%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP150^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 76.59s 15.20s
% Output : Refutation 66.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 214
% Syntax : Number of formulae : 430 ( 341 unt; 0 typ; 0 def)
% Number of atoms : 821 ( 683 equ; 0 cnn)
% Maximal formula atoms : 17 ( 1 avg)
% Number of connectives : 2711 ( 96 ~; 21 |; 30 &;2396 @)
% ( 0 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 10 con; 0-3 aty)
% Number of variables : 1091 ( 56 ^;1013 !; 22 ?;1091 :)
% Comments :
%------------------------------------------------------------------------------
thf(polyno1532895200ly_nat_type,type,
polyno1532895200ly_nat: $tType ).
thf(polyno727731844poly_a_type,type,
polyno727731844poly_a: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(one_one_a_decl,type,
one_one_a: a ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > nat > nat ).
thf(plus_plus_a_decl,type,
plus_plus_a: a > a > a ).
thf(times_times_a_decl,type,
times_times_a: a > a > a ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(zero_zero_a_decl,type,
zero_zero_a: a ).
thf(if_nat_decl,type,
if_nat: $o > nat > nat > nat ).
thf(compow1114216044poly_a_decl,type,
compow1114216044poly_a: nat > ( polyno727731844poly_a > polyno727731844poly_a ) > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno422358502poly_a_decl,type,
polyno422358502poly_a: list_a > polyno727731844poly_a > a ).
thf(polyno1465139388head_a_decl,type,
polyno1465139388head_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno578545843gree_a_decl,type,
polyno578545843gree_a: polyno727731844poly_a > nat ).
thf(polyno1674775833reen_a_decl,type,
polyno1674775833reen_a: polyno727731844poly_a > nat > nat ).
thf(polyno1884029055head_a_decl,type,
polyno1884029055head_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno2115742616onst_a_decl,type,
polyno2115742616onst_a: polyno727731844poly_a > a ).
thf(polyno567601229eadn_a_decl,type,
polyno567601229eadn_a: polyno727731844poly_a > nat > polyno727731844poly_a ).
thf(polyno190918219poly_a_decl,type,
polyno190918219poly_a: polyno727731844poly_a > $o ).
thf(polyno1372495879olyh_a_decl,type,
polyno1372495879olyh_a: polyno727731844poly_a > nat > $o ).
thf(polyno1623170614_Add_a_decl,type,
polyno1623170614_Add_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno2024845497ound_a_decl,type,
polyno2024845497ound_a: nat > polyno727731844poly_a ).
thf(polyno1057396216e_CN_a_decl,type,
polyno1057396216e_CN_a: polyno727731844poly_a > nat > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno439679028le_C_a_decl,type,
polyno439679028le_C_a: a > polyno727731844poly_a ).
thf(polyno1491482291_Mul_a_decl,type,
polyno1491482291_Mul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno96675367_Neg_a_decl,type,
polyno96675367_Neg_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno1538138524e_Pw_a_decl,type,
polyno1538138524e_Pw_a: polyno727731844poly_a > nat > polyno727731844poly_a ).
thf(polyno975704247_Sub_a_decl,type,
polyno975704247_Sub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno562434098cmul_a_decl,type,
polyno562434098cmul_a: a > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno212464073eriv_a_decl,type,
polyno212464073eriv_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno1006823949_aux_a_decl,type,
polyno1006823949_aux_a: a > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno1934269411ymul_a_decl,type,
polyno1934269411ymul_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno955999183nate_a_decl,type,
polyno955999183nate_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno1371724751ypow_a_decl,type,
polyno1371724751ypow_a: nat > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno1418491367ysub_a_decl,type,
polyno1418491367ysub_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno1397854436bst0_a_decl,type,
polyno1397854436bst0_a: polyno727731844poly_a > polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno784948432ift1_a_decl,type,
polyno784948432ift1_a: polyno727731844poly_a > polyno727731844poly_a ).
thf(polyno896877631f_bs_a_decl,type,
polyno896877631f_bs_a: list_a > polyno727731844poly_a > $o ).
thf(n0_decl,type,
n0: nat ).
thf(n1_decl,type,
n1: nat ).
thf(p_decl,type,
p: polyno727731844poly_a ).
thf(q_decl,type,
q: polyno727731844poly_a ).
thf(141,axiom,
! [A: a] :
( ( times_times_a @ one_one_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_comm__monoid__mult__class_Omult__1) ).
thf(709,plain,
! [A: a] :
( ( times_times_a @ one_one_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(121,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( ( polyno2115742616onst_a @ A )
= zero_zero_a )
= ( A
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_headconst__zero) ).
thf(645,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( ( polyno2115742616onst_a @ A )
= zero_zero_a )
= ( A
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(168,axiom,
! [A: list_a,B: a,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno562434098cmul_a @ B @ C ) )
= ( polyno422358502poly_a @ A @ ( polyno1491482291_Mul_a @ ( polyno439679028le_C_a @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_poly__cmul) ).
thf(809,plain,
! [A: list_a,B: a,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno562434098cmul_a @ B @ C ) )
= ( polyno422358502poly_a @ A @ ( polyno1491482291_Mul_a @ ( polyno439679028le_C_a @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(41,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ D )
=> ( ( polyno578545843gree_a @ A )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_degree__npolyhCN) ).
thf(347,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ D )
=> ( ( polyno578545843gree_a @ A )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(179,axiom,
! [A: a,B: a] :
( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno439679028le_C_a @ B ) )
= ( polyno439679028le_C_a @ ( times_times_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_polymul_Osimps_I1_J) ).
thf(846,plain,
! [A: a,B: a] :
( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno439679028le_C_a @ B ) )
= ( polyno439679028le_C_a @ ( times_times_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(195,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno2024845497ound_a @ D ) )
= ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno2024845497ound_a @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_polymul_Osimps_I11_J) ).
thf(893,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno2024845497ound_a @ D ) )
= ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno2024845497ound_a @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(8,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_plus__nat_Oadd__0) ).
thf(234,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(209,axiom,
! [A: a,B: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno96675367_Neg_a @ B ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno96675367_Neg_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_poly__cmul_Osimps_I7_J) ).
thf(941,plain,
! [A: a,B: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno96675367_Neg_a @ B ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno96675367_Neg_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(93,axiom,
( times_times_a
= ( ^ [A: a,B: a] : ( times_times_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_mult_Ocommute) ).
thf(555,plain,
( times_times_a
= ( ^ [A: a,B: a] : ( times_times_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(11,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_Nat_Oadd__0__right) ).
thf(249,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,axiom,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_comm__semiring__class_Odistrib) ).
thf(333,plain,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(116,axiom,
! [A: a,B: nat] :
( ( polyno439679028le_C_a @ A )
!= ( polyno2024845497ound_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_poly_Odistinct_I1_J) ).
thf(628,plain,
! [A: a,B: nat] :
( ( polyno439679028le_C_a @ A )
!= ( polyno2024845497ound_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(62,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_verit__sum__simplify) ).
thf(408,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(155,axiom,
! [A: a] :
( ( polyno2115742616onst_a @ ( polyno439679028le_C_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_headconst_Osimps_I2_J) ).
thf(762,plain,
! [A: a] :
( ( polyno2115742616onst_a @ ( polyno439679028le_C_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(124,axiom,
! [A: nat] :
( ( polyno1372495879olyh_a @ ( polyno2024845497ound_a @ A ) )
= ( ^ [B: nat] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_isnpolyh_Osimps_I3_J) ).
thf(655,plain,
! [A: nat] :
( ( polyno1372495879olyh_a @ ( polyno2024845497ound_a @ A ) )
= ( ^ [B: nat] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(184,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno975704247_Sub_a @ A @ B ) @ C )
= ( polyno1491482291_Mul_a @ ( polyno975704247_Sub_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_polymul_Osimps_I7_J) ).
thf(861,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno975704247_Sub_a @ A @ B ) @ C )
= ( polyno1491482291_Mul_a @ ( polyno975704247_Sub_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(145,axiom,
zero_zero_a != one_one_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_zero__neq__one) ).
thf(730,plain,
zero_zero_a != one_one_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(20,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_nat @ A @ C )
= ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_add__mono__thms__linordered__semiring_I4_J) ).
thf(276,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_nat @ A @ C )
= ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(53,axiom,
! [A: a,B: a,C: a,D: a] :
( ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( plus_plus_a @ ( times_times_a @ C @ B ) @ D ) )
= ( plus_plus_a @ ( times_times_a @ ( plus_plus_a @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_combine__common__factor) ).
thf(385,plain,
! [A: a,B: a,C: a,D: a] :
( ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( plus_plus_a @ ( times_times_a @ C @ B ) @ D ) )
= ( plus_plus_a @ ( times_times_a @ ( plus_plus_a @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(164,axiom,
! [A: a,B: a] :
( ( polyno1006823949_aux_a @ A @ ( polyno439679028le_C_a @ B ) )
= ( polyno562434098cmul_a @ A @ ( polyno439679028le_C_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_poly__deriv__aux_Osimps_I2_J) ).
thf(797,plain,
! [A: a,B: a] :
( ( polyno1006823949_aux_a @ A @ ( polyno439679028le_C_a @ B ) )
= ( polyno562434098cmul_a @ A @ ( polyno439679028le_C_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(88,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( ( polyno1884029055head_a @ A )
= ( polyno439679028le_C_a @ zero_zero_a ) )
= ( A
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_head__nz) ).
thf(538,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( ( polyno1884029055head_a @ A )
= ( polyno439679028le_C_a @ zero_zero_a ) )
= ( A
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(55,axiom,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_add_Ocommute) ).
thf(389,plain,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(103,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ ( polyno1538138524e_Pw_a @ A @ B ) )
= ( ^ [C: nat] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_isnpolyh_Osimps_I8_J) ).
