%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP043^2 : 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 : n011.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 24.13s 6.34s
% Output : Refutation 25.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 303
% Syntax : Number of formulae : 608 ( 230 unt; 0 typ; 0 def)
% Number of atoms : 1672 ( 681 equ; 2 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 6977 ( 154 ~; 20 |; 78 &;5911 @)
% ( 0 <=>; 814 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 174 ( 174 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 9 con; 0-3 aty)
% Number of variables : 1866 ( 26 ^;1800 !; 40 ?;1866 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(a_type,type,
a: $tType ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(type_decl,type,
type:
!>[TA: $tType] : $o ).
thf(size_decl,type,
size:
!>[TA: $tType] : $o ).
thf(plus_decl,type,
plus:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(semigroup_add_decl,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_decl,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_decl,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(ordere1818651114id_add_decl,type,
ordere1818651114id_add:
!>[TA: $tType] : $o ).
thf(strict797366125id_add_decl,type,
strict797366125id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_decl,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(strict2144017051up_add_decl,type,
strict2144017051up_add:
!>[TA: $tType] : $o ).
thf(ordere516151231imp_le_decl,type,
ordere516151231imp_le:
!>[TA: $tType] : $o ).
thf(descar1668888542_psums_decl,type,
descar1668888542_psums:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > 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(last_decl,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(nth_decl,type,
nth:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA ) ).
thf(replicate_decl,type,
replicate:
!>[TA: $tType] : ( nat > TA > ( list @ TA ) ) ).
thf(take_decl,type,
take:
!>[TA: $tType] : ( nat > ( list @ TA ) > ( list @ TA ) ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(p_decl,type,
p: nat ).
thf(v_decl,type,
v: ( list @ a ) > int ).
thf(xa_decl,type,
xa: a ).
thf(xs_decl,type,
xs: list @ a ).
thf(xs1_decl,type,
xs1: list @ a ).
thf(xs2_decl,type,
xs2: list @ a ).
thf(xsa_decl,type,
xsa: list @ a ).
thf(232,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_not__Cons__self2) ).
thf(1036,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(181,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_85_Cons__eq__append__conv) ).
thf(809,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)],[181]) ).
thf(251,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_74_neq__Nil__conv) ).
thf(1105,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)],[251]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_add__less__le__mono) ).
thf(468,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(208,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_add__increasing) ).
thf(941,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(29,axiom,
strict2144017051up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_5) ).
thf(365,plain,
strict2144017051up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(278,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_17_Cons__eq__appendI) ).
thf(1190,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)],[278]) ).
thf(17,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere779506340up_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add) ).
thf(333,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere779506340up_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(139,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_add__nonpos__eq__0__iff) ).
thf(628,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(44,axiom,
ordere1818651114id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_9) ).
thf(408,plain,
ordere1818651114id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(92,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_add__le__imp__le__left) ).
thf(523,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(4,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_add_Oleft__commute) ).
thf(308,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(61,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder_18) ).
thf(449,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(262,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_add__nonpos__nonpos) ).
thf(1142,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(135,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_66_sorted__wrt_Oinduct) ).
thf(614,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)],[135]) ).
thf(153,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( size_size @ ( list @ TA ) @ B ) )
=> ( A
!= ( cons @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_impossible__Cons) ).
thf(677,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( size_size @ ( list @ TA ) @ B ) )
=> ( A
!= ( cons @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(161,axiom,
( xs
!= ( nil @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_assms_I1_J) ).
thf(715,plain,
( xs
!= ( nil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(239,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( last @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_last__snoc) ).
thf(1063,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( last @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(288,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_less__nat__zero__code) ).
thf(1222,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(41,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_minf_I8_J) ).
thf(404,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_le__funE) ).
thf(436,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(290,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_append__Nil) ).
thf(1228,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(144,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_3_psums__0__Cons) ).
thf(651,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)],[144]) ).
thf(219,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_add__neg__nonpos) ).
thf(973,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(199,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_add__nonneg__pos) ).
thf(885,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(36,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_length__induct) ).
thf(389,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(164,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A != B )
=> ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ? [C: list @ TA,D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( D != F )
& ( A
= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ D @ ( nil @ TA ) ) @ E ) ) )
& ( B
= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ F @ ( nil @ TA ) ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_same__length__different) ).
thf(724,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A != B )
=> ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ? [C: list @ TA,D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( D != F )
& ( A
= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ D @ ( nil @ TA ) ) @ E ) ) )
& ( B
= ( append @ TA @ C @ ( append @ TA @ ( cons @ TA @ F @ ( nil @ TA ) ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(114,axiom,
semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__add) ).
thf(570,plain,
semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(34,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_le__cases3) ).
thf(372,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(84,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_add__less__cancel__left) ).
thf(504,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(124,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_add__le__imp__le__right) ).
thf(587,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(202,axiom,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_list_Osize_I3_J) ).
thf(917,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(304,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_add__increasing2) ).
thf(1279,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(103,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_add__le__cancel__right) ).
thf(542,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(67,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ozero) ).
thf(460,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( zero @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(264,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_add__less__same__cancel2) ).
thf(1147,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(130,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linorder @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Orderings_Olinorder) ).
thf(606,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linorder @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(49,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_group__cancel_Oadd2) ).
thf(416,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(12,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_14) ).
thf(325,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_add__left__imp__eq) ).
thf(316,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(292,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_add__cancel__right__right) ).
thf(1232,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(77,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ( take @ TA @ A @ B )
= B )
= ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_take__all__iff) ).
thf(485,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ( take @ TA @ A @ B )
= B )
= ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(180,axiom,
! [TA: $tType,A: nat,B: nat,C: list @ TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( nth @ TA @ ( take @ TA @ B @ C ) @ A )
= ( nth @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_nth__take) ).
thf(806,plain,
! [TA: $tType,A: nat,B: nat,C: list @ TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( nth @ TA @ ( take @ TA @ B @ C ) @ A )
= ( nth @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_le__fun__def) ).
thf(480,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_le__funD) ).
thf(348,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(117,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_add__left__mono) ).
thf(574,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(237,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ! [C: TA] :
( ( B
= ( plus_plus @ TA @ A @ C ) )
=> ( C
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_canonically__ordered__monoid__add__class_OlessE) ).
thf(1051,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ! [C: TA] :
( ( B
= ( plus_plus @ TA @ A @ C ) )
=> ( C
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(185,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_37_append1__eq__conv) ).
thf(821,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)],[185]) ).
thf(129,axiom,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_size__neq__size__imp__neq) ).
thf(602,plain,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(271,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_add_Oleft__neutral) ).
