%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP043^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 20.86s 5.44s
% Output : Refutation 21.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 307
% Syntax : Number of formulae : 616 ( 356 unt; 0 typ; 0 def)
% Number of atoms : 1342 ( 995 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 4446 ( 210 ~; 30 |; 102 &;3558 @)
% ( 0 <=>; 546 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 226 ( 226 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 13 con; 0-2 aty)
% Number of variables : 1790 ( 18 ^;1726 !; 46 ?;1790 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_list_nat_type,type,
list_list_nat: $tType ).
thf(list_list_a_type,type,
list_list_a: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(a_type,type,
a: $tType ).
thf(descar226543321ms_nat_decl,type,
descar226543321ms_nat: list_nat > list_nat ).
thf(descar1375166517sums_a_decl,type,
descar1375166517sums_a: list_a > list_a ).
thf(plus_plus_int_decl,type,
plus_plus_int: int > int > int ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > nat > nat ).
thf(plus_plus_a_decl,type,
plus_plus_a: a > a > a ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(zero_zero_a_decl,type,
zero_zero_a: a ).
thf(append_nat_decl,type,
append_nat: list_nat > list_nat > list_nat ).
thf(append_a_decl,type,
append_a: list_a > list_a > list_a ).
thf(last_nat_decl,type,
last_nat: list_nat > nat ).
thf(last_a_decl,type,
last_a: list_a > a ).
thf(cons_list_nat_decl,type,
cons_list_nat: list_nat > list_list_nat > list_list_nat ).
thf(cons_list_a_decl,type,
cons_list_a: list_a > list_list_a > list_list_a ).
thf(cons_nat_decl,type,
cons_nat: nat > list_nat > list_nat ).
thf(cons_a_decl,type,
cons_a: a > list_a > list_a ).
thf(nil_list_nat_decl,type,
nil_list_nat: list_list_nat ).
thf(nil_list_a_decl,type,
nil_list_a: list_list_a ).
thf(nil_nat_decl,type,
nil_nat: list_nat ).
thf(nil_a_decl,type,
nil_a: list_a ).
thf(nth_nat_decl,type,
nth_nat: list_nat > nat > nat ).
thf(nth_a_decl,type,
nth_a: list_a > nat > a ).
thf(replicate_nat_decl,type,
replicate_nat: nat > nat > list_nat ).
thf(replicate_a_decl,type,
replicate_a: nat > a > list_a ).
thf(take_a_decl,type,
take_a: nat > list_a > list_a ).
thf(size_size_list_nat_decl,type,
size_size_list_nat: list_nat > nat ).
thf(size_size_list_a_decl,type,
size_size_list_a: list_a > nat ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_a_decl,type,
ord_less_a: a > a > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_a_decl,type,
ord_less_eq_a: a > a > $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(154,axiom,
! [A: nat] :
( ( replicate_nat @ zero_zero_nat @ A )
= nil_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_replicate__0) ).
thf(892,plain,
! [A: nat] :
( ( replicate_nat @ zero_zero_nat @ A )
= nil_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(18,axiom,
! [A: list_nat,B: list_nat] :
( ( ( append_nat @ A @ B )
= nil_nat )
= ( ( A = nil_nat )
& ( B = nil_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_append__is__Nil__conv) ).
thf(365,plain,
! [A: list_nat,B: list_nat] :
( ( ( append_nat @ A @ B )
= nil_nat )
= ( ( A = nil_nat )
& ( B = nil_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(121,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_le__add__same__cancel2) ).
thf(760,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(125,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_le__neq__implies__less) ).
thf(777,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)],[125]) ).
thf(97,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_add__right__cancel) ).
thf(666,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(306,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ A )
= ( ord_less_eq_a @ B @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_add__le__same__cancel1) ).
thf(1549,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ A )
= ( ord_less_eq_a @ B @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(208,axiom,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a] : ( A @ D @ ( cons_a @ E @ nil_a ) )
=> ( ! [D: a > a > $o,E: a,F: a,G: list_a] :
( ( A @ D @ ( cons_a @ F @ G ) )
=> ( A @ D @ ( cons_a @ E @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_successively_Oinduct) ).
thf(1110,plain,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a] : ( A @ D @ ( cons_a @ E @ nil_a ) )
=> ( ! [D: a > a > $o,E: a,F: a,G: list_a] :
( ( A @ D @ ( cons_a @ F @ G ) )
=> ( A @ D @ ( cons_a @ E @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( replicate_nat @ A @ B )
= ( replicate_nat @ C @ D ) )
= ( ( A = C )
& ( ( A != zero_zero_nat )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_replicate__eq__replicate) ).
thf(481,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( replicate_nat @ A @ B )
= ( replicate_nat @ C @ D ) )
= ( ( A = C )
& ( ( A != zero_zero_nat )
=> ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(199,axiom,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_add_Oleft__neutral) ).
thf(1083,plain,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(170,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_add__left__cancel) ).
thf(962,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(66,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_add__left__mono) ).
thf(523,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(102,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_add__mono) ).
thf(683,plain,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(299,axiom,
! [A: a,B: a] :
( ( ord_less_a @ A @ ( plus_plus_a @ A @ B ) )
= ( ord_less_a @ zero_zero_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_less__add__same__cancel1) ).
thf(1522,plain,
! [A: a,B: a] :
( ( ord_less_a @ A @ ( plus_plus_a @ A @ B ) )
= ( ord_less_a @ zero_zero_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(217,axiom,
! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= A )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_add__cancel__left__right) ).
thf(1142,plain,
! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= A )
= ( B = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(302,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ! [B: list_list_a] :
( A
!= ( cons_list_a @ nil_a @ B ) )
=> ~ ! [B: a,C: list_a,D: list_list_a] :
( A
!= ( cons_list_a @ ( cons_a @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_transpose_Ocases) ).
thf(1533,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ! [B: list_list_a] :
( A
!= ( cons_list_a @ nil_a @ B ) )
=> ~ ! [B: a,C: list_a,D: list_list_a] :
( A
!= ( cons_list_a @ ( cons_a @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(116,axiom,
! [A: nat,B: list_nat,C: nat,D: list_nat] :
( ( ( cons_nat @ A @ B )
= ( cons_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_list_Oinject) ).
thf(741,plain,
! [A: nat,B: list_nat,C: nat,D: list_nat] :
( ( ( cons_nat @ A @ B )
= ( cons_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(197,axiom,
! [A: list_a,B: list_a] :
( ( A = nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_last__appendL) ).
thf(1073,plain,
! [A: list_a,B: list_a] :
( ( A = nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(94,axiom,
! [A: list_nat > list_nat > $o,B: list_nat,C: list_nat] :
( ! [D: list_nat] : ( A @ D @ nil_nat )
=> ( ! [D: nat,E: list_nat] : ( A @ nil_nat @ ( cons_nat @ D @ E ) )
=> ( ! [D: nat,E: list_nat,F: nat,G: list_nat] :
( ( A @ E @ G )
=> ( A @ ( cons_nat @ D @ E ) @ ( cons_nat @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_plus__coeffs_Oinduct) ).
thf(655,plain,
! [A: list_nat > list_nat > $o,B: list_nat,C: list_nat] :
( ! [D: list_nat] : ( A @ D @ nil_nat )
=> ( ! [D: nat,E: list_nat] : ( A @ nil_nat @ ( cons_nat @ D @ E ) )
=> ( ! [D: nat,E: list_nat,F: nat,G: list_nat] :
( ( A @ E @ G )
=> ( A @ ( cons_nat @ D @ E ) @ ( cons_nat @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(62,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_add__le__imp__le__right) ).
thf(511,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(198,axiom,
! [A: ( a > a ) > list_a > list_a > $o,B: a > a,C: list_a,D: list_a] :
( ! [E: a > a,F: list_a] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > a,F: a,G: list_a,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_map__tailrec__rev_Oinduct) ).
thf(1078,plain,
! [A: ( a > a ) > list_a > list_a > $o,B: a > a,C: list_a,D: list_a] :
( ! [E: a > a,F: list_a] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > a,F: a,G: list_a,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(25,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_add__right__mono) ).
thf(384,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(74,axiom,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat] : ( A @ ( cons_nat @ C @ nil_nat ) )
=> ( ! [C: nat,D: nat,E: list_nat] :
( ( ( C = D )
=> ( A @ ( cons_nat @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_nat @ D @ E ) ) )
=> ( A @ ( cons_nat @ C @ ( cons_nat @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_remdups__adj_Oinduct) ).