thf(587,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ ( polyno1538138524e_Pw_a @ A @ B ) )
= ( ^ [C: nat] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(138,axiom,
( ( polyno1371724751ypow_a @ zero_zero_nat )
= ( ^ [A: polyno727731844poly_a] : ( polyno439679028le_C_a @ one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_polypow_Osimps_I1_J) ).
thf(702,plain,
( ( polyno1371724751ypow_a @ zero_zero_nat )
= ( ^ [A: polyno727731844poly_a] : ( polyno439679028le_C_a @ one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_add_Oleft__commute) ).
thf(344,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(44,axiom,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_ring__class_Oring__distribs_I2_J) ).
thf(357,plain,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(89,axiom,
! [A: a] :
( ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ A ) )
= ( ^ [B: nat] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_isnpolyh_Osimps_I1_J) ).
thf(542,plain,
! [A: a] :
( ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ A ) )
= ( ^ [B: nat] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(171,axiom,
! [A: polyno727731844poly_a] : ( polyno190918219poly_a @ ( polyno955999183nate_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_polynate__norm) ).
thf(817,plain,
! [A: polyno727731844poly_a] : ( polyno190918219poly_a @ ( polyno955999183nate_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(181,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1538138524e_Pw_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_polymul_Osimps_I28_J) ).
thf(853,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1538138524e_Pw_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(187,axiom,
polyno1372495879olyh_a @ p @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_np) ).
thf(870,plain,
polyno1372495879olyh_a @ p @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(157,axiom,
! [A: a] :
( ( times_times_a @ A @ one_one_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_mult_Oright__neutral) ).
thf(770,plain,
! [A: a] :
( ( times_times_a @ A @ one_one_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(191,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno190918219poly_a @ A )
=> ( ( polyno190918219poly_a @ B )
=> ( polyno190918219poly_a @ ( polyno1934269411ymul_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_polymul__norm) ).
thf(881,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno190918219poly_a @ A )
=> ( ( polyno190918219poly_a @ B )
=> ( polyno190918219poly_a @ ( polyno1934269411ymul_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(6,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1674775833reen_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( ^ [C: nat] : zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_degreen_Osimps_I4_J) ).
thf(228,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1674775833reen_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( ^ [C: nat] : zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_add__cancel__right__right) ).
thf(261,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(216,plain,
( ( polyno1934269411ymul_a @ p @ q )
!= ( polyno1934269411ymul_a @ q @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(153,axiom,
! [A: a,B: a] :
( ( A
= ( times_times_a @ B @ A ) )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_mult__cancel__right1) ).
thf(756,plain,
! [A: a,B: a] :
( ( A
= ( times_times_a @ B @ A ) )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= B )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_add__cancel__left__left) ).
thf(321,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= B )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(175,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_poly__deriv_Osimps_I4_J) ).
thf(834,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(167,axiom,
! [A: a] :
( ( polyno955999183nate_a @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_polynate_Osimps_I8_J) ).
thf(806,plain,
! [A: a] :
( ( polyno955999183nate_a @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(215,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1623170614_Add_a @ A @ B ) @ C )
= ( polyno1491482291_Mul_a @ ( polyno1623170614_Add_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_polymul_Osimps_I6_J) ).
thf(966,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1623170614_Add_a @ A @ B ) @ C )
= ( polyno1491482291_Mul_a @ ( polyno1623170614_Add_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(108,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1397854436bst0_a @ A @ ( polyno1623170614_Add_a @ B @ C ) )
= ( polyno1623170614_Add_a @ ( polyno1397854436bst0_a @ A @ B ) @ ( polyno1397854436bst0_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_polysubst0_Osimps_I4_J) ).
thf(602,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1397854436bst0_a @ A @ ( polyno1623170614_Add_a @ B @ C ) )
= ( polyno1623170614_Add_a @ ( polyno1397854436bst0_a @ A @ B ) @ ( polyno1397854436bst0_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(21,axiom,
! [A: a,B: a,C: a] :
( ( times_times_a @ A @ ( plus_plus_a @ B @ C ) )
= ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_ring__class_Oring__distribs_I1_J) ).
thf(280,plain,
! [A: a,B: a,C: a] :
( ( times_times_a @ A @ ( plus_plus_a @ B @ C ) )
= ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( polyno1372495879olyh_a @ ( polyno1884029055head_a @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_head__isnpolyh) ).
thf(221,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( polyno1372495879olyh_a @ ( polyno1884029055head_a @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_add__eq__self__zero) ).
thf(293,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(58,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_add__0__iff) ).
thf(396,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( if_nat @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Nat__Onat_T) ).
thf(411,plain,
! [A: nat,B: nat] :
( ( if_nat @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(68,axiom,
! [A: nat] :
( ( polyno1465139388head_a @ ( polyno2024845497ound_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_behead_Osimps_I3_J) ).
thf(428,plain,
! [A: nat] :
( ( polyno1465139388head_a @ ( polyno2024845497ound_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(180,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ A )
= ( polyno439679028le_C_a @ zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_polymul__0_I2_J) ).
thf(849,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ A )
= ( polyno439679028le_C_a @ zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(30,axiom,
! [A: a] :
( ( polyno578545843gree_a @ ( polyno439679028le_C_a @ A ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_degree_Osimps_I2_J) ).
thf(312,plain,
! [A: a] :
( ( polyno578545843gree_a @ ( polyno439679028le_C_a @ A ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(190,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1934269411ymul_a @ A @ ( polyno439679028le_C_a @ one_one_a ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_polymul__1_I1_J) ).
thf(877,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1934269411ymul_a @ A @ ( polyno439679028le_C_a @ one_one_a ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(135,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1372495879olyh_a @ C @ D )
=> ( ( ( polyno1418491367ysub_a @ A @ C )
= ( polyno439679028le_C_a @ zero_zero_a ) )
= ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_polysub__0) ).
thf(692,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1372495879olyh_a @ C @ D )
=> ( ( ( polyno1418491367ysub_a @ A @ C )
= ( polyno439679028le_C_a @ zero_zero_a ) )
= ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(51,axiom,
( polyno1884029055head_a
= ( ^ [A: polyno727731844poly_a] : ( polyno567601229eadn_a @ A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_head__eq__headn0) ).
thf(380,plain,
( polyno1884029055head_a
= ( ^ [A: polyno727731844poly_a] : ( polyno567601229eadn_a @ A @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(80,axiom,
! [A: a] :
( ( times_times_a @ A @ one_one_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_mult_Ocomm__neutral) ).
thf(512,plain,
! [A: a] :
( ( times_times_a @ A @ one_one_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(18,axiom,
! [A: a] :
( ( polyno1674775833reen_a @ ( polyno439679028le_C_a @ A ) )
= ( ^ [B: nat] : zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_degreen_Osimps_I2_J) ).
thf(270,plain,
! [A: a] :
( ( polyno1674775833reen_a @ ( polyno439679028le_C_a @ A ) )
= ( ^ [B: nat] : zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(204,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ one_one_a ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_polymul__1_I2_J) ).
thf(925,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ one_one_a ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(47,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_add__left__imp__eq) ).
thf(366,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(212,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1491482291_Mul_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1491482291_Mul_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_polymul_Osimps_I26_J) ).
thf(957,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1491482291_Mul_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1491482291_Mul_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(150,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1465139388head_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_behead_Osimps_I6_J) ).
thf(746,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1465139388head_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(95,axiom,
( polyno784948432ift1_a
= ( polyno1057396216e_CN_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_shift1__def) ).
thf(561,plain,
( polyno784948432ift1_a
= ( polyno1057396216e_CN_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(170,axiom,
! [A: nat] : ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ one_one_a ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_one__normh) ).
thf(815,plain,
! [A: nat] : ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ one_one_a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(12,axiom,
! [A: a] :
( ( polyno567601229eadn_a @ ( polyno439679028le_C_a @ A ) )
= ( ^ [B: nat] : ( polyno439679028le_C_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_headn_Osimps_I2_J) ).
thf(252,plain,
! [A: a] :
( ( polyno567601229eadn_a @ ( polyno439679028le_C_a @ A ) )
= ( ^ [B: nat] : ( polyno439679028le_C_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(127,axiom,
! [A: nat,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno2024845497ound_a @ A )
!= ( polyno1491482291_Mul_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_poly_Odistinct_I19_J) ).
thf(665,plain,
! [A: nat,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno2024845497ound_a @ A )
!= ( polyno1491482291_Mul_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(83,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1465139388head_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_behead_Osimps_I4_J) ).
thf(522,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1465139388head_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(74,axiom,
! [A: a,B: a] :
( ( ( polyno439679028le_C_a @ A )
= ( polyno439679028le_C_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_poly_Oinject_I1_J) ).
thf(493,plain,
! [A: a,B: a] :
( ( ( polyno439679028le_C_a @ A )
= ( polyno439679028le_C_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(132,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1372495879olyh_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( ^ [C: nat] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_isnpolyh_Osimps_I4_J) ).
thf(682,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1372495879olyh_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( ^ [C: nat] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(92,axiom,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno439679028le_C_a @ A )
!= ( polyno1623170614_Add_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_poly_Odistinct_I3_J) ).
thf(551,plain,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno439679028le_C_a @ A )
!= ( polyno1623170614_Add_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(34,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno578545843gree_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_degree_Osimps_I6_J) ).
thf(324,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno578545843gree_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(97,axiom,
! [A: polyno727731844poly_a] :
( ( polyno190918219poly_a @ A )
=> ( ( A
!= ( polyno439679028le_C_a @ zero_zero_a ) )
=> ( polyno190918219poly_a @ ( polyno784948432ift1_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_shift1__isnpoly) ).
thf(566,plain,
! [A: polyno727731844poly_a] :
( ( polyno190918219poly_a @ A )
=> ( ( A
!= ( polyno439679028le_C_a @ zero_zero_a ) )
=> ( polyno190918219poly_a @ ( polyno784948432ift1_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(71,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1465139388head_a @ ( polyno975704247_Sub_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_behead_Osimps_I5_J) ).