thf(1169,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: list @ TC,B: list @ TB,C: list @ TD,D: list @ TA,E: ( list @ TC ) > ( list @ TB ) > ( list @ TD ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TC ) @ A )
= ( size_size @ ( list @ TB ) @ B ) )
=> ( ( ( size_size @ ( list @ TB ) @ B )
= ( size_size @ ( list @ TD ) @ C ) )
=> ( ( ( size_size @ ( list @ TD ) @ C )
= ( size_size @ ( list @ TA ) @ D ) )
=> ( ( E @ ( nil @ TC ) @ ( nil @ TB ) @ ( nil @ TD ) @ ( nil @ TA ) )
=> ( ! [F: TC,G: list @ TC,H: TB,I: list @ TB,J: TD,K: list @ TD,L: TA,M: list @ TA] :
( ( ( size_size @ ( list @ TC ) @ G )
= ( size_size @ ( list @ TB ) @ I ) )
=> ( ( ( size_size @ ( list @ TB ) @ I )
= ( size_size @ ( list @ TD ) @ K ) )
=> ( ( ( size_size @ ( list @ TD ) @ K )
= ( size_size @ ( list @ TA ) @ M ) )
=> ( ( E @ G @ I @ K @ M )
=> ( E @ ( cons @ TC @ F @ G ) @ ( cons @ TB @ H @ I ) @ ( cons @ TD @ J @ K ) @ ( cons @ TA @ L @ M ) ) ) ) ) )
=> ( E @ A @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_list__induct4) ).
thf(692,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: list @ TC,B: list @ TB,C: list @ TD,D: list @ TA,E: ( list @ TC ) > ( list @ TB ) > ( list @ TD ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TC ) @ A )
= ( size_size @ ( list @ TB ) @ B ) )
=> ( ( ( size_size @ ( list @ TB ) @ B )
= ( size_size @ ( list @ TD ) @ C ) )
=> ( ( ( size_size @ ( list @ TD ) @ C )
= ( size_size @ ( list @ TA ) @ D ) )
=> ( ( E @ ( nil @ TC ) @ ( nil @ TB ) @ ( nil @ TD ) @ ( nil @ TA ) )
=> ( ! [F: TC,G: list @ TC,H: TB,I: list @ TB,J: TD,K: list @ TD,L: TA,M: list @ TA] :
( ( ( size_size @ ( list @ TC ) @ G )
= ( size_size @ ( list @ TB ) @ I ) )
=> ( ( ( size_size @ ( list @ TB ) @ I )
= ( size_size @ ( list @ TD ) @ K ) )
=> ( ( ( size_size @ ( list @ TD ) @ K )
= ( size_size @ ( list @ TA ) @ M ) )
=> ( ( E @ G @ I @ K @ M )
=> ( E @ ( cons @ TC @ F @ G ) @ ( cons @ TB @ H @ I ) @ ( cons @ TD @ J @ K ) @ ( cons @ TA @ L @ M ) ) ) ) ) )
=> ( E @ A @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(242,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_59_strict__sorted_Oinduct) ).
thf(1072,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)],[242]) ).
thf(147,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_27_append__self__conv2) ).
thf(660,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)],[147]) ).
thf(224,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_add__decreasing2) ).
thf(998,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(296,axiom,
! [TA: $tType,A: nat,B: TA] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( cons @ TA @ B @ ( replicate @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_replicate__append__same) ).
thf(1242,plain,
! [TA: $tType,A: nat,B: TA] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( cons @ TA @ B @ ( replicate @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(85,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere216010020id_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__comm__monoid__add) ).
thf(507,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere216010020id_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(94,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_27) ).
thf(527,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_ord__le__eq__subst) ).
thf(428,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(281,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( nth @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ C ) ) @ ( size_size @ ( list @ TA ) @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_nth__append__length) ).
thf(1201,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( nth @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ C ) ) @ ( size_size @ ( list @ TA ) @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(3,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_13) ).
thf(307,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(63,axiom,
! [TA: $tType] :
( ( strict2144017051up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_add__strict__mono) ).
thf(452,plain,
! [TA: $tType] :
( ( strict2144017051up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(203,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_57_gr__zeroI) ).
thf(920,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)],[203]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_le__neq__implies__less) ).
thf(439,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(176,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_le__add__same__cancel2) ).
thf(793,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(266,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_72_splice_Oinduct) ).
thf(1153,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)],[266]) ).
thf(30,axiom,
! [TA: $tType,A: list @ TA,B: nat] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( take @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_take__all) ).
thf(366,plain,
! [TA: $tType,A: list @ TA,B: nat] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( take @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(98,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(534,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(238,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
| ( ( size_size @ ( list @ TA ) @ C )
= ( size_size @ ( list @ TA ) @ D ) ) )
=> ( ( ( append @ TA @ A @ C )
= ( append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_append__eq__append__conv) ).
thf(1057,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
| ( ( size_size @ ( list @ TA ) @ C )
= ( size_size @ ( list @ TA ) @ D ) ) )
=> ( ( ( append @ TA @ A @ C )
= ( append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(269,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_le0) ).
thf(1163,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(214,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_neq0__conv) ).
thf(957,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(234,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_le__0__eq) ).
thf(1042,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(298,axiom,
! [TA: $tType] :
( ( take @ TA @ ( zero_zero @ nat ) )
= ( ^ [A: list @ TA] : ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_take0) ).
thf(1255,plain,
! [TA: $tType] :
( ( take @ TA @ ( zero_zero @ nat ) )
= ( ^ [A: list @ TA] : ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(196,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_62_list__nonempty__induct) ).
thf(862,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)],[196]) ).
thf(128,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_neq__if__length__neq) ).
thf(598,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(51,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_minf_I6_J) ).
thf(424,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(43,axiom,
plus @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oplus_23) ).
thf(407,plain,
plus @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(183,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_10_append_Oassoc) ).
thf(815,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)],[183]) ).
thf(294,axiom,
linordered_idom @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
thf(1238,plain,
linordered_idom @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(170,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_29_append__self__conv) ).
thf(746,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)],[170]) ).
thf(246,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_append__Nil2) ).
thf(1091,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(70,axiom,
ordere1818651114id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__cancel__comm__monoid__add) ).
thf(467,plain,
ordere1818651114id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(27,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_add__less__imp__less__left) ).
thf(361,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(198,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_nth__equalityI) ).
thf(879,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(192,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_add__neg__neg) ).
thf(852,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(149,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_15_list_Oinject) ).
thf(665,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)],[149]) ).
thf(201,axiom,
! [TA: $tType] :
( ( ( plus @ TA )
& ( zero @ TA ) )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: list @ TA] :
( ( A @ C )
=> ( A @ ( cons @ TA @ ( zero_zero @ TA ) @ C ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( C
!= ( zero_zero @ TA ) )
=> ( ( A @ ( cons @ TA @ ( plus_plus @ TA @ C @ D ) @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_sign__changes__induct) ).
