%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP044^2 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:32 AM UTC 2026
% Result : Theorem 15.38s 4.03s
% Output : Refutation 15.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 349
% Syntax : Number of formulae : 700 ( 180 unt; 0 typ; 0 def)
% Number of atoms : 1958 ( 735 equ; 2 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 6882 ( 194 ~; 54 |; 90 &;5710 @)
% ( 0 <=>; 834 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 142 ( 142 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 7 con; 0-3 aty)
% Number of variables : 1692 ( 10 ^;1664 !; 18 ?;1692 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(comm_ring_1_decl,type,
comm_ring_1:
!>[TA: $tType] : $o ).
thf(type_decl,type,
type:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(sgn_decl,type,
sgn:
!>[TA: $tType] : $o ).
thf(idom_decl,type,
idom:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(plus_decl,type,
plus:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(neg_numeral_decl,type,
neg_numeral:
!>[TA: $tType] : $o ).
thf(comm_ring_decl,type,
comm_ring:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(idom_abs_sgn_decl,type,
idom_abs_sgn:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(ab_group_add_decl,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(wellorder_decl,type,
wellorder:
!>[TA: $tType] : $o ).
thf(zero_less_one_decl,type,
zero_less_one:
!>[TA: $tType] : $o ).
thf(semigroup_mult_decl,type,
semigroup_mult:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_decl,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_ring_decl,type,
linordered_ring:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_decl,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(boolean_algebra_decl,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(linord581940658strict_decl,type,
linord581940658strict:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(semiri1193490041visors_decl,type,
semiri1193490041visors:
!>[TA: $tType] : $o ).
thf(linord20386208strict_decl,type,
linord20386208strict:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_decl,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(linord893533164strict_decl,type,
linord893533164strict:
!>[TA: $tType] : $o ).
thf(semiri1923998003cancel_decl,type,
semiri1923998003cancel:
!>[TA: $tType] : $o ).
thf(descar1668888542_psums_decl,type,
descar1668888542_psums:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(descar316357986e_root_decl,type,
descar316357986e_root:
!>[TA: $tType] : ( TA > ( poly @ TA ) > ( poly @ TA ) ) ).
thf(descar149487500hanges_decl,type,
descar149487500hanges:
!>[TA: $tType] : ( ( list @ TA ) > nat ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(append_decl,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(n_lists_decl,type,
n_lists:
!>[TA: $tType] : ( nat > ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(null_decl,type,
null:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(neg_numeral_dbl_dec_decl,type,
neg_numeral_dbl_dec:
!>[TA: $tType] : ( TA > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(poly2_decl,type,
poly2:
!>[TA: $tType] : ( ( list @ TA ) > ( poly @ TA ) ) ).
thf(coeffs_decl,type,
coeffs:
!>[TA: $tType] : ( ( poly @ TA ) > ( list @ TA ) ) ).
thf(is_zero_decl,type,
is_zero:
!>[TA: $tType] : ( ( poly @ TA ) > $o ) ).
thf(pCons_decl,type,
pCons:
!>[TA: $tType] : ( TA > ( poly @ TA ) > ( poly @ TA ) ) ).
thf(poly_cutoff_decl,type,
poly_cutoff:
!>[TA: $tType] : ( nat > ( poly @ TA ) > ( poly @ TA ) ) ).
thf(smult_decl,type,
smult:
!>[TA: $tType] : ( TA > ( poly @ TA ) > ( poly @ TA ) ) ).
thf(g_decl,type,
g: poly @ a ).
thf(v_decl,type,
v: ( poly @ a ) > nat ).
thf(xs_decl,type,
xs: list @ a ).
thf(ys_decl,type,
ys: list @ a ).
thf(191,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord893533164strict @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Olinordered__comm__semiring__strict) ).
thf(892,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord893533164strict @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(320,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( one @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oone_28) ).
thf(1322,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( one @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(232,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_self__append__conv2) ).
thf(1036,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(326,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( sgn @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Osgn) ).
thf(1337,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( sgn @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(349,axiom,
( ys
= ( descar1668888542_psums @ a @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_ys) ).
thf(1411,plain,
( ys
= ( descar1668888542_psums @ a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(252,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_mult__0__right) ).
thf(1105,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(292,axiom,
! [A: nat,B: nat] :
( ( ( one_one @ nat )
= ( times_times @ nat @ A @ B ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_nat__1__eq__mult__iff) ).
thf(1237,plain,
! [A: nat,B: nat] :
( ( ( one_one @ nat )
= ( times_times @ nat @ A @ B ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(230,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= B )
= ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_mult__cancel__right2) ).
thf(1031,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= B )
= ( ( B
= ( zero_zero @ TA ) )
| ( A
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(317,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_gr0I) ).
thf(1315,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(309,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_ring @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__ring) ).
thf(1295,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_ring @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(254,axiom,
zero_less_one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__less__one) ).
thf(1110,plain,
zero_less_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(270,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( idom_abs_sgn @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oidom__abs__sgn) ).
thf(1158,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( idom_abs_sgn @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(241,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly @ TA,C: poly @ TA] :
( ( times_times @ ( poly @ TA ) @ ( smult @ TA @ A @ B ) @ C )
= ( smult @ TA @ A @ ( times_times @ ( poly @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_mult__smult__left) ).
thf(1073,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly @ TA,C: poly @ TA] :
( ( times_times @ ( poly @ TA ) @ ( smult @ TA @ A @ B ) @ C )
= ( smult @ TA @ A @ ( times_times @ ( poly @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(53,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( mult_zero @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Omult__zero) ).
thf(449,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( mult_zero @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(17,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(379,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( uminus_uminus @ ( poly @ TA ) @ ( pCons @ TA @ A @ B ) )
= ( pCons @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ ( poly @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_minus__pCons) ).
thf(614,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( uminus_uminus @ ( poly @ TA ) @ ( pCons @ TA @ A @ B ) )
= ( pCons @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ ( poly @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(408,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(215,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord219039673up_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Olinordered__ab__group__add) ).
thf(977,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord219039673up_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(21,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).
thf(385,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(20,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(384,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(83,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_mult__neg__neg) ).
thf(533,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(132,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ( ( descar1668888542_psums @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_psums_Osimps_I1_J) ).
thf(715,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ( ( descar1668888542_psums @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(322,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Cons__eq__append__conv) ).
thf(1327,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(204,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( descar316357986e_root @ TA @ A @ B )
!= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_reduce__root__nonzero) ).
thf(945,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( descar316357986e_root @ TA @ A @ B )
!= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(119,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_mult__pos__neg) ).
thf(670,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(328,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA,C: list @ TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( descar149487500hanges @ TA @ ( cons @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_sign__changes__Cons__Cons__same) ).
thf(1342,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA,C: list @ TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( descar149487500hanges @ TA @ ( cons @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(197,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_mult__less__cancel2) ).
thf(913,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(248,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_1 @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Oring__1) ).
thf(1095,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_1 @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(294,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_nat__mult__1__right) ).
thf(1243,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(37,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( plus @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oplus) ).
thf(417,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( plus @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(334,axiom,
( v
= ( ^ [A: poly @ a] : ( descar149487500hanges @ a @ ( coeffs @ a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_v__def) ).
thf(1359,plain,
( v
= ( ^ [A: poly @ a] : ( descar149487500hanges @ a @ ( coeffs @ a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(23,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( monoid_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Omonoid__add_22) ).
thf(389,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( monoid_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( mult_zero @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Omult__zero_23) ).
thf(372,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( mult_zero @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(323,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_mult__right__cancel) ).
thf(1330,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(129,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_infinite__descent__measure) ).
thf(702,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(303,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordered_ab_group_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oordered__ab__group__add) ).
thf(1279,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordered_ab_group_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(108,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_less__irrefl__nat) ).
thf(638,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(296,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_neq__Nil__conv) ).
thf(1247,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(39,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( semiri1193490041visors @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors) ).
thf(421,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( semiri1193490041visors @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(212,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_compl__less__swap1) ).
thf(969,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(226,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_strict__sorted_Oinduct) ).
thf(1013,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(250,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( semigroup_mult @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Osemigroup__mult) ).