thf(484,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1465139388head_a @ ( polyno975704247_Sub_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(82,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a] :
( ( polyno955999183nate_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) )
= ( polyno955999183nate_a @ ( polyno1623170614_Add_a @ A @ ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_polynate_Osimps_I7_J) ).
thf(519,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a] :
( ( polyno955999183nate_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) )
= ( polyno955999183nate_a @ ( polyno1623170614_Add_a @ A @ ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(189,axiom,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno896877631f_bs_a @ A @ B )
=> ( ( polyno896877631f_bs_a @ A @ C )
=> ( polyno896877631f_bs_a @ A @ ( polyno1934269411ymul_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_wf__bs__polyul) ).
thf(874,plain,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno896877631f_bs_a @ A @ B )
=> ( ( polyno896877631f_bs_a @ A @ C )
=> ( polyno896877631f_bs_a @ A @ ( polyno1934269411ymul_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(54,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Nat__Onat_T) ).
thf(388,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(105,axiom,
! [A: nat,B: nat] :
( ( ( polyno2024845497ound_a @ A )
= ( polyno2024845497ound_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_poly_Oinject_I2_J) ).
thf(593,plain,
! [A: nat,B: nat] :
( ( ( polyno2024845497ound_a @ A )
= ( polyno2024845497ound_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(111,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a] :
( ( polyno2115742616onst_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) )
= ( polyno2115742616onst_a @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_headconst_Osimps_I1_J) ).
thf(610,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a] :
( ( polyno2115742616onst_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) )
= ( polyno2115742616onst_a @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(76,axiom,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( times_times_a @ ( polyno422358502poly_a @ A @ B ) @ ( polyno422358502poly_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Ipoly_Osimps_I6_J) ).
thf(499,plain,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( times_times_a @ ( polyno422358502poly_a @ A @ B ) @ ( polyno422358502poly_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(192,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: polyno727731844poly_a,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1491482291_Mul_a @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1491482291_Mul_a @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_polymul_Osimps_I14_J) ).
thf(884,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: polyno727731844poly_a,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1491482291_Mul_a @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1491482291_Mul_a @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(128,axiom,
! [A: nat,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( polyno2024845497ound_a @ A )
!= ( polyno1057396216e_CN_a @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_poly_Odistinct_I25_J) ).
thf(669,plain,
! [A: nat,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( polyno2024845497ound_a @ A )
!= ( polyno1057396216e_CN_a @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(120,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: polyno727731844poly_a,E: nat,F: polyno727731844poly_a] :
( ( ( polyno1057396216e_CN_a @ A @ B @ C )
= ( polyno1057396216e_CN_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_poly_Oinject_I8_J) ).
thf(642,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: polyno727731844poly_a,E: nat,F: polyno727731844poly_a] :
( ( ( polyno1057396216e_CN_a @ A @ B @ C )
= ( polyno1057396216e_CN_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(104,axiom,
! [A: a,B: a] :
( ( A
= ( times_times_a @ A @ B ) )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_mult__cancel__left1) ).
thf(590,plain,
! [A: a,B: a] :
( ( A
= ( times_times_a @ A @ B ) )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(131,axiom,
! [A: polyno727731844poly_a > polyno727731844poly_a,B: nat,C: polyno727731844poly_a] :
( ( A @ ( compow1114216044poly_a @ B @ A @ C ) )
= ( compow1114216044poly_a @ B @ A @ ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_funpow__swap1) ).
thf(679,plain,
! [A: polyno727731844poly_a > polyno727731844poly_a,B: nat,C: polyno727731844poly_a] :
( ( A @ ( compow1114216044poly_a @ B @ A @ C ) )
= ( compow1114216044poly_a @ B @ A @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(140,axiom,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( times_times_a @ A @ B ) @ C )
= ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_mult_Oassoc) ).
thf(706,plain,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( times_times_a @ A @ B ) @ C )
= ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(176,axiom,
! [A: list_a,B: a] :
( ( polyno422358502poly_a @ A @ ( polyno439679028le_C_a @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Ipoly_Osimps_I1_J) ).
thf(837,plain,
! [A: list_a,B: a] :
( ( polyno422358502poly_a @ A @ ( polyno439679028le_C_a @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(81,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat] :
( ( polyno1491482291_Mul_a @ A @ B )
!= ( polyno1538138524e_Pw_a @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_poly_Odistinct_I47_J) ).
thf(515,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat] :
( ( polyno1491482291_Mul_a @ A @ B )
!= ( polyno1538138524e_Pw_a @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(143,axiom,
! [A: a,B: a,C: a,D: a,E: a] :
( ( A != zero_zero_a )
=> ( ( ( B = C )
& ( D != E ) )
=> ( ( plus_plus_a @ B @ ( times_times_a @ A @ D ) )
!= ( plus_plus_a @ C @ ( times_times_a @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_add__scale__eq__noteq) ).
thf(721,plain,
! [A: a,B: a,C: a,D: a,E: a] :
( ( A != zero_zero_a )
=> ( ( ( B = C )
& ( D != E ) )
=> ( ( plus_plus_a @ B @ ( times_times_a @ A @ D ) )
!= ( plus_plus_a @ C @ ( times_times_a @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(98,axiom,
! [A: polyno727731844poly_a,B: nat,C: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( A
!= ( polyno439679028le_C_a @ zero_zero_a ) )
=> ( ( polyno567601229eadn_a @ A @ C )
!= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_headnz) ).
thf(569,plain,
! [A: polyno727731844poly_a,B: nat,C: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( A
!= ( polyno439679028le_C_a @ zero_zero_a ) )
=> ( ( polyno567601229eadn_a @ A @ C )
!= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_add__is__0) ).
thf(371,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)],[48]) ).
thf(109,axiom,
( polyno190918219poly_a
= ( ^ [A: polyno727731844poly_a] : ( polyno1372495879olyh_a @ A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_isnpoly__def) ).
thf(605,plain,
( polyno190918219poly_a
= ( ^ [A: polyno727731844poly_a] : ( polyno1372495879olyh_a @ A @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(9,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1674775833reen_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( ^ [C: nat] : zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_degreen_Osimps_I6_J) ).
thf(237,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1674775833reen_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( ^ [C: nat] : zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(208,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: polyno727731844poly_a,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1623170614_Add_a @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1623170614_Add_a @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_polymul_Osimps_I12_J) ).
thf(938,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: polyno727731844poly_a,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1623170614_Add_a @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1623170614_Add_a @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(45,axiom,
! [A: nat] :
( ( polyno1884029055head_a @ ( polyno2024845497ound_a @ A ) )
= ( polyno2024845497ound_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_head_Osimps_I3_J) ).
thf(360,plain,
! [A: nat] :
( ( polyno1884029055head_a @ ( polyno2024845497ound_a @ A ) )
= ( polyno2024845497ound_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(156,axiom,
! [A: nat,B: polyno727731844poly_a > polyno727731844poly_a,C: polyno727731844poly_a,D: nat] :
( ! [E: polyno727731844poly_a] :
( ( polyno1372495879olyh_a @ E @ A )
=> ( polyno1372495879olyh_a @ ( B @ E ) @ A ) )
=> ( ( polyno1372495879olyh_a @ C @ A )
=> ( polyno1372495879olyh_a @ ( compow1114216044poly_a @ D @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_funpow__isnpolyh) ).
thf(765,plain,
! [A: nat,B: polyno727731844poly_a > polyno727731844poly_a,C: polyno727731844poly_a,D: nat] :
( ! [E: polyno727731844poly_a] :
( ( polyno1372495879olyh_a @ E @ A )
=> ( polyno1372495879olyh_a @ ( B @ E ) @ A ) )
=> ( ( polyno1372495879olyh_a @ C @ A )
=> ( polyno1372495879olyh_a @ ( compow1114216044poly_a @ D @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(211,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1372495879olyh_a @ C @ D )
=> ( ( ( polyno1934269411ymul_a @ A @ C )
= ( polyno439679028le_C_a @ zero_zero_a ) )
= ( ( A
= ( polyno439679028le_C_a @ zero_zero_a ) )
| ( C
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_polymul__eq0__iff) ).
thf(953,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1372495879olyh_a @ C @ D )
=> ( ( ( polyno1934269411ymul_a @ A @ C )
= ( polyno439679028le_C_a @ zero_zero_a ) )
= ( ( A
= ( polyno439679028le_C_a @ zero_zero_a ) )
| ( C
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(126,axiom,
! [A: a,B: a,C: a] :
( ( ( times_times_a @ A @ B )
= ( times_times_a @ A @ C ) )
= ( ( A = zero_zero_a )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_mult__cancel__left) ).
thf(662,plain,
! [A: a,B: a,C: a] :
( ( ( times_times_a @ A @ B )
= ( times_times_a @ A @ C ) )
= ( ( A = zero_zero_a )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(158,axiom,
! [A: nat] :
( ( polyno567601229eadn_a @ ( polyno2024845497ound_a @ A ) )
= ( ^ [B: nat] : ( polyno2024845497ound_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_headn_Osimps_I3_J) ).
thf(773,plain,
! [A: nat] :
( ( polyno567601229eadn_a @ ( polyno2024845497ound_a @ A ) )
= ( ^ [B: nat] : ( polyno2024845497ound_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(163,axiom,
! [A: a] :
( ( polyno1465139388head_a @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_behead_Osimps_I2_J) ).
thf(794,plain,
! [A: a] :
( ( polyno1465139388head_a @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(200,axiom,
! [A: a,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( ( A = zero_zero_a )
=> ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1057396216e_CN_a @ B @ C @ D ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ) )
& ( ( A != zero_zero_a )
=> ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1057396216e_CN_a @ B @ C @ D ) )
= ( polyno1057396216e_CN_a @ ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ B ) @ C @ ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_polymul_Osimps_I2_J) ).