thf(889,plain,
! [TA: $tType] :
( ( ( plus @ TA )
& ( zero @ TA ) )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: list @ TA] :
( ( A @ C )
=> ( A @ ( cons @ TA @ ( zero_zero @ TA ) @ C ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( C
!= ( zero_zero @ TA ) )
=> ( ( A @ ( cons @ TA @ ( plus_plus @ TA @ C @ D ) @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(284,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_double__zero__sym) ).
thf(1210,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(190,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_length__0__conv) ).
thf(842,plain,
! [TA: $tType,A: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(11,axiom,
ordere223160158up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add_6) ).
thf(324,plain,
ordere223160158up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(113,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_group__cancel_Oadd1) ).
thf(566,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(76,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add_15) ).
thf(484,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(15,axiom,
ordere779506340up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_10) ).
thf(329,plain,
ordere779506340up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(274,axiom,
( ( last @ a @ xs )
!= ( zero_zero @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_assms_I2_J) ).
thf(1178,plain,
( ( last @ a @ xs )
!= ( zero_zero @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(121,axiom,
ordere216010020id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__comm__monoid__add) ).
thf(583,plain,
ordere216010020id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(188,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_last__append) ).
thf(830,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(211,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_zero__le) ).
thf(948,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(253,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ 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 ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_add__pos__pos) ).
thf(1111,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ 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 ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(226,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_24_append__is__Nil__conv) ).
thf(1006,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)],[226]) ).
thf(126,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ! [C: nat] :
( ( take @ TA @ C @ A )
= ( take @ TA @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_take__equalityI) ).
thf(593,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ! [C: nat] :
( ( take @ TA @ C @ A )
= ( take @ TA @ C @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(133,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add__le__cancel__left) ).
thf(610,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(50,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_ord__le__eq__trans) ).
thf(420,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(168,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_add__decreasing) ).
thf(742,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(119,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_add__right__mono) ).
thf(578,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(260,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_le__add__same__cancel1) ).
thf(1138,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(25,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_le__iff__add) ).
thf(356,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_7) ).
thf(328,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(268,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_95_append__Cons) ).
thf(1160,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)],[268]) ).
thf(78,axiom,
strict2144017051up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(488,plain,
strict2144017051up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(106,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_add__mono__thms__linordered__field_I3_J) ).
thf(554,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(100,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ab_semigroup_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oab__semigroup__add) ).
thf(537,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ab_semigroup_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(156,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_84_append__eq__Cons__conv) ).
thf(686,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)],[156]) ).
thf(79,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( group_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ogroup__add) ).
thf(489,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( group_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(283,axiom,
( xsa
!= ( nil @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_nonneg_Ohyps_I1_J) ).
thf(1207,plain,
( xsa
!= ( nil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(233,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( descar1668888542_psums @ TA @ A ) )
= ( size_size @ ( list @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_length__psums) ).
thf(1039,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( descar1668888542_psums @ TA @ A ) )
= ( size_size @ ( list @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(229,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_bot__nat__0_Oextremum) ).
thf(1028,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
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_22_not__gr__zero) ).
thf(1082,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(189,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_68_shuffles_Oinduct) ).
thf(837,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)],[189]) ).
thf(249,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_less__add__same__cancel1) ).
thf(1099,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(265,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_bot__nat__0_Oextremum__uniqueI) ).
thf(1150,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(145,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_double__add__le__zero__iff__single__add__le__zero) ).
thf(654,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(163,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_zero__less__double__add__iff__zero__less__single__add) ).
thf(721,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(33,axiom,
size @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(371,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(143,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_61_map__tailrec__rev_Oinduct) ).
thf(647,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)],[143]) ).
thf(301,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_zero__reorient) ).
thf(1263,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(302,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_75_list_Oinducts) ).
thf(1266,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)],[302]) ).
thf(291,axiom,
ord_less_eq @ a @ ( zero_zero @ a ) @ xa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_nonneg_Ohyps_I4_J) ).
thf(1231,plain,
ord_less_eq @ a @ ( zero_zero @ a ) @ xa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(5,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(311,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(102,axiom,
strict797366125id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_8) ).
thf(541,plain,
strict797366125id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(146,axiom,
! [TA: $tType,A: nat,B: TA] :
( ( ( replicate @ TA @ A @ B )
= ( nil @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_replicate__empty) ).
thf(657,plain,
! [TA: $tType,A: nat,B: TA] :
( ( ( replicate @ TA @ A @ B )
= ( nil @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(38,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_linear) ).
thf(398,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(108,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( cancel1352612707id_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ocancel__comm__monoid__add) ).
thf(558,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( cancel1352612707id_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(96,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_add__mono__thms__linordered__semiring_I1_J) ).
thf(530,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(162,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_11_append__assoc) ).
thf(718,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)],[162]) ).
thf(277,axiom,
! [TA: $tType,A: list @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ TA ) @ A ) )
= ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_length__greater__0__conv) ).
thf(1187,plain,
! [TA: $tType,A: list @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ TA ) @ A ) )
= ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(152,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_add__eq__0__iff__both__eq__0) ).
thf(674,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(173,axiom,
( ( nth @ a @ xsa @ p )
!= ( zero_zero @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_p__nz) ).
thf(773,plain,
( ( nth @ a @ xsa @ p )
!= ( zero_zero @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(123,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_21) ).
thf(586,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(259,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_double__add__less__zero__iff__single__add__less__zero) ).
thf(1135,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(136,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: nat,B: list @ TA] :
( ( descar1668888542_psums @ TA @ ( append @ TA @ ( replicate @ TA @ A @ ( zero_zero @ TA ) ) @ B ) )
= ( append @ TA @ ( replicate @ TA @ A @ ( zero_zero @ TA ) ) @ ( descar1668888542_psums @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_psums__replicate__0__append) ).
thf(618,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: nat,B: list @ TA] :
( ( descar1668888542_psums @ TA @ ( append @ TA @ ( replicate @ TA @ A @ ( zero_zero @ TA ) ) @ B ) )
= ( append @ TA @ ( replicate @ TA @ A @ ( zero_zero @ TA ) ) @ ( descar1668888542_psums @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(88,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_add_Oleft__cancel) ).
thf(513,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(194,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_bot__nat__0_Onot__eq__extremum) ).
thf(856,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(116,axiom,
cancel1352612707id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add) ).
thf(573,plain,
cancel1352612707id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(157,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_zero__eq__add__iff__both__eq__0) ).
thf(689,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(59,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_less__eqE) ).
thf(444,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(287,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_82_psums_Ocases) ).
thf(1219,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)],[287]) ).
thf(186,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_le__zero__eq) ).
thf(824,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(122,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_less__imp__le__nat) ).
thf(584,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_le__funI) ).
thf(402,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(165,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_add__cancel__left__right) ).
thf(732,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_ord__eq__le__subst) ).
thf(545,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(110,axiom,
semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_16) ).
thf(562,plain,
semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(220,axiom,
! [TA: $tType,A: list @ TA] :
( ( take @ TA @ ( zero_zero @ nat ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_take__0) ).