thf(1100,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( semigroup_mult @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(290,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: list @ TA] :
( ( poly2 @ TA @ ( cons @ TA @ A @ B ) )
= ( pCons @ TA @ A @ ( poly2 @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Poly_Osimps_I2_J) ).
thf(1232,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: list @ TA] :
( ( poly2 @ TA @ ( cons @ TA @ A @ B ) )
= ( pCons @ TA @ A @ ( poly2 @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_nat__0__less__mult__iff) ).
thf(756,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(51,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_minus__equation__iff) ).
thf(443,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(262,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_no__zero__divisors) ).
thf(1136,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(305,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_less__one) ).
thf(1283,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(238,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_nat__mult__eq__cancel__disj) ).
thf(1051,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(353,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(211,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_nat__mult__less__cancel__disj) ).
thf(966,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(194,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( times_times @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_mult__cancel__left1) ).
thf(905,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( times_times @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(65,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_append_Oright__neutral) ).
thf(480,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(186,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_minus__less__iff) ).
thf(877,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(208,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_neq0__conv) ).
thf(956,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(55,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_mult__strict__right__mono) ).
thf(453,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(343,axiom,
! [TA: $tType] :
( ( ( sgn @ TA )
& ( zero @ TA ) )
=> ! [A: TA] :
( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_sign__changes__singleton) ).
thf(1394,plain,
! [TA: $tType] :
( ( ( sgn @ TA )
& ( zero @ TA ) )
=> ! [A: TA] :
( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(331,axiom,
( ys
= ( append @ a @ ( coeffs @ a @ g ) @ ( cons @ a @ ( zero_zero @ a ) @ ( nil @ a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_ys__def) ).
thf(1351,plain,
( ys
= ( append @ a @ ( coeffs @ a @ g ) @ ( cons @ a @ ( zero_zero @ a ) @ ( nil @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(115,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_zero__neq__one) ).
thf(660,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(221,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_zero__less__mult__pos2) ).
thf(998,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(347,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( ( coeffs @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_coeffs__eq__Nil) ).
thf(1405,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( ( coeffs @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(43,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_11004092258visors @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Oring__1__no__zero__divisors) ).
thf(428,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_11004092258visors @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(176,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_mult__less__cancel__left__neg) ).
thf(849,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(81,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_gr__zeroI) ).
thf(527,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(274,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_infinite__descent) ).
thf(1169,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(27,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( ring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oring__1) ).
thf(397,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( ring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(34,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordered_ab_group_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__ab__group__add) ).
thf(411,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordered_ab_group_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(329,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( descar149487500hanges @ TA @ ( coeffs @ TA @ ( smult @ TA @ A @ B ) ) )
= ( descar149487500hanges @ TA @ ( coeffs @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_coeff__sign__changes__smult) ).
thf(1345,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( descar149487500hanges @ TA @ ( coeffs @ TA @ ( smult @ TA @ A @ B ) ) )
= ( descar149487500hanges @ TA @ ( coeffs @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(18,axiom,
plus @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oplus) ).
thf(380,plain,
plus @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(121,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_mult__is__0) ).
thf(678,plain,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(201,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_self__append__conv) ).
thf(925,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(279,axiom,
! [A: nat,B: nat] :
( ( A
= ( times_times @ nat @ A @ B ) )
=> ( ( B
= ( one_one @ nat ) )
| ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_mult__eq__self__implies__10) ).
thf(1199,plain,
! [A: nat,B: nat] :
( ( A
= ( times_times @ nat @ A @ B ) )
=> ( ( B
= ( one_one @ nat ) )
| ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(268,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_less__numeral__extra_I3_J) ).
thf(1153,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(162,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ozero) ).
thf(810,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(19,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_equation__minus__iff) ).
thf(381,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord20386208strict @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Olinordered__semiring__strict) ).
thf(366,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord20386208strict @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_mult__less__mono2) ).
thf(512,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(203,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( poly_cutoff @ TA @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_poly__cutoff__0) ).
thf(942,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( poly_cutoff @ TA @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(49,axiom,
! [TA: $tType] :
( ( ( comm_semiring_0 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ( semiri1193490041visors @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors_10) ).
thf(439,plain,
! [TA: $tType] :
( ( ( comm_semiring_0 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ( semiri1193490041visors @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(236,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord20386208strict @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__semiring__strict_9) ).
thf(1047,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord20386208strict @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(158,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_append_Oassoc) ).
thf(798,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(272,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_less__neg__neg) ).
thf(1163,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(246,axiom,
comm_monoid_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(1091,plain,
comm_monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(168,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( poly2 @ TA @ ( nil @ TA ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Poly_Osimps_I1_J) ).
thf(825,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( poly2 @ TA @ ( nil @ TA ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(234,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_append__eq__Cons__conv) ).
thf(1042,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(299,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(1255,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ C @ B ) )
= ( ( A = C )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_mult__cancel2) ).
thf(862,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ C @ B ) )
= ( ( A = C )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(95,axiom,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ( comm_ring @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__ring) ).
thf(598,plain,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ( comm_ring @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(166,axiom,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_nat__mult__1) ).
thf(820,plain,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(41,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( semiri1923998003cancel @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors__cancel) ).
thf(424,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( semiri1923998003cancel @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(105,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_zero__less__mult__iff) ).
thf(630,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(154,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_ring @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Ocomm__ring) ).
thf(788,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_ring @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(164,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_not__gr__zero) ).
thf(815,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(137,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_compl__less__swap2) ).
thf(729,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(341,axiom,
( g
!= ( zero_zero @ ( poly @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nz) ).
thf(1387,plain,
( g
!= ( zero_zero @ ( poly @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(196,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_append__is__Nil__conv) ).
thf(910,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(287,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_not__less__zero) ).
thf(1223,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(192,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_comm__monoid__mult__class_Omult__1) ).
thf(894,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(198,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
~ ! [B: TA,C: poly @ TA] :
( A
!= ( pCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_pCons__cases) ).
thf(916,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
~ ! [B: TA,C: poly @ TA] :
( A
!= ( pCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(175,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_char_0 @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Nat_Oring__char__0) ).
thf(847,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_char_0 @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(7,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA ) )
=> ( ring_char_0 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Nat_Oring__char__0) ).
thf(361,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA ) )
=> ( ring_char_0 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(275,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_infinite__descent0__measure) ).
thf(1178,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(190,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: TA,C: poly @ TA] :
( ( descar316357986e_root @ TA @ A @ ( pCons @ TA @ B @ C ) )
= ( pCons @ TA @ B @ ( smult @ TA @ A @ ( descar316357986e_root @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_reduce__root__pCons) ).
thf(889,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: TA,C: poly @ TA] :
( ( descar316357986e_root @ TA @ A @ ( pCons @ TA @ B @ C ) )
= ( pCons @ TA @ B @ ( smult @ TA @ A @ ( descar316357986e_root @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(243,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_zero__less__iff__neq__zero) ).
thf(1079,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(278,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_gr__implies__not__zero) ).
thf(1195,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(259,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_append__self__conv) ).
thf(1128,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(304,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_semidom @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Olinordered__semidom) ).
thf(1281,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_semidom @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(57,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_append__same__eq) ).
thf(456,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(214,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_rev__exhaust) ).
thf(974,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(177,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_less__numeral__extra_I4_J) ).
thf(852,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(47,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_16) ).
thf(435,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(70,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: poly @ TA] :
( ( smult @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_smult__1__left) ).
thf(493,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: poly @ TA] :
( ( smult @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(283,axiom,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_null__rec_I2_J) ).
thf(1210,plain,
! [TA: $tType] : ( null @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(346,axiom,
! [TA: $tType] :
( ( idom_abs_sgn @ TA )
=> ! [A: list @ TA] :
( ( descar149487500hanges @ TA @ ( cons @ TA @ ( zero_zero @ TA ) @ A ) )
= ( descar149487500hanges @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_sign__changes__0__Cons) ).
thf(1402,plain,
! [TA: $tType] :
( ( idom_abs_sgn @ TA )
=> ! [A: list @ TA] :
( ( descar149487500hanges @ TA @ ( cons @ TA @ ( zero_zero @ TA ) @ A ) )
= ( descar149487500hanges @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(78,axiom,
! [TA: $tType] :
( ( linordered_ring @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( times_times @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_not__square__less__zero) ).