thf(550,plain,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat] : ( A @ ( cons_nat @ C @ nil_nat ) )
=> ( ! [C: nat,D: nat,E: list_nat] :
( ( ( C = D )
=> ( A @ ( cons_nat @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_nat @ D @ E ) ) )
=> ( A @ ( cons_nat @ C @ ( cons_nat @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(112,axiom,
! [A: nat,B: list_a] :
( ( ( take_a @ A @ B )
= B )
= ( ord_less_eq_nat @ ( size_size_list_a @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_take__all__iff) ).
thf(715,plain,
! [A: nat,B: list_a] :
( ( ( take_a @ A @ B )
= B )
= ( ord_less_eq_nat @ ( size_size_list_a @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(50,axiom,
! [A: list_nat,B: nat] :
( ( last_nat @ ( append_nat @ A @ ( cons_nat @ B @ nil_nat ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_last__snoc) ).
thf(472,plain,
! [A: list_nat,B: nat] :
( ( last_nat @ ( append_nat @ A @ ( cons_nat @ B @ nil_nat ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(227,axiom,
! [A: list_nat > list_a > $o,B: list_nat,C: list_a] :
( ( A @ nil_nat @ nil_a )
=> ( ! [D: nat,E: list_nat] : ( A @ ( cons_nat @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_nat @ ( cons_a @ D @ E ) )
=> ( ! [D: nat,E: list_nat,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_nat @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_list__induct2_H) ).
thf(1196,plain,
! [A: list_nat > list_a > $o,B: list_nat,C: list_a] :
( ( A @ nil_nat @ nil_a )
=> ( ! [D: nat,E: list_nat] : ( A @ ( cons_nat @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_nat @ ( cons_a @ D @ E ) )
=> ( ! [D: nat,E: list_nat,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_nat @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(212,axiom,
! [A: a,B: list_a,C: a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_list_Oinject) ).
thf(1127,plain,
! [A: a,B: list_a,C: a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(110,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_not__less__zero) ).
thf(709,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(141,axiom,
! [A: list_nat] :
( ( A != nil_nat )
=> ( ! [B: nat] :
( A
!= ( cons_nat @ B @ nil_nat ) )
=> ~ ! [B: nat,C: nat,D: list_nat] :
( A
!= ( cons_nat @ B @ ( cons_nat @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_psums_Ocases) ).
thf(841,plain,
! [A: list_nat] :
( ( A != nil_nat )
=> ( ! [B: nat] :
( A
!= ( cons_nat @ B @ nil_nat ) )
=> ~ ! [B: nat,C: nat,D: list_nat] :
( A
!= ( cons_nat @ B @ ( cons_nat @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(192,axiom,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( cons_a @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_list__nonempty__induct) ).
thf(1046,plain,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( cons_a @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(266,axiom,
! [A: list_a,B: a] :
( ( A = nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_last__ConsL) ).
thf(1366,plain,
! [A: list_a,B: a] :
( ( A = nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(298,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_psums_Ocases) ).
thf(1518,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(242,axiom,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ B ) ) )
& ( ( A != nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_last__append) ).
thf(1254,plain,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ B ) ) )
& ( ( A != nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(127,axiom,
( ( descar226543321ms_nat @ nil_nat )
= nil_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_psums_Osimps_I1_J) ).
thf(785,plain,
( ( descar226543321ms_nat @ nil_nat )
= nil_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C: nat] :
( B
!= ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_less__eqE) ).
thf(504,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C: nat] :
( B
!= ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(165,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_bot__nat__0_Oextremum__uniqueI) ).
thf(949,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(48,axiom,
! [A: list_nat] :
( ( append_nat @ A @ nil_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_append_Oright__neutral) ).
thf(460,plain,
! [A: list_nat] :
( ( append_nat @ A @ nil_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(108,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_zero__less__iff__neq__zero) ).
thf(702,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(120,axiom,
! [A: list_a > $o,B: list_a] :
( ! [C: list_a] :
( ! [D: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ D ) @ ( size_size_list_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_length__induct) ).
thf(751,plain,
! [A: list_a > $o,B: list_a] :
( ! [C: list_a] :
( ! [D: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ D ) @ ( size_size_list_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(157,axiom,
xs != nil_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_assms_I1_J) ).
thf(902,plain,
xs != nil_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(209,axiom,
! [A: list_a,B: list_a,C: list_a,D: list_a] :
( ( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
| ( ( size_size_list_a @ C )
= ( size_size_list_a @ D ) ) )
=> ( ( ( append_a @ A @ C )
= ( append_a @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_append__eq__append__conv) ).
thf(1115,plain,
! [A: list_a,B: list_a,C: list_a,D: list_a] :
( ( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
| ( ( size_size_list_a @ C )
= ( size_size_list_a @ D ) ) )
=> ( ( ( append_a @ A @ C )
= ( append_a @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(44,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_add__less__imp__less__left) ).
thf(448,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(235,axiom,
! [A: nat,B: a] :
( ( nil_a
= ( replicate_a @ A @ B ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_empty__replicate) ).
thf(1232,plain,
! [A: nat,B: a] :
( ( nil_a
= ( replicate_a @ A @ B ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(277,axiom,
! [A: list_a,B: a] :
( ( ( A = nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= B ) )
& ( ( A != nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= ( last_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_last_Osimps) ).
thf(1415,plain,
! [A: list_a,B: a] :
( ( ( A = nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= B ) )
& ( ( A != nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= ( last_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_add__less__cancel__left) ).
thf(475,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(56,axiom,
! [A: nat,B: nat,C: list_nat] :
( ( append_nat @ ( replicate_nat @ A @ B ) @ ( cons_nat @ B @ C ) )
= ( cons_nat @ B @ ( append_nat @ ( replicate_nat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_replicate__app__Cons__same) ).
thf(492,plain,
! [A: nat,B: nat,C: list_nat] :
( ( append_nat @ ( replicate_nat @ A @ B ) @ ( cons_nat @ B @ C ) )
= ( cons_nat @ B @ ( append_nat @ ( replicate_nat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(129,axiom,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat,D: list_nat] :
( ( A @ D )
=> ( A @ ( append_nat @ D @ ( cons_nat @ C @ nil_nat ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rev__induct) ).
thf(789,plain,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat,D: list_nat] :
( ( A @ D )
=> ( A @ ( append_nat @ D @ ( cons_nat @ C @ nil_nat ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(285,axiom,
! [A: list_a > $o,B: list_a] :
( ! [C: a,D: list_a] :
( ! [E: a,F: list_a] :
( ( D
= ( cons_a @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( ( A @ nil_a )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_min__list_Oinduct) ).
thf(1450,plain,
! [A: list_a > $o,B: list_a] :
( ! [C: a,D: list_a] :
( ! [E: a,F: list_a] :
( ( D
= ( cons_a @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( ( A @ nil_a )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(42,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_add__le__imp__le__left) ).
thf(443,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(22,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_nat @ A @ B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_add__mono__thms__linordered__field_I5_J) ).
thf(376,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_nat @ A @ B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(215,axiom,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_comm__monoid__add__class_Oadd__0) ).
thf(1136,plain,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(13,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_comm__monoid__add__class_Oadd__0) ).
thf(348,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(132,axiom,
! [A: list_list_nat] :
( ( A != nil_list_nat )
=> ( ! [B: list_list_nat] :
( A
!= ( cons_list_nat @ nil_nat @ B ) )
=> ~ ! [B: nat,C: list_nat,D: list_list_nat] :
( A
!= ( cons_list_nat @ ( cons_nat @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_transpose_Ocases) ).
thf(806,plain,
! [A: list_list_nat] :
( ( A != nil_list_nat )
=> ( ! [B: list_list_nat] :
( A
!= ( cons_list_nat @ nil_nat @ B ) )
=> ~ ! [B: nat,C: list_nat,D: list_list_nat] :
( A
!= ( cons_list_nat @ ( cons_nat @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(158,axiom,
! [A: a] : ( ord_less_eq_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_order__refl) ).
thf(905,plain,
! [A: a] : ( ord_less_eq_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(190,axiom,
! [A: a,B: a] :
( ( ord_less_a @ ( plus_plus_a @ A @ B ) @ A )
= ( ord_less_a @ B @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_add__less__same__cancel1) ).
