyno649217638_Bound @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_polymul_Osimps_I5_J) ).
thf(1012,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: nat,B: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno649217638_Bound @ TA @ A ) @ B )
= ( polyno850874092le_Mul @ TA @ ( polyno649217638_Bound @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(116,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mult__zero__right) ).
thf(583,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(186,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno86455060npolyh @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( ^ [C: nat] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_isnpolyh_Osimps_I6_J) ).
thf(830,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno86455060npolyh @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( ^ [C: nat] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(251,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) @ C )
= ( polyno850874092le_Mul @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_polymul_Osimps_I6_J) ).
thf(1017,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) @ C )
= ( polyno850874092le_Mul @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(267,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) @ A )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_polymul__0_I2_J) ).
thf(1064,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) @ A )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(277,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno156741596_wf_bs @ TA @ A @ B )
=> ( ( polyno156741596_wf_bs @ TA @ A @ C )
=> ( polyno156741596_wf_bs @ TA @ A @ ( polyno452058812olymul @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_wf__bs__polyul) ).
thf(1096,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno156741596_wf_bs @ TA @ A @ B )
=> ( ( polyno156741596_wf_bs @ TA @ A @ C )
=> ( polyno156741596_wf_bs @ TA @ A @ ( polyno452058812olymul @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(247,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_polymul__1_I2_J) ).
thf(1006,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(56,axiom,
! [TA: $tType,A: TA] :
( ( polyno47817938_headn @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( ^ [B: nat] : ( polyno333904939elle_C @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_headn_Osimps_I2_J) ).
thf(420,plain,
! [TA: $tType,A: TA] :
( ( polyno47817938_headn @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( ^ [B: nat] : ( polyno333904939elle_C @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(86,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( polyno86455060npolyh @ TA @ ( polyno476449744olypow @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_polypow__normh) ).
thf(499,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( polyno86455060npolyh @ TA @ ( polyno476449744olypow @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(76,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: TA] :
( ( polyno1789993463subst0 @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) )
= ( polyno333904939elle_C @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_polysubst0_Osimps_I1_J) ).
thf(471,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: TA] :
( ( polyno1789993463subst0 @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) )
= ( polyno333904939elle_C @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(106,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: TA] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_poly__deriv__aux_Osimps_I2_J) ).
thf(554,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: TA] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(100,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( ( polyno900443112le_Sub @ TA @ A @ B )
= ( polyno900443112le_Sub @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_poly_Oinject_I4_J) ).
thf(537,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( ( polyno900443112le_Sub @ TA @ A @ B )
= ( polyno900443112le_Sub @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(146,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( polyno86455060npolyh @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( ^ [B: nat] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_isnpolyh_Osimps_I3_J) ).
thf(669,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( polyno86455060npolyh @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( ^ [B: nat] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(152,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno427297311behead @ TA @ ( polyno900443112le_Sub @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_behead_Osimps_I5_J) ).
thf(686,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno427297311behead @ TA @ ( polyno900443112le_Sub @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(136,axiom,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_mult__0) ).
thf(642,plain,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(96,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno75289385y_cmul @ TA @ A @ B ) @ C @ ( polyno75289385y_cmul @ TA @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_poly__cmul_Osimps_I2_J) ).
thf(526,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno75289385y_cmul @ TA @ A @ B ) @ C @ ( polyno75289385y_cmul @ TA @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(134,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA] :
( ( polyno2122670676snpoly @ TA @ A )
=> ( ( A
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
=> ( polyno2122670676snpoly @ TA @ ( polyno222789899shift1 @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_shift1__isnpoly) ).
thf(637,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA] :
( ( polyno2122670676snpoly @ TA @ A )
=> ( ( A
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
=> ( polyno2122670676snpoly @ TA @ ( polyno222789899shift1 @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(47,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_ring__class_Oring__distribs_I2_J) ).
thf(393,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(158,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( A
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
=> ( polyno86455060npolyh @ TA @ ( polyno222789899shift1 @ TA @ A ) @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_shift1__isnpolyh) ).
thf(701,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( A
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
=> ( polyno86455060npolyh @ TA @ ( polyno222789899shift1 @ TA @ A ) @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(92,axiom,
! [TA: $tType,A: TA > TA,B: TA] :
( ( compow @ ( TA > TA ) @ ( zero_zero @ nat ) @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_funpow__0) ).
thf(515,plain,
! [TA: $tType,A: TA > TA,B: TA] :
( ( compow @ ( TA > TA ) @ ( zero_zero @ nat ) @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(72,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( A @ D @ E )
= ( A @ E @ D ) )
=> ( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ D @ ( plus_plus @ nat @ D @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_Euclid__induct) ).
thf(457,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( A @ D @ E )
= ( A @ E @ D ) )
=> ( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ D @ ( plus_plus @ nat @ D @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(241,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( times_times @ TA @ B @ A ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__cancel__right1) ).
thf(984,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( times_times @ TA @ B @ A ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(169,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ( ( polyno476449744olypow @ TA @ ( zero_zero @ nat ) )
= ( ^ [A: polyno1783536151e_poly @ TA] : ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_polypow_Osimps_I1_J) ).
thf(779,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ( ( polyno476449744olypow @ TA @ ( zero_zero @ nat ) )
= ( ^ [A: polyno1783536151e_poly @ TA] : ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TA )
=> ( minus @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ominus) ).
thf(343,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TA )
=> ( minus @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(224,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno1644367587lle_CN @ TA @ A @ ( zero_zero @ nat ) @ B ) )
= ( polyno1211105166iv_aux @ TA @ ( one_one @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_poly__deriv_Osimps_I1_J) ).
thf(938,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno1644367587lle_CN @ TA @ A @ ( zero_zero @ nat ) @ B ) )
= ( polyno1211105166iv_aux @ TA @ ( one_one @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(35,axiom,
! [TA: $tType,A: TA] :
( ( polyno367318022egreen @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( ^ [B: nat] : ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_degreen_Osimps_I2_J) ).
thf(360,plain,
! [TA: $tType,A: TA] :
( ( polyno367318022egreen @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( ^ [B: nat] : ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(921,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(254,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno86455060npolyh @ TA @ C @ D )
=> ( ( ( polyno452058812olymul @ TA @ A @ C )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
| ( C
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_polymul__eq0__iff) ).
thf(1026,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno86455060npolyh @ TA @ C @ D )
=> ( ( ( polyno452058812olymul @ TA @ A @ C )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
| ( C
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(229,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_poly__deriv_Osimps_I6_J) ).
thf(953,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(164,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( polyno86455060npolyh @ TA @ ( polyno545456796e_head @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_head__isnpolyh) ).
thf(718,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( polyno86455060npolyh @ TA @ ( polyno545456796e_head @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(220,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mult__eq__0__iff) ).
thf(926,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(167,axiom,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno649217638_Bound @ TA @ A )
!= ( polyno850874092le_Mul @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_poly_Odistinct_I19_J) ).
thf(773,plain,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno649217638_Bound @ TA @ A )
!= ( polyno850874092le_Mul @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(117,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mult__zero__left) ).
thf(586,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(213,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( polyno2122670676snpoly @ TA )
= ( ^ [A: polyno1783536151e_poly @ TA] : ( polyno86455060npolyh @ TA @ A @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_isnpoly__def) ).