thf(975,plain,
! [TA: $tType,A: list @ TA] :
( ( take @ TA @ ( zero_zero @ nat ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(141,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_25_Nil__is__append__conv) ).
thf(641,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)],[141]) ).
thf(295,axiom,
! [TA: $tType,A: nat,B: TA] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ( last @ TA @ ( replicate @ TA @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_last__replicate) ).
thf(1239,plain,
! [TA: $tType,A: nat,B: TA] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ( last @ TA @ ( replicate @ TA @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(18,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_add__right__cancel) ).
thf(335,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_less__or__eq__imp__le) ).
thf(350,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(299,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_13_same__append__eq) ).
thf(1258,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)],[299]) ).
thf(159,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( B
= ( append @ TA @ E @ C ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( last @ TA @ D )
!= ( last @ TA @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_longest__common__suffix) ).
thf(704,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( B
= ( append @ TA @ E @ C ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( last @ TA @ D )
!= ( last @ TA @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(279,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_add_Ocomm__neutral) ).
thf(1194,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(42,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(406,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(154,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_bot__nat__0_Oextremum__unique) ).
thf(681,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(236,axiom,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( cons @ TA @ B @ C ) )
= ( cons @ TA @ B @ ( append @ TA @ ( replicate @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_replicate__app__Cons__same) ).
thf(1048,plain,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( cons @ TA @ B @ C ) )
= ( cons @ TA @ B @ ( append @ TA @ ( replicate @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(263,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ( ( descar1668888542_psums @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_psums_Osimps_I1_J) ).
thf(1144,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ( ( descar1668888542_psums @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(86,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__add) ).
thf(509,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(273,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_append_Oright__neutral) ).
thf(1175,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_add__strict__left__mono) ).
thf(387,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(140,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_87_rev__induct) ).
thf(631,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)],[140]) ).
thf(21,axiom,
ordere779506340up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
thf(345,plain,
ordere779506340up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(99,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( cancel_semigroup_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ocancel__semigroup__add) ).
thf(535,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( cancel_semigroup_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(132,axiom,
monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__add) ).
thf(609,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(10,axiom,
ordere223160158up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(323,plain,
ordere223160158up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(178,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_81_eq__Nil__appendI) ).
thf(799,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)],[178]) ).
thf(137,axiom,
! [TA: $tType,A: nat,B: TA,C: nat] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( replicate @ TA @ C @ B ) )
= ( append @ TA @ ( replicate @ TA @ C @ B ) @ ( replicate @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_append__replicate__commute) ).
thf(621,plain,
! [TA: $tType,A: nat,B: TA,C: nat] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( replicate @ TA @ C @ B ) )
= ( append @ TA @ ( replicate @ TA @ C @ B ) @ ( replicate @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(75,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(483,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(216,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_last__appendL) ).
thf(964,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(209,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_add_Oright__neutral) ).
thf(943,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(150,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_90_psums_Osimps_I2_J) ).
thf(668,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)],[150]) ).
thf(16,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_add__right__imp__eq) ).
thf(330,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(68,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_add_Oassoc) ).
thf(462,plain,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(91,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( strict797366125id_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ostrict__ordered__comm__monoid__add) ).
thf(521,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( strict797366125id_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(297,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [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 @ ( cons @ TA @ ( plus_plus @ TA @ C @ D ) @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_psums_Oinduct) ).
thf(1245,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [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 @ ( cons @ TA @ ( plus_plus @ TA @ C @ D ) @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(240,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_add__le__same__cancel1) ).
thf(1066,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(65,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_add__less__cancel__right) ).
thf(455,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(131,axiom,
ordere216010020id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_11) ).
thf(608,plain,
ordere216010020id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(225,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA] :
( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ C ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( ( nth @ TA @ B @ D )
= ( nth @ TA @ C @ D ) ) )
=> ( ( take @ TA @ A @ B )
= ( take @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_nth__take__lemma) ).
thf(1000,plain,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA] :
( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ C ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( ( nth @ TA @ B @ D )
= ( nth @ TA @ C @ D ) ) )
=> ( ( take @ TA @ A @ B )
= ( take @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(250,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_26_self__append__conv2) ).
thf(1102,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)],[250]) ).
thf(56,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_22) ).
thf(438,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(285,axiom,
! [TA: $tType,A: nat,B: TA,C: nat,D: TA] :
( ( ( replicate @ TA @ A @ B )
= ( replicate @ TA @ C @ D ) )
= ( ( A = C )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_replicate__eq__replicate) ).
thf(1213,plain,
! [TA: $tType,A: nat,B: TA,C: nat,D: TA] :
( ( ( replicate @ TA @ A @ B )
= ( replicate @ TA @ C @ D ) )
= ( ( A = C )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(187,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_list_Odistinct_I1_J) ).
thf(827,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(254,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_12_append__same__eq) ).
thf(1113,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)],[254]) ).
thf(111,axiom,
ordere516151231imp_le @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(563,plain,
ordere516151231imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(52,axiom,
strict797366125id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ostrict__ordered__comm__monoid__add) ).
thf(426,plain,
strict797366125id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(125,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_add__mono__thms__linordered__field_I1_J) ).
thf(589,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(148,axiom,
! [TA: $tType] :
( ( ordere1818651114id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_add__strict__increasing) ).
thf(663,plain,
! [TA: $tType] :
( ( ordere1818651114id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(205,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( C @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ E )
= ( size_size @ ( list @ TA ) @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_list__induct2) ).
thf(927,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( C @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ E )
= ( size_size @ ( list @ TA ) @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(182,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_add_Ogroup__left__neutral) ).
thf(812,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(171,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_69_min__list_Oinduct) ).
thf(749,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)],[171]) ).
thf(89,axiom,
group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add) ).
thf(516,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(207,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_add__nonneg__nonneg) ).
thf(939,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(20,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_add_Ocommute) ).
thf(342,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(105,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(553,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(217,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_last__appendR) ).
thf(968,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(66,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_add__mono) ).
thf(458,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(275,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ p )
=> ( ( nth @ a @ xsa @ A )
= ( zero_zero @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__p__zero) ).
thf(1181,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ p )
=> ( ( nth @ a @ xsa @ A )
= ( zero_zero @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(174,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_83_rev__nonempty__induct) ).
thf(776,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)],[174]) ).
thf(93,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_le__cases) ).
thf(525,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(160,axiom,
! [TA: $tType,A: TA] :
( ( replicate @ TA @ ( zero_zero @ nat ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_replicate__0) ).
thf(712,plain,
! [TA: $tType,A: TA] :
( ( replicate @ TA @ ( zero_zero @ nat ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(120,axiom,
! [TA: $tType,A: nat] :
( ( take @ TA @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_take__Nil) ).