thf(1040,plain,
! [A: a,B: a] :
( ( ord_less_a @ ( plus_plus_a @ A @ B ) @ A )
= ( ord_less_a @ B @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(6,axiom,
! [A: list_nat,B: list_nat,C: list_nat,D: list_nat] :
( ( ( ( size_size_list_nat @ A )
= ( size_size_list_nat @ B ) )
| ( ( size_size_list_nat @ C )
= ( size_size_list_nat @ D ) ) )
=> ( ( ( append_nat @ A @ C )
= ( append_nat @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_append__eq__append__conv) ).
thf(321,plain,
! [A: list_nat,B: list_nat,C: list_nat,D: list_nat] :
( ( ( ( size_size_list_nat @ A )
= ( size_size_list_nat @ B ) )
| ( ( size_size_list_nat @ C )
= ( size_size_list_nat @ D ) ) )
=> ( ( ( append_nat @ A @ C )
= ( append_nat @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(220,axiom,
! [A: list_a,B: list_a,C: a] :
( ( ord_less_eq_nat @ ( size_size_list_a @ A ) @ ( size_size_list_a @ B ) )
=> ( A
!= ( cons_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_impossible__Cons) ).
thf(1151,plain,
! [A: list_a,B: list_a,C: a] :
( ( ord_less_eq_nat @ ( size_size_list_a @ A ) @ ( size_size_list_a @ B ) )
=> ( A
!= ( cons_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(161,axiom,
! [A: list_a,B: nat] :
( ( ord_less_eq_nat @ ( size_size_list_a @ A ) @ B )
=> ( ( take_a @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_take__all) ).
thf(937,plain,
! [A: list_a,B: nat] :
( ( ord_less_eq_nat @ ( size_size_list_a @ A ) @ B )
=> ( ( take_a @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(86,axiom,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat,D: list_nat] :
( ( A @ D )
=> ( A @ ( cons_nat @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_strict__sorted_Oinduct) ).
thf(602,plain,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat,D: list_nat] :
( ( A @ D )
=> ( A @ ( cons_nat @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(91,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_zero__le) ).
thf(634,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(284,axiom,
! [A: nat,B: a] :
( ( ( replicate_a @ A @ B )
= nil_a )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_replicate__empty) ).
thf(1447,plain,
! [A: nat,B: a] :
( ( ( replicate_a @ A @ B )
= nil_a )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(148,axiom,
! [A: list_nat,B: nat] :
( ( ( A = nil_nat )
=> ( ( last_nat @ ( cons_nat @ B @ A ) )
= B ) )
& ( ( A != nil_nat )
=> ( ( last_nat @ ( cons_nat @ B @ A ) )
= ( last_nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_last_Osimps) ).
thf(866,plain,
! [A: list_nat,B: nat] :
( ( ( A = nil_nat )
=> ( ( last_nat @ ( cons_nat @ B @ A ) )
= B ) )
& ( ( A != nil_nat )
=> ( ( last_nat @ ( cons_nat @ B @ A ) )
= ( last_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(46,axiom,
! [A: list_nat,B: list_nat] :
( ( A
= ( append_nat @ B @ A ) )
= ( B = nil_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_self__append__conv2) ).
thf(453,plain,
! [A: list_nat,B: list_nat] :
( ( A
= ( append_nat @ B @ A ) )
= ( B = nil_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(95,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_gr__zeroI) ).
thf(660,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(262,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: list_a,C: a] :
( A
!= ( append_a @ B @ ( cons_a @ C @ nil_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_rev__exhaust) ).
thf(1345,plain,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: list_a,C: a] :
( A
!= ( append_a @ B @ ( cons_a @ C @ nil_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(280,axiom,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_add_Ocomm__neutral) ).
thf(1433,plain,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(228,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ ( cons_a @ F @ G ) )
=> ( ( A @ ( cons_a @ D @ E ) @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_shuffles_Oinduct) ).
thf(1201,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ ( cons_a @ F @ G ) )
=> ( ( A @ ( cons_a @ D @ E ) @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(206,axiom,
! [A: a,B: list_a] :
( ( nth_a @ ( cons_a @ A @ B ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_nth__Cons__0) ).
thf(1104,plain,
! [A: a,B: list_a] :
( ( nth_a @ ( cons_a @ A @ B ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(238,axiom,
! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= B )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_add__cancel__left__left) ).
thf(1242,plain,
! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= B )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(143,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_add__right__imp__eq) ).
thf(849,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(68,axiom,
! [A: list_nat,B: list_nat] :
( ( ( append_nat @ A @ B )
= B )
= ( A = nil_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_append__self__conv2) ).
thf(529,plain,
! [A: list_nat,B: list_nat] :
( ( ( append_nat @ A @ B )
= B )
= ( A = nil_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(133,axiom,
! [A: nat,B: list_nat] :
( ( nth_nat @ ( cons_nat @ A @ B ) @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_nth__Cons__0) ).
thf(810,plain,
! [A: nat,B: list_nat] :
( ( nth_nat @ ( cons_nat @ A @ B ) @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(260,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ ( plus_plus_a @ A @ B ) )
= ( ord_less_eq_a @ zero_zero_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_le__add__same__cancel1) ).
thf(1338,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ ( plus_plus_a @ A @ B ) )
= ( ord_less_eq_a @ zero_zero_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ A @ B ) )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_zero__eq__add__iff__both__eq__0) ).
thf(381,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ A @ B ) )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(254,axiom,
! [A: a] :
( ( descar1375166517sums_a @ ( cons_a @ A @ nil_a ) )
= ( cons_a @ A @ nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_psums_Osimps_I2_J) ).
thf(1311,plain,
! [A: a] :
( ( descar1375166517sums_a @ ( cons_a @ A @ nil_a ) )
= ( cons_a @ A @ nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(195,axiom,
! [A: a] :
( ( ord_less_a @ zero_zero_a @ ( plus_plus_a @ A @ A ) )
= ( ord_less_a @ zero_zero_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_zero__less__double__add__iff__zero__less__single__add) ).
thf(1067,plain,
! [A: a] :
( ( ord_less_a @ zero_zero_a @ ( plus_plus_a @ A @ A ) )
= ( ord_less_a @ zero_zero_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(168,axiom,
! [A: list_a,B: list_a] :
( ! [C: nat] :
( ( take_a @ C @ A )
= ( take_a @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_take__equalityI) ).
thf(957,plain,
! [A: list_a,B: list_a] :
( ! [C: nat] :
( ( take_a @ C @ A )
= ( take_a @ C @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(118,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_le__zero__eq) ).
thf(746,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(166,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_bot__nat__0_Oextremum__unique) ).
thf(952,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_add__nonpos__eq__0__iff) ).
thf(862,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(232,axiom,
! [A: list_a,B: list_a] :
? [C: list_a,D: list_a,E: list_a] :
( ( A
= ( append_a @ D @ C ) )
& ( B
= ( append_a @ E @ C ) )
& ( ( D = nil_a )
| ( E = nil_a )
| ( ( last_a @ D )
!= ( last_a @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_longest__common__suffix) ).
thf(1217,plain,
! [A: list_a,B: list_a] :
? [C: list_a,D: list_a,E: list_a] :
( ( A
= ( append_a @ D @ C ) )
& ( B
= ( append_a @ E @ C ) )
& ( ( D = nil_a )
| ( E = nil_a )
| ( ( last_a @ D )
!= ( last_a @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(292,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_same__append__eq) ).
thf(1487,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(37,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add__less__cancel__right) ).
thf(429,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(135,axiom,
! [A: nat,B: list_nat] :
( nil_nat
!= ( cons_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_list_Odistinct_I1_J) ).
thf(815,plain,
! [A: nat,B: list_nat] :
( nil_nat
!= ( cons_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(237,axiom,
! [A: a,B: list_a] :
( nil_a
!= ( cons_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_list_Odistinct_I1_J) ).
thf(1238,plain,
! [A: a,B: list_a] :
( nil_a
!= ( cons_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(54,axiom,
! [A: list_nat,B: list_nat] :
( ( nil_nat
= ( append_nat @ A @ B ) )
= ( ( A = nil_nat )
& ( B = nil_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_Nil__is__append__conv) ).
thf(484,plain,
! [A: list_nat,B: list_nat] :
( ( nil_nat
= ( append_nat @ A @ B ) )
= ( ( A = nil_nat )
& ( B = nil_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(150,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_add__less__same__cancel2) ).
thf(879,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_nat @ A @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(153,axiom,
! [A: list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ A ) )
= ( A != nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_length__greater__0__conv) ).
thf(889,plain,
! [A: list_a] :
( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ A ) )
= ( A != nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(222,axiom,
! [A: a,B: list_a,C: list_a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ( ( C = nil_a )
& ( ( cons_a @ A @ B )
= D ) )
| ? [E: list_a] :
( ( ( cons_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Cons__eq__append__conv) ).