thf(519,plain,
! [TA: $tType] :
( ( linordered_ring @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( times_times @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(245,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_ring @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Olinordered__ring) ).
thf(1089,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_ring @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(265,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( B = C )
| ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_mult__cancel1) ).
thf(1143,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( B = C )
| ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(255,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_min__list_Oinduct) ).
thf(1111,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(30,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_double__compl) ).
thf(403,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(152,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_zero__reorient) ).
thf(783,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(72,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_plus__coeffs_Oinduct) ).
thf(499,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(344,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( A
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( coeffs @ TA @ A )
!= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_not__0__coeffs__not__Nil) ).
thf(1397,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( A
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( coeffs @ TA @ A )
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(113,axiom,
! [TA: $tType,A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( n_lists @ TA @ A @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( n_lists @ TA @ A @ ( nil @ TA ) )
= ( nil @ ( list @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_n__lists__Nil) ).
thf(650,plain,
! [TA: $tType,A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( n_lists @ TA @ A @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( n_lists @ TA @ A @ ( nil @ TA ) )
= ( nil @ ( list @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(205,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ( ab_group_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oab__group__add) ).
thf(948,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ( ab_group_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(336,axiom,
linordered_idom @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
thf(1375,plain,
linordered_idom @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(256,axiom,
wellorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(1121,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(62,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_list_Oexhaust) ).
thf(471,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(271,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_mult__minus1__right) ).
thf(1160,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
= ( uminus_uminus @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(244,axiom,
! [TA: $tType] :
( ( ( comm_semiring_1 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ! [A: ( poly @ TA ) > $o,B: poly @ TA] :
( ! [C: TA,D: poly @ TA] :
( ( ( D
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( A @ D ) )
=> ( A @ ( pCons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_pderiv_Oinduct) ).
thf(1082,plain,
! [TA: $tType] :
( ( ( comm_semiring_1 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ! [A: ( poly @ TA ) > $o,B: poly @ TA] :
( ! [C: TA,D: poly @ TA] :
( ( ( D
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( A @ D ) )
=> ( A @ ( pCons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(68,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( times_times @ ( poly @ TA ) @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_mult__poly__0__right) ).
thf(488,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( times_times @ ( poly @ TA ) @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(335,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) )
=> ( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= ( one_one @ nat ) ) )
& ( ~ ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) )
=> ( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_sign__changes__two) ).
thf(1361,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) )
=> ( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= ( one_one @ nat ) ) )
& ( ~ ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) )
=> ( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(308,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_not__gr0) ).
thf(1292,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(85,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_mult__cancel__right) ).
thf(537,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(124,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_shuffles_Oinduct) ).
thf(686,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(110,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_less__minus__one__simps_I1_J) ).
thf(642,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(285,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ozero_26) ).
thf(1214,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(282,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( times_times @ ( poly @ TA ) @ ( zero_zero @ ( poly @ TA ) ) @ A )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_mult__poly__0__left) ).
thf(1207,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( times_times @ ( poly @ TA ) @ ( zero_zero @ ( poly @ TA ) ) @ A )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(233,axiom,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( smult @ TA @ A @ ( uminus_uminus @ ( poly @ TA ) @ B ) )
= ( uminus_uminus @ ( poly @ TA ) @ ( smult @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_smult__minus__right) ).
thf(1039,plain,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( smult @ TA @ A @ ( uminus_uminus @ ( poly @ TA ) @ B ) )
= ( uminus_uminus @ ( poly @ TA ) @ ( smult @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(269,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_less__zeroE) ).
thf(1155,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(87,axiom,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_mult__0) ).
thf(554,plain,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(142,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_nat__mult__eq__1__iff) ).
thf(753,plain,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(172,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_less__minus__iff) ).
thf(837,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(112,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_one__reorient) ).
thf(647,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(218,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__neq__one) ).
thf(985,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(310,axiom,
! [TA: $tType] :
( ( zero_less_one @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_zero__less__one) ).
thf(1297,plain,
! [TA: $tType] :
( ( zero_less_one @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(260,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( monoid_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Omonoid__add) ).
thf(1131,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( monoid_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(277,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_neg__equal__0__iff__equal) ).
thf(1192,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(134,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero_neq_one @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Ozero__neq__one) ).
thf(721,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero_neq_one @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(295,axiom,
semigroup_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult) ).
thf(1246,plain,
semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(150,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_15) ).
thf(779,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(73,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= A )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mult__cancel__left2) ).
thf(503,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= A )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(321,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_nat__neq__iff) ).
thf(1324,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(25,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord581940658strict @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Olinordered__ring__strict) ).
thf(393,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord581940658strict @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(77,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_nat__mult__less__cancel1) ).
thf(515,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(267,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_mult__zero__left) ).
thf(1150,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(324,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_linorder__neqE__linordered__idom) ).
thf(1333,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(318,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__idom) ).
thf(1318,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(200,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_less__not__refl3) ).
thf(921,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_linorder__neqE__nat) ).
thf(657,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(306,axiom,
! [TA: $tType] :
( ( semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_mult_Oassoc) ).
thf(1286,plain,
! [TA: $tType] :
( ( semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(228,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( times_times @ TA @ A @ ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_minus__mult__commute) ).
thf(1026,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( times_times @ TA @ A @ ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_list_Odistinct_I1_J) ).
thf(530,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(207,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ A )
= ( times_times @ TA @ B @ B ) )
= ( ( A = B )
| ( A
= ( uminus_uminus @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_square__eq__iff) ).
thf(953,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ A )
= ( times_times @ TA @ B @ B ) )
= ( ( A = B )
| ( A
= ( uminus_uminus @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(148,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA] :
( ( ( times_times @ TA @ A @ A )
= ( one_one @ TA ) )
= ( ( A
= ( one_one @ TA ) )
| ( A
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_square__eq__1__iff) ).
thf(773,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA] :
( ( ( times_times @ TA @ A @ A )
= ( one_one @ TA ) )
= ( ( A
= ( one_one @ TA ) )
| ( A
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(133,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_less__not__refl) ).
thf(718,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(280,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_monoid_mult @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ocomm__monoid__mult_13) ).
thf(1202,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_monoid_mult @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(156,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_less__nat__zero__code) ).
thf(792,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(106,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( pCons @ TA @ ( one_one @ TA ) @ ( zero_zero @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_pCons__one) ).
thf(633,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( pCons @ TA @ ( one_one @ TA ) @ ( zero_zero @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(6,axiom,
comm_semiring_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__0) ).
thf(360,plain,
comm_semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(145,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_mult__left__cancel) ).
thf(765,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(239,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_remdups__adj_Oinduct) ).
thf(1054,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(141,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ C ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_mult__less__cancel__right__disj) ).
thf(750,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ C ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(301,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_mult__eq__0__iff) ).
thf(1273,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(179,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_divisors__zero) ).
thf(856,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(312,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( times_times @ TA @ B @ A ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_mult__cancel__right1) ).
thf(1301,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( times_times @ TA @ B @ A ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(97,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_neg__less__iff__less) ).
thf(601,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(266,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_list_OdiscI) ).
thf(1146,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(44,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( semiri1923998003cancel @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors__cancel_6) ).
thf(430,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( semiri1923998003cancel @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(14,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( neg_numeral @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Num_Oneg__numeral) ).
thf(375,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( neg_numeral @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(139,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: ( poly @ TA ) > $o,B: poly @ TA] :
( ( A @ ( zero_zero @ ( poly @ TA ) ) )
=> ( ! [C: TA,D: poly @ TA] :
( ( ( C
!= ( zero_zero @ TA ) )
| ( D
!= ( zero_zero @ ( poly @ TA ) ) ) )
=> ( ( A @ D )
=> ( A @ ( pCons @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_pCons__induct) ).
thf(733,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: ( poly @ TA ) > $o,B: poly @ TA] :
( ( A @ ( zero_zero @ ( poly @ TA ) ) )
=> ( ! [C: TA,D: poly @ TA] :
( ( ( C
!= ( zero_zero @ TA ) )
| ( D
!= ( zero_zero @ ( poly @ TA ) ) ) )
=> ( ( A @ D )
=> ( A @ ( pCons @ TA @ C @ D ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(94,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_rev__nonempty__induct) ).