thf(580,plain,
! [TA: $tType,A: nat] :
( ( take @ TA @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(228,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_86_rev__exhaust) ).
thf(1025,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)],[228]) ).
thf(289,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_append_Oleft__neutral) ).
thf(1225,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(200,axiom,
! [TA: $tType] :
( ( ordere1818651114id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_add__strict__increasing2) ).
thf(887,plain,
! [TA: $tType] :
( ( ordere1818651114id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(213,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add__cancel__right__left) ).
thf(954,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(167,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_less__add__same__cancel2) ).
thf(739,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(45,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_25) ).
thf(409,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(47,axiom,
plus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oplus) ).
thf(414,plain,
plus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(218,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_not__less__zero) ).
thf(971,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(32,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_12) ).
thf(370,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(83,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere516151231imp_le @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(502,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere516151231imp_le @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(293,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_28_self__append__conv) ).
thf(1235,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)],[293]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_add__mono__thms__linordered__semiring_I4_J) ).
thf(338,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_add__strict__right__mono) ).
thf(359,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(257,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_67_remdups__adj_Ocases) ).
thf(1130,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)],[257]) ).
thf(244,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nth @ TA @ ( cons @ TA @ A @ B ) @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_nth__Cons__0) ).
thf(1085,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nth @ TA @ ( cons @ TA @ A @ B ) @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(72,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_add__mono__thms__linordered__field_I2_J) ).
thf(470,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(118,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( strict2144017051up_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(576,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( strict2144017051up_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(169,axiom,
! [TA: $tType] :
( ( strict797366125id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_pos__add__strict) ).
thf(744,plain,
! [TA: $tType] :
( ( strict797366125id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(261,axiom,
ord_less @ nat @ p @ ( size_size @ ( list @ a ) @ xsa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_p__less__length) ).
thf(1141,plain,
ord_less @ nat @ p @ ( size_size @ ( list @ a ) @ xsa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(134,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add_19) ).
thf(613,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(6,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere223160158up_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(314,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere223160158up_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(115,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( plus @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oplus) ).
thf(571,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( plus @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(195,axiom,
! [TA: $tType,A: nat,B: TA] :
( ( size_size @ ( list @ TA ) @ ( replicate @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_length__replicate) ).
thf(859,plain,
! [TA: $tType,A: nat,B: TA] :
( ( size_size @ ( list @ TA ) @ ( replicate @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(247,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_comm__monoid__add__class_Oadd__0) ).
thf(1094,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(221,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_71_induct__list012) ).
thf(978,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)],[221]) ).
thf(82,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_less__mono__imp__le__mono) ).
thf(497,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(197,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_add__less__same__cancel1) ).
thf(876,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(191,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_last_Osimps) ).
thf(845,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(69,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_le__eq__less__or__eq) ).
thf(465,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(62,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_add__less__imp__less__right) ).
thf(450,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(101,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( monoid_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Omonoid__add) ).
thf(539,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( monoid_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(151,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_zero__le__double__add__iff__zero__le__single__add) ).
thf(671,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(267,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_add__cancel__left__left) ).
thf(1157,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(81,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_add__mono__thms__linordered__field_I5_J) ).
thf(495,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(172,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_ex__least__nat__le) ).
thf(759,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(286,axiom,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_Skolem__list__nth) ).
thf(1216,plain,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(256,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_last__ConsL) ).
thf(1126,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(252,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_last__ConsR) ).
thf(1108,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(28,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___HOL_Otype) ).
thf(363,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(107,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere1818651114id_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__cancel__comm__monoid__add) ).
thf(556,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere1818651114id_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(303,axiom,
! [A: list @ a] :
( ( v @ ( append @ a @ A @ xsa ) )
= ( plus_plus @ int @ ( v @ ( append @ a @ A @ ( cons @ a @ ( nth @ a @ xsa @ p ) @ ( nil @ a ) ) ) ) @ ( v @ ( cons @ a @ ( nth @ a @ xsa @ p ) @ xs2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_v__decompose) ).
thf(1276,plain,
! [A: list @ a] :
( ( v @ ( append @ a @ A @ xsa ) )
= ( plus_plus @ int @ ( v @ ( append @ a @ A @ ( cons @ a @ ( nth @ a @ xsa @ p ) @ ( nil @ a ) ) ) ) @ ( v @ ( cons @ a @ ( nth @ a @ xsa @ p ) @ xs2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(90,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_add__mono__thms__linordered__semiring_I2_J) ).
thf(517,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(8,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_add__left__cancel) ).
thf(319,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(210,axiom,
( xs1
= ( replicate @ a @ p @ ( zero_zero @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_xs1__def) ).
thf(946,plain,
( xs1
= ( replicate @ a @ p @ ( zero_zero @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(223,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_76_list_Oexhaust) ).
thf(995,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)],[223]) ).
thf(230,axiom,
! [TA: $tType,A: nat,B: TA] :
( ( ( nil @ TA )
= ( replicate @ TA @ A @ B ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_empty__replicate) ).
thf(1030,plain,
! [TA: $tType,A: nat,B: TA] :
( ( ( nil @ TA )
= ( replicate @ TA @ A @ B ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(87,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_add_Oright__cancel) ).
thf(510,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(155,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_add__nonpos__neg) ).
thf(684,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(22,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_add__le__less__mono) ).
thf(346,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(235,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_add__le__same__cancel2) ).
thf(1045,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(255,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: list @ TA,D: ( list @ TB ) > ( list @ TC ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( ( size_size @ ( list @ TC ) @ B )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: list @ TB,G: TC,H: list @ TC,I: TA,J: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ F )
= ( size_size @ ( list @ TC ) @ H ) )
=> ( ( ( size_size @ ( list @ TC ) @ H )
= ( size_size @ ( list @ TA ) @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons @ TB @ E @ F ) @ ( cons @ TC @ G @ H ) @ ( cons @ TA @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_list__induct3) ).
thf(1116,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: list @ TA,D: ( list @ TB ) > ( list @ TC ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( ( size_size @ ( list @ TC ) @ B )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: list @ TB,G: TC,H: list @ TC,I: TA,J: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ F )
= ( size_size @ ( list @ TC ) @ H ) )
=> ( ( ( size_size @ ( list @ TC ) @ H )
= ( size_size @ ( list @ TA ) @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons @ TB @ E @ F ) @ ( cons @ TC @ G @ H ) @ ( cons @ TA @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(258,axiom,
( ( take @ a @ p @ xsa )
= ( replicate @ a @ p @ ( zero_zero @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062take_Ap_Axs_A_061_Areplicate_Ap_A_I0_058_058_Ha_J_092_060close_062) ).
thf(1133,plain,
( ( take @ a @ p @ xsa )
= ( replicate @ a @ p @ ( zero_zero @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(60,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(447,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( comm_monoid_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(46,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_add__mono__thms__linordered__semiring_I3_J) ).