thf(1159,plain,
! [A: a,B: list_a,C: list_a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ( ( C = nil_a )
& ( ( cons_a @ A @ B )
= D ) )
| ? [E: list_a] :
( ( ( cons_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(274,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_append_Oassoc) ).
thf(1392,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(47,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_add__mono__thms__linordered__field_I2_J) ).
thf(456,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( ord_less_nat @ C @ D ) )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(308,axiom,
! [A: nat,B: a] :
( ( size_size_list_a @ ( replicate_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_length__replicate) ).
thf(1555,plain,
! [A: nat,B: a] :
( ( size_size_list_a @ ( replicate_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_add__cancel__right__left) ).
thf(435,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(80,axiom,
! [A: list_nat] :
( ( A != nil_nat )
= ( ? [B: nat,C: list_nat] :
( A
= ( cons_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_neq__Nil__conv) ).
thf(583,plain,
! [A: list_nat] :
( ( A != nil_nat )
= ( ? [B: nat,C: list_nat] :
( A
= ( cons_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(137,axiom,
! [A: list_nat] :
( ( descar226543321ms_nat @ ( cons_nat @ zero_zero_nat @ A ) )
= ( cons_nat @ zero_zero_nat @ ( descar226543321ms_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_psums__0__Cons) ).
thf(830,plain,
! [A: list_nat] :
( ( descar226543321ms_nat @ ( cons_nat @ zero_zero_nat @ A ) )
= ( cons_nat @ zero_zero_nat @ ( descar226543321ms_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(264,axiom,
! [A: a,B: a] :
( ( ord_less_a @ A @ ( plus_plus_a @ B @ A ) )
= ( ord_less_a @ zero_zero_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_less__add__same__cancel2) ).
thf(1360,plain,
! [A: a,B: a] :
( ( ord_less_a @ A @ ( plus_plus_a @ B @ A ) )
= ( ord_less_a @ zero_zero_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(78,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_nat__less__le) ).
thf(578,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(201,axiom,
! [A: nat,B: nat,C: a] :
( ( ord_less_nat @ A @ B )
=> ( ( nth_a @ ( replicate_a @ B @ C ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_nth__replicate) ).
thf(1089,plain,
! [A: nat,B: nat,C: a] :
( ( ord_less_nat @ A @ B )
=> ( ( nth_a @ ( replicate_a @ B @ C ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(245,axiom,
! [A: list_a] :
( ( size_size_list_a @ ( descar1375166517sums_a @ A ) )
= ( size_size_list_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_length__psums) ).
thf(1270,plain,
! [A: list_a] :
( ( size_size_list_a @ ( descar1375166517sums_a @ A ) )
= ( size_size_list_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(257,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_plus__coeffs_Oinduct) ).
thf(1328,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(194,axiom,
! [A: a] :
( ( zero_zero_a
= ( plus_plus_a @ A @ A ) )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_double__zero__sym) ).
thf(1064,plain,
! [A: a] :
( ( zero_zero_a
= ( plus_plus_a @ A @ A ) )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(29,axiom,
! [A: nat,B: list_nat,C: list_nat] :
( ( append_nat @ ( cons_nat @ A @ B ) @ C )
= ( cons_nat @ A @ ( append_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_append__Cons) ).
thf(403,plain,
! [A: nat,B: list_nat,C: list_nat] :
( ( append_nat @ ( cons_nat @ A @ B ) @ C )
= ( cons_nat @ A @ ( append_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(203,axiom,
! [A: list_a,B: a,C: list_a] :
( ( nth_a @ ( append_a @ A @ ( cons_a @ B @ C ) ) @ ( size_size_list_a @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_nth__append__length) ).
thf(1096,plain,
! [A: list_a,B: a,C: list_a] :
( ( nth_a @ ( append_a @ A @ ( cons_a @ B @ C ) ) @ ( size_size_list_a @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_add__strict__mono) ).
thf(356,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ D )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(83,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_a @ C @ B ) )
= ( ord_less_eq_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_add__le__cancel__right) ).
thf(593,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_a @ C @ B ) )
= ( ord_less_eq_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(269,axiom,
! [A: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ A ) @ zero_zero_a )
= ( ord_less_eq_a @ A @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_double__add__le__zero__iff__single__add__le__zero) ).
thf(1375,plain,
! [A: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ A ) @ zero_zero_a )
= ( ord_less_eq_a @ A @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(210,axiom,
( ( nth_a @ xsa @ p )
!= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_p__nz) ).
thf(1121,plain,
( ( nth_a @ xsa @ p )
!= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_add__mono) ).
thf(339,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(98,axiom,
! [A: list_nat,B: nat] :
( ( A != nil_nat )
=> ( ( last_nat @ ( cons_nat @ B @ A ) )
= ( last_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_last__ConsR) ).
thf(669,plain,
! [A: list_nat,B: nat] :
( ( A != nil_nat )
=> ( ( last_nat @ ( cons_nat @ B @ A ) )
= ( last_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(103,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_add__left__imp__eq) ).
thf(686,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(278,axiom,
! [A: nat,B: list_a,C: list_a] :
( ( ord_less_eq_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ord_less_eq_nat @ A @ ( size_size_list_a @ C ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( ( nth_a @ B @ D )
= ( nth_a @ C @ D ) ) )
=> ( ( take_a @ A @ B )
= ( take_a @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_nth__take__lemma) ).
thf(1424,plain,
! [A: nat,B: list_a,C: list_a] :
( ( ord_less_eq_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ord_less_eq_nat @ A @ ( size_size_list_a @ C ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( ( nth_a @ B @ D )
= ( nth_a @ C @ D ) ) )
=> ( ( take_a @ A @ B )
= ( take_a @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= B )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_add__cancel__left__left) ).
thf(526,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= B )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(229,axiom,
( ( take_a @ p @ xsa )
= ( replicate_a @ p @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062take_Ap_Axs_A_061_Areplicate_Ap_A_I0_058_058_Ha_J_092_060close_062) ).
thf(1207,plain,
( ( take_a @ p @ xsa )
= ( replicate_a @ p @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(73,axiom,
! [A: list_nat,B: nat,C: list_nat,D: nat] :
( ( ( append_nat @ A @ ( cons_nat @ B @ nil_nat ) )
= ( append_nat @ C @ ( cons_nat @ D @ nil_nat ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_append1__eq__conv) ).
thf(547,plain,
! [A: list_nat,B: nat,C: list_nat,D: nat] :
( ( ( append_nat @ A @ ( cons_nat @ B @ nil_nat ) )
= ( append_nat @ C @ ( cons_nat @ D @ nil_nat ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(243,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ p )
=> ( ( nth_a @ xsa @ A )
= zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_less__p__zero) ).
thf(1263,plain,
! [A: nat] :
( ( ord_less_nat @ A @ p )
=> ( ( nth_a @ xsa @ A )
= zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(204,axiom,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ B @ A ) )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add__cancel__right__left) ).
thf(1099,plain,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ B @ A ) )
= ( B = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(252,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_strict__sorted_Oinduct) ).
thf(1297,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(244,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ zero_zero_a @ A )
=> ( ( ord_less_eq_a @ zero_zero_a @ B )
=> ( ( ( plus_plus_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
& ( B = zero_zero_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_add__nonneg__eq__0__iff) ).
thf(1266,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ zero_zero_a @ A )
=> ( ( ord_less_eq_a @ zero_zero_a @ B )
=> ( ( ( plus_plus_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
& ( B = zero_zero_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(307,axiom,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ A @ B ) )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_add__cancel__right__right) ).
thf(1552,plain,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ A @ B ) )
= ( B = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(300,axiom,
! [A: nat,B: a] :
( ( append_a @ ( replicate_a @ A @ B ) @ ( cons_a @ B @ nil_a ) )
= ( cons_a @ B @ ( replicate_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_replicate__append__same) ).
thf(1525,plain,
! [A: nat,B: a] :
( ( append_a @ ( replicate_a @ A @ B ) @ ( cons_a @ B @ nil_a ) )
= ( cons_a @ B @ ( replicate_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(258,axiom,
( xs1
= ( replicate_a @ p @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_xs1__def) ).
thf(1333,plain,
( xs1
= ( replicate_a @ p @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(200,axiom,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_append__Nil) ).
thf(1086,plain,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(61,axiom,
! [A: list_nat] :
( ( size_size_list_nat @ ( descar226543321ms_nat @ A ) )
= ( size_size_list_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_length__psums) ).