thf(584,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(40,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_1) ).
thf(423,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(92,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( monoid_mult @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Omonoid__mult) ).
thf(579,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( monoid_mult @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(300,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_infinite__descent0) ).
thf(1256,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(35,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Orderings_Oord) ).
thf(413,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(224,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( pCons @ TA @ ( one_one @ TA ) @ ( zero_zero @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_one__poly__eq__simps_I2_J) ).
thf(1007,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( pCons @ TA @ ( one_one @ TA ) @ ( zero_zero @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(126,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_less__numeral__extra_I1_J) ).
thf(694,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(174,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Cons__eq__appendI) ).
thf(843,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(258,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_bot__nat__0_Oextremum__strict) ).
thf(1125,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(185,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ B )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_less__1__mult) ).
thf(875,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ B )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(131,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_successively_Oinduct) ).
thf(711,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(109,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(641,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(316,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: TA,C: poly @ TA] :
( ( smult @ TA @ A @ ( pCons @ TA @ B @ C ) )
= ( pCons @ TA @ ( times_times @ TA @ A @ B ) @ ( smult @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_smult__pCons) ).
thf(1312,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: TA,C: poly @ TA] :
( ( smult @ TA @ A @ ( pCons @ TA @ B @ C ) )
= ( pCons @ TA @ ( times_times @ TA @ A @ B ) @ ( smult @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(101,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_mult_Oright__neutral) ).
thf(611,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(333,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( descar149487500hanges @ TA @ ( coeffs @ TA @ ( descar316357986e_root @ TA @ A @ B ) ) )
= ( descar149487500hanges @ TA @ ( coeffs @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_coeff__sign__changes__reduce__root) ).
thf(1356,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( descar149487500hanges @ TA @ ( coeffs @ TA @ ( descar316357986e_root @ TA @ A @ B ) ) )
= ( descar149487500hanges @ TA @ ( coeffs @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(86,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_list__nonempty__induct) ).
thf(540,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_measure__induct__rule) ).
thf(672,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( group_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ogroup__add) ).
thf(391,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( group_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(263,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero_less_one @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ozero__less__one_18) ).
thf(1139,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero_less_one @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(60,axiom,
! [TA: $tType,A: list @ TA] :
( ( n_lists @ TA @ ( zero_zero @ nat ) @ A )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_n__lists_Osimps_I1_J) ).
thf(466,plain,
! [TA: $tType,A: list @ TA] :
( ( n_lists @ TA @ ( zero_zero @ nat ) @ A )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(247,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_neg__less__0__iff__less) ).
thf(1092,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(199,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_semidom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__semidom_11) ).
thf(919,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_semidom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_list__induct2_H) ).
thf(804,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(31,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_semiring_0 @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__0) ).
thf(406,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_semiring_0 @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(38,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oidom) ).
thf(419,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
semiri1923998003cancel @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel) ).
thf(377,plain,
semiri1923998003cancel @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(257,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
= ( nil @ TA ) )
= ( null @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_eq__Nil__null) ).
thf(1122,plain,
! [TA: $tType,A: list @ TA] :
( ( A
= ( nil @ TA ) )
= ( null @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(337,axiom,
( ( descar149487500hanges @ a @ xs )
= ( v @ ( times_times @ ( poly @ a ) @ ( pCons @ a @ ( one_one @ a ) @ ( pCons @ a @ ( uminus_uminus @ a @ ( one_one @ a ) ) @ ( zero_zero @ ( poly @ a ) ) ) ) @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062) ).
thf(1376,plain,
( ( descar149487500hanges @ a @ xs )
= ( v @ ( times_times @ ( poly @ a ) @ ( pCons @ a @ ( one_one @ a ) @ ( pCons @ a @ ( uminus_uminus @ a @ ( one_one @ a ) ) @ ( zero_zero @ ( poly @ a ) ) ) ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(314,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_monoid_mult @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__mult) ).
thf(1307,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_monoid_mult @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(216,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA] :
( ( descar1668888542_psums @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_psums_Osimps_I2_J) ).
thf(979,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA] :
( ( descar1668888542_psums @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(98,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: TA,C: poly @ TA] :
( ( smult @ TA @ A @ ( smult @ TA @ B @ C ) )
= ( smult @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_smult__smult) ).
thf(604,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: TA,C: poly @ TA] :
( ( smult @ TA @ A @ ( smult @ TA @ B @ C ) )
= ( smult @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(122,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( smult @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( pCons @ TA @ A @ ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_smult__one) ).
thf(681,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( smult @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( pCons @ TA @ A @ ( zero_zero @ ( poly @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(348,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( coeffs @ TA @ ( one_one @ ( poly @ TA ) ) )
= ( cons @ TA @ ( one_one @ TA ) @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_coeffs__1__eq) ).
thf(1408,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( coeffs @ TA @ ( one_one @ ( poly @ TA ) ) )
= ( cons @ TA @ ( one_one @ TA ) @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(54,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linorder @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Orderings_Olinorder) ).
thf(451,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linorder @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType] :
( ( ( zero @ TA )
& ( zero @ TB ) )
=> ! [A: ( poly @ TB ) > ( poly @ TA ) > $o,B: poly @ TB,C: poly @ TA] :
( ( A @ ( zero_zero @ ( poly @ TB ) ) @ ( zero_zero @ ( poly @ TA ) ) )
=> ( ! [D: TB,E: poly @ TB,F: TA,G: poly @ TA] :
( ( A @ E @ G )
=> ( A @ ( pCons @ TB @ D @ E ) @ ( pCons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_poly__induct2) ).
thf(567,plain,
! [TA: $tType,TB: $tType] :
( ( ( zero @ TA )
& ( zero @ TB ) )
=> ! [A: ( poly @ TB ) > ( poly @ TA ) > $o,B: poly @ TB,C: poly @ TA] :
( ( A @ ( zero_zero @ ( poly @ TB ) ) @ ( zero_zero @ ( poly @ TA ) ) )
=> ( ! [D: TB,E: poly @ TB,F: TA,G: poly @ TA] :
( ( A @ E @ G )
=> ( A @ ( pCons @ TB @ D @ E ) @ ( pCons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(75,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_equal__neg__zero) ).
thf(509,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(187,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_append__Nil2) ).
thf(880,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(46,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Omult__zero) ).
thf(434,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(64,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( smult @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_smult__0__left) ).
thf(477,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( smult @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(327,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ( ( zero_zero @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_zero__neq__neg__one) ).
thf(1339,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ( ( zero_zero @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(84,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Orderings_Oord_24) ).
thf(535,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(100,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( idom_abs_sgn @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Oidom__abs__sgn) ).
thf(609,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( idom_abs_sgn @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(136,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_mult__zero__right) ).
thf(726,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(66,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_append__self__conv2) ).
thf(483,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(229,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_mult__neg__pos) ).
thf(1029,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(339,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: list @ TA] :
( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( cons @ TA @ ( zero_zero @ TA ) @ B ) ) )
= ( descar149487500hanges @ TA @ ( cons @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_sign__changes__Cons__Cons__0) ).
thf(1381,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: list @ TA] :
( ( descar149487500hanges @ TA @ ( cons @ TA @ A @ ( cons @ TA @ ( zero_zero @ TA ) @ B ) ) )
= ( descar149487500hanges @ TA @ ( cons @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_eq__Nil__appendI) ).
thf(462,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(79,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( one_one @ ( poly @ TA ) )
= ( pCons @ TA @ ( one_one @ TA ) @ ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_one__poly__eq__simps_I1_J) ).
thf(521,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( one_one @ ( poly @ TA ) )
= ( pCons @ TA @ ( one_one @ TA ) @ ( zero_zero @ ( poly @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ( group_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ogroup__add) ).
thf(399,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ( group_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(209,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_splice_Oinduct) ).
thf(959,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(146,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_bot__nat__0_Onot__eq__extremum) ).
thf(768,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(107,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_mult__strict__left__mono__neg) ).
thf(636,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(183,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_sorted__wrt_Oinduct) ).
thf(868,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(219,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_nat__less__induct) ).
thf(986,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(222,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly @ TA,C: TA] :
( ( ( smult @ TA @ A @ B )
= ( pCons @ TA @ C @ B ) )
=> ( B
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_synthetic__div__unique__lemma) ).