thf(906,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( polyno2122670676snpoly @ TA )
= ( ^ [A: polyno1783536151e_poly @ TA] : ( polyno86455060npolyh @ TA @ A @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(8,axiom,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_distrib__left) ).
thf(298,plain,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(60,axiom,
semiri1193490041visors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors) ).
thf(430,plain,
semiri1193490041visors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(184,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/sandbox2/benchmark/theBenchmark.p',fact_105_nat__mult__eq__cancel__disj) ).
thf(824,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)],[184]) ).
thf(66,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_add_Oright__neutral) ).
thf(444,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(122,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA] :
( ( polyno620195148lynate @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_polynate_Osimps_I8_J) ).
thf(601,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA] :
( ( polyno620195148lynate @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(153,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( monoid_add @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Omonoid__add) ).
thf(689,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( monoid_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(6,axiom,
minus @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ominus_3) ).
thf(296,plain,
minus @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(57,axiom,
! [TA: $tType,A: TA] :
( ( polyno545456796e_head @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_head_Osimps_I2_J) ).
thf(423,plain,
! [TA: $tType,A: TA] :
( ( polyno545456796e_head @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(155,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( zero @ TA ) )
=> ! [A: nat] : ( polyno86455060npolyh @ TA @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_one__normh) ).
thf(694,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( zero @ TA ) )
=> ! [A: nat] : ( polyno86455060npolyh @ TA @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(50,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_add_Oleft__commute) ).
thf(402,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(191,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( A
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
=> ( ( polyno47817938_headn @ TA @ A @ C )
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_headnz) ).
thf(843,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( A
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
=> ( ( polyno47817938_headn @ TA @ A @ C )
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(114,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) )
= ( polyno333904939elle_C @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_poly__cmul_Osimps_I1_J) ).
thf(577,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno333904939elle_C @ TA @ B ) )
= ( polyno333904939elle_C @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(103,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA,E: nat,F: polyno1783536151e_poly @ TA] :
( ( ( polyno1644367587lle_CN @ TA @ A @ B @ C )
= ( polyno1644367587lle_CN @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_poly_Oinject_I8_J) ).
thf(545,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA,E: nat,F: polyno1783536151e_poly @ TA] :
( ( ( polyno1644367587lle_CN @ TA @ A @ B @ C )
= ( polyno1644367587lle_CN @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(109,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA] :
( ( polyno427297311behead @ TA @ ( polyno858086008le_Neg @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_behead_Osimps_I7_J) ).
thf(562,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA] :
( ( polyno427297311behead @ TA @ ( polyno858086008le_Neg @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(212,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___HOL_Otype) ).
thf(904,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(43,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( minus @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Ominus) ).
thf(382,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( minus @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(126,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mult_Oleft__neutral) ).
thf(611,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(275,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno452058812olymul @ TA @ A @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_polymul__1_I1_J) ).
thf(1090,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno452058812olymul @ TA @ A @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(177,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( mult_zero @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Omult__zero) ).
thf(804,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( mult_zero @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(159,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno1789993463subst0 @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) )
= ( polyno1645220415lle_Pw @ TA @ ( polyno1789993463subst0 @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_polysubst0_Osimps_I7_J) ).
thf(704,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno1789993463subst0 @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) )
= ( polyno1645220415lle_Pw @ TA @ ( polyno1789993463subst0 @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(101,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ab_semigroup_mult @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Oab__semigroup__mult) ).
thf(540,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ab_semigroup_mult @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(147,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno900443112le_Sub @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_poly__deriv_Osimps_I5_J) ).
thf(672,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno900443112le_Sub @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(265,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno850874092le_Mul @ TA @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno850874092le_Mul @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_polymul_Osimps_I14_J) ).
thf(1058,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno850874092le_Mul @ TA @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno850874092le_Mul @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(281,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno452058812olymul @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) )
= ( polyno850874092le_Mul @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_polymul_Osimps_I22_J) ).
thf(1107,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno452058812olymul @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) )
= ( polyno850874092le_Mul @ TA @ A @ ( polyno1645220415lle_Pw @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(150,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( ( polyno750620841le_Add @ TA @ A @ B )
= ( polyno750620841le_Add @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_poly_Oinject_I3_J) ).
thf(681,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( ( ( polyno750620841le_Add @ TA @ A @ B )
= ( polyno750620841le_Add @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(55,axiom,
comm_monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(419,plain,
comm_monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(69,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(451,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(15,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(318,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(239,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( zero_neq_one @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Ozero__neq__one) ).
thf(979,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( zero_neq_one @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(123,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( zero @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Ozero) ).
thf(604,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( zero @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(243,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( polyno86455060npolyh @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( ^ [B: nat] : $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_isnpolyh_Osimps_I1_J) ).
thf(990,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( polyno86455060npolyh @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( ^ [B: nat] : $true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(245,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_mult__not__zero) ).
thf(996,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',fact_93_mult__cancel2) ).
thf(509,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)],[90]) ).
thf(62,axiom,
! [TA: $tType,A: TA > TA > $o] :
( ( compow @ ( TA > TA > $o ) @ ( one_one @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_relpowp__1) ).
thf(434,plain,
! [TA: $tType,A: TA > TA > $o] :
( ( compow @ ( TA > TA > $o ) @ ( one_one @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(10,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(303,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(286,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno649217638_Bound @ TA @ D ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno649217638_Bound @ TA @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_polymul_Osimps_I11_J) ).
thf(1122,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno649217638_Bound @ TA @ D ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ ( polyno649217638_Bound @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(207,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_zero__neq__one) ).
thf(890,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(78,axiom,
ab_semigroup_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(477,plain,
ab_semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(45,axiom,
! [TA: $tType,A: TA] :
( ( polyno498386536degree @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_degree_Osimps_I2_J) ).
thf(387,plain,
! [TA: $tType,A: TA] :
( ( polyno498386536degree @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(273,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno452058812olymul @ TA @ B @ ( polyno333904939elle_C @ TA @ A ) ) @ C @ ( polyno452058812olymul @ TA @ D @ ( polyno333904939elle_C @ TA @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_polymul_Osimps_I3_J) ).
thf(1080,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( polyno452058812olymul @ TA @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno452058812olymul @ TA @ B @ ( polyno333904939elle_C @ TA @ A ) ) @ C @ ( polyno452058812olymul @ TA @ D @ ( polyno333904939elle_C @ TA @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(18,axiom,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_distrib__right) ).
thf(323,plain,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(128,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semiring @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Osemiring) ).
thf(621,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semiring @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(94,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno750620841le_Add @ TA @ A @ B )
!= ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_poly_Odistinct_I35_J) ).
thf(520,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno750620841le_Add @ TA @ A @ B )
!= ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(255,axiom,
field_char_0 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(1029,plain,
field_char_0 @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(233,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semigroup_add @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Osemigroup__add) ).
thf(964,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semigroup_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(21,axiom,
plus @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oplus) ).
thf(330,plain,
plus @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__mult) ).
thf(345,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(196,axiom,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno649217638_Bound @ TA @ A )
!= ( polyno1645220415lle_Pw @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_poly_Odistinct_I23_J) ).