thf(508,plain,
! [A: list_nat] :
( ( size_size_list_nat @ ( descar226543321ms_nat @ A ) )
= ( size_size_list_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(3,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_add_Oright__neutral) ).
thf(311,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(71,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_add_Oleft__cancel) ).
thf(541,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(225,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( A @ E )
=> ( ( A @ ( cons_a @ D @ E ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_induct__list012) ).
thf(1170,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( A @ E )
=> ( ( A @ ( cons_a @ D @ E ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(249,axiom,
! [A: list_a,B: list_a,C: list_a,D: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ? [E: list_a] :
( ( ( A
= ( append_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) )
| ( ( ( append_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_append__eq__append__conv2) ).
thf(1286,plain,
! [A: list_a,B: list_a,C: list_a,D: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ? [E: list_a] :
( ( ( A
= ( append_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) )
| ( ( ( append_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(188,axiom,
! [A: list_nat > list_nat > $o,B: list_nat,C: list_nat] :
( ( A @ nil_nat @ nil_nat )
=> ( ! [D: nat,E: list_nat] : ( A @ ( cons_nat @ D @ E ) @ nil_nat )
=> ( ! [D: nat,E: list_nat] : ( A @ nil_nat @ ( cons_nat @ D @ E ) )
=> ( ! [D: nat,E: list_nat,F: nat,G: list_nat] :
( ( A @ E @ G )
=> ( A @ ( cons_nat @ D @ E ) @ ( cons_nat @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_list__induct2_H) ).
thf(1026,plain,
! [A: list_nat > list_nat > $o,B: list_nat,C: list_nat] :
( ( A @ nil_nat @ nil_nat )
=> ( ! [D: nat,E: list_nat] : ( A @ ( cons_nat @ D @ E ) @ nil_nat )
=> ( ! [D: nat,E: list_nat] : ( A @ nil_nat @ ( cons_nat @ D @ E ) )
=> ( ! [D: nat,E: list_nat,F: nat,G: list_nat] :
( ( A @ E @ G )
=> ( A @ ( cons_nat @ D @ E ) @ ( cons_nat @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(226,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_list_Oinducts) ).
thf(1185,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_less__add__same__cancel2) ).
thf(586,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(113,axiom,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat] : ( A @ ( cons_nat @ C @ nil_nat ) )
=> ( ! [C: nat,D: nat,E: list_nat] :
( ( A @ E )
=> ( ( A @ ( cons_nat @ D @ E ) )
=> ( A @ ( cons_nat @ C @ ( cons_nat @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_induct__list012) ).
thf(718,plain,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat] : ( A @ ( cons_nat @ C @ nil_nat ) )
=> ( ! [C: nat,D: nat,E: list_nat] :
( ( A @ E )
=> ( ( A @ ( cons_nat @ D @ E ) )
=> ( A @ ( cons_nat @ C @ ( cons_nat @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_add__strict__right__mono) ).
thf(412,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(171,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_le0) ).
thf(965,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(63,axiom,
! [A: list_nat,B: list_nat] :
( ( A != nil_nat )
=> ( ( last_nat @ ( append_nat @ B @ A ) )
= ( last_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_last__appendR) ).
thf(513,plain,
! [A: list_nat,B: list_nat] :
( ( A != nil_nat )
=> ( ( last_nat @ ( append_nat @ B @ A ) )
= ( last_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(291,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_list_Oexhaust) ).
thf(1483,plain,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(246,axiom,
! [A: a,B: list_a] :
( ( cons_a @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_not__Cons__self2) ).
thf(1273,plain,
! [A: a,B: list_a] :
( ( cons_a @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(145,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_le__0__eq) ).
thf(856,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(76,axiom,
( ( size_size_list_a @ nil_a )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_list_Osize_I3_J) ).
thf(573,plain,
( ( size_size_list_a @ nil_a )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(114,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(733,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(241,axiom,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_append__Nil2) ).
thf(1251,plain,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(89,axiom,
! [A: list_nat > $o,B: list_nat] :
( ! [C: nat,D: list_nat] :
( ! [E: nat,F: list_nat] :
( ( D
= ( cons_nat @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons_nat @ C @ D ) ) )
=> ( ( A @ nil_nat )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_min__list_Oinduct) ).
thf(618,plain,
! [A: list_nat > $o,B: list_nat] :
( ! [C: nat,D: list_nat] :
( ! [E: nat,F: list_nat] :
( ( D
= ( cons_nat @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons_nat @ C @ D ) ) )
=> ( ( A @ nil_nat )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(136,axiom,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat,D: list_nat] :
( ( A @ D )
=> ( A @ ( cons_nat @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_list_Oinducts) ).
thf(819,plain,
! [A: list_nat > $o,B: list_nat] :
( ( A @ nil_nat )
=> ( ! [C: nat,D: list_nat] :
( ( A @ D )
=> ( A @ ( cons_nat @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(35,axiom,
! [A: list_nat] :
( ( append_nat @ nil_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_append__Nil) ).
thf(423,plain,
! [A: list_nat] :
( ( append_nat @ nil_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(105,axiom,
! [A: a] :
? [B: a] :
! [C: a] :
( ( ord_less_a @ C @ B )
=> ( ord_less_eq_a @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_minf_I6_J) ).
thf(694,plain,
! [A: a] :
? [B: a] :
! [C: a] :
( ( ord_less_a @ C @ B )
=> ( ord_less_eq_a @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(273,axiom,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_zero__reorient) ).
thf(1389,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(124,axiom,
! [A: list_nat > list_nat > $o,B: list_nat,C: list_nat] :
( ! [D: list_nat] : ( A @ nil_nat @ D )
=> ( ! [D: nat,E: list_nat,F: list_nat] :
( ( A @ F @ E )
=> ( A @ ( cons_nat @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_splice_Oinduct) ).
thf(772,plain,
! [A: list_nat > list_nat > $o,B: list_nat,C: list_nat] :
( ! [D: list_nat] : ( A @ nil_nat @ D )
=> ( ! [D: nat,E: list_nat,F: list_nat] :
( ( A @ F @ E )
=> ( A @ ( cons_nat @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(149,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_gr__implies__not__zero) ).
thf(875,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(211,axiom,
! [A: nat,B: list_a] :
( ( descar1375166517sums_a @ ( append_a @ ( replicate_a @ A @ zero_zero_a ) @ B ) )
= ( append_a @ ( replicate_a @ A @ zero_zero_a ) @ ( descar1375166517sums_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_psums__replicate__0__append) ).
thf(1124,plain,
! [A: nat,B: list_a] :
( ( descar1375166517sums_a @ ( append_a @ ( replicate_a @ A @ zero_zero_a ) @ B ) )
= ( append_a @ ( replicate_a @ A @ zero_zero_a ) @ ( descar1375166517sums_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(233,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_append__same__eq) ).
thf(1226,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',fact_290_ex__least__nat__le) ).
thf(641,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)],[93]) ).
thf(43,axiom,
! [A: list_nat,B: list_nat,C: list_nat] :
( ( ( append_nat @ A @ B )
= ( append_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_same__append__eq) ).
thf(445,plain,
! [A: list_nat,B: list_nat,C: list_nat] :
( ( ( append_nat @ A @ B )
= ( append_nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(267,axiom,
ord_less_nat @ p @ ( size_size_list_a @ xsa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_p__less__length) ).
thf(1371,plain,
ord_less_nat @ p @ ( size_size_list_a @ xsa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(128,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_less__eq__nat_Osimps_I1_J) ).
thf(787,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(58,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( nth_nat @ ( replicate_nat @ B @ C ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_nth__replicate) ).
thf(498,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( nth_nat @ ( replicate_nat @ B @ C ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(207,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ ( plus_plus_a @ B @ A ) )
= ( ord_less_eq_a @ zero_zero_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_le__add__same__cancel2) ).
thf(1107,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ ( plus_plus_a @ B @ A ) )
= ( ord_less_eq_a @ zero_zero_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(9,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_nat @ A @ B )
& ( C = D ) )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_add__mono__thms__linordered__field_I1_J) ).
thf(335,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_nat @ A @ B )
& ( C = D ) )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ( size_size_list_nat @ ( replicate_nat @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_length__replicate) ).
thf(391,plain,
! [A: nat,B: nat] :
( ( size_size_list_nat @ ( replicate_nat @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(216,axiom,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= nil_a )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_append__is__Nil__conv) ).