thf(1000,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly @ TA,C: TA] :
( ( ( smult @ TA @ A @ B )
= ( pCons @ TA @ C @ B ) )
=> ( B
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(297,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_zero__less__mult__pos) ).
thf(1250,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(251,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_append__Cons) ).
thf(1102,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(56,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom) ).
thf(455,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(188,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mult_Oleft__neutral) ).
thf(883,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(231,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_semiring_1 @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__1) ).
thf(1034,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_semiring_1 @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(313,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( times_times @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_minus__mult__minus) ).
thf(1304,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( times_times @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(157,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA,B: TA,C: poly @ TA] :
( ( times_times @ ( poly @ TA ) @ A @ ( smult @ TA @ B @ C ) )
= ( smult @ TA @ B @ ( times_times @ ( poly @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_mult__smult__right) ).
thf(795,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA,B: TA,C: poly @ TA] :
( ( times_times @ ( poly @ TA ) @ A @ ( smult @ TA @ B @ C ) )
= ( smult @ TA @ B @ ( times_times @ ( poly @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(116,axiom,
linord893533164strict @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).
thf(663,plain,
linord893533164strict @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(13,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(374,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(163,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ C @ A ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_mult__less__iff1) ).
thf(812,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ C @ A ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(103,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ A )
= ( uminus_uminus @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mult__minus1) ).
thf(617,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ A )
= ( uminus_uminus @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(4,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_neg__equal__iff__equal) ).
thf(355,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(167,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord581940658strict @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__ring__strict) ).
thf(823,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord581940658strict @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(237,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( neg_numeral @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Num_Oneg__numeral) ).
thf(1049,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( neg_numeral @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(350,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( (=) @ ( poly @ TA ) )
= ( ^ [A: poly @ TA,B: poly @ TA] :
( ( coeffs @ TA @ A )
= ( coeffs @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_coeffs__eq__iff) ).
thf(1413,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( (=) @ ( poly @ TA ) )
= ( ^ [A: poly @ TA,B: poly @ TA] :
( ( coeffs @ TA @ A )
= ( coeffs @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(242,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_same__append__eq) ).
thf(1076,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(42,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_11004092258visors @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oring__1__no__zero__divisors) ).
thf(426,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_11004092258visors @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(273,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_transpose_Ocases) ).
thf(1166,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(149,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_neg__0__less__iff__less) ).
thf(776,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(213,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( uminus_uminus @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_mult__minus__left) ).
thf(971,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( uminus_uminus @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(298,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_min__list_Ocases) ).
thf(1252,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(88,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_list_Oinducts) ).
thf(557,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(223,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_nat__mult__eq__cancel1) ).
thf(1003,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(240,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( pCons @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_pCons__0__0) ).
thf(1070,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( pCons @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(184,axiom,
! [TA: $tType] :
( ( ( comm_semiring_0 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ! [A: TA,B: poly @ TA] :
( ( ( smult @ TA @ A @ B )
= ( zero_zero @ ( poly @ TA ) ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_smult__eq__0__iff) ).
thf(872,plain,
! [TA: $tType] :
( ( ( comm_semiring_0 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ! [A: TA,B: poly @ TA] :
( ( ( smult @ TA @ A @ B )
= ( zero_zero @ ( poly @ TA ) ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(288,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_minus__poly__rev__list_Oinduct) ).
thf(1225,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(345,axiom,
( xs
= ( coeffs @ a @ ( times_times @ ( poly @ a ) @ ( pCons @ a @ ( one_one @ a ) @ ( pCons @ a @ ( uminus_uminus @ a @ ( one_one @ a ) ) @ ( zero_zero @ ( poly @ a ) ) ) ) @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_xs__def) ).
thf(1400,plain,
( xs
= ( coeffs @ a @ ( times_times @ ( poly @ a ) @ ( pCons @ a @ ( one_one @ a ) @ ( pCons @ a @ ( uminus_uminus @ a @ ( one_one @ a ) ) @ ( zero_zero @ ( poly @ a ) ) ) ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(276,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_less__not__refl2) ).
thf(1188,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(50,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_14) ).
thf(441,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(11,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord219039673up_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Olinordered__ab__group__add) ).
thf(370,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord219039673up_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(173,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA] :
( ( descar1668888542_psums @ TA @ ( cons @ TA @ ( zero_zero @ TA ) @ A ) )
= ( cons @ TA @ ( zero_zero @ TA ) @ ( descar1668888542_psums @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_psums__0__Cons) ).
thf(840,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA] :
( ( descar1668888542_psums @ TA @ ( cons @ TA @ ( zero_zero @ TA ) @ A ) )
= ( cons @ TA @ ( zero_zero @ TA ) @ ( descar1668888542_psums @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(291,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_mult__pos__neg2) ).
thf(1235,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(161,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ab_group_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oab__group__add) ).
thf(808,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ab_group_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(325,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add) ).
thf(1336,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero_less_one @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Ozero__less__one) ).
thf(1141,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero_less_one @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(227,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_append_Oleft__neutral) ).
thf(1023,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(22,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_compl__eq__compl__iff) ).
thf(386,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(180,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_mult__cancel__left) ).
thf(859,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(293,axiom,
! [TA: $tType] :
( ( ( comm_semiring_1 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ! [A: poly @ TA] :
~ ! [B: TA,C: poly @ TA] :
( A
!= ( pCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_pderiv_Ocases) ).
thf(1240,plain,
! [TA: $tType] :
( ( ( comm_semiring_1 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ! [A: poly @ TA] :
~ ! [B: TA,C: poly @ TA] :
( A
!= ( pCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(332,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( poly2 @ TA @ ( coeffs @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Poly__coeffs) ).
thf(1353,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( poly2 @ TA @ ( coeffs @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(96,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(600,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(52,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl_dec @ TA @ ( one_one @ TA ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_dbl__dec__simps_I3_J) ).
thf(446,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl_dec @ TA @ ( one_one @ TA ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_arg__min__list_Oinduct) ).
thf(571,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(8,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_add_Oinverse__inverse) ).
thf(363,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_measure__induct) ).
thf(759,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(286,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( poly_cutoff @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( poly_cutoff @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_poly__cutoff__1) ).
thf(1216,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( poly_cutoff @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( poly_cutoff @ TA @ A @ ( one_one @ ( poly @ TA ) ) )
= ( one_one @ ( poly @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(147,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( zero_neq_one @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ozero__neq__one_19) ).
thf(771,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( zero_neq_one @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(253,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__ring__1) ).
thf(1108,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_mult__less__mono1) ).
thf(524,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(93,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_remdups__adj_Ocases) ).
thf(581,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(225,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_append__assoc) ).
thf(1010,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(342,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: list @ TA,B: poly @ TA] :
( ( ( poly2 @ TA @ A )
= B )
=> ( ( descar149487500hanges @ TA @ A )
= ( descar149487500hanges @ TA @ ( coeffs @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_sign__changes__coeff__sign__changes) ).
thf(1390,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: list @ TA,B: poly @ TA] :
( ( ( poly2 @ TA @ A )
= B )
=> ( ( descar149487500hanges @ TA @ A )
= ( descar149487500hanges @ TA @ ( coeffs @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(307,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_neg__equal__zero) ).
thf(1289,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(10,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( semigroup_mult @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Osemigroup__mult_17) ).
thf(368,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( semigroup_mult @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(302,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( ( pCons @ TA @ A @ B )
= ( zero_zero @ ( poly @ TA ) ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_pCons__eq__0__iff) ).
thf(1276,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( ( pCons @ TA @ A @ B )
= ( zero_zero @ ( poly @ TA ) ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(128,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_psums_Ocases) ).
thf(699,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(210,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_one__neq__neg__one) ).
thf(963,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ( ( one_one @ TA )
!= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(140,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linorder @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Orderings_Olinorder_20) ).
thf(748,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linorder @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1,conjecture,
( ( descar149487500hanges @ a @ ys )
= ( descar149487500hanges @ a @ ( coeffs @ a @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( descar149487500hanges @ a @ ys )
!= ( descar149487500hanges @ a @ ( coeffs @ a @ g ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(351,plain,
( ( descar149487500hanges @ a @ ys )
!= ( descar149487500hanges @ a @ ( coeffs @ a @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,axiom,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ( ring @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oring) ).