thf(410,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(184,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_51_transpose_Ocases) ).
thf(818,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)],[184]) ).
thf(193,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_add__pos__nonneg) ).
thf(854,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(175,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_list__eq__iff__nth__eq) ).
thf(790,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(166,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_77_list_OdiscI) ).
thf(735,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)],[166]) ).
thf(212,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_73_list__induct2_H) ).
thf(950,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)],[212]) ).
thf(248,axiom,
( xsa
= ( append @ a @ xs1 @ ( cons @ a @ ( nth @ a @ xsa @ p ) @ xs2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_xs__decompose) ).
thf(1097,plain,
( xsa
= ( append @ a @ xs1 @ ( cons @ a @ ( nth @ a @ xsa @ p ) @ xs2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(112,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Orderings_Oord) ).
thf(564,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1,conjecture,
( ( descar1668888542_psums @ a @ xsa )
= ( append @ a @ ( replicate @ a @ p @ ( zero_zero @ a ) ) @ ( descar1668888542_psums @ a @ ( cons @ a @ ( nth @ a @ xsa @ p ) @ xs2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( descar1668888542_psums @ a @ xsa )
!= ( append @ a @ ( replicate @ a @ p @ ( zero_zero @ a ) ) @ ( descar1668888542_psums @ a @ ( cons @ a @ ( nth @ a @ xsa @ p ) @ xs2 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(305,plain,
( ( descar1668888542_psums @ a @ xsa )
!= ( append @ a @ ( replicate @ a @ p @ ( zero_zero @ a ) ) @ ( descar1668888542_psums @ a @ ( cons @ a @ ( nth @ a @ xsa @ p ) @ xs2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere236663937imp_le @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(326,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere236663937imp_le @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(215,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_94_append__eq__appendI) ).
thf(960,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)],[215]) ).
thf(97,axiom,
! [TA: $tType] : ( size @ ( list @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_28) ).
thf(532,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(270,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_63_successively_Oinduct) ).
thf(1165,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)],[270]) ).
thf(177,axiom,
! [TA: $tType,A: nat,B: nat,C: TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( nth @ TA @ ( replicate @ TA @ B @ C ) @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_nth__replicate) ).
thf(796,plain,
! [TA: $tType,A: nat,B: nat,C: TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( nth @ TA @ ( replicate @ TA @ B @ C ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(48,axiom,
ordere516151231imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_4) ).
thf(415,plain,
ordere516151231imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(272,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ( take @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_take__eq__Nil) ).
thf(1172,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ( take @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(73,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_linorder__wlog) ).
thf(474,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(231,axiom,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: TA,C: list @ TA] :
( ( descar1668888542_psums @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( cons @ TA @ A @ ( descar1668888542_psums @ TA @ ( cons @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_psums_Osimps_I3_J) ).
thf(1033,plain,
! [TA: $tType] :
( ( plus @ TA )
=> ! [A: TA,B: TA,C: list @ TA] :
( ( descar1668888542_psums @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( cons @ TA @ A @ ( descar1668888542_psums @ TA @ ( cons @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(39,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(400,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord219039673up_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(280,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_55_gr__implies__not__zero) ).
thf(1197,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)],[280]) ).
thf(300,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_less__eq__nat_Osimps_I1_J) ).
thf(1261,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(53,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(427,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(127,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_add__mono__thms__linordered__field_I4_J) ).
thf(596,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(95,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_nat__less__le) ).
thf(528,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(142,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_70_min__list_Ocases) ).
thf(644,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)],[142]) ).
thf(222,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_double__zero) ).
thf(992,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(58,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( semigroup_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Osemigroup__add) ).
thf(442,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( semigroup_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(31,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Olinorder) ).
thf(369,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(37,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_Ex__list__of__length) ).
thf(395,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(138,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_64_arg__min__list_Oinduct) ).
thf(624,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)],[138]) ).
thf(9,axiom,
ordere236663937imp_le @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(322,plain,
ordere236663937imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(179,axiom,
( ( last @ a @ xsa )
!= ( zero_zero @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_nonneg_Ohyps_I2_J) ).
thf(803,plain,
( ( last @ a @ xsa )
!= ( zero_zero @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(204,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_103_plus__coeffs_Oinduct) ).
thf(923,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)],[204]) ).
thf(276,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_60_strict__sorted_Ocases) ).
thf(1184,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)],[276]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(560,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(282,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_54_zero__less__iff__neq__zero) ).
thf(1204,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)],[282]) ).
thf(206,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_102_minus__poly__rev__list_Oinduct) ).
thf(935,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)],[206]) ).
thf(227,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_65_remdups__adj_Oinduct) ).
thf(1009,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)],[227]) ).
thf(80,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_ord__eq__le__trans) ).
thf(491,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(245,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_add__nonneg__eq__0__iff) ).
thf(1088,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(64,axiom,
ord @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oord_3) ).
thf(454,plain,
ord @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(241,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_93_append__eq__append__conv2) ).
thf(1069,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)],[241]) ).
thf(1342,plain,
$false,
inference(e,[status(thm)],[1036,809,1105,468,941,365,1190,333,628,408,523,308,449,1142,614,677,715,1063,1222,404,436,1228,651,973,885,389,724,570,372,504,587,917,1279,542,460,1147,606,416,325,316,1232,485,806,480,348,574,1051,821,602,1169,692,1072,660,998,1242,507,527,428,1201,307,452,920,439,793,1153,366,534,1057,1163,957,1042,1255,862,598,424,407,815,1238,746,1091,467,361,879,852,665,889,1210,842,324,566,484,329,1178,583,830,948,1111,1006,593,610,420,742,578,1138,356,328,1160,488,554,537,686,489,1207,1039,1028,1082,837,1099,1150,654,721,371,647,1263,1266,1231,311,541,657,398,558,530,718,1187,674,773,586,1135,618,513,856,573,689,444,1219,824,584,402,732,545,562,975,641,1239,335,350,1258,704,1194,406,681,1048,1144,509,1175,387,631,345,535,609,323,799,621,483,964,943,668,330,462,521,1245,1066,455,608,1000,1102,438,1213,827,1113,563,426,589,663,927,812,749,516,939,342,553,968,458,1181,776,525,712,580,1025,1225,887,954,739,409,414,971,370,502,1235,338,359,1130,1085,470,576,744,1141,613,314,571,859,1094,978,497,876,845,465,450,539,671,1157,495,759,1216,1126,1108,363,556,1276,517,319,946,995,1030,510,684,346,1045,1116,1133,447,410,818,854,790,735,950,1097,564,305,326,960,532,1165,796,415,1172,474,1033,400,1197,1261,427,596,528,644,992,442,369,395,624,322,803,923,1184,560,1204,935,1009,491,1088,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP043^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:40:46 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.65/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.92/0.86 % [INFO] Parsing done (350ms).