thf(906,plain,
! [A: a,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( ( A = zero_zero_a )
=> ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1057396216e_CN_a @ B @ C @ D ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ) )
& ( ( A != zero_zero_a )
=> ( ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1057396216e_CN_a @ B @ C @ D ) )
= ( polyno1057396216e_CN_a @ ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ B ) @ C @ ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(67,axiom,
! [A: polyno727731844poly_a > polyno727731844poly_a,B: polyno727731844poly_a] :
( ( compow1114216044poly_a @ zero_zero_nat @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_funpow__0) ).
thf(425,plain,
! [A: polyno727731844poly_a > polyno727731844poly_a,B: polyno727731844poly_a] :
( ( compow1114216044poly_a @ zero_zero_nat @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(16,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1884029055head_a @ ( polyno1057396216e_CN_a @ A @ zero_zero_nat @ B ) )
= ( polyno1884029055head_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_head_Osimps_I1_J) ).
thf(264,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1884029055head_a @ ( polyno1057396216e_CN_a @ A @ zero_zero_nat @ B ) )
= ( polyno1884029055head_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(182,axiom,
( ( ! [A: list_a] :
( ( polyno422358502poly_a @ A @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ A @ ( polyno1934269411ymul_a @ q @ p ) ) ) )
= ( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ) ),
file('/export/starexec/sandbox/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(856,plain,
( ( ! [A: list_a] :
( ( polyno422358502poly_a @ A @ ( polyno1934269411ymul_a @ p @ q ) )
= ( polyno422358502poly_a @ A @ ( polyno1934269411ymul_a @ q @ p ) ) ) )
= ( ( polyno1934269411ymul_a @ p @ q )
= ( polyno1934269411ymul_a @ q @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(99,axiom,
! [A: a,B: a,C: a] :
( ( A != zero_zero_a )
=> ( ( ( times_times_a @ B @ A )
= ( times_times_a @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_mult__right__cancel) ).
thf(573,plain,
! [A: a,B: a,C: a] :
( ( A != zero_zero_a )
=> ( ( ( times_times_a @ B @ A )
= ( times_times_a @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_333_Euclid__induct) ).
thf(296,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)],[26]) ).
thf(146,axiom,
! [A: a] :
( ( times_times_a @ A @ zero_zero_a )
= zero_zero_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_mult__zero__right) ).
thf(733,plain,
! [A: a] :
( ( times_times_a @ A @ zero_zero_a )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(102,axiom,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( times_times_a @ A @ B ) @ C )
= ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(584,plain,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( times_times_a @ A @ B ) @ C )
= ( times_times_a @ A @ ( times_times_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(172,axiom,
! [A: a,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( polyno439679028le_C_a @ A )
!= ( polyno1057396216e_CN_a @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_poly_Odistinct_I13_J) ).
thf(819,plain,
! [A: a,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( polyno439679028le_C_a @ A )
!= ( polyno1057396216e_CN_a @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_add__cancel__left__right) ).
thf(402,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(178,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1934269411ymul_a @ A @ ( polyno2024845497ound_a @ B ) )
= ( polyno1491482291_Mul_a @ A @ ( polyno2024845497ound_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_polymul_Osimps_I17_J) ).
thf(843,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1934269411ymul_a @ A @ ( polyno2024845497ound_a @ B ) )
= ( polyno1491482291_Mul_a @ A @ ( polyno2024845497ound_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(23,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ D )
=> ( ( polyno1674775833reen_a @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_degreen__npolyhCN) ).
thf(286,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ D )
=> ( ( polyno1674775833reen_a @ A @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(149,axiom,
! [A: polyno727731844poly_a] :
( ( polyno1465139388head_a @ ( polyno96675367_Neg_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_behead_Osimps_I7_J) ).
thf(743,plain,
! [A: polyno727731844poly_a] :
( ( polyno1465139388head_a @ ( polyno96675367_Neg_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(100,axiom,
! [A: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno96675367_Neg_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_poly__deriv_Osimps_I7_J) ).
thf(577,plain,
! [A: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno96675367_Neg_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(90,axiom,
! [A: a,B: a,C: a] :
( ( times_times_a @ A @ ( times_times_a @ B @ C ) )
= ( times_times_a @ B @ ( times_times_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_mult_Oleft__commute) ).
thf(545,plain,
! [A: a,B: a,C: a] :
( ( times_times_a @ A @ ( times_times_a @ B @ C ) )
= ( times_times_a @ B @ ( times_times_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_add__eq__0__iff__both__eq__0) ).
thf(391,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)],[56]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(382,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(161,axiom,
! [A: a,B: a,C: a] :
( ( A != zero_zero_a )
=> ( ( ( times_times_a @ A @ B )
= ( times_times_a @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_mult__left__cancel) ).
thf(787,plain,
! [A: a,B: a,C: a] :
( ( A != zero_zero_a )
=> ( ( ( times_times_a @ A @ B )
= ( times_times_a @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(139,axiom,
! [A: nat] : ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_zero__normh) ).
thf(704,plain,
! [A: nat] : ( polyno1372495879olyh_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(198,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: nat] :
( ( polyno1934269411ymul_a @ A @ ( polyno1538138524e_Pw_a @ B @ C ) )
= ( polyno1491482291_Mul_a @ A @ ( polyno1538138524e_Pw_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_polymul_Osimps_I22_J) ).
thf(900,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: nat] :
( ( polyno1934269411ymul_a @ A @ ( polyno1538138524e_Pw_a @ B @ C ) )
= ( polyno1491482291_Mul_a @ A @ ( polyno1538138524e_Pw_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(174,axiom,
! [A: a,B: a,C: a] :
( ( ( times_times_a @ A @ B )
= ( times_times_a @ C @ B ) )
= ( ( B = zero_zero_a )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_mult__cancel__right) ).
thf(831,plain,
! [A: a,B: a,C: a] :
( ( ( times_times_a @ A @ B )
= ( times_times_a @ C @ B ) )
= ( ( B = zero_zero_a )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( if_nat @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Nat__Onat_T) ).
thf(419,plain,
! [A: nat,B: nat] :
( ( if_nat @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(147,axiom,
! [A: polyno727731844poly_a,B: nat,C: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( ( polyno567601229eadn_a @ A @ C )
= ( polyno439679028le_C_a @ zero_zero_a ) )
= ( A
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_headn__nz) ).
thf(736,plain,
! [A: polyno727731844poly_a,B: nat,C: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( ( polyno567601229eadn_a @ A @ C )
= ( polyno439679028le_C_a @ zero_zero_a ) )
= ( A
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(50,axiom,
! [A: nat] :
( ( polyno1674775833reen_a @ ( polyno2024845497ound_a @ A ) )
= ( ^ [B: nat] : zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_degreen_Osimps_I3_J) ).
thf(377,plain,
! [A: nat] :
( ( polyno1674775833reen_a @ ( polyno2024845497ound_a @ A ) )
= ( ^ [B: nat] : zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_add__right__cancel) ).
thf(318,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(107,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
=> ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_divisors__zero) ).
thf(599,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
=> ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(79,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1465139388head_a @ ( polyno1538138524e_Pw_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_behead_Osimps_I8_J) ).
thf(509,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1465139388head_a @ ( polyno1538138524e_Pw_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(122,axiom,
! [A: a] :
( ( times_times_a @ zero_zero_a @ A )
= zero_zero_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_mult__zero__left) ).
thf(649,plain,
! [A: a] :
( ( times_times_a @ zero_zero_a @ A )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(70,axiom,
! [A: polyno727731844poly_a,B: nat > nat] :
( ( ( polyno1674775833reen_a @ A )
= B )
=> ( ! [C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( A
= ( polyno1057396216e_CN_a @ C @ D @ E ) )
=> ( B
!= ( ^ [F: nat] : ( if_nat @ ( D = F ) @ ( plus_plus_nat @ one_one_nat @ ( polyno1674775833reen_a @ E @ D ) ) @ zero_zero_nat ) ) ) )
=> ( ( ? [C: a] :
( A
= ( polyno439679028le_C_a @ C ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: nat] :
( A
= ( polyno2024845497ound_a @ C ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: polyno727731844poly_a,D: polyno727731844poly_a] :
( A
= ( polyno1623170614_Add_a @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: polyno727731844poly_a,D: polyno727731844poly_a] :
( A
= ( polyno975704247_Sub_a @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: polyno727731844poly_a,D: polyno727731844poly_a] :
( A
= ( polyno1491482291_Mul_a @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: polyno727731844poly_a] :
( A
= ( polyno96675367_Neg_a @ C ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ~ ( ? [C: polyno727731844poly_a,D: nat] :
( A
= ( polyno1538138524e_Pw_a @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_degreen_Oelims) ).
thf(434,plain,
! [A: polyno727731844poly_a,B: nat > nat] :
( ( ( polyno1674775833reen_a @ A )
= B )
=> ( ! [C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( A
= ( polyno1057396216e_CN_a @ C @ D @ E ) )
=> ( B
!= ( ^ [F: nat] : ( if_nat @ ( D = F ) @ ( plus_plus_nat @ one_one_nat @ ( polyno1674775833reen_a @ E @ D ) ) @ zero_zero_nat ) ) ) )
=> ( ( ? [C: a] :
( A
= ( polyno439679028le_C_a @ C ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: nat] :
( A
= ( polyno2024845497ound_a @ C ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: polyno727731844poly_a,D: polyno727731844poly_a] :
( A
= ( polyno1623170614_Add_a @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: polyno727731844poly_a,D: polyno727731844poly_a] :
( A
= ( polyno975704247_Sub_a @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: polyno727731844poly_a,D: polyno727731844poly_a] :
( A
= ( polyno1491482291_Mul_a @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ( ( ? [C: polyno727731844poly_a] :
( A
= ( polyno96675367_Neg_a @ C ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) )
=> ~ ( ? [C: polyno727731844poly_a,D: nat] :
( A
= ( polyno1538138524e_Pw_a @ C @ D ) )
=> ( B
!= ( ^ [C: nat] : zero_zero_nat ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(113,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1623170614_Add_a @ A @ B )
!= ( polyno1057396216e_CN_a @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_poly_Odistinct_I35_J) ).