thf(1139,plain,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= nil_a )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(230,axiom,
! [A: list_a] :
( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ A ) )
= ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_psums__0__Cons) ).
thf(1209,plain,
! [A: list_a] :
( ( descar1375166517sums_a @ ( cons_a @ zero_zero_a @ A ) )
= ( cons_a @ zero_zero_a @ ( descar1375166517sums_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(248,axiom,
! [A: list_a] :
( ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) )
=> ( A = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_min__list_Ocases) ).
thf(1282,plain,
! [A: list_a] :
( ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) )
=> ( A = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',fact_285_less__mono__imp__le__mono) ).
thf(736,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)],[115]) ).
thf(263,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ( A @ nil_a @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_list__induct2_H) ).
thf(1349,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ( A @ nil_a @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(304,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ zero_zero_a )
=> ( ( ord_less_eq_a @ B @ zero_zero_a )
=> ( ( ( plus_plus_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
& ( B = zero_zero_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_add__nonpos__eq__0__iff) ).
thf(1542,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ zero_zero_a )
=> ( ( ord_less_eq_a @ B @ zero_zero_a )
=> ( ( ( plus_plus_a @ A @ B )
= zero_zero_a )
= ( ( A = zero_zero_a )
& ( B = zero_zero_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(5,axiom,
! [A: list_nat,B: list_nat] :
( ( ( append_nat @ A @ B )
= A )
= ( B = nil_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_append__self__conv) ).
thf(318,plain,
! [A: list_nat,B: list_nat] :
( ( ( append_nat @ A @ B )
= A )
= ( B = nil_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(191,axiom,
! [A: nat,B: a,C: nat] :
( ( append_a @ ( replicate_a @ A @ B ) @ ( replicate_a @ C @ B ) )
= ( append_a @ ( replicate_a @ C @ B ) @ ( replicate_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_append__replicate__commute) ).
thf(1043,plain,
! [A: nat,B: a,C: nat] :
( ( append_a @ ( replicate_a @ A @ B ) @ ( replicate_a @ C @ B ) )
= ( append_a @ ( replicate_a @ C @ B ) @ ( replicate_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(88,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_a @ C @ B ) )
=> ( ord_less_eq_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_add__le__imp__le__right) ).
thf(616,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_a @ C @ B ) )
=> ( ord_less_eq_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(156,axiom,
( ( take_a @ zero_zero_nat )
= ( ^ [A: list_a] : nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_take0) ).
thf(900,plain,
( ( take_a @ zero_zero_nat )
= ( ^ [A: list_a] : nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_add__cancel__right__right) ).
thf(406,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(184,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_add__nonneg__eq__0__iff) ).
thf(1011,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(34,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_add__mono__thms__linordered__semiring_I3_J) ).
thf(419,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(178,axiom,
! [A: list_nat,B: list_nat,C: nat,D: list_nat] :
( ( ( append_nat @ A @ B )
= ( cons_nat @ C @ D ) )
= ( ( ( A = nil_nat )
& ( B
= ( cons_nat @ C @ D ) ) )
| ? [E: list_nat] :
( ( A
= ( cons_nat @ C @ E ) )
& ( ( append_nat @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_append__eq__Cons__conv) ).
thf(990,plain,
! [A: list_nat,B: list_nat,C: nat,D: list_nat] :
( ( ( append_nat @ A @ B )
= ( cons_nat @ C @ D ) )
= ( ( ( A = nil_nat )
& ( B
= ( cons_nat @ C @ D ) ) )
| ? [E: list_nat] :
( ( A
= ( cons_nat @ C @ E ) )
& ( ( append_nat @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(180,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_add__right__mono) ).
thf(996,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(17,axiom,
! [A: list_nat,B: list_nat] :
( ( A
= ( append_nat @ A @ B ) )
= ( B = nil_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_self__append__conv) ).
thf(362,plain,
! [A: list_nat,B: list_nat] :
( ( A
= ( append_nat @ A @ B ) )
= ( B = nil_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(75,axiom,
! [A: list_nat > list_nat > $o,B: list_nat,C: list_nat] :
( ! [D: list_nat] : ( A @ nil_nat @ D )
=> ( ! [D: list_nat] : ( A @ D @ nil_nat )
=> ( ! [D: nat,E: list_nat,F: nat,G: list_nat] :
( ( A @ E @ ( cons_nat @ F @ G ) )
=> ( ( A @ ( cons_nat @ D @ E ) @ G )
=> ( A @ ( cons_nat @ D @ E ) @ ( cons_nat @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_shuffles_Oinduct) ).
thf(567,plain,
! [A: list_nat > list_nat > $o,B: list_nat,C: list_nat] :
( ! [D: list_nat] : ( A @ nil_nat @ D )
=> ( ! [D: list_nat] : ( A @ D @ nil_nat )
=> ( ! [D: nat,E: list_nat,F: nat,G: list_nat] :
( ( A @ E @ ( cons_nat @ F @ G ) )
=> ( ( A @ ( cons_nat @ D @ E ) @ G )
=> ( A @ ( cons_nat @ D @ E ) @ ( cons_nat @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( ( replicate_nat @ A @ B )
= nil_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_replicate__empty) ).
thf(599,plain,
! [A: nat,B: nat] :
( ( ( replicate_nat @ A @ B )
= nil_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(282,axiom,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_add_Oright__neutral) ).
thf(1439,plain,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(26,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_add__mono__thms__linordered__semiring_I2_J) ).
thf(387,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( nil_nat
= ( replicate_nat @ A @ B ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_empty__replicate) ).
thf(631,plain,
! [A: nat,B: nat] :
( ( nil_nat
= ( replicate_nat @ A @ B ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(12,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_add_Oleft__neutral) ).
thf(345,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_less__or__eq__imp__le) ).
thf(535,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)],[70]) ).
thf(223,axiom,
! [A: list_a,B: list_a] :
( ( A != nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_last__appendR) ).
thf(1162,plain,
! [A: list_a,B: list_a] :
( ( A != nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(256,axiom,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= A )
= ( B = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_append__self__conv) ).
thf(1325,plain,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= A )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(155,axiom,
! [A: ( nat > nat ) > list_nat > list_nat > $o,B: nat > nat,C: list_nat,D: list_nat] :
( ! [E: nat > nat,F: list_nat] : ( A @ E @ nil_nat @ F )
=> ( ! [E: nat > nat,F: nat,G: list_nat,H: list_nat] :
( ( A @ E @ G @ ( cons_nat @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_nat @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_map__tailrec__rev_Oinduct) ).
thf(895,plain,
! [A: ( nat > nat ) > list_nat > list_nat > $o,B: nat > nat,C: list_nat,D: list_nat] :
( ! [E: nat > nat,F: list_nat] : ( A @ E @ nil_nat @ F )
=> ( ! [E: nat > nat,F: nat,G: list_nat,H: list_nat] :
( ( A @ E @ G @ ( cons_nat @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_nat @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(251,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_remdups__adj_Ocases) ).
thf(1293,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',fact_169_v__decompose) ).
thf(1381,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)],[271]) ).
thf(8,axiom,
! [A: list_nat,B: list_nat,C: list_nat,D: list_nat,E: list_nat] :
( ( ( append_nat @ A @ B )
= C )
=> ( ( D
= ( append_nat @ B @ E ) )
=> ( ( append_nat @ A @ D )
= ( append_nat @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_append__eq__appendI) ).
thf(330,plain,
! [A: list_nat,B: list_nat,C: list_nat,D: list_nat,E: list_nat] :
( ( ( append_nat @ A @ B )
= C )
=> ( ( D
= ( append_nat @ B @ E ) )
=> ( ( append_nat @ A @ D )
= ( append_nat @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(193,axiom,
! [A: list_a,B: list_a] :
( ( nil_a
= ( append_a @ A @ B ) )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Nil__is__append__conv) ).
thf(1061,plain,
! [A: list_a,B: list_a] :
( ( nil_a
= ( append_a @ A @ B ) )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(107,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_eq_nat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_minf_I6_J) ).
thf(700,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_eq_nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(65,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_add_Ocomm__neutral) ).
thf(520,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(163,axiom,
! [A: list_a] :
( ( take_a @ zero_zero_nat @ A )
= nil_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_take__0) ).
thf(943,plain,
! [A: list_a] :
( ( take_a @ zero_zero_nat @ A )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(187,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_int @ A @ C )
= ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_add__mono__thms__linordered__semiring_I4_J) ).