thf(858,plain,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno649217638_Bound @ TA @ A )
!= ( polyno1645220415lle_Pw @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(130,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA] :
( ( polyno222789899shift1 @ TA @ A )
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_shift1__nz) ).
thf(626,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA] :
( ( polyno222789899shift1 @ TA @ A )
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(216,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: list @ TA,B: TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno75289385y_cmul @ TA @ B @ C ) )
= ( polyno1341257465_Ipoly @ TA @ A @ ( polyno850874092le_Mul @ TA @ ( polyno333904939elle_C @ TA @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_poly__cmul) ).
thf(915,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: list @ TA,B: TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno75289385y_cmul @ TA @ B @ C ) )
= ( polyno1341257465_Ipoly @ TA @ A @ ( polyno850874092le_Mul @ TA @ ( polyno333904939elle_C @ TA @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(222,axiom,
! [TA: $tType] :
( ( polyno1549699593char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno86455060npolyh @ TA @ C @ D )
=> ( ( ! [E: list @ TA] :
( ( polyno1341257465_Ipoly @ TA @ E @ A )
= ( polyno1341257465_Ipoly @ TA @ E @ C ) ) )
= ( A = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_isnpolyh__unique) ).
thf(932,plain,
! [TA: $tType] :
( ( polyno1549699593char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno86455060npolyh @ TA @ C @ D )
=> ( ( ! [E: list @ TA] :
( ( polyno1341257465_Ipoly @ TA @ E @ A )
= ( polyno1341257465_Ipoly @ TA @ E @ C ) ) )
= ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(266,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: TA] :
( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno333904939elle_C @ TA @ B ) )
= ( polyno333904939elle_C @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_polymul_Osimps_I1_J) ).
thf(1061,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: TA] :
( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno333904939elle_C @ TA @ B ) )
= ( polyno333904939elle_C @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(215,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno427297311behead @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_behead_Osimps_I8_J) ).
thf(912,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno427297311behead @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(49,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_add_Ocommute) ).
thf(399,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(231,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( uminus @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Ouminus) ).
thf(959,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( uminus @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(185,axiom,
! [TA: $tType,A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno850874092le_Mul @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_poly_Odistinct_I7_J) ).
thf(827,plain,
! [TA: $tType,A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno850874092le_Mul @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(250,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno2122670676snpoly @ TA @ A )
=> ( ( polyno2122670676snpoly @ TA @ B )
=> ( polyno2122670676snpoly @ TA @ ( polyno452058812olymul @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_polymul__norm) ).
thf(1015,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno2122670676snpoly @ TA @ A )
=> ( ( polyno2122670676snpoly @ TA @ B )
=> ( polyno2122670676snpoly @ TA @ ( polyno452058812olymul @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(125,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: nat] :
( ( polyno1008312662_deriv @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_poly__deriv_Osimps_I3_J) ).
thf(608,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: nat] :
( ( polyno1008312662_deriv @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(11,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA] :
( ( compow @ ( TA > TA > $o ) @ ( zero_zero @ nat ) @ A @ B @ C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_relpowp__0__E) ).
thf(306,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA] :
( ( compow @ ( TA > TA > $o ) @ ( zero_zero @ nat ) @ A @ B @ C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(283,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno750620841le_Add @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_poly__cmul_Osimps_I4_J) ).
thf(1113,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno750620841le_Add @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(61,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( plus_plus @ nat @ ( times_times @ nat @ C @ B ) @ D ) )
= ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_left__add__mult__distrib) ).
thf(431,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( plus_plus @ nat @ ( times_times @ nat @ C @ B ) @ D ) )
= ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(142,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno2122670676snpoly @ TA @ A )
=> ( ( A
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
=> ( polyno2122670676snpoly @ TA @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ B @ ( polyno222789899shift1 @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_funpow__shift1__isnpoly) ).
thf(658,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno2122670676snpoly @ TA @ A )
=> ( ( A
!= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
=> ( polyno2122670676snpoly @ TA @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ B @ ( polyno222789899shift1 @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(271,axiom,
polyno86455060npolyh @ a @ p @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_np) ).
thf(1076,plain,
polyno86455060npolyh @ a @ p @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(58,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_add_Oleft__cancel) ).
thf(426,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(118,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( ( polyno545456796e_head @ TA @ A )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_head__nz) ).
thf(589,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( ( polyno545456796e_head @ TA @ A )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno1645220415lle_Pw @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_poly_Odistinct_I11_J) ).
thf(548,plain,
! [TA: $tType,A: TA,B: polyno1783536151e_poly @ TA,C: nat] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno1645220415lle_Pw @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(180,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_poly__deriv_Osimps_I2_J) ).
thf(812,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno333904939elle_C @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(33,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno498386536degree @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_degree_Osimps_I6_J) ).
thf(355,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno498386536degree @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(235,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( polyno333904939elle_C @ TA @ A )
= ( polyno333904939elle_C @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_poly_Oinject_I1_J) ).
thf(968,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( polyno333904939elle_C @ TA @ A )
= ( polyno333904939elle_C @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(188,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( comm_ring_1 @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Ocomm__ring__1) ).
thf(836,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( comm_ring_1 @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(83,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(490,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(148,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno850874092le_Mul @ TA @ A @ B )
!= ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_poly_Odistinct_I49_J) ).
thf(675,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno850874092le_Mul @ TA @ A @ B )
!= ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(98,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_mult__cancel__left) ).
thf(531,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(226,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semiri1193490041visors @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Osemiring__no__zero__divisors) ).
thf(944,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semiri1193490041visors @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(138,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno222789899shift1 @ TA @ B ) )
= ( polyno1341257465_Ipoly @ TA @ A @ ( polyno850874092le_Mul @ TA @ ( polyno649217638_Bound @ TA @ ( zero_zero @ nat ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_shift1) ).
thf(648,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno222789899shift1 @ TA @ B ) )
= ( polyno1341257465_Ipoly @ TA @ A @ ( polyno850874092le_Mul @ TA @ ( polyno649217638_Bound @ TA @ ( zero_zero @ nat ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(82,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Nat_Oadd__0__right) ).
thf(487,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(168,axiom,
! [TA: $tType] :
( ( ( minus @ TA )
& ( plus @ TA )
& ( uminus @ TA )
& ( zero @ TA )
& ( power @ TA ) )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( polyno1341257465_Ipoly @ TA @ A @ B ) @ ( polyno1341257465_Ipoly @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_Ipoly_Osimps_I4_J) ).
thf(776,plain,
! [TA: $tType] :
( ( ( minus @ TA )
& ( plus @ TA )
& ( uminus @ TA )
& ( zero @ TA )
& ( power @ TA ) )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( polyno1341257465_Ipoly @ TA @ A @ B ) @ ( polyno1341257465_Ipoly @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(135,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: polyno1783536151e_poly @ TA] : ( polyno2122670676snpoly @ TA @ ( polyno620195148lynate @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_polynate__norm) ).
thf(640,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: polyno1783536151e_poly @ TA] : ( polyno2122670676snpoly @ TA @ ( polyno620195148lynate @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(269,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno452058812olymul @ TA @ A @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_polymul__0_I1_J) ).