thf(616,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1623170614_Add_a @ A @ B )
!= ( polyno1057396216e_CN_a @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(27,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( A != B )
& ( C != D ) )
= ( ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ D ) )
!= ( plus_plus_a @ ( times_times_a @ A @ D ) @ ( times_times_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_crossproduct__noteq) ).
thf(303,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( A != B )
& ( C != D ) )
= ( ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ D ) )
!= ( plus_plus_a @ ( times_times_a @ A @ D ) @ ( times_times_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(194,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1623170614_Add_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1623170614_Add_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_polymul_Osimps_I24_J) ).
thf(890,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1623170614_Add_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1623170614_Add_a @ A @ B ) @ ( polyno1057396216e_CN_a @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(183,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1538138524e_Pw_a @ A @ B ) @ C )
= ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_polymul_Osimps_I10_J) ).
thf(858,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1538138524e_Pw_a @ A @ B ) @ C )
= ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(87,axiom,
! [A: list_a,B: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno955999183nate_a @ B ) )
= ( polyno422358502poly_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_polynate) ).
thf(535,plain,
! [A: list_a,B: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno955999183nate_a @ B ) )
= ( polyno422358502poly_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(144,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1491482291_Mul_a @ A @ B )
!= ( polyno1057396216e_CN_a @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_poly_Odistinct_I49_J) ).
thf(726,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: nat,E: polyno727731844poly_a] :
( ( polyno1491482291_Mul_a @ A @ B )
!= ( polyno1057396216e_CN_a @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(10,axiom,
! [A: nat,B: polyno727731844poly_a] :
( ( ( A = zero_zero_nat )
=> ( ( polyno1397854436bst0_a @ B @ ( polyno2024845497ound_a @ A ) )
= B ) )
& ( ( A != zero_zero_nat )
=> ( ( polyno1397854436bst0_a @ B @ ( polyno2024845497ound_a @ A ) )
= ( polyno2024845497ound_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_polysubst0_Osimps_I2_J) ).
thf(240,plain,
! [A: nat,B: polyno727731844poly_a] :
( ( ( A = zero_zero_nat )
=> ( ( polyno1397854436bst0_a @ B @ ( polyno2024845497ound_a @ A ) )
= B ) )
& ( ( A != zero_zero_nat )
=> ( ( polyno1397854436bst0_a @ B @ ( polyno2024845497ound_a @ A ) )
= ( polyno2024845497ound_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(201,axiom,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno1623170614_Add_a @ B @ C ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1623170614_Add_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_poly__cmul_Osimps_I4_J) ).
thf(915,plain,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno1623170614_Add_a @ B @ C ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1623170614_Add_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(36,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_comm__monoid__add__class_Oadd__0) ).
thf(330,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(206,axiom,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno975704247_Sub_a @ B @ C ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno975704247_Sub_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_poly__cmul_Osimps_I5_J) ).
thf(932,plain,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno975704247_Sub_a @ B @ C ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno975704247_Sub_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(133,axiom,
! [A: polyno727731844poly_a,B: nat,C: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( polyno1372495879olyh_a @ ( polyno1371724751ypow_a @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_polypow__normh) ).
thf(685,plain,
! [A: polyno727731844poly_a,B: nat,C: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( polyno1372495879olyh_a @ ( polyno1371724751ypow_a @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(59,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_zero__neq__one) ).
thf(399,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(160,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ! [C: list_a] :
( ( polyno896877631f_bs_a @ C @ A )
=> ( ( polyno422358502poly_a @ C @ A )
= zero_zero_a ) )
=> ( A
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_isnpolyh__zero__iff) ).
thf(780,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ! [C: list_a] :
( ( polyno896877631f_bs_a @ C @ A )
=> ( ( polyno422358502poly_a @ C @ A )
= zero_zero_a ) )
=> ( A
= ( polyno439679028le_C_a @ zero_zero_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ B @ C ) )
=> ( ( plus_plus_nat @ D @ A )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_group__cancel_Oadd2) ).
thf(223,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ B @ C ) )
=> ( ( plus_plus_nat @ D @ A )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(96,axiom,
! [A: a] :
( ( times_times_a @ one_one_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_mult_Oleft__neutral) ).
thf(563,plain,
! [A: a] :
( ( times_times_a @ one_one_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(17,axiom,
! [A: a,B: a,C: a] :
( ( times_times_a @ A @ ( plus_plus_a @ B @ C ) )
= ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_distrib__left) ).
thf(267,plain,
! [A: a,B: a,C: a] :
( ( times_times_a @ A @ ( plus_plus_a @ B @ C ) )
= ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(78,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1418491367ysub_a @ A @ A )
= ( polyno439679028le_C_a @ zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_polysub__same__0) ).
thf(505,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1418491367ysub_a @ A @ A )
= ( polyno439679028le_C_a @ zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(69,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= B )
= ( ( B = zero_zero_a )
| ( A = one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_mult__cancel__right2) ).
thf(431,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= B )
= ( ( B = zero_zero_a )
| ( A = one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(203,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( polyno1491482291_Mul_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_polymul_Osimps_I20_J) ).
thf(922,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( polyno1491482291_Mul_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(125,axiom,
! [A: polyno727731844poly_a,B: nat,C: list_a] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno422358502poly_a @ C @ ( polyno1623170614_Add_a @ ( polyno1491482291_Mul_a @ ( polyno1884029055head_a @ A ) @ ( polyno1538138524e_Pw_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ ( polyno578545843gree_a @ A ) ) ) @ ( polyno1465139388head_a @ A ) ) )
= ( polyno422358502poly_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_behead) ).
thf(658,plain,
! [A: polyno727731844poly_a,B: nat,C: list_a] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno422358502poly_a @ C @ ( polyno1623170614_Add_a @ ( polyno1491482291_Mul_a @ ( polyno1884029055head_a @ A ) @ ( polyno1538138524e_Pw_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ ( polyno578545843gree_a @ A ) ) ) @ ( polyno1465139388head_a @ A ) ) )
= ( polyno422358502poly_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(57,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( polyno1372495879olyh_a @ ( polyno1465139388head_a @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_behead__isnpolyh) ).
thf(394,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( polyno1372495879olyh_a @ ( polyno1465139388head_a @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_add__cancel__right__left) ).
thf(306,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(73,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: polyno727731844poly_a] :
( ( ( polyno1623170614_Add_a @ A @ B )
= ( polyno1623170614_Add_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_poly_Oinject_I3_J) ).
thf(490,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: polyno727731844poly_a] :
( ( ( polyno1623170614_Add_a @ A @ B )
= ( polyno1623170614_Add_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(210,axiom,
! [A: a,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( ( A = zero_zero_a )
=> ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ B @ C @ D ) @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ) )
& ( ( A != zero_zero_a )
=> ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ B @ C @ D ) @ ( polyno439679028le_C_a @ A ) )
= ( polyno1057396216e_CN_a @ ( polyno1934269411ymul_a @ B @ ( polyno439679028le_C_a @ A ) ) @ C @ ( polyno1934269411ymul_a @ D @ ( polyno439679028le_C_a @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_polymul_Osimps_I3_J) ).
thf(944,plain,
! [A: a,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( ( A = zero_zero_a )
=> ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ B @ C @ D ) @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ) )
& ( ( A != zero_zero_a )
=> ( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ B @ C @ D ) @ ( polyno439679028le_C_a @ A ) )
= ( polyno1057396216e_CN_a @ ( polyno1934269411ymul_a @ B @ ( polyno439679028le_C_a @ A ) ) @ C @ ( polyno1934269411ymul_a @ D @ ( polyno439679028le_C_a @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(91,axiom,
! [A: list_a,B: nat,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( compow1114216044poly_a @ B @ polyno784948432ift1_a @ C ) )
= ( polyno422358502poly_a @ A @ ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_funpow__shift1) ).
thf(548,plain,
! [A: list_a,B: nat,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( compow1114216044poly_a @ B @ polyno784948432ift1_a @ C ) )
= ( polyno422358502poly_a @ A @ ( polyno1491482291_Mul_a @ ( polyno1538138524e_Pw_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(49,axiom,
! [A: a] :
( ( polyno1884029055head_a @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_head_Osimps_I2_J) ).
thf(374,plain,
! [A: a] :
( ( polyno1884029055head_a @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(13,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_add_Oleft__neutral) ).
thf(255,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(72,axiom,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno896877631f_bs_a @ A @ B )
=> ( ( polyno896877631f_bs_a @ A @ C )
=> ( polyno896877631f_bs_a @ A @ ( polyno1418491367ysub_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_wf__bs__polysub) ).
thf(487,plain,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno896877631f_bs_a @ A @ B )
=> ( ( polyno896877631f_bs_a @ A @ C )
=> ( polyno896877631f_bs_a @ A @ ( polyno1418491367ysub_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(169,axiom,
! [A: nat] :
( ( polyno212464073eriv_a @ ( polyno2024845497ound_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_poly__deriv_Osimps_I3_J) ).
thf(812,plain,
! [A: nat] :
( ( polyno212464073eriv_a @ ( polyno2024845497ound_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(151,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1397854436bst0_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( polyno1491482291_Mul_a @ ( polyno1397854436bst0_a @ A @ B ) @ ( polyno1397854436bst0_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_polysubst0_Osimps_I6_J) ).
thf(749,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1397854436bst0_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( polyno1491482291_Mul_a @ ( polyno1397854436bst0_a @ A @ B ) @ ( polyno1397854436bst0_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(173,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
!= zero_zero_a )
=> ( ( A != zero_zero_a )
& ( B != zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_mult__not__zero) ).
thf(823,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
!= zero_zero_a )
=> ( ( A != zero_zero_a )
& ( B != zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(159,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: polyno727731844poly_a] :
( ( polyno1623170614_Add_a @ A @ B )
!= ( polyno1491482291_Mul_a @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_poly_Odistinct_I29_J) ).