thf(1022,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_int @ A @ C )
= ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(301,axiom,
! [A: list_a,B: a,C: list_a] :
( ( A
= ( cons_a @ B @ C ) )
=> ( A != nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_list_OdiscI) ).
thf(1528,plain,
! [A: list_a,B: a,C: list_a] :
( ( A
= ( cons_a @ B @ C ) )
=> ( A != nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(126,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( plus_plus_int @ A @ D )
= ( plus_plus_int @ B @ ( plus_plus_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_group__cancel_Oadd1) ).
thf(780,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( plus_plus_int @ A @ D )
= ( plus_plus_int @ B @ ( plus_plus_int @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(185,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( ord_less_eq_a @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_add__mono__thms__linordered__semiring_I3_J) ).
thf(1015,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( ord_less_eq_a @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(28,axiom,
! [A: list_nat,B: list_nat] :
( ( ( A = nil_nat )
=> ( ( last_nat @ ( append_nat @ B @ A ) )
= ( last_nat @ B ) ) )
& ( ( A != nil_nat )
=> ( ( last_nat @ ( append_nat @ B @ A ) )
= ( last_nat @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_last__append) ).
thf(394,plain,
! [A: list_nat,B: list_nat] :
( ( ( A = nil_nat )
=> ( ( last_nat @ ( append_nat @ B @ A ) )
= ( last_nat @ B ) ) )
& ( ( A != nil_nat )
=> ( ( last_nat @ ( append_nat @ B @ A ) )
= ( last_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(289,axiom,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ B @ A ) )
= ( B = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_self__append__conv2) ).
thf(1477,plain,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ B @ A ) )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(205,axiom,
( ( descar1375166517sums_a @ nil_a )
= nil_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_psums_Osimps_I1_J) ).
thf(1102,plain,
( ( descar1375166517sums_a @ nil_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(40,axiom,
! [A: list_nat,B: list_nat,C: list_nat] :
( ( append_nat @ ( append_nat @ A @ B ) @ C )
= ( append_nat @ A @ ( append_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_append_Oassoc) ).
thf(438,plain,
! [A: list_nat,B: list_nat,C: list_nat] :
( ( append_nat @ ( append_nat @ A @ B ) @ C )
= ( append_nat @ A @ ( append_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(160,axiom,
! [A: list_nat,B: list_nat > $o] :
( ( A != nil_nat )
=> ( ! [C: nat] : ( B @ ( cons_nat @ C @ nil_nat ) )
=> ( ! [C: nat,D: list_nat] :
( ( D != nil_nat )
=> ( ( B @ D )
=> ( B @ ( cons_nat @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_list__nonempty__induct) ).
thf(922,plain,
! [A: list_nat,B: list_nat > $o] :
( ( A != nil_nat )
=> ( ! [C: nat] : ( B @ ( cons_nat @ C @ nil_nat ) )
=> ( ! [C: nat,D: list_nat] :
( ( D != nil_nat )
=> ( ( B @ D )
=> ( B @ ( cons_nat @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(92,axiom,
! [A: ( nat > nat > $o ) > list_nat > $o,B: nat > nat > $o,C: list_nat] :
( ! [D: nat > nat > $o] : ( A @ D @ nil_nat )
=> ( ! [D: nat > nat > $o,E: nat,F: list_nat] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_nat @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_sorted__wrt_Oinduct) ).
thf(636,plain,
! [A: ( nat > nat > $o ) > list_nat > $o,B: nat > nat > $o,C: list_nat] :
( ! [D: nat > nat > $o] : ( A @ D @ nil_nat )
=> ( ! [D: nat > nat > $o,E: nat,F: list_nat] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_nat @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(239,axiom,
! [A: a] :
( ( ( plus_plus_a @ A @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_double__zero) ).
thf(1245,plain,
! [A: a] :
( ( ( plus_plus_a @ A @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(100,axiom,
! [A: list_nat,B: nat] :
( ( A = nil_nat )
=> ( ( last_nat @ ( cons_nat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_last__ConsL) ).
thf(675,plain,
! [A: list_nat,B: nat] :
( ( A = nil_nat )
=> ( ( last_nat @ ( cons_nat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(82,axiom,
! [A: list_nat] :
( ! [B: nat,C: list_nat] :
( A
!= ( cons_nat @ B @ C ) )
=> ( A = nil_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_min__list_Ocases) ).
thf(589,plain,
! [A: list_nat] :
( ! [B: nat,C: list_nat] :
( A
!= ( cons_nat @ B @ C ) )
=> ( A = nil_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(101,axiom,
! [A: nat] :
( ( take_a @ A @ nil_a )
= nil_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_take__Nil) ).
thf(680,plain,
! [A: nat] :
( ( take_a @ A @ nil_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(96,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_not__gr__zero) ).
thf(663,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(247,axiom,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a,F: list_a] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_a @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_sorted__wrt_Oinduct) ).
thf(1277,plain,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a,F: list_a] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_a @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(55,axiom,
! [A: nat,B: list_nat,C: list_nat,D: list_nat,E: list_nat] :
( ( ( cons_nat @ A @ B )
= C )
=> ( ( D
= ( append_nat @ B @ E ) )
=> ( ( cons_nat @ A @ D )
= ( append_nat @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Cons__eq__appendI) ).
thf(487,plain,
! [A: nat,B: list_nat,C: list_nat,D: list_nat,E: list_nat] :
( ( ( cons_nat @ A @ B )
= C )
=> ( ( D
= ( append_nat @ B @ E ) )
=> ( ( cons_nat @ A @ D )
= ( append_nat @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(119,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_bot__nat__0_Oextremum) ).
thf(749,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(11,axiom,
! [A: list_nat,B: list_nat,C: list_nat,D: list_nat] :
( ( ( append_nat @ A @ B )
= ( append_nat @ C @ D ) )
= ( ? [E: list_nat] :
( ( ( A
= ( append_nat @ C @ E ) )
& ( ( append_nat @ E @ B )
= D ) )
| ( ( ( append_nat @ A @ E )
= C )
& ( B
= ( append_nat @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_append__eq__append__conv2) ).
thf(342,plain,
! [A: list_nat,B: list_nat,C: list_nat,D: list_nat] :
( ( ( append_nat @ A @ B )
= ( append_nat @ C @ D ) )
= ( ? [E: list_nat] :
( ( ( A
= ( append_nat @ C @ E ) )
& ( ( append_nat @ E @ B )
= D ) )
| ( ( ( append_nat @ A @ E )
= C )
& ( B
= ( append_nat @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(218,axiom,
! [A: a,B: a] :
( ( ord_less_a @ ( plus_plus_a @ A @ B ) @ B )
= ( ord_less_a @ A @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_add__less__same__cancel2) ).
thf(1145,plain,
! [A: a,B: a] :
( ( ord_less_a @ ( plus_plus_a @ A @ B ) @ B )
= ( ord_less_a @ A @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(139,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_add__left__mono) ).
thf(836,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( plus_plus_a @ C @ A ) @ ( plus_plus_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(36,axiom,
! [A: list_nat,B: list_nat,C: list_nat] :
( ( ( append_nat @ A @ B )
= ( append_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_append__same__eq) ).
thf(426,plain,
! [A: list_nat,B: list_nat,C: list_nat] :
( ( ( append_nat @ A @ B )
= ( append_nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(224,axiom,
! [A: list_a,B: a] :
( ( A != nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= ( last_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_last__ConsR) ).
thf(1166,plain,
! [A: list_a,B: a] :
( ( A != nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= ( last_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(79,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_neq0__conv) ).
thf(580,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(196,axiom,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= B )
= ( A = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_append__self__conv2) ).
thf(1070,plain,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= B )
= ( A = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(7,axiom,
! [A: nat,B: nat,C: nat] :
( ( append_nat @ ( replicate_nat @ A @ B ) @ ( replicate_nat @ C @ B ) )
= ( append_nat @ ( replicate_nat @ C @ B ) @ ( replicate_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_append__replicate__commute) ).
thf(327,plain,
! [A: nat,B: nat,C: nat] :
( ( append_nat @ ( replicate_nat @ A @ B ) @ ( replicate_nat @ C @ B ) )
= ( append_nat @ ( replicate_nat @ C @ B ) @ ( replicate_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_add__cancel__left__right) ).
thf(409,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(179,axiom,
! [A: nat,B: list_nat,C: list_nat,D: list_nat] :
( ( ( cons_nat @ A @ B )
= ( append_nat @ C @ D ) )
= ( ( ( C = nil_nat )
& ( ( cons_nat @ A @ B )
= D ) )
| ? [E: list_nat] :
( ( ( cons_nat @ A @ E )
= C )
& ( B
= ( append_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_Cons__eq__append__conv) ).