thf(401,plain,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ( ring @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(151,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_mult__pos__pos) ).
thf(781,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(220,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_list_Oinject) ).
thf(995,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(138,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
~ ( null @ TA @ ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_null__rec_I1_J) ).
thf(731,plain,
! [TA: $tType,A: TA,B: list @ TA] :
~ ( null @ TA @ ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(153,axiom,
! [TA: $tType] :
( ( linord893533164strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(786,plain,
! [TA: $tType] :
( ( linord893533164strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(16,axiom,
linord20386208strict @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semiring__strict) ).
thf(378,plain,
linord20386208strict @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(118,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( uminus_uminus @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult__minus__right) ).
thf(667,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( uminus_uminus @ TA @ ( times_times @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(284,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_less__minus__one__simps_I4_J) ).
thf(1212,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(315,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ C ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_mult__less__cancel__left__disj) ).
thf(1309,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ C ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(235,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_not__one__less__zero) ).
thf(1045,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(170,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__mult) ).
thf(832,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(123,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_ring_1 @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Ocomm__ring__1) ).
thf(684,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_ring_1 @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(261,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_mult__less__cancel__left__pos) ).
thf(1133,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(330,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( is_zero @ TA )
= ( ^ [A: poly @ TA] : ( null @ TA @ ( coeffs @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_is__zero__def) ).
thf(1348,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( is_zero @ TA )
= ( ^ [A: poly @ TA] : ( null @ TA @ ( coeffs @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(104,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_rev__induct) ).
thf(620,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(45,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_monoid_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add) ).
thf(432,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_monoid_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(289,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
= ( ( zero_zero @ TA )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_neg__0__equal__iff__equal) ).
thf(1229,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
= ( ( zero_zero @ TA )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(165,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_less__minus__one__simps_I3_J) ).
thf(818,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(178,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord893533164strict @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__comm__semiring__strict_7) ).
thf(854,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord893533164strict @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(155,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( one @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oone) ).
thf(790,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( one @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(182,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_add_Oinverse__neutral) ).
thf(865,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(171,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_gr__implies__not0) ).
thf(833,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(33,axiom,
semiri1193490041visors @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors) ).
thf(410,plain,
semiri1193490041visors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(206,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: list @ TA] :
( ( poly2 @ TA @ ( append @ TA @ A @ ( cons @ TA @ ( zero_zero @ TA ) @ ( nil @ TA ) ) ) )
= ( poly2 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Poly__snoc__zero) ).
thf(950,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: list @ TA] :
( ( poly2 @ TA @ ( append @ TA @ A @ ( cons @ TA @ ( zero_zero @ TA ) @ ( nil @ TA ) ) ) )
= ( poly2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(249,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: poly @ TA,C: TA,D: poly @ TA] :
( ( ( pCons @ TA @ A @ B )
= ( pCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_pCons__eq__iff) ).
thf(1097,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: poly @ TA,C: TA,D: poly @ TA] :
( ( ( pCons @ TA @ A @ B )
= ( pCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(159,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_not__Cons__self2) ).
thf(801,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(74,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_mult_Ocomm__neutral) ).
thf(506,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(5,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( plus @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oplus_27) ).
thf(358,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( plus @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Oring) ).
thf(437,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(117,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( is_zero @ TA )
= ( ^ [A: poly @ TA] :
( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_is__zero__null) ).
thf(664,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( is_zero @ TA )
= ( ^ [A: poly @ TA] :
( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(169,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_append__eq__appendI) ).
thf(828,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(127,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_mult__less__0__iff) ).
thf(696,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(193,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_mult__not__zero) ).
thf(897,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(63,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Nil__is__append__conv) ).
thf(474,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(189,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_strict__sorted_Ocases) ).
thf(886,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(202,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_induct__list012) ).
thf(928,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(36,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord1659791738miring @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Olinordered__nonzero__semiring) ).
thf(415,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord1659791738miring @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(26,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( idom @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Rings_Oidom) ).
thf(395,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( idom @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_map__tailrec__rev_Oinduct) ).
thf(575,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(340,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( coeffs @ TA @ ( zero_zero @ ( poly @ TA ) ) )
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_coeffs__0__eq__Nil) ).
thf(1384,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( coeffs @ TA @ ( zero_zero @ ( poly @ TA ) ) )
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(338,axiom,
! [TA: $tType] :
( ( ( sgn @ TA )
& ( zero @ TA ) )
=> ( ( descar149487500hanges @ TA @ ( nil @ TA ) )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_sign__changes__Nil) ).
thf(1378,plain,
! [TA: $tType] :
( ( ( sgn @ TA )
& ( zero @ TA ) )
=> ( ( descar149487500hanges @ TA @ ( nil @ TA ) )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(111,axiom,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( smult @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( uminus_uminus @ ( poly @ TA ) @ ( smult @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_smult__minus__left) ).
thf(644,plain,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ! [A: TA,B: poly @ TA] :
( ( smult @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( uminus_uminus @ ( poly @ TA ) @ ( smult @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(58,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_append1__eq__conv) ).
thf(459,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(195,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_less__minus__one__simps_I2_J) ).
thf(908,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord_less @ TA @ ( uminus_uminus @ TA @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(135,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_neg__less__pos) ).
thf(723,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(217,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_append__Nil) ).
thf(982,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(311,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_mult__strict__right__mono__neg) ).
thf(1299,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(125,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_not__less0) ).
thf(691,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(99,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( monoid_mult @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Omonoid__mult_21) ).
thf(607,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( monoid_mult @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(67,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___HOL_Otype) ).
thf(486,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(319,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( sgn @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Osgn) ).
thf(1320,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( sgn @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(61,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord1659791738miring @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_8) ).
thf(469,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord1659791738miring @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(69,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_mult__strict__left__mono) ).
thf(491,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(281,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( smult @ TA @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_smult__0__right) ).
thf(1204,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( smult @ TA @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(71,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_append__eq__append__conv2) ).
thf(496,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(130,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl_dec @ TA @ ( zero_zero @ TA ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_dbl__dec__simps_I2_J) ).
thf(708,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl_dec @ TA @ ( zero_zero @ TA ) )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1437,plain,
$false,
inference(e,[status(thm)],[892,1322,1036,1337,1411,1105,1237,1031,1315,1295,1110,1158,1073,449,379,614,408,977,385,384,533,715,1327,945,670,1342,913,1095,1243,417,1359,389,372,1330,702,1279,638,1247,421,969,1013,1100,1232,756,443,1136,1283,1051,353,966,905,480,877,956,453,1394,1351,660,998,1405,428,849,527,1169,397,411,1345,380,678,925,1199,1153,810,381,366,512,942,439,1047,798,1163,1091,825,1042,1255,862,598,820,424,630,788,815,729,1387,910,1223,894,916,847,361,1178,889,1079,1195,1128,1281,456,974,852,435,493,1210,1402,519,1089,1143,1111,403,783,499,1397,650,948,1375,1121,471,1160,1082,488,1361,1292,537,686,642,1214,1207,1039,1155,554,753,837,647,985,1297,1131,1192,721,1246,779,503,1324,393,515,1150,1333,1318,921,657,1286,1026,530,953,773,718,1202,792,633,360,765,1054,750,1273,856,1301,601,1146,430,375,733,584,423,579,1256,413,1007,694,843,1125,875,711,641,1312,611,1356,540,672,391,1139,466,1092,919,804,406,419,377,1122,1376,1307,979,604,681,1408,451,567,509,880,434,477,1339,535,609,726,483,1029,1381,462,521,399,959,768,636,868,986,1000,1250,1102,455,883,1034,1304,795,663,374,812,617,355,823,1049,1413,1076,426,1166,776,971,1252,557,1003,1070,872,1225,1400,1188,441,370,840,1235,808,1336,1141,1023,386,859,1240,1353,600,446,571,363,759,1216,771,1108,524,581,1010,1390,1289,368,1276,699,963,748,351,401,781,995,731,786,378,667,1212,1309,1045,832,684,1133,1348,620,432,1229,818,854,790,865,833,410,950,1097,801,506,358,437,664,828,696,897,474,886,928,415,395,575,1384,1378,644,459,908,723,982,1299,691,607,486,1320,469,491,1204,496,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP044^2 : 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
% 0.12/0.22 % Computer : n018.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 19:43:56 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.40/1.23 % [INFO] Parsing done (428ms).