thf(776,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: polyno727731844poly_a] :
( ( polyno1623170614_Add_a @ A @ B )
!= ( polyno1491482291_Mul_a @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(84,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= A )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_mult__cancel__left2) ).
thf(525,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= A )
= ( ( A = zero_zero_a )
| ( B = one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(101,axiom,
! [A: a,B: polyno727731844poly_a,C: nat] :
( ( polyno439679028le_C_a @ A )
!= ( polyno1538138524e_Pw_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_poly_Odistinct_I11_J) ).
thf(580,plain,
! [A: a,B: polyno727731844poly_a,C: nat] :
( ( polyno439679028le_C_a @ A )
!= ( polyno1538138524e_Pw_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(193,axiom,
! [A: a,B: nat] :
( ( polyno562434098cmul_a @ A @ ( polyno2024845497ound_a @ B ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno2024845497ound_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_poly__cmul_Osimps_I3_J) ).
thf(887,plain,
! [A: a,B: nat] :
( ( polyno562434098cmul_a @ A @ ( polyno2024845497ound_a @ B ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno2024845497ound_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(64,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_add__right__imp__eq) ).
thf(414,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(35,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_add_Oright__neutral) ).
thf(327,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(142,axiom,
! [A: nat,B: polyno727731844poly_a,C: polyno727731844poly_a,D: polyno727731844poly_a] :
( ( ( A = zero_zero_nat )
=> ( ( polyno1397854436bst0_a @ B @ ( polyno1057396216e_CN_a @ C @ A @ D ) )
= ( polyno1623170614_Add_a @ ( polyno1397854436bst0_a @ B @ C ) @ ( polyno1491482291_Mul_a @ B @ ( polyno1397854436bst0_a @ B @ D ) ) ) ) )
& ( ( A != zero_zero_nat )
=> ( ( polyno1397854436bst0_a @ B @ ( polyno1057396216e_CN_a @ C @ A @ D ) )
= ( polyno1057396216e_CN_a @ ( polyno1397854436bst0_a @ B @ C ) @ A @ ( polyno1397854436bst0_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_polysubst0_Osimps_I8_J) ).
thf(712,plain,
! [A: nat,B: polyno727731844poly_a,C: polyno727731844poly_a,D: polyno727731844poly_a] :
( ( ( A = zero_zero_nat )
=> ( ( polyno1397854436bst0_a @ B @ ( polyno1057396216e_CN_a @ C @ A @ D ) )
= ( polyno1623170614_Add_a @ ( polyno1397854436bst0_a @ B @ C ) @ ( polyno1491482291_Mul_a @ B @ ( polyno1397854436bst0_a @ B @ D ) ) ) ) )
& ( ( A != zero_zero_nat )
=> ( ( polyno1397854436bst0_a @ B @ ( polyno1057396216e_CN_a @ C @ A @ D ) )
= ( polyno1057396216e_CN_a @ ( polyno1397854436bst0_a @ B @ C ) @ A @ ( polyno1397854436bst0_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(94,axiom,
! [A: nat,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno2024845497ound_a @ A )
!= ( polyno1623170614_Add_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_poly_Odistinct_I15_J) ).
thf(557,plain,
! [A: nat,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno2024845497ound_a @ A )
!= ( polyno1623170614_Add_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(129,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno975704247_Sub_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_poly__deriv_Osimps_I5_J) ).
thf(673,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno975704247_Sub_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(162,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno212464073eriv_a @ ( polyno1538138524e_Pw_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_poly__deriv_Osimps_I8_J) ).
thf(791,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno212464073eriv_a @ ( polyno1538138524e_Pw_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(77,axiom,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_mult__eq__0__iff) ).
thf(502,plain,
! [A: a,B: a] :
( ( ( times_times_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
| ( B = zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(177,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno955999183nate_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( polyno1934269411ymul_a @ ( polyno955999183nate_a @ A ) @ ( polyno955999183nate_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_polynate_Osimps_I4_J) ).
thf(840,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno955999183nate_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( polyno1934269411ymul_a @ ( polyno955999183nate_a @ A ) @ ( polyno955999183nate_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ B @ C ) )
=> ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_group__cancel_Oadd1) ).
thf(336,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ B @ C ) )
=> ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(112,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno190918219poly_a @ A )
=> ( ( polyno190918219poly_a @ B )
=> ( polyno190918219poly_a @ ( polyno1418491367ysub_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_polysub__norm) ).
thf(613,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno190918219poly_a @ A )
=> ( ( polyno190918219poly_a @ B )
=> ( polyno190918219poly_a @ ( polyno1418491367ysub_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(185,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1491482291_Mul_a @ A @ B ) @ C )
= ( polyno1491482291_Mul_a @ ( polyno1491482291_Mul_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_polymul_Osimps_I8_J) ).
thf(864,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno1491482291_Mul_a @ A @ B ) @ C )
= ( polyno1491482291_Mul_a @ ( polyno1491482291_Mul_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(7,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ C @ D ) )
= ( plus_plus_a @ ( times_times_a @ A @ D ) @ ( times_times_a @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_crossproduct__eq) ).
thf(231,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( plus_plus_a @ ( times_times_a @ A @ B ) @ ( times_times_a @ C @ D ) )
= ( plus_plus_a @ ( times_times_a @ A @ D ) @ ( times_times_a @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(46,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1884029055head_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( polyno1491482291_Mul_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_head_Osimps_I6_J) ).
thf(363,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1884029055head_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( polyno1491482291_Mul_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(154,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_poly__deriv_Osimps_I6_J) ).
thf(759,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_add__left__cancel) ).
thf(218,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(134,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1372495879olyh_a @ C @ D )
=> ( ( ! [E: list_a] :
( ( polyno422358502poly_a @ E @ A )
= ( polyno422358502poly_a @ E @ C ) ) )
= ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_isnpolyh__unique) ).
thf(688,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1372495879olyh_a @ C @ D )
=> ( ( ! [E: list_a] :
( ( polyno422358502poly_a @ E @ A )
= ( polyno422358502poly_a @ E @ C ) ) )
= ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(199,axiom,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: polyno727731844poly_a,E: nat] :
( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1538138524e_Pw_a @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1538138524e_Pw_a @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_polymul_Osimps_I16_J) ).
thf(903,plain,
! [A: polyno727731844poly_a,B: nat,C: polyno727731844poly_a,D: polyno727731844poly_a,E: nat] :
( ( polyno1934269411ymul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1538138524e_Pw_a @ D @ E ) )
= ( polyno1491482291_Mul_a @ ( polyno1057396216e_CN_a @ A @ B @ C ) @ ( polyno1538138524e_Pw_a @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(137,axiom,
! [A: a,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno1057396216e_CN_a @ B @ C @ D ) )
= ( polyno1057396216e_CN_a @ ( polyno562434098cmul_a @ A @ B ) @ C @ ( polyno562434098cmul_a @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_poly__cmul_Osimps_I2_J) ).
thf(699,plain,
! [A: a,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno1057396216e_CN_a @ B @ C @ D ) )
= ( polyno1057396216e_CN_a @ ( polyno562434098cmul_a @ A @ B ) @ C @ ( polyno562434098cmul_a @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(214,axiom,
! [A: list_a,B: nat,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( compow1114216044poly_a @ B @ polyno784948432ift1_a @ C ) )
= ( polyno422358502poly_a @ A @ ( polyno1934269411ymul_a @ ( compow1114216044poly_a @ B @ polyno784948432ift1_a @ ( polyno439679028le_C_a @ one_one_a ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_funpow__shift1__1) ).
thf(963,plain,
! [A: list_a,B: nat,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( compow1114216044poly_a @ B @ polyno784948432ift1_a @ C ) )
= ( polyno422358502poly_a @ A @ ( polyno1934269411ymul_a @ ( compow1114216044poly_a @ B @ polyno784948432ift1_a @ ( polyno439679028le_C_a @ one_one_a ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(196,axiom,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1491482291_Mul_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_poly__cmul_Osimps_I6_J) ).
thf(896,plain,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno562434098cmul_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1491482291_Mul_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(14,axiom,
! [A: nat] :
( ( polyno578545843gree_a @ ( polyno2024845497ound_a @ A ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_degree_Osimps_I3_J) ).
thf(258,plain,
! [A: nat] :
( ( polyno578545843gree_a @ ( polyno2024845497ound_a @ A ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(117,axiom,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1006823949_aux_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( polyno562434098cmul_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_poly__deriv__aux_Osimps_I6_J) ).
thf(632,plain,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1006823949_aux_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) )
= ( polyno562434098cmul_a @ A @ ( polyno1491482291_Mul_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(123,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1372495879olyh_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( ^ [C: nat] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_isnpolyh_Osimps_I6_J) ).
thf(652,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1372495879olyh_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( ^ [C: nat] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(42,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_add_Ocomm__neutral) ).
thf(351,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(24,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno567601229eadn_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( ^ [C: nat] : ( polyno1491482291_Mul_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_headn_Osimps_I6_J) ).
thf(290,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno567601229eadn_a @ ( polyno1491482291_Mul_a @ A @ B ) )
= ( ^ [C: nat] : ( polyno1491482291_Mul_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(205,axiom,
! [A: nat,B: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno2024845497ound_a @ A ) @ B )
= ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_polymul_Osimps_I5_J) ).
thf(929,plain,
! [A: nat,B: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno2024845497ound_a @ A ) @ B )
= ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(197,axiom,
polyno1372495879olyh_a @ q @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_nq) ).
thf(899,plain,
polyno1372495879olyh_a @ q @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(165,axiom,
! [A: a] :
( ( one_one_a = A )
= ( A = one_one_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_one__reorient) ).
thf(800,plain,
! [A: a] :
( ( one_one_a = A )
= ( A = one_one_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(114,axiom,
! [A: polyno727731844poly_a] :
( ( polyno784948432ift1_a @ A )
!= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_shift1__nz) ).
thf(620,plain,
! [A: polyno727731844poly_a] :
( ( polyno784948432ift1_a @ A )
!= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(152,axiom,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno439679028le_C_a @ A )
!= ( polyno1491482291_Mul_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_poly_Odistinct_I7_J) ).