thf(993,plain,
! [A: nat,B: list_nat,C: list_nat,D: list_nat] :
( ( ( cons_nat @ A @ B )
= ( append_nat @ C @ D ) )
= ( ( ( C = nil_nat )
& ( ( cons_nat @ A @ B )
= D ) )
| ? [E: list_nat] :
( ( ( cons_nat @ A @ E )
= C )
& ( B
= ( append_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(111,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_add_Oleft__commute) ).
thf(712,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(182,axiom,
! [A: ( nat > nat > $o ) > list_nat > $o,B: nat > nat > $o,C: list_nat] :
( ! [D: nat > nat > $o] : ( A @ D @ nil_nat )
=> ( ! [D: nat > nat > $o,E: nat] : ( A @ D @ ( cons_nat @ E @ nil_nat ) )
=> ( ! [D: nat > nat > $o,E: nat,F: nat,G: list_nat] :
( ( A @ D @ ( cons_nat @ F @ G ) )
=> ( A @ D @ ( cons_nat @ E @ ( cons_nat @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_successively_Oinduct) ).
thf(1003,plain,
! [A: ( nat > nat > $o ) > list_nat > $o,B: nat > nat > $o,C: list_nat] :
( ! [D: nat > nat > $o] : ( A @ D @ nil_nat )
=> ( ! [D: nat > nat > $o,E: nat] : ( A @ D @ ( cons_nat @ E @ nil_nat ) )
=> ( ! [D: nat > nat > $o,E: nat,F: nat,G: list_nat] :
( ( A @ D @ ( cons_nat @ F @ G ) )
=> ( A @ D @ ( cons_nat @ E @ ( cons_nat @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(109,axiom,
! [A: list_nat] :
( ( A != nil_nat )
=> ~ ! [B: nat,C: list_nat] :
( A
!= ( cons_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_strict__sorted_Ocases) ).
thf(705,plain,
! [A: list_nat] :
( ( A != nil_nat )
=> ~ ! [B: nat,C: list_nat] :
( A
!= ( cons_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(221,axiom,
! [A: list_a,B: a,C: list_a,D: a] :
( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
= ( append_a @ C @ ( cons_a @ D @ nil_a ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_append1__eq__conv) ).
thf(1156,plain,
! [A: list_a,B: a,C: list_a,D: a] :
( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
= ( append_a @ C @ ( cons_a @ D @ nil_a ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(99,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_order__refl) ).
thf(673,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_add__less__imp__less__right) ).
thf(441,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(20,axiom,
! [A: list_nat] :
( ( append_nat @ nil_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_append_Oleft__neutral) ).
thf(370,plain,
! [A: list_nat] :
( ( append_nat @ nil_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(59,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_le__iff__add) ).
thf(502,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(236,axiom,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_append_Oright__neutral) ).
thf(1235,plain,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(49,axiom,
! [A: list_nat,B: list_nat] :
? [C: list_nat,D: list_nat,E: list_nat] :
( ( A
= ( append_nat @ D @ C ) )
& ( B
= ( append_nat @ E @ C ) )
& ( ( D = nil_nat )
| ( E = nil_nat )
| ( ( last_nat @ D )
!= ( last_nat @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_longest__common__suffix) ).
thf(463,plain,
! [A: list_nat,B: list_nat] :
? [C: list_nat,D: list_nat,E: list_nat] :
( ( A
= ( append_nat @ D @ C ) )
& ( B
= ( append_nat @ E @ C ) )
& ( ( D = nil_nat )
| ( E = nil_nat )
| ( ( last_nat @ D )
!= ( last_nat @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(16,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_add__strict__left__mono) ).
thf(359,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(213,axiom,
! [A: a] :
( ( replicate_a @ zero_zero_nat @ A )
= nil_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_replicate__0) ).
thf(1130,plain,
! [A: a] :
( ( replicate_a @ zero_zero_nat @ A )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(72,axiom,
! [A: nat] :
( ( descar226543321ms_nat @ ( cons_nat @ A @ nil_nat ) )
= ( cons_nat @ A @ nil_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_psums_Osimps_I2_J) ).
thf(544,plain,
! [A: nat] :
( ( descar226543321ms_nat @ ( cons_nat @ A @ nil_nat ) )
= ( cons_nat @ A @ nil_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(159,axiom,
! [A: list_nat,B: list_nat > $o] :
( ( A != nil_nat )
=> ( ! [C: nat] : ( B @ ( cons_nat @ C @ nil_nat ) )
=> ( ! [C: nat,D: list_nat] :
( ( D != nil_nat )
=> ( ( B @ D )
=> ( B @ ( append_nat @ D @ ( cons_nat @ C @ nil_nat ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_rev__nonempty__induct) ).
thf(907,plain,
! [A: list_nat,B: list_nat > $o] :
( ( A != nil_nat )
=> ( ! [C: nat] : ( B @ ( cons_nat @ C @ nil_nat ) )
=> ( ! [C: nat,D: list_nat] :
( ( D != nil_nat )
=> ( ( B @ D )
=> ( B @ ( append_nat @ D @ ( cons_nat @ C @ nil_nat ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(117,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ C @ D ) )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_add__mono__thms__linordered__semiring_I1_J) ).
thf(744,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( ord_less_eq_a @ A @ B )
& ( ord_less_eq_a @ C @ D ) )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(87,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_zero__reorient) ).
thf(613,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(175,axiom,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_size__neq__size__imp__neq) ).
thf(978,plain,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(183,axiom,
! [A: nat,B: list_a] :
( ( ( take_a @ A @ B )
= nil_a )
= ( ( A = zero_zero_nat )
| ( B = nil_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_take__eq__Nil) ).
thf(1008,plain,
! [A: nat,B: list_a] :
( ( ( take_a @ A @ B )
= nil_a )
= ( ( A = zero_zero_nat )
| ( B = nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(4,axiom,
! [A: list_nat,B: list_nat] :
( ( A = B )
=> ( A
= ( append_nat @ nil_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_eq__Nil__appendI) ).
thf(314,plain,
! [A: list_nat,B: list_nat] :
( ( A = B )
=> ( A
= ( append_nat @ nil_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(268,axiom,
! [A: list_a] :
( ( A != nil_a )
= ( ? [B: a,C: list_a] :
( A
= ( cons_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_neq__Nil__conv) ).
thf(1372,plain,
! [A: list_a] :
( ( A != nil_a )
= ( ? [B: a,C: list_a] :
( A
= ( cons_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ A )
= ( ord_less_eq_nat @ B @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_add__le__same__cancel1) ).
thf(859,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ A )
= ( ord_less_eq_nat @ B @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(142,axiom,
! [A: list_nat] :
( ( A != nil_nat )
=> ( ! [B: nat] :
( A
!= ( cons_nat @ B @ nil_nat ) )
=> ~ ! [B: nat,C: nat,D: list_nat] :
( A
!= ( cons_nat @ B @ ( cons_nat @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_remdups__adj_Ocases) ).
thf(845,plain,
! [A: list_nat] :
( ( A != nil_nat )
=> ( ! [B: nat] :
( A
!= ( cons_nat @ B @ nil_nat ) )
=> ~ ! [B: nat,C: nat,D: list_nat] :
( A
!= ( cons_nat @ B @ ( cons_nat @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(45,axiom,
! [A: nat,B: list_nat] :
( ( descar226543321ms_nat @ ( append_nat @ ( replicate_nat @ A @ zero_zero_nat ) @ B ) )
= ( append_nat @ ( replicate_nat @ A @ zero_zero_nat ) @ ( descar226543321ms_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_psums__replicate__0__append) ).
thf(450,plain,
! [A: nat,B: list_nat] :
( ( descar226543321ms_nat @ ( append_nat @ ( replicate_nat @ A @ zero_zero_nat ) @ B ) )
= ( append_nat @ ( replicate_nat @ A @ zero_zero_nat ) @ ( descar226543321ms_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(174,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_le__eq__less__or__eq) ).
thf(976,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(297,axiom,
ord_less_eq_a @ zero_zero_a @ xa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_nonneg_Ohyps_I4_J) ).
thf(1517,plain,
ord_less_eq_a @ zero_zero_a @ xa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(57,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_add__le__cancel__right) ).
thf(495,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(276,axiom,
( ( last_a @ xsa )
!= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_nonneg_Ohyps_I2_