thf(1070,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno452058812olymul @ TA @ A @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(160,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( plus @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Oplus) ).
thf(707,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( plus @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(206,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mult_Ocomm__neutral) ).
thf(887,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(236,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( monoid_mult @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Omonoid__mult) ).
thf(971,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( monoid_mult @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(20,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add__eq__self__zero) ).
thf(327,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(53,axiom,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( polyno1789993463subst0 @ TA @ B @ ( polyno649217638_Bound @ TA @ A ) )
= B ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( polyno1789993463subst0 @ TA @ B @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno649217638_Bound @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_polysubst0_Osimps_I2_J) ).
thf(409,plain,
! [TA: $tType,A: nat,B: polyno1783536151e_poly @ TA] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( polyno1789993463subst0 @ TA @ B @ ( polyno649217638_Bound @ TA @ A ) )
= B ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( polyno1789993463subst0 @ TA @ B @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno649217638_Bound @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(278,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno452058812olymul @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) )
= ( polyno850874092le_Mul @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_polymul_Osimps_I17_J) ).
thf(1098,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno452058812olymul @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) )
= ( polyno850874092le_Mul @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(244,axiom,
! [TA: $tType,A: TA > TA,B: nat,C: TA] :
( ( A @ ( compow @ ( TA > TA ) @ B @ A @ C ) )
= ( compow @ ( TA > TA ) @ B @ A @ ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_funpow__swap1) ).
thf(993,plain,
! [TA: $tType,A: TA > TA,B: nat,C: TA] :
( ( A @ ( compow @ ( TA > TA ) @ B @ A @ C ) )
= ( compow @ ( TA > TA ) @ B @ A @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(162,axiom,
! [A: nat,B: nat] :
( ( ( one_one @ nat )
= ( times_times @ nat @ A @ B ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_nat__1__eq__mult__iff) ).
thf(712,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)],[162]) ).
thf(107,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno1645220415lle_Pw @ TA @ A @ B )
!= ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_poly_Odistinct_I55_J) ).
thf(557,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno1645220415lle_Pw @ TA @ A @ B )
!= ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(115,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: list @ TA] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno1341257465_Ipoly @ TA @ C @ ( polyno750620841le_Add @ TA @ ( polyno850874092le_Mul @ TA @ ( polyno545456796e_head @ TA @ A ) @ ( polyno1645220415lle_Pw @ TA @ ( polyno649217638_Bound @ TA @ ( zero_zero @ nat ) ) @ ( polyno498386536degree @ TA @ A ) ) ) @ ( polyno427297311behead @ TA @ A ) ) )
= ( polyno1341257465_Ipoly @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_behead) ).
thf(580,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: list @ TA] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( polyno1341257465_Ipoly @ TA @ C @ ( polyno750620841le_Add @ TA @ ( polyno850874092le_Mul @ TA @ ( polyno545456796e_head @ TA @ A ) @ ( polyno1645220415lle_Pw @ TA @ ( polyno649217638_Bound @ TA @ ( zero_zero @ nat ) ) @ ( polyno498386536degree @ TA @ A ) ) ) @ ( polyno427297311behead @ TA @ A ) ) )
= ( polyno1341257465_Ipoly @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(195,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( ^ [C: nat] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_isnpolyh_Osimps_I8_J) ).
thf(855,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( ^ [C: nat] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(22,axiom,
power @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Power_Opower) ).
thf(331,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(39,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno47817938_headn @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( ^ [C: nat] : ( polyno850874092le_Mul @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_headn_Osimps_I6_J) ).
thf(370,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno47817938_headn @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( ^ [C: nat] : ( polyno850874092le_Mul @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(253,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno620195148lynate @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( polyno452058812olymul @ TA @ ( polyno620195148lynate @ TA @ A ) @ ( polyno620195148lynate @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_polynate_Osimps_I4_J) ).
thf(1023,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno620195148lynate @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( polyno452058812olymul @ TA @ ( polyno620195148lynate @ TA @ A ) @ ( polyno620195148lynate @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(263,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno452058812olymul @ TA @ B @ C ) )
= ( times_times @ TA @ ( polyno1341257465_Ipoly @ TA @ A @ B ) @ ( polyno1341257465_Ipoly @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_polymul) ).
thf(1052,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno452058812olymul @ TA @ B @ C ) )
= ( times_times @ TA @ ( polyno1341257465_Ipoly @ TA @ A @ B ) @ ( polyno1341257465_Ipoly @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(198,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( ( polyno646301383dconst @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_headconst__zero) ).
thf(864,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( ( polyno646301383dconst @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(112,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ D )
=> ( ( polyno498386536degree @ TA @ A )
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_degree__npolyhCN) ).
thf(571,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno86455060npolyh @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) @ D )
=> ( ( polyno498386536degree @ TA @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(120,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno427297311behead @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_behead_Osimps_I6_J) ).
thf(595,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno427297311behead @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(202,axiom,
! [A: nat,B: nat] :
( ( A
= ( times_times @ nat @ A @ B ) )
=> ( ( B
= ( one_one @ nat ) )
| ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_mult__eq__self__implies__10) ).
thf(876,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)],[202]) ).
thf(74,axiom,
! [TA: $tType,A: nat] :
( ( polyno498386536degree @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_degree_Osimps_I3_J) ).
thf(465,plain,
! [TA: $tType,A: nat] :
( ( polyno498386536degree @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(68,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(450,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(36,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno47817938_headn @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( ^ [C: nat] : ( polyno1645220415lle_Pw @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_headn_Osimps_I8_J) ).
thf(363,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno47817938_headn @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( ^ [C: nat] : ( polyno1645220415lle_Pw @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(238,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( polyno427297311behead @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_behead_Osimps_I3_J) ).
thf(976,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( polyno427297311behead @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(157,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( times @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Otimes) ).
thf(699,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( times @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(232,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1789993463subst0 @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( polyno750620841le_Add @ TA @ ( polyno1789993463subst0 @ TA @ A @ B ) @ ( polyno1789993463subst0 @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_polysubst0_Osimps_I4_J) ).
thf(961,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno1789993463subst0 @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( polyno750620841le_Add @ TA @ ( polyno1789993463subst0 @ TA @ A @ B ) @ ( polyno1789993463subst0 @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(16,axiom,
semiri1923998003cancel @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel) ).
thf(319,plain,
semiri1923998003cancel @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(209,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno750620841le_Add @ TA @ A @ B )
!= ( polyno1645220415lle_Pw @ TA @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_poly_Odistinct_I33_J) ).
thf(896,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA,D: nat] :
( ( polyno750620841le_Add @ TA @ A @ B )
!= ( polyno1645220415lle_Pw @ TA @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(140,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: list @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ B @ ( polyno222789899shift1 @ TA ) @ C ) )
= ( polyno1341257465_Ipoly @ TA @ A @ ( polyno850874092le_Mul @ TA @ ( polyno1645220415lle_Pw @ TA @ ( polyno649217638_Bound @ TA @ ( zero_zero @ nat ) ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_funpow__shift1) ).