thf(752,plain,
! [A: a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno439679028le_C_a @ A )
!= ( polyno1491482291_Mul_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(31,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno578545843gree_a @ ( polyno1623170614_Add_a @ A @ B ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_degree_Osimps_I4_J) ).
thf(315,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno578545843gree_a @ ( polyno1623170614_Add_a @ A @ B ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(61,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_zero__reorient) ).
thf(405,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ A @ B ) )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_zero__eq__add__iff__both__eq__0) ).
thf(422,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ A @ B ) )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(186,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ A @ ( polyno1623170614_Add_a @ B @ C ) )
= ( polyno1491482291_Mul_a @ A @ ( polyno1623170614_Add_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_polymul_Osimps_I18_J) ).
thf(867,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ A @ ( polyno1623170614_Add_a @ B @ C ) )
= ( polyno1491482291_Mul_a @ A @ ( polyno1623170614_Add_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(19,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1884029055head_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( polyno1623170614_Add_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_head_Osimps_I4_J) ).
thf(273,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno1884029055head_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( polyno1623170614_Add_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(202,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1934269411ymul_a @ A @ ( polyno439679028le_C_a @ zero_zero_a ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_polymul__0_I1_J) ).
thf(918,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( polyno1934269411ymul_a @ A @ ( polyno439679028le_C_a @ zero_zero_a ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(39,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_one__reorient) ).
thf(341,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(86,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: polyno727731844poly_a] :
( ( ( polyno1491482291_Mul_a @ A @ B )
= ( polyno1491482291_Mul_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_poly_Oinject_I5_J) ).
thf(532,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a,C: polyno727731844poly_a,D: polyno727731844poly_a] :
( ( ( polyno1491482291_Mul_a @ A @ B )
= ( polyno1491482291_Mul_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(136,axiom,
! [A: a,B: a] :
( ( polyno562434098cmul_a @ A @ ( polyno439679028le_C_a @ B ) )
= ( polyno439679028le_C_a @ ( times_times_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_poly__cmul_Osimps_I1_J) ).
thf(696,plain,
! [A: a,B: a] :
( ( polyno562434098cmul_a @ A @ ( polyno439679028le_C_a @ B ) )
= ( polyno439679028le_C_a @ ( times_times_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(22,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno1057396216e_CN_a @ A @ zero_zero_nat @ B ) )
= ( polyno1006823949_aux_a @ one_one_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_poly__deriv_Osimps_I1_J) ).
thf(283,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno212464073eriv_a @ ( polyno1057396216e_CN_a @ A @ zero_zero_nat @ B ) )
= ( polyno1006823949_aux_a @ one_one_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(213,axiom,
! [A: nat,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno2024845497ound_a @ A ) @ ( polyno1057396216e_CN_a @ B @ C @ D ) )
= ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ A ) @ ( polyno1057396216e_CN_a @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_polymul_Osimps_I23_J) ).
thf(960,plain,
! [A: nat,B: polyno727731844poly_a,C: nat,D: polyno727731844poly_a] :
( ( polyno1934269411ymul_a @ ( polyno2024845497ound_a @ A ) @ ( polyno1057396216e_CN_a @ B @ C @ D ) )
= ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ A ) @ ( polyno1057396216e_CN_a @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(118,axiom,
! [A: a,B: a] :
( ( A != zero_zero_a )
=> ( ( B != zero_zero_a )
=> ( ( times_times_a @ A @ B )
!= zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_no__zero__divisors) ).
thf(635,plain,
! [A: a,B: a] :
( ( A != zero_zero_a )
=> ( ( B != zero_zero_a )
=> ( ( times_times_a @ A @ B )
!= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(115,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno190918219poly_a @ A )
=> ( ( A
!= ( polyno439679028le_C_a @ zero_zero_a ) )
=> ( polyno190918219poly_a @ ( compow1114216044poly_a @ B @ polyno784948432ift1_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_funpow__shift1__isnpoly) ).
thf(624,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno190918219poly_a @ A )
=> ( ( A
!= ( polyno439679028le_C_a @ zero_zero_a ) )
=> ( polyno190918219poly_a @ ( compow1114216044poly_a @ B @ polyno784948432ift1_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(148,axiom,
! [A: a] :
( ( polyno212464073eriv_a @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_poly__deriv_Osimps_I2_J) ).
thf(740,plain,
! [A: a] :
( ( polyno212464073eriv_a @ ( polyno439679028le_C_a @ A ) )
= ( polyno439679028le_C_a @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(106,axiom,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_zero__reorient) ).
thf(596,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(85,axiom,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( A
!= ( polyno439679028le_C_a @ zero_zero_a ) )
=> ( polyno1372495879olyh_a @ ( polyno784948432ift1_a @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_shift1__isnpolyh) ).
thf(528,plain,
! [A: polyno727731844poly_a,B: nat] :
( ( polyno1372495879olyh_a @ A @ B )
=> ( ( A
!= ( polyno439679028le_C_a @ zero_zero_a ) )
=> ( polyno1372495879olyh_a @ ( polyno784948432ift1_a @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(188,axiom,
! [A: a,B: polyno727731844poly_a,C: nat] :
( ( polyno562434098cmul_a @ A @ ( polyno1538138524e_Pw_a @ B @ C ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1538138524e_Pw_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_poly__cmul_Osimps_I8_J) ).
thf(871,plain,
! [A: a,B: polyno727731844poly_a,C: nat] :
( ( polyno562434098cmul_a @ A @ ( polyno1538138524e_Pw_a @ B @ C ) )
= ( polyno1934269411ymul_a @ ( polyno439679028le_C_a @ A ) @ ( polyno1538138524e_Pw_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(110,axiom,
! [A: polyno727731844poly_a,B: a] :
( ( polyno1397854436bst0_a @ A @ ( polyno439679028le_C_a @ B ) )
= ( polyno439679028le_C_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_polysubst0_Osimps_I1_J) ).
thf(607,plain,
! [A: polyno727731844poly_a,B: a] :
( ( polyno1397854436bst0_a @ A @ ( polyno439679028le_C_a @ B ) )
= ( polyno439679028le_C_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(166,axiom,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno1623170614_Add_a @ B @ C ) )
= ( plus_plus_a @ ( polyno422358502poly_a @ A @ B ) @ ( polyno422358502poly_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_Ipoly_Osimps_I4_J) ).
thf(803,plain,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno1623170614_Add_a @ B @ C ) )
= ( plus_plus_a @ ( polyno422358502poly_a @ A @ B ) @ ( polyno422358502poly_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(43,axiom,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_distrib__right) ).
thf(354,plain,
! [A: a,B: a,C: a] :
( ( times_times_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ ( times_times_a @ A @ C ) @ ( times_times_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(207,axiom,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno1934269411ymul_a @ B @ C ) )
= ( times_times_a @ ( polyno422358502poly_a @ A @ B ) @ ( polyno422358502poly_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_polymul) ).
thf(935,plain,
! [A: list_a,B: polyno727731844poly_a,C: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno1934269411ymul_a @ B @ C ) )
= ( times_times_a @ ( polyno422358502poly_a @ A @ B ) @ ( polyno422358502poly_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_add_Oassoc) ).
thf(309,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(119,axiom,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno567601229eadn_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( ^ [C: nat] : ( polyno1623170614_Add_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_headn_Osimps_I4_J) ).
thf(639,plain,
! [A: polyno727731844poly_a,B: polyno727731844poly_a] :
( ( polyno567601229eadn_a @ ( polyno1623170614_Add_a @ A @ B ) )
= ( ^ [C: nat] : ( polyno1623170614_Add_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(130,axiom,
! [A: list_a,B: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno784948432ift1_a @ B ) )
= ( polyno422358502poly_a @ A @ ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_shift1) ).
thf(676,plain,
! [A: list_a,B: polyno727731844poly_a] :
( ( polyno422358502poly_a @ A @ ( polyno784948432ift1_a @ B ) )
= ( polyno422358502poly_a @ A @ ( polyno1491482291_Mul_a @ ( polyno2024845497ound_a @ zero_zero_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(75,axiom,
! [A: nat] :
( ( polyno955999183nate_a @ ( polyno2024845497ound_a @ A ) )
= ( polyno1057396216e_CN_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ A @ ( polyno439679028le_C_a @ one_one_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_polynate_Osimps_I1_J) ).
thf(496,plain,
! [A: nat] :
( ( polyno955999183nate_a @ ( polyno2024845497ound_a @ A ) )
= ( polyno1057396216e_CN_a @ ( polyno439679028le_C_a @ zero_zero_a ) @ A @ ( polyno439679028le_C_a @ one_one_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(15448,plain,
$false,
inference(e,[status(thm)],[709,645,809,347,846,893,234,941,555,249,333,628,408,762,655,861,730,276,385,797,538,389,587,702,344,357,542,817,853,870,770,881,228,261,216,756,321,834,806,966,602,280,221,293,396,411,428,849,312,877,692,380,512,270,925,366,957,746,561,815,252,665,522,493,682,551,324,566,484,519,874,388,593,610,499,884,669,642,590,679,706,837,515,721,569,371,605,237,938,360,765,953,662,773,794,906,425,264,856,573,296,733,584,819,402,843,286,743,577,545,391,382,787,704,900,831,419,736,377,318,599,509,649,434,616,303,890,858,535,726,240,915,330,932,685,399,780,223,563,267,505,431,922,658,394,306,490,944,548,374,255,487,812,749,823,776,525,580,887,414,327,712,557,673,791,502,840,336,613,864,231,363,759,218,688,903,699,963,896,258,632,652,351,290,929,899,800,620,752,315,405,422,867,273,918,341,532,696,283,960,635,624,740,596,528,871,607,803,354,935,309,639,676,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP150^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n006.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 20:01:51 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.99/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.94/1.16 % [INFO] Parsing done (340ms).