% 1.92/0.89 % [INFO] Running in sequential loop mode.
% 3.07/1.28 % [INFO] eprover registered as external prover.
% 3.07/1.29 % [INFO] Scanning for conjecture ...
% 3.48/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 329 axioms. Running axiom selection ...
% 4.06/1.60 % [INFO] Axiom selection finished. Selected 302 axioms (removed 27 axioms).
% 5.04/1.91 % [INFO] Problem is higher-order (TPTP THF).
% 5.04/1.94 % [INFO] Type checking passed.
% 5.04/1.94 % [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 ...
% 24.13/6.34 % External prover 'e' found a proof!
% 24.13/6.34 % [INFO] Killing All external provers ...
% 24.13/6.34 % Time passed: 6055ms (effective reasoning time: 5442ms)
% 24.13/6.34 % 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)>
% 24.13/6.34 % Axioms used in derivation (302): subcl_Rings_Olinordered__idom___Groups_Ogroup__add, fact_225_same__length__different, fact_187_add__strict__mono, tcon_HOL_Obool___Orderings_Olinorder_25, fact_136_double__add__less__zero__iff__single__add__less__zero, subcl_Rings_Olinordered__idom___Orderings_Olinorder, fact_197_add__nonneg__nonneg, fact_182_add__mono__thms__linordered__semiring_I3_J, tfree_0, fact_103_plus__coeffs_Oinduct, fact_214_list__eq__iff__nth__eq, fact_162_size__neq__size__imp__neq, fact_94_append__eq__appendI, fact_219_add__strict__increasing, fact_5_xs__decompose, tcon_Int_Oint___Groups_Oplus, fact_20_replicate__eq__replicate, fact_154_bot__nat__0_Oextremum__uniqueI, fact_152_group__cancel_Oadd2, tcon_Nat_Onat___Groups_Ocancel__semigroup__add_13, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_7, fact_57_gr__zeroI, tcon_HOL_Obool___Orderings_Oord_27, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_4, fact_204_add__pos__pos, fact_113_double__zero__sym, fact_61_map__tailrec__rev_Oinduct, fact_0_nonneg_Ohyps_I1_J, subcl_Rings_Olinordered__idom___Groups_Oordered__cancel__ab__semigroup__add, tcon_Nat_Onat___Nat_Osize, fact_249_le__funI, tcon_Nat_Onat___Groups_Ostrict__ordered__comm__monoid__add_8, fact_31_nth__Cons__0, fact_155_add_Oassoc, tcon_Int_Oint___Groups_Ostrict__ordered__ab__semigroup__add, fact_70_min__list_Ocases, fact_147_le__0__eq, fact_11_append__assoc, fact_129_zero__le__double__add__iff__zero__le__single__add, fact_157_add_Oright__cancel, tcon_Int_Oint___Groups_Ozero, fact_39_last__appendL, fact_105_minf_I6_J, fact_80_append__Nil, fact_161_add__right__imp__eq, fact_10_append_Oassoc, fact_189_add__mono__thms__linordered__field_I2_J, fact_140_add__less__same__cancel1, fact_82_psums_Ocases, fact_171_add_Ocomm__neutral, fact_60_strict__sorted_Ocases, subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_93_append__eq__append__conv2, fact_30_append__Nil2, fact_126_take__all, fact_53_replicate__0, fact_241_linear, fact_217_psums_Osimps_I3_J, fact_224_sign__changes__induct, tcon_fun___Orderings_Oord, fact_180_add__mono__thms__linordered__semiring_I1_J, fact_143_nth__append__length, fact_156_add_Oleft__cancel, fact_78_list_Odistinct_I1_J, fact_166_le__eq__less__or__eq, fact_32_take0, fact_137_less__add__same__cancel2, fact_14_nonneg_Ohyps_I4_J, fact_19_assms_I2_J, fact_213_psums_Oinduct, fact_42_last__snoc, fact_123_add__less__cancel__left, fact_144_less__eq__nat_Osimps_I1_J, subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add, fact_176_add__right__mono, fact_8__092_060open_062take_Ap_Axs_A_061_Areplicate_Ap_A_I0_058_058_Ha_J_092_060close_062, subcl_Rings_Olinordered__idom___Groups_Ozero, fact_69_min__list_Oinduct, fact_89_replicate__append__same, fact_183_add__less__imp__less__right, tcon_Int_Oint___Groups_Oordered__comm__monoid__add, fact_63_successively_Oinduct, fact_237_le__cases3, fact_244_ord__le__eq__subst, fact_115_add__cancel__left__right, fact_34_empty__replicate, fact_141_length__0__conv, fact_195_add__nonneg__eq__0__iff, tcon_Int_Oint___Groups_Ocancel__semigroup__add, fact_23_append_Oright__neutral, subcl_Rings_Olinordered__idom___Groups_Ocancel__comm__monoid__add, fact_222_add__nonneg__pos, subcl_Rings_Olinordered__idom___HOL_Otype, tcon_Nat_Onat___Groups_Omonoid__add_19, fact_194_add__nonpos__eq__0__iff, tcon_Int_Oint___Groups_Omonoid__add, fact_202_pos__add__strict, fact_29_append__self__conv, fact_88_psums_Osimps_I1_J, tcon_Int_Oint___Groups_Oab__semigroup__add, fact_87_rev__induct, tcon_Int_Oint___Groups_Osemigroup__add, fact_168_ex__least__nat__le, fact_35_replicate__empty, fact_209_add__mono__thms__linordered__field_I4_J, fact_75_list_Oinducts, fact_130_double__add__le__zero__iff__single__add__le__zero, fact_164_le__neq__implies__less, fact_245_ord__eq__le__subst, fact_95_append__Cons, fact_206_add__less__le__mono, fact_119_zero__eq__add__iff__both__eq__0, fact_47_last__ConsR, fact_163_less__mono__imp__le__mono, fact_122_add__less__cancel__right, fact_36_last__replicate, fact_83_rev__nonempty__induct, fact_216_nth__equalityI, fact_106_add__left__cancel, fact_51_transpose_Ocases, fact_184_add__less__imp__less__left, fact_165_less__or__eq__imp__le, fact_208_add__mono__thms__linordered__field_I3_J, fact_186_add__strict__left__mono, fact_233_ord__le__eq__trans, fact_150_neq__if__length__neq, fact_177_less__eqE, tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le, tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__add_9, fact_146_add__mono__thms__linordered__semiring_I4_J, tcon_Int_Oint___Groups_Ocancel__comm__monoid__add, fact_181_add__mono__thms__linordered__semiring_I2_J, fact_139_add__less__same__cancel2, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_12, subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add, fact_117_add__cancel__right__right, fact_102_minus__poly__rev__list_Oinduct, fact_41_nth__replicate, tcon_Nat_Onat___Groups_Oordered__comm__monoid__add_11, fact