thf(652,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: list @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ B @ ( polyno222789899shift1 @ TA ) @ C ) )
= ( polyno1341257465_Ipoly @ TA @ A @ ( polyno850874092le_Mul @ TA @ ( polyno1645220415lle_Pw @ TA @ ( polyno649217638_Bound @ TA @ ( zero_zero @ nat ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(46,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_add_Oleft__neutral) ).
thf(390,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(132,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semigroup_mult @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Osemigroup__mult) ).
thf(632,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( semigroup_mult @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(227,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno620195148lynate @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) )
= ( polyno620195148lynate @ TA @ ( polyno750620841le_Add @ TA @ A @ ( polyno850874092le_Mul @ TA @ ( polyno649217638_Bound @ TA @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_polynate_Osimps_I7_J) ).
thf(946,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno620195148lynate @ TA @ ( polyno1644367587lle_CN @ TA @ A @ B @ C ) )
= ( polyno620195148lynate @ TA @ ( polyno750620841le_Add @ TA @ A @ ( polyno850874092le_Mul @ TA @ ( polyno649217638_Bound @ TA @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(279,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno900443112le_Sub @ TA @ B @ C ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno900443112le_Sub @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_poly__cmul_Osimps_I5_J) ).
thf(1101,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno900443112le_Sub @ TA @ B @ C ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno900443112le_Sub @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(256,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( polyno850874092le_Mul @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_polymul_Osimps_I18_J) ).
thf(1030,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) )
= ( polyno850874092le_Mul @ TA @ A @ ( polyno750620841le_Add @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(111,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno858086008le_Neg @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_poly__deriv_Osimps_I7_J) ).
thf(568,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA] :
( ( polyno1008312662_deriv @ TA @ ( polyno858086008le_Neg @ TA @ A ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_add__is__0) ).
thf(290,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(221,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno1008312662_deriv @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_poly__deriv_Osimps_I8_J) ).
thf(929,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno1008312662_deriv @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(210,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno620195148lynate @ TA @ B ) )
= ( polyno1341257465_Ipoly @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_polynate) ).
thf(899,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: list @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( polyno620195148lynate @ TA @ B ) )
= ( polyno1341257465_Ipoly @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(151,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( power @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Power_Opower) ).
thf(684,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( power @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(30,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ A @ ( plus_plus @ nat @ B @ C ) )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_add__mult__distrib2) ).
thf(346,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ A @ ( plus_plus @ nat @ B @ C ) )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(262,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ B ) @ C @ ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_polymul_Osimps_I2_J) ).
thf(1045,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ B ) @ C @ ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1,conjecture,
( ( polyno452058812olymul @ a @ p @ q )
= ( polyno452058812olymul @ a @ q @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( polyno452058812olymul @ a @ p @ q )
!= ( polyno452058812olymul @ a @ q @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(287,plain,
( ( polyno452058812olymul @ a @ p @ q )
!= ( polyno452058812olymul @ a @ q @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(272,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_polymul_Osimps_I28_J) ).
thf(1077,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) )
= ( polyno850874092le_Mul @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) @ ( polyno1644367587lle_CN @ TA @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(79,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_plus__nat_Oadd__0) ).
thf(478,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(284,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno850874092le_Mul @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_poly__cmul_Osimps_I6_J) ).
thf(1116,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno850874092le_Mul @ TA @ B @ C ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno850874092le_Mul @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(67,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_add_Oright__cancel) ).
thf(447,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(315,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(187,axiom,
! [TA: $tType,A: TA,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno1644367587lle_CN @ TA @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_poly_Odistinct_I13_J) ).
thf(833,plain,
! [TA: $tType,A: TA,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno1644367587lle_CN @ TA @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(182,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= B )
= ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mult__cancel__right2) ).
thf(818,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= B )
= ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(51,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno545456796e_head @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( polyno1645220415lle_Pw @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_head_Osimps_I8_J) ).
thf(405,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat] :
( ( polyno545456796e_head @ TA @ ( polyno1645220415lle_Pw @ TA @ A @ B ) )
= ( polyno1645220415lle_Pw @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(173,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( times_times @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_mult__cancel__left1) ).
thf(790,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( times_times @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(199,axiom,
! [TA: $tType,A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno750620841le_Add @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_poly_Odistinct_I3_J) ).
thf(867,plain,
! [TA: $tType,A: TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno333904939elle_C @ TA @ A )
!= ( polyno750620841le_Add @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(40,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno545456796e_head @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( polyno750620841le_Add @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_head_Osimps_I4_J) ).
thf(373,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno545456796e_head @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( polyno750620841le_Add @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(19,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Omult__zero) ).
thf(326,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(217,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( ( polyno47817938_headn @ TA @ A @ C )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_headn__nz) ).
thf(918,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: nat,C: nat] :
( ( polyno86455060npolyh @ TA @ A @ B )
=> ( ( ( polyno47817938_headn @ TA @ A @ C )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) )
= ( A
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(89,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_mult__cancel__right) ).
thf(506,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(34,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( compow @ ( TA > TA > $o ) @ ( zero_zero @ nat ) @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_relpowp__0__I) ).
thf(358,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( compow @ ( TA > TA > $o ) @ ( zero_zero @ nat ) @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(63,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno498386536degree @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_degree_Osimps_I4_J) ).
thf(437,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno498386536degree @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(77,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno47817938_headn @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( ^ [C: nat] : ( polyno750620841le_Add @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_headn_Osimps_I4_J) ).
thf(474,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno47817938_headn @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( ^ [C: nat] : ( polyno750620841le_Add @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(144,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( group_add @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Ogroup__add) ).
thf(664,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( group_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(257,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: nat,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno649217638_Bound @ TA @ A ) @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) )
= ( polyno850874092le_Mul @ TA @ ( polyno649217638_Bound @ TA @ A ) @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_polymul_Osimps_I23_J) ).
thf(1033,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: nat,B: polyno1783536151e_poly @ TA,C: nat,D: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno649217638_Bound @ TA @ A ) @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) )
= ( polyno850874092le_Mul @ TA @ ( polyno649217638_Bound @ TA @ A ) @ ( polyno1644367587lle_CN @ TA @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(156,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_mult__0__right) ).
thf(696,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(165,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno86455060npolyh @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( ^ [C: nat] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_isnpolyh_Osimps_I4_J) ).
thf(720,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno86455060npolyh @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( ^ [C: nat] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(175,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ring_11004092258visors @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Oring__1__no__zero__divisors) ).
thf(796,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ring_11004092258visors @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(276,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: nat] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno649217638_Bound @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_poly__cmul_Osimps_I3_J) ).
thf(1093,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: nat] :
( ( polyno75289385y_cmul @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) )
= ( polyno452058812olymul @ TA @ ( polyno333904939elle_C @ TA @ A ) @ ( polyno649217638_Bound @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(242,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: nat] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_poly__deriv__aux_Osimps_I3_J) ).
thf(987,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: TA,B: nat] :
( ( polyno1211105166iv_aux @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) )
= ( polyno75289385y_cmul @ TA @ A @ ( polyno649217638_Bound @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(73,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add) ).
thf(464,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(23,axiom,
semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add) ).