% 2.40/1.25 % [INFO] Running in sequential loop mode.
% 3.29/1.45 % [INFO] eprover registered as external prover.
% 3.29/1.46 % [INFO] Scanning for conjecture ...
% 3.75/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 364 axioms. Running axiom selection ...
% 4.15/1.65 % [INFO] Axiom selection finished. Selected 348 axioms (removed 16 axioms).
% 4.99/1.85 % [INFO] Problem is higher-order (TPTP THF).
% 4.99/1.87 % [INFO] Type checking passed.
% 4.99/1.87 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 14.82/4.03 % External prover 'e' found a proof!
% 15.38/4.03 % [INFO] Killing All external provers ...
% 15.38/4.03 % Time passed: 3662ms (effective reasoning time: 2778ms)
% 15.38/4.03 % 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)>
% 15.38/4.03 % Axioms used in derivation (348): fact_38_psums_Osimps_I2_J, fact_242_nat__mult__eq__cancel__disj, fact_163_null__rec_I2_J, subcl_Rings_Olinordered__idom___Groups_Ogroup__add, fact_130_minus__less__iff, fact_4_sign__changes__coeff__sign__changes, subcl_Rings_Olinordered__idom___Orderings_Olinorder, subcl_Rings_Olinordered__idom___Groups_Oab__group__add, fact_206_less__nat__zero__code, tfree_0, fact_221_nat__less__induct, fact_124_divisors__zero, tcon_Polynomial_Opoly___Num_Oneg__numeral, fact_68_mult__cancel__right2, tcon_Polynomial_Opoly___Groups_Oab__group__add, fact_183_not__one__less__zero, fact_117_gr__implies__not__zero, fact_136_strict__sorted_Ocases, tcon_Nat_Onat___Orderings_Olinorder, fact_173_zero__less__mult__pos2, tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors__cancel_6, fact_32_coeffs__1__eq, fact_195_rev__induct, fact_1_nz, fact_71_list_Oinject, fact_93_append_Oright__neutral, fact_44_pderiv_Ocases, fact_188_less__minus__one__simps_I2_J, subcl_Rings_Olinordered__idom___Groups_Oordered__ab__group__add, fact_16_smult__smult, fact_229_gr0I, fact_210_mult__cancel1, fact_170_mult__strict__left__mono__neg, fact_129_comm__monoid__mult__class_Omult__1, fact_251_compl__less__swap2, subcl_Rings_Olinordered__idom___Rings_Oidom__abs__sgn, fact_137_map__tailrec__rev_Oinduct, fact_34__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062, fact_78_mult__cancel__left, tcon_Nat_Onat___Rings_Ozero__neq__one, fact_213_dbl__dec__simps_I3_J, fact_219_linorder__neqE__nat, tcon_fun___Orderings_Oord, fact_131_less__minus__iff, fact_62_neg__less__pos, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors, tcon_Nat_Onat___Orderings_Oord_1, fact_14_pCons__eq__iff, tcon_Polynomial_Opoly___Groups_Osemigroup__mult_17, fact_204_mult__cancel2, fact_223_less__not__refl3, fact_107_mult_Oassoc, fact_116_zero__less__iff__neq__zero, tcon_Nat_Onat___Rings_Ozero__less__one, fact_49_mult__poly__0__right, tcon_Nat_Onat___Groups_Ocomm__monoid__mult, fact_228_measure__induct__rule, fact_54_psums_Ocases, fact_29_coeffs__eq__Nil, fact_77_mult__cancel__right, fact_175_zero__less__mult__iff, tcon_Polynomial_Opoly___Rings_Oidom, fact_132_minus__mult__commute, subcl_Rings_Olinordered__idom___Rings_Ocomm__ring, fact_231_not__less0, fact_187_zero__neq__neg__one, tcon_Polynomial_Opoly___Rings_Ozero__less__one_18, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, fact_67_mult__cancel__right1, fact_193_Cons__eq__append__conv, subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add, fact_158_append_Oleft__neutral, fact_181_not__square__less__zero, subcl_Rings_Olinordered__idom___Groups_Ozero, fact_139_successively_Oinduct, tcon_Polynomial_Opoly___Rings_Ocomm__ring__1, fact_201_nat__mult__less__cancel__disj, fact_169_mult__strict__left__mono, fact_155_list_Odistinct_I1_J, fact_51_not__0__coeffs__not__Nil, tcon_Polynomial_Opoly___Rings_Ozero__neq__one_19, fact_184_zero__less__one, subcl_Rings_Olinordered__idom___Rings_Ocomm__ring__1, tcon_Nat_Onat___Groups_Ocomm__monoid__add, fact_91_minus__mult__minus, fact_0_v__def, subcl_Rings_Olinordered__idom___Rings_Oring, fact_159_append__Nil, fact_7_is__zero__def, fact_112_not__Cons__self2, subcl_Rings_Olinordered__idom___HOL_Otype, fact_211_nat__1__eq__mult__iff, fact_28_smult__pCons, tcon_Nat_Onat___Groups_Oone, tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_8, fact_30_coeffs__0__eq__Nil, tcon_Nat_Onat___Rings_Olinordered__semidom, subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__0, fact_199_mult__less__iff1, fact_42_is__zero__null, fact_144_transpose_Ocases, fact_186_less__1__mult, fact_217_nat__mult__1__right, tcon_Nat_Onat___Groups_Oplus, fact_90_mult__minus__right, tcon_Nat_Onat___Groups_Omonoid__add, fact_174_zero__less__mult__pos, fact_74_append__assoc, fact_59_mult__minus1, fact_194_rev__exhaust, fact_202_nat__0__less__mult__iff, fact_140_arg__min__list_Oinduct, fact_226_nat__neq__iff, fact_92_mult__minus__left, tcon_Polynomial_Opoly___Groups_Oone_28, fact_3_ys, fact_47_pderiv_Oinduct, fact_121_mult__right__cancel, fact_31_psums__0__Cons, fact_2_coeffs__eq__iff, subcl_Rings_Olinordered__idom___Nat_Oring__char__0, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel, fact_212_nat__mult__eq__1__iff, fact_104_linorder__neqE__linordered__idom, fact_166_mult__strict__right__mono, fact_179_mult__neg__pos, fact_103_zero__reorient, fact_125_mult__not__zero, fact_97_append__self__conv2, fact_89_neg__less__iff__less, fact_48_mult__poly__0__left, fact_237_mult__less__mono1, fact_244_n__lists__Nil, fact_100_append__Nil2, fact_232_less__zeroE, tcon_Polynomial_Opoly___Rings_Olinordered__ring, fact_36_Poly_Osimps_I2_J, fact_135_strict__sorted_Oinduct, fact_198_poly__cutoff__1, fact_114_append__eq__appendI, fact_220_infinite__descent, fact_80_mult__zero__right, fact_10_xs__def, fact_196_less__minus__one__simps_I1_J, tcon_Polynomial_Opoly___Rings_Ocomm__ring, fact_43_pCons__induct, fact_13_sign__changes__Cons__Cons__0, fact_50_plus__coeffs_Oinduct, fact_168_mult__less__cancel__left__disj, fact_115_sign__changes__two, subcl_Rings_Olinordered__idom___Rings_Oring__1__no__zero__divisors, fact_17_smult__1__left, fact_110_minus__equation__iff, subcl_Rings_Olinordered__idom___Rings_Ozero__less__one, tcon_Nat_Onat___Groups_Ozero, fact_101_smult__minus__right, fact_122_mult__left__cancel, fact_96_self__append__conv2, fact_164_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_218_infinite__descent__measure, fact_21_mult__smult__right, fact_241_nat__mult__less__cancel1, tcon_Nat_Onat___Orderings_Owellorder, fact_207_bot__nat__0_Onot__eq__extremum, fact_65_mult__cancel__left1, fact_15_minus__pCons, fact_156_append__Cons, fact_126_zero__neq__one, fact_39_psums_Osimps_I1_J, tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_16, fact_172_mult__less__cancel__left__neg, fact_147_min__list_Ocases, fact_152_list_Oinducts, tcon_Polynomial_