_86_rev__exhaust, fact_149_Ex__list__of__length, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_10, fact_100_bot__nat__0_Onot__eq__extremum, fact_62_list__nonempty__induct, tcon_Int_Oint___Orderings_Olinorder, fact_85_Cons__eq__append__conv, fact_239_le__cases, fact_91_zero__reorient, fact_1_p__nz, fact_17_Cons__eq__appendI, fact_201_add__decreasing, subcl_Rings_Olinordered__idom___Groups_Ocancel__semigroup__add, fact_108_le0, fact_116_add__cancel__right__left, fact_193_nth__take__lemma, fact_27_append__self__conv2, fact_151_group__cancel_Oadd1, tcon_Nat_Onat___Groups_Oplus_23, fact_4_xs1__def, tcon_Nat_Onat___Orderings_Oord_21, fact_234_ord__eq__le__trans, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add, tcon_Nat_Onat___Groups_Ocomm__monoid__add_15, subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add__imp__le, fact_207_add__le__less__mono, fact_33_take__eq__Nil, fact_98_neq0__conv, subcl_Rings_Olinordered__idom___Groups_Oordered__cancel__comm__monoid__add, fact_221_add__nonpos__neg, fact_3_psums__0__Cons, tcon_Int_Oint___Groups_Ocomm__monoid__add, fact_40_last__appendR, fact_248_le__fun__def, fact_24_append__is__Nil__conv, fact_18_assms_I1_J, tcon_Nat_Onat___Groups_Ozero_22, fact_71_induct__list012, fact_170_comm__monoid__add__class_Oadd__0, fact_16_append__replicate__commute, fact_191_list_Osize_I3_J, fact_50_take__equalityI, fact_148_impossible__Cons, fact_111_add_Oright__neutral, fact_109_bot__nat__0_Oextremum, tcon_Int_Oint___Groups_Ogroup__add, tcon_Nat_Onat___Groups_Osemigroup__add_16, subcl_Rings_Olinordered__idom___Groups_Osemigroup__add, subcl_Rings_Olinordered__idom___Groups_Ostrict__ordered__comm__monoid__add, fact_125_take__all__iff, fact_9_replicate__app__Cons__same, fact_112_double__zero, fact_46_last__ConsL, fact_153_bot__nat__0_Oextremum__unique, fact_200_add__increasing, fact_22_not__gr__zero, fact_99_less__nat__zero__code, fact_81_eq__Nil__appendI, fact_192_length__induct, fact_124_append__eq__append__conv, fact_26_self__append__conv2, fact_28_self__append__conv, tcon_Int_Oint___Groups_Olinordered__ab__group__add, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, subcl_Rings_Olinordered__idom___Groups_Oab__semigroup__add, fact_203_canonically__ordered__monoid__add__class_OlessE, fact_67_remdups__adj_Ocases, fact_21_le__zero__eq, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_5, fact_79_append_Oleft__neutral, fact_179_add__mono, fact_223_add__neg__nonpos, fact_135_zero__less__double__add__iff__zero__less__single__add, fact_145_ab__semigroup__add__class_Oadd__ac_I1_J, fact_169_nat__less__le, fact_68_shuffles_Oinduct, fact_138_less__add__same__cancel1, fact_118_add__eq__0__iff__both__eq__0, subcl_Rings_Olinordered__idom___Groups_Olinordered__ab__group__add, fact_174_add__le__imp__le__left, fact_54_zero__less__iff__neq__zero, fact_72_splice_Oinduct, fact_84_append__eq__Cons__conv, fact_199_add__decreasing2, fact_159_add_Oleft__commute, fact_172_add_Ogroup__left__neutral, fact_66_sorted__wrt_Oinduct, fact_76_list_Oexhaust, fact_52_longest__common__suffix, fact_37_append1__eq__conv, fact_77_list_OdiscI, fact_215_Skolem__list__nth, fact_114_add__cancel__left__left, tcon_Nat_Onat___Groups_Oab__semigroup__add_14, fact_132_le__add__same__cancel1, fact_198_add__increasing2, fact_110_add_Oleft__neutral, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add_6, fact_160_add__left__imp__eq, fact_185_add__strict__right__mono, fact_107_add__right__cancel, fact_38_nth__take, subcl_Rings_Olinordered__idom___Groups_Oordered__comm__monoid__add, fact_229_linorder__wlog, subcl_Rings_Olinordered__idom___Orderings_Oord, fact_49_take__Nil, fact_120_add__le__cancel__right, fact_96_v__decompose, fact_251_le__funD, fact_59_strict__sorted_Oinduct, fact_250_le__funE, fact_134_add__le__same__cancel1, fact_45_last_Osimps, fact_92_not__Cons__self2, fact_167_less__imp__le__nat, fact_65_remdups__adj_Oinduct, subcl_Rings_Olinordered__idom___Groups_Omonoid__add, fact_25_Nil__is__append__conv, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_74_neq__Nil__conv, fact_48_last__append, fact_133_add__le__same__cancel2, fact_43_take__0, fact_58_zero__le, fact_90_psums_Osimps_I2_J, fact_158_add_Ocommute, tcon_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add, fact_211_list__induct3, subcl_Rings_Olinordered__idom___Groups_Ostrict__ordered__ab__semigroup__add, tcon_Int_Oint___Orderings_Oord_3, tcon_Int_Oint___Groups_Oordered__cancel__comm__monoid__add, tcon_List_Olist___Nat_Osize_28, fact_212_list__induct2, fact_13_same__append__eq, fact_218_add__strict__increasing2, fact_128_length__psums, fact_12_append__same__eq, fact_64_arg__min__list_Oinduct, fact_56_not__less__zero, fact_104_minf_I8_J, fact_188_add__mono__thms__linordered__field_I1_J, fact_210_list__induct4, subcl_Rings_Olinordered__idom___Groups_Oplus, fact_2_nonneg_Ohyps_I2_J, fact_127_length__replicate, fact_55_gr__implies__not__zero, fact_220_add__pos__nonneg, fact_196_add__nonpos__nonpos, fact_131_le__add__same__cancel2, tcon_Int_Oint___Groups_Ostrict__ordered__comm__monoid__add, fact_190_add__mono__thms__linordered__field_I5_J, tcon_Nat_Onat___Orderings_Olinorder_18, fact_142_length__greater__0__conv, fact_178_add__left__mono, fact_97_p__less__length, fact_173_add__le__imp__le__right, fact_121_add__le__cancel__left, fact_73_list__induct2_H, fact_205_add__neg__neg, fact_6_psums__replicate__0__append, fact_175_le__iff__add, fact_7_less__p__zero, fact_15_list_Oinject
% 24.13/6.34 % No. of inferences in proof: 608
% 24.13/6.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6055 ms resp. 5442 ms w/o parsing
% 25.11/6.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.11/6.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------