thf(332,plain,
semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(166,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat > nat] :
( ( ( polyno367318022egreen @ TA @ A )
= B )
=> ( ! [C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( A
= ( polyno1644367587lle_CN @ TA @ C @ D @ E ) )
=> ( B
!= ( ^ [F: nat] : ( if @ nat @ ( D = F ) @ ( plus_plus @ nat @ ( one_one @ nat ) @ ( polyno367318022egreen @ TA @ E @ D ) ) @ ( zero_zero @ nat ) ) ) ) )
=> ( ( ? [C: TA] :
( A
= ( polyno333904939elle_C @ TA @ C ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: nat] :
( A
= ( polyno649217638_Bound @ TA @ C ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( A
= ( polyno750620841le_Add @ TA @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( A
= ( polyno900443112le_Sub @ TA @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( A
= ( polyno850874092le_Mul @ TA @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: polyno1783536151e_poly @ TA] :
( A
= ( polyno858086008le_Neg @ TA @ C ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ~ ( ? [C: polyno1783536151e_poly @ TA,D: nat] :
( A
= ( polyno1645220415lle_Pw @ TA @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_degreen_Oelims) ).
thf(723,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: nat > nat] :
( ( ( polyno367318022egreen @ TA @ A )
= B )
=> ( ! [C: polyno1783536151e_poly @ TA,D: nat,E: polyno1783536151e_poly @ TA] :
( ( A
= ( polyno1644367587lle_CN @ TA @ C @ D @ E ) )
=> ( B
!= ( ^ [F: nat] : ( if @ nat @ ( D = F ) @ ( plus_plus @ nat @ ( one_one @ nat ) @ ( polyno367318022egreen @ TA @ E @ D ) ) @ ( zero_zero @ nat ) ) ) ) )
=> ( ( ? [C: TA] :
( A
= ( polyno333904939elle_C @ TA @ C ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: nat] :
( A
= ( polyno649217638_Bound @ TA @ C ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( A
= ( polyno750620841le_Add @ TA @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( A
= ( polyno900443112le_Sub @ TA @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: polyno1783536151e_poly @ TA,D: polyno1783536151e_poly @ TA] :
( A
= ( polyno850874092le_Mul @ TA @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ( ( ? [C: polyno1783536151e_poly @ TA] :
( A
= ( polyno858086008le_Neg @ TA @ C ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) )
=> ~ ( ? [C: polyno1783536151e_poly @ TA,D: nat] :
( A
= ( polyno1645220415lle_Pw @ TA @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : ( zero_zero @ nat ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(246,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( comm_monoid_mult @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Groups_Ocomm__monoid__mult) ).
thf(1004,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( comm_monoid_mult @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(154,axiom,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: nat] :
( ( polyno620195148lynate @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) @ A @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_polynate_Osimps_I1_J) ).
thf(691,plain,
! [TA: $tType] :
( ( ( one @ TA )
& ( plus @ TA )
& ( times @ TA )
& ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: nat] :
( ( polyno620195148lynate @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( polyno1644367587lle_CN @ TA @ ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) @ A @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(87,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult__is__0) ).
thf(501,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)],[87]) ).
thf(38,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__neq__one) ).
thf(369,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(26,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_add_Ogroup__left__neutral) ).
thf(337,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(219,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno427297311behead @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_behead_Osimps_I4_J) ).
thf(923,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( polyno427297311behead @ TA @ ( polyno750620841le_Add @ TA @ A @ B ) )
= ( polyno333904939elle_C @ TA @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(12,axiom,
! [TA: $tType,A: nat] :
( ( polyno367318022egreen @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( ^ [B: nat] : ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_degreen_Osimps_I3_J) ).
thf(309,plain,
! [TA: $tType,A: nat] :
( ( polyno367318022egreen @ TA @ ( polyno649217638_Bound @ TA @ A ) )
= ( ^ [B: nat] : ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(119,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_mult_Oleft__commute) ).
thf(592,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(204,axiom,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_nat__mult__1) ).
thf(882,plain,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(223,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(935,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(248,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) @ C )
= ( polyno850874092le_Mul @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_polymul_Osimps_I8_J) ).
thf(1009,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( times @ TA )
& ( zero @ TA ) )
=> ! [A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA,C: polyno1783536151e_poly @ TA] :
( ( polyno452058812olymul @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) @ C )
= ( polyno850874092le_Mul @ TA @ ( polyno850874092le_Mul @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(259,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: list @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ B @ ( polyno222789899shift1 @ TA ) @ C ) )
= ( polyno1341257465_Ipoly @ TA @ A @ ( polyno452058812olymul @ TA @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ B @ ( polyno222789899shift1 @ TA ) @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_funpow__shift1__1) ).
thf(1037,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: list @ TA,B: nat,C: polyno1783536151e_poly @ TA] :
( ( polyno1341257465_Ipoly @ TA @ A @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ B @ ( polyno222789899shift1 @ TA ) @ C ) )
= ( polyno1341257465_Ipoly @ TA @ A @ ( polyno452058812olymul @ TA @ ( compow @ ( ( polyno1783536151e_poly @ TA ) > ( polyno1783536151e_poly @ TA ) ) @ B @ ( polyno222789899shift1 @ TA ) @ ( polyno333904939elle_C @ TA @ ( one_one @ TA ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(108,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ring @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Fields_Ofield__char__0___Rings_Oring) ).
thf(560,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ring @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(85,axiom,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( ( polyno858086008le_Neg @ TA @ A )
= ( polyno858086008le_Neg @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_poly_Oinject_I6_J) ).
thf(496,plain,
! [TA: $tType,A: polyno1783536151e_poly @ TA,B: polyno1783536151e_poly @ TA] :
( ( ( polyno858086008le_Neg @ TA @ A )
= ( polyno858086008le_Neg @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_ring__class_Oring__distribs_I1_J) ).
thf(454,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1790,plain,
$false,
inference(e,[status(thm)],[645,1036,809,629,846,893,518,468,941,666,1110,909,333,481,352,408,523,1073,873,379,614,861,440,655,384,715,340,782,709,841,301,651,973,885,320,565,1055,785,504,838,949,542,902,1087,870,606,416,289,443,1040,376,623,806,966,821,1020,574,981,634,1119,396,312,293,956,1104,849,452,512,678,529,661,793,366,534,1067,798,334,1042,349,598,297,429,788,815,484,879,852,493,551,1012,583,830,1017,1064,1096,1006,420,499,471,554,537,669,686,642,526,637,393,701,515,457,984,779,343,938,360,921,1026,953,718,926,773,586,906,298,430,824,444,601,689,296,423,694,402,843,577,545,562,904,382,611,1090,804,704,540,672,1058,1107,681,419,451,318,979,604,990,996,509,434,303,1122,890,477,387,1080,323,621,520,1029,964,330,345,858,626,915,932,1061,912,399,959,827,1015,608,306,1113,431,658,1076,426,589,548,812,355,968,836,490,675,531,944,648,487,776,640,1070,707,887,971,327,409,1098,993,712,557,580,855,331,370,1023,1052,864,571,595,876,465,450,363,976,699,961,319,896,652,390,632,946,1101,1030,568,290,929,899,684,346,1045,287,1077,478,1116,447,315,833,818,405,790,867,373,326,918,506,358,437,474,664,1033,696,720,796,1093,987,464,332,723,1004,691,501,369,337,923,309,592,882,935,1009,1037,560,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP150^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n015.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 20:05:18 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.02/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.33/1.25 % [INFO] Parsing done (442ms).