% 1.94/1.18 % [INFO] Running in sequential loop mode.
% 3.13/1.56 % [INFO] eprover registered as external prover.
% 3.13/1.57 % [INFO] Scanning for conjecture ...
% 3.66/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ...
% 3.86/1.83 % [INFO] Axiom selection finished. Selected 213 axioms (removed 142 axioms).
% 4.26/2.02 % [INFO] Problem is higher-order (TPTP THF).
% 4.61/2.04 % [INFO] Type checking passed.
% 4.61/2.04 % [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 ...
% 76.24/15.20 % External prover 'e' found a proof!
% 76.59/15.20 % [INFO] Killing All external provers ...
% 76.59/15.20 % Time passed: 14825ms (effective reasoning time: 14018ms)
% 76.59/15.20 % 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)>
% 76.59/15.20 % Axioms used in derivation (213): fact_17_polymul_Osimps_I14_J, fact_288_combine__common__factor, fact_29_Ipoly_Osimps_I6_J, fact_341_poly__cmul_Osimps_I5_J, fact_279_add__mono__thms__linordered__semiring_I4_J, fact_207_poly__deriv_Osimps_I3_J, fact_33_poly_Odistinct_I35_J, fact_198_headconst_Osimps_I2_J, fact_256_poly__deriv__aux_Osimps_I6_J, fact_262_add__is__0, fact_126_zero__reorient, fact_32_poly_Odistinct_I49_J, fact_44_polymul_Osimps_I24_J, fact_166_shift1__nz, fact_275_isnpolyh_Osimps_I8_J, fact_170_shift1__def, fact_290_distrib__right, help_If_2_1_If_001t__Nat__Onat_T, fact_249_degreen_Osimps_I3_J, fact_144_mult__left__cancel, fact_332_crossproduct__eq, fact_65_polymul__eq0__iff, fact_62_polymul__1_I2_J, fact_50_isnpolyh_Osimps_I4_J, fact_206_degree__npolyhCN, fact_284_add_Oleft__commute, fact_36_poly_Odistinct_I29_J, fact_110_mult__cancel__right2, fact_246_degreen_Osimps_I6_J, fact_150_comm__monoid__mult__class_Omult__1, fact_104_polymul_Osimps_I23_J, fact_52_isnpolyh_Osimps_I1_J, fact_57_polymul_Osimps_I6_J, fact_83_poly_Odistinct_I15_J, fact_169_shift1__isnpoly, fact_324_behead_Osimps_I8_J, fact_348_poly__deriv_Osimps_I7_J, fact_333_Euclid__induct, fact_322_behead_Osimps_I3_J, fact_7_polymul_Osimps_I20_J, fact_72_poly_Oinject_I2_J, fact_30_Ipoly_Osimps_I1_J, fact_107_mult__cancel__left1, fact_138_mult__not__zero, fact_124_mult__eq__0__iff, fact_147_zero__neq__one, fact_176_headconst__zero, fact_300_poly_Odistinct_I11_J, fact_92_polymul_Osimps_I5_J, fact_77_poly_Odistinct_I25_J, fact_261_add__right__cancel, fact_216_degree_Osimps_I3_J, fact_310_polymul_Osimps_I28_J, fact_267_add__cancel__right__left, fact_316_behead_Osimps_I2_J, fact_179_polysubst0_Osimps_I8_J, fact_90_polymul_Osimps_I17_J, fact_292_distrib__left, fact_70_polymul_Osimps_I3_J, fact_5_wf__bs__polyul, fact_15_polymul_Osimps_I26_J, fact_230_funpow__isnpolyh, fact_303_polymul_Osimps_I22_J, fact_213_degree_Osimps_I6_J, fact_306_Ipoly_Osimps_I4_J, fact_58_isnpolyh__zero__iff, fact_75_poly__cmul_Osimps_I3_J, fact_100_isnpoly__def, fact_264_zero__eq__add__iff__both__eq__0, fact_140_divisors__zero, fact_61_polymul__0_I1_J, fact_20_poly_Oinject_I8_J, fact_180_polysubst0_Osimps_I1_J, fact_26_poly_Oinject_I3_J, fact_280_group__cancel_Oadd1, fact_98_zero__normh, fact_152_mult_Ocomm__neutral, fact_2_nq, fact_260_add__left__cancel, fact_251_head_Osimps_I1_J, fact_12_polymul_Osimps_I1_J, fact_258_funpow__shift1__isnpoly, fact_136_one__reorient, fact_25_poly_Oinject_I5_J, fact_305_polymul_Osimps_I10_J, fact_335_polypow_Osimps_I1_J, fact_320_behead_Osimps_I4_J, fact_54_polynate__norm, fact_274_add__eq__self__zero, fact_351_polymul_Osimps_I7_J, fact_343_behead_Osimps_I7_J, fact_281_group__cancel_Oadd2, help_If_3_1_If_001t__Nat__Onat_T, fact_130_mult_Oassoc, fact_132_mult_Ocommute, fact_134_mult_Oleft__commute, fact_311_poly__cmul_Osimps_I8_J, fact_253_head__eq__headn0, fact_200_polysubst0_Osimps_I2_J, fact_116_mult__cancel__right, fact_259_funpow__shift1, fact_192_headn_Osimps_I3_J, fact_74_polynate_Osimps_I1_J, fact_294_comm__semiring__class_Odistrib, help_If_1_1_If_001t__Nat__Onat_T, fact_308_polymul_Osimps_I16_J, fact_339_behead_Osimps_I5_J, fact_69_poly__cmul_Osimps_I6_J, fact_105_polymul_Osimps_I2_J, fact_295_ring__class_Oring__distribs_I1_J, fact_214_degree_Osimps_I4_J, fact_159_shift1__isnpolyh, fact_55_isnpolyh__unique, fact_108_mult__cancel__left2, fact_142_no__zero__divisors, fact_194_wf__bs__polysub, fact_285_add__left__imp__eq, fact_109_mult__cancel__right1, fact_283_add_Ocommute, fact_190_headn_Osimps_I4_J, fact_28_polynate, fact_146_mult__right__cancel, fact_263_Nat_Oadd__0__right, fact_86_isnpolyh_Osimps_I3_J, fact_328_add__0__iff, fact_219_poly__deriv_Osimps_I1_J, fact_266_add__cancel__right__right, fact_298_add_Ocomm__neutral, fact_225_funpow__0, fact_114_mult_Oleft__neutral, fact_184_polysubst0_Osimps_I4_J, fact_1_np, fact_334_verit__sum__simplify, fact_210_degree_Osimps_I2_J, fact_195_polysub__norm, fact_79_poly_Odistinct_I1_J, fact_239_head_Osimps_I3_J, fact_53_polynate_Osimps_I8_J, fact_327_add__scale__eq__noteq, fact_222_head__nz, fact_3_polymul__norm, fact_66_poly__cmul_Osimps_I4_J, fact_202_polysub__0, fact_338_degreen_Oelims, fact_347_poly__deriv_Osimps_I5_J, fact_242_head__isnpolyh, fact_330_crossproduct__noteq, fact_269_add__cancel__left__left, fact_148_zero__neq__one, fact_296_ring__class_Oring__distribs_I2_J, fact_218_poly__deriv_Osimps_I2_J, fact_60_polymul__0_I2_J, fact_174_headn__nz, fact_93_poly__cmul_Osimps_I1_J, fact_10_polymul, fact_59_poly__cmul, fact_189_headn_Osimps_I6_J, fact_40_poly_Odistinct_I7_J, fact_314_behead, fact_64_polynate_Osimps_I7_J, fact_22_poly_Oinject_I1_J, fact_122_mult__zero__right, fact_349_polypow__normh, fact_278_ab__semigroup__add__class_Oadd__ac_I1_J, fact_282_add_Oassoc, fact_345_poly__cmul_Osimps_I7_J, fact_118_mult__cancel__left, fact_299_comm__monoid__add__class_Oadd__0, fact_37_poly_Odistinct_I13_J, fact_227_funpow__swap1, fact_243_degreen_Osimps_I2_J, fact_237_head_Osimps_I4_J, fact_128_ab__semigroup__mult__class_Omult__ac_I1_J, fact_9_polymul_Osimps_I8_J, fact_41_poly_Odistinct_I3_J, fact_13_polynate_Osimps_I4_J, fact_48_isnpolyh_Osimps_I6_J, fact_247_degreen_Osimps_I4_J, fact_96_one__normh, fact_63_polymul__1_I1_J, fact_233_head_Osimps_I2_J, fact_271_add_Oleft__neutral, fact_220_funpow__shift1__1, fact_135_one__reorient, fact_265_add__eq__0__iff__both__eq__0, fact_19_polymul_Osimps_I18_J, fact_102_polymul_Osimps_I11_J, fact_112_mult_Oright__neutral, fact_236_head_Osimps_I6_J, fact_255_poly__deriv__aux_Osimps_I2_J, fact_268_add__cancel__left__right, fact_286_add__right__imp__eq, 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_125_zero__reorient, fact_224_degreen__npolyhCN, fact_209_poly__deriv_Osimps_I6_J, fact_82_poly_Odistinct_I19_J, fact_315_behead__isnpolyh, fact_87_poly__cmul_Osimps_I2_J, fact_208_poly__deriv_Osimps_I4_J, fact_319_behead_Osimps_I6_J, fact_183_polysubst0_Osimps_I6_J, fact_186_headn_Osimps_I2_J, fact_297_poly_Odistinct_I47_J, fact_120_mult__zero__left, fact_157_shift1, fact_313_poly__deriv_Osimps_I8_J, fact_270_add_Oright__neutral, fact_177_polysub__same__0, fact_204_headnz, fact_196_headconst_Osimps_I1_J, fact_46_polymul_Osimps_I12_J, fact_273_plus__nat_Oadd__0
% 76.59/15.20 % No. of inferences in proof: 430
% 76.59/15.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14825 ms resp. 14018 ms w/o parsing
% 66.41/15.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 66.41/15.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------