Opoly___Rings_Olinordered__semidom_11, fact_239_mult__0, fact_191_rev__nonempty__induct, fact_225_less__not__refl, tcon_Polynomial_Opoly___Groups_Omonoid__add_22, fact_35_Poly__snoc__zero, tcon_Nat_Onat___Rings_Ocomm__semiring__0, tcon_Nat_Onat___Groups_Omonoid__mult, fact_154_list_OdiscI, fact_177_mult__pos__pos, tcon_Polynomial_Opoly___Groups_Osgn, subcl_Rings_Olinordered__idom___Num_Oneg__numeral, fact_85_neg__0__equal__iff__equal, fact_98_self__append__conv, fact_243_mult__eq__self__implies__10, fact_79_mult__eq__0__iff, fact_81_mult__zero__left, subcl_Rings_Olinordered__idom___Rings_Oidom, fact_11_coeff__sign__changes__smult, fact_157_Cons__eq__appendI, fact_5_ys__def, fact_53_synthetic__div__unique__lemma, subcl_Rings_Olinordered__idom___Rings_Omult__zero, tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict, fact_197_less__minus__one__simps_I3_J, fact_190_square__eq__1__iff, fact_148_induct__list012, fact_153_list_Oexhaust, fact_176_mult__pos__neg2, tcon_Polynomial_Opoly___Rings_Olinordered__idom, subcl_Rings_Olinordered__idom___Groups_Osgn, subcl_Rings_Olinordered__idom___Groups_Oone, fact_245_n__lists_Osimps_I1_J, fact_150_list__induct2_H, fact_66_mult__cancel__left2, fact_60_mult__minus1__right, fact_63_neg__0__less__iff__less, fact_128_mult_Ocomm__neutral, subcl_Rings_Olinordered__idom___Rings_Olinordered__ring__strict, tcon_Nat_Onat___Rings_Omult__zero, fact_37_Poly_Osimps_I1_J, fact_149_splice_Oinduct, fact_109_one__reorient, subcl_Rings_Olinordered__idom___Rings_Ozero__neq__one, fact_118_not__less__zero, fact_73_append__same__eq, fact_84_neg__equal__0__iff__equal, fact_57_sign__changes__Cons__Cons__same, fact_82_neg__equal__zero, tcon_fun___Lattices_Oboolean__algebra, tcon_Polynomial_Opoly___Rings_Oidom__abs__sgn, fact_76_not__gr__zero, fact_40_pCons__one, fact_94_append__is__Nil__conv, fact_162_eq__Nil__null, fact_165_mult__less__cancel__right__disj, fact_250_compl__less__swap1, fact_24_one__poly__eq__simps_I2_J, fact_64_neg__less__0__iff__less, fact_55_reduce__root__pCons, tcon_Polynomial_Opoly___Groups_Ozero_26, fact_208_mult__is__0, fact_200_dbl__dec__simps_I2_J, fact_8_Poly__coeffs, tcon_Polynomial_Opoly___Orderings_Olinorder_20, tcon_Polynomial_Opoly___Groups_Ocomm__monoid__mult_13, fact_33_sign__changes__singleton, subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__mult, fact_240_nat__mult__eq__cancel1, fact_27_smult__eq__0__iff, subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__1, tcon_Nat_Onat___Rings_Ocomm__semiring__1, fact_138_list__nonempty__induct, tcon_Polynomial_Opoly___Groups_Olinordered__ab__group__add, fact_18_smult__minus__left, fact_185_less__numeral__extra_I1_J, subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors__cancel, fact_127_less__numeral__extra_I4_J, fact_26_smult__0__left, fact_72_same__append__eq, fact_180_mult__less__0__iff, tcon_Polynomial_Opoly___Rings_Olinordered__ring__strict, fact_102_smult__one, tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_15, fact_58_append1__eq__conv, fact_160_eq__Nil__appendI, tcon_Polynomial_Opoly___Groups_Omonoid__mult_21, fact_151_neq__Nil__conv, subcl_Rings_Olinordered__idom___Rings_Olinordered__semidom, fact_113_append__eq__append__conv2, tcon_Polynomial_Opoly___Groups_Oplus_27, fact_161_null__rec_I1_J, subcl_Rings_Olinordered__idom___Groups_Olinordered__ab__group__add, fact_86_add_Oinverse__neutral, fact_88_mult_Oleft__neutral, fact_119_gr__zeroI, fact_120_less__numeral__extra_I3_J, tcon_Polynomial_Opoly___Rings_Olinordered__comm__semiring__strict_7, tcon_Polynomial_Opoly___Groups_Ogroup__add, fact_75_append_Oassoc, fact_123_no__zero__divisors, subcl_Rings_Olinordered__idom___Rings_Olinordered__ring, fact_23_pCons__eq__0__iff, fact_171_mult__less__cancel__left__pos, fact_235_bot__nat__0_Oextremum__strict, fact_145_shuffles_Oinduct, fact_143_remdups__adj_Ocases, fact_83_equal__neg__zero, fact_209_mult__0__right, subcl_Rings_Olinordered__idom___Rings_Oring__1, fact_141_remdups__adj_Oinduct, tcon_Polynomial_Opoly___Rings_Oring, fact_247_double__compl, tcon_Polynomial_Opoly___Nat_Oring__char__0, fact_99_append__self__conv, fact_227_measure__induct, fact_61_less__neg__neg, subcl_Rings_Olinordered__idom___Orderings_Oord, fact_22_pCons__0__0, fact_12_sign__changes__0__Cons, tcon_Nat_Onat___Groups_Osemigroup__mult, tcon_Polynomial_Opoly___Rings_Olinordered__semiring__strict_9, fact_56_reduce__root__nonzero, fact_189_less__minus__one__simps_I4_J, subcl_Rings_Olinordered__idom___Rings_Olinordered__semiring__strict, fact_87_mult_Oright__neutral, tcon_Polynomial_Opoly___Rings_Oring__1, fact_19_smult__0__right, subcl_Rings_Olinordered__idom___Groups_Omonoid__add, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, subcl_Rings_Olinordered__idom___Rings_Olinordered__nonzero__semiring, fact_69_neg__equal__iff__equal, fact_238_mult__less__mono2, fact_178_mult__pos__neg, subcl_Rings_Olinordered__idom___Rings_Olinordered__comm__semiring__strict, fact_6_coeff__sign__changes__reduce__root, fact_25_one__poly__eq__simps_I1_J, fact_233_gr__implies__not0, fact_246_compl__eq__compl__iff, fact_20_mult__smult__left, fact_46_poly__induct2, fact_95_Nil__is__append__conv, fact_134_one__neq__neg__one, fact_142_sorted__wrt_Oinduct, fact_215_less__one, fact_230_not__gr0, subcl_Rings_Olinordered__idom___Groups_Omonoid__mult, fact_70_add_Oinverse__inverse, fact_167_mult__strict__right__mono__neg, fact_203_mult__less__cancel2, subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors, tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_14, tcon_Nat_Onat___Rings_Olinordered__semiring__strict, fact_234_infinite__descent0, fact_111_equation__minus__iff, fact_214_poly__cutoff__0, tcon_Polynomial_Opoly___Orderings_Oord_24, fact_224_less__not__refl2, fact_41_pCons__cases, fact_216_nat__mult__1, fact_133_square__eq__iff, fact_52_minus__poly__rev__list_Oinduct, fact_146_min__list_Oinduct, tcon_Polynomial_Opoly___Groups_Oordered__ab__group__add, fact_222_less__irrefl__nat, subcl_Rings_Olinordered__idom___Groups_Oplus, fact_236_infinite__descent0__measure, fact_192_append__eq__Cons__conv, tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors_10, fact_205_neq0__conv, fact_182_mult__neg__neg, fact_9_sign__changes__Nil, tcon_Polynomial_Opoly___Rings_Omult__zero_23, subcl_Rings_Olinordered__idom___Groups_Osemigroup__mult, tcon_Polynomial_Opoly___Rings_Oring__1__no__zero__divisors
% 15.38/4.03 % No. of inferences in proof: 700
% 15.38/4.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3662 ms resp. 2778 ms w/o parsing
% 15.96/4.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.96/4.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------