% 2.33/1.27 % [INFO] Running in sequential loop mode.
% 3.55/1.65 % [INFO] eprover registered as external prover.
% 3.55/1.66 % [INFO] Scanning for conjecture ...
% 4.02/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 318 axioms. Running axiom selection ...
% 4.23/2.01 % [INFO] Axiom selection finished. Selected 284 axioms (removed 34 axioms).
% 5.58/2.34 % [INFO] Problem is higher-order (TPTP THF).
% 5.58/2.37 % [INFO] Type checking passed.
% 5.58/2.38 % [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 ...
% 30.07/7.41 % External prover 'e' found a proof!
% 30.07/7.41 % [INFO] Killing All external provers ...
% 30.07/7.42 % Time passed: 7053ms (effective reasoning time: 6143ms)
% 30.07/7.42 % 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)>
% 30.07/7.42 % Axioms used in derivation (284): fact_54_isnpolyh_Osimps_I3_J, fact_9_polynate_Osimps_I4_J, fact_69_mult_Oright__neutral, fact_60_zero__normh, fact_218_poly__cmul_Osimps_I8_J, fact_211_polymul_Osimps_I10_J, tcon_fun___Groups_Ominus, subcl_Fields_Ofield__char__0___Groups_Oab__semigroup__add, fact_248_poly__cmul_Osimps_I7_J, tfree_0, fact_83_divisors__zero, fact_225_behead__isnpolyh, fact_175_add_Oleft__neutral, fact_68_mult__cancel__right2, fact_164_Nat_Oadd__0__right, fact_105_nat__mult__eq__cancel__disj, fact_56_polymul_Osimps_I17_J, fact_182_add__mult__distrib, fact_112_polysubst0_Osimps_I4_J, fact_20_poly_Odistinct_I49_J, fact_151_head__eq__headn0, fact_91_mult__0__right, fact_94_shift1, fact_181_add__mult__distrib2, fact_14_poly_Oinject_I1_J, fact_24_poly_Odistinct_I7_J, fact_113_headn_Osimps_I2_J, tcon_HOL_Obool___Groups_Ominus_3, fact_34_polymul_Osimps_I6_J, fact_44_poly__cmul_Osimps_I6_J, fact_217_polymul_Osimps_I28_J, fact_246_poly__cmul_Osimps_I5_J, fact_43_poly__cmul_Osimps_I4_J, subcl_Fields_Ofield__char__0___Rings_Ocomm__ring__1, fact_19_Ipoly_Osimps_I1_J, fact_214_Ipoly_Osimps_I4_J, fact_194_poly_Odistinct_I23_J, fact_92_mult__cancel1, fact_202_poly_Odistinct_I47_J, fact_188_add_Oleft__cancel, fact_156_funpow__shift1__isnpoly, fact_154_poly__deriv__aux_Osimps_I4_J, fact_108_polysub__same__0, tcon_Nat_Onat___Rings_Ozero__neq__one, fact_139_funpow__isnpolyh, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors, fact_183_ab__semigroup__add__class_Oadd__ac_I1_J, fact_213_degree_Osimps_I8_J, fact_145_head__isnpolyh, fact_100_mult__eq__self__implies__10, fact_101_mult__0, fact_133_poly__deriv_Osimps_I1_J, fact_241_polypow_Osimps_I1_J, fact_132_poly__deriv_Osimps_I2_J, fact_11_polymul_Osimps_I14_J, tcon_Nat_Onat___Power_Opower, fact_149_degreen_Osimps_I3_J, tcon_Nat_Onat___Groups_Ocomm__monoid__mult, subcl_Fields_Ofield__char__0___Groups_Ogroup__add, subcl_Fields_Ofield__char__0___Groups_Ocomm__monoid__mult, fact_247_behead_Osimps_I7_J, fact_142_head_Osimps_I6_J, fact_251_polypow__normh, fact_99_nat__mult__1, fact_196_distrib__right, fact_220_degreen_Osimps_I1_J, fact_67_mult__cancel__right1, fact_150_head_Osimps_I1_J, fact_126_poly__deriv_Osimps_I4_J, fact_109_polysubst0_Osimps_I8_J, tcon_HOL_Obool___Groups_Ouminus_2, fact_41_polynate_Osimps_I7_J, fact_191_add_Oleft__commute, subcl_Fields_Ofield__char__0___Groups_Ouminus, fact_235_relpowp__0__I, fact_95_shift1__isnpolyh, fact_81_one__reorient, fact_157_funpow__code__def, fact_119_headconst_Osimps_I1_J, fact_137_funpow__0, fact_28_isnpolyh_Osimps_I6_J, tcon_Nat_Onat___Groups_Oone, fact_190_add_Ocommute, fact_130_degree_Osimps_I4_J, tcon_Nat_Onat___Groups_Oab__semigroup__mult, fact_35_isnpolyh__zero__iff, subcl_Fields_Ofield__char__0___Power_Opower, fact_187_add_Oassoc, fact_163_add__is__0, subcl_Fields_Ofield__char__0___Rings_Oring__1__no__zero__divisors, subcl_Fields_Ofield__char__0___Rings_Osemiring__no__zero__divisors, fact_25_poly_Odistinct_I3_J, fact_97_nat__1__eq__mult__iff, fact_39_polymul__1_I2_J, fact_222_sum__squares__eq__zero__iff, tcon_Nat_Onat___Groups_Oplus, fact_8_polymul_Osimps_I1_J, fact_29_isnpolyh_Osimps_I4_J, fact_42_polymul__eq0__iff, fact_21_poly_Odistinct_I35_J, fact_131_degree_Osimps_I3_J, tcon_Nat_Onat___Groups_Omonoid__add, fact_2_nq, fact_57_polymul_Osimps_I5_J, fact_30_isnpolyh_Osimps_I1_J, fact_73_mult__zero__left, subcl_Fields_Ofield__char__0___Groups_Ominus, fact_76_zero__reorient, fact_93_mult__cancel2, fact_195_combine__common__factor, fact_135_head__nz, fact_63_polymul_Osimps_I23_J, subcl_Fields_Ofield__char__0___Rings_Ozero__neq__one, fact_32_polynate__norm, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel, fact_242_degreen_Oelims, help_If_1_1_T, fact_38_polymul__0_I1_J, fact_210_polymul_Osimps_I22_J, fact_85_mult__left__cancel, fact_40_polymul__1_I1_J, fact_228_behead_Osimps_I4_J, fact_12_polymul_Osimps_I18_J, subcl_Fields_Ofield__char__0___Rings_Osemiring, fact_18_Ipoly_Osimps_I6_J, fact_118_polysub__norm, fact_33_isnpolyh__unique, fact_244_poly_Oinject_I4_J, fact_58_poly__cmul_Osimps_I1_J, fact_37_polymul__0_I2_J, fact_207_poly_Odistinct_I55_J, fact_209_polysubst0_Osimps_I7_J, fact_165_poly_Oinject_I7_J, fact_17_polynate, fact_121_polysubst0_Osimps_I2_J, fact_36_poly__cmul, fact_200_ring__class_Oring__distribs_I2_J, fact_49_poly__cmul_Osimps_I3_J, subcl_Fields_Ofield__char__0___Polynomial__List_Oidom__char__0, fact_117_wf__bs__polysub, fact_229_behead_Osimps_I3_J, fact_245_behead_Osimps_I5_J, fact_65_mult__cancel__left1, subcl_Fields_Ofield__char__0___Groups_Ozero, fact_107_headconst__zero, tcon_Nat_Onat___Groups_Ozero, fact_219_poly__deriv_Osimps_I8_J, tcon_Nat_Onat___Groups_Omonoid__mult, fact_89_mult_Ocomm__neutral, fact_111_polysubst0_Osimps_I6_J, fact_75_mult__eq__0__iff, fact_88_comm__monoid__mult__class_Omult__1, fact_55_poly__cmul_Osimps_I2_J, fact_148_degreen_Osimps_I4_J, fact_189_add_Oright__cancel, fact_48_polynate_Osimps_I1_J, tcon_Nat_Onat___Rings_Ocomm__semiring, fact_71_mult__cancel__right, fact_174_add_Oright__neutral, fact_115_headn_Osimps_I4_J, subcl_Fields_Ofield__char__0___Rings_Osemiring__no__zero__divisors__cancel, fact_177_left__add__mult__distrib, fact_1_np, fact_5_polymul_Osimps_I20_J, fact_90_mult__is__0, fact_7_polymul, fact_127_poly__deriv_Osimps_I6_J, fact_23_poly_Odistinct_I13_J, tcon_Nat_Onat___Rings_Osemiring, tcon_Nat_Onat___Rings_Omult__zero, fact_122_polysub__0, subcl_Fields_Ofield__char__0___Rings_Omult__zero, fact_66_mult__cancel__left2, fact_158_funpow__shift1, fact_146_degreen_Osimps_I2_J, help_If_3_1_T, fact_206_poly_Odistinct_I11_J, fact_86_mult__right__cancel, fact_52_poly_Odistinct_I19_J, fact_10_polymul_Osimps_I26_J, fact_116_headn_Osimps_I3_J, fact_134_funpow__shift1__1, fact_82_mult__not__zero, fact_124_degree__npolyhCN, fact_106_headn__nz, help_If_2_1_T, fact_87_zero__neq__one, fact_3_polymul__norm, fact_203_add_Ogroup__left__neutral, fact_144_head_Osimps_I3_J, fact_98_nat__mult__1__right, subcl_Fields_Ofield__char__0___Groups_Osemigroup__mult, fact_53_poly_Odistinct_I15_J, subcl_Fields_Ofield__char__0___HOL_Otype, subcl_Fields_Ofield__char__0___Groups_Osemigroup__add, fact_6_polymul_Osimps_I8_J, subcl_Fields_Ofield__char__0___Groups_Omonoid__mult, subcl_Fields_Ofield__char__0___Rings_Oring__1, fact_27_polymul_Osimps_I12_J, subcl_Fields_Ofield__char__0___Rings_Oring, fact_70_mult_Oleft__neutral, fact_239_Euclid__induct, fact_51_poly_Odistinct_I1_J, fact_4_wf__bs__polyul, fact_226_behead_Osimps_I2_J, fact_136_degreen__npolyhCN, fact_129_degree_Osimps_I6_J, fact_178_plus__nat_Oadd__0, fact_201_poly_Odistinct_I33_J, fact_50_poly_Odistinct_I25_J, fact_64_polymul_Osimps_I2_J, fact_140_funpow__mult, fact_212_degreen_Osimps_I8_J, subcl_Fields_Ofield__char__0___Groups_Oone, fact_26_polymul_Osimps_I24_J, fact_13_poly_Oinject_I8_J, fact_104_shift1__def, subcl_Fields_Ofield__char__0___Groups_Omonoid__add, fact_79_mult_Ocommute, fact_72_mult__cancel__left, fact_123_headnz, fact_74_mult__zero__right, fact_138_funpow__swap1, fact_249_poly__deriv_Osimps_I5_J, fact_221_degree_Osimps_I1_J, fact_232_relpowp__1, fact_22_poly_Odistinct_I29_J, fact_15_poly_Oinject_I5_J, fact_159_polydivide__def, fact_110_polysubst0_Osimps_I1_J, fact_243_poly_Oinject_I6_J, fact_84_no__zero__divisors, tcon_Nat_Onat___Groups_Osemigroup__add, tcon_Nat_Onat___Groups_Otimes, fact_233_relpowp_Osimps_I1_J, fact_227_behead_Osimps_I6_J, fact_152_poly__deriv__aux_Osimps_I2_J, fact_180_isnpolyh_Osimps_I8_J, fact_153_poly__deriv__aux_Osimps_I6_J, tcon_Nat_Onat___Groups_Osemigroup__mult, fact_160_poly__deriv__aux_Osimps_I1_J, fact_114_headn_Osimps_I6_J, tcon_fun___Groups_Ouminus, fact_77_ab__semigroup__mult__class_Omult__ac_I1_J, fact_102_shift1__nz, fact_47_poly_Oinject_I2_J, fact_125_poly__deriv_Osimps_I3_J, fact_80_mult_Oleft__commute, fact_234_relpowp__0__E, fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062, fact_61_isnpoly__def, fact_155_poly__deriv__aux_Osimps_I3_J, subcl_Fields_Ofield__char__0___Groups_Oplus, fact_176_head_Osimps_I8_J, subcl_Fields_Ofield__char__0___Groups_Otimes, subcl_Fields_Ofield__char__0___Rings_Ocomm__semiring, fact_31_polynate_Osimps_I8_J, fact_216_polymul_Osimps_I16_J, fact_46_polymul_Osimps_I3_J, fact_197_distrib__left, fact_143_head_Osimps_I4_J, fact_96_nat__mult__eq__1__iff, tcon_Nat_Onat___Groups_Oab__semigroup__add, fact_224_behead, fact_198_comm__semiring__class_Odistrib, fact_250_poly__deriv_Osimps_I7_J, fact_62_polymul_Osimps_I11_J, fact_208_headn_Osimps_I8_J, fact_230_behead_Osimps_I8_J, fact_215_poly__deriv__aux_Osimps_I8_J, fact_252_polymul_Osimps_I7_J, subcl_Fields_Ofield__char__0___Fields_Ofield, fact_16_poly_Oinject_I3_J, tcon_Nat_Onat___Groups_Ominus_1, subcl_Fields_Ofield__char__0___Groups_Oab__semigroup__mult, fact_199_ring__class_Oring__distribs_I1_J, fact_103_shift1__isnpoly, fact_179_add__eq__self__zero, fact_59_one__normh, fact_147_degreen_Osimps_I6_J, fact_128_degree_Osimps_I2_J, fact_141_head_Osimps_I2_J, fact_120_headconst_Osimps_I2_J, fact_78_mult_Oassoc
% 30.07/7.42 % No. of inferences in proof: 572
% 30.07/7.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7053 ms resp. 6143 ms w/o parsing
% 29.59/7.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.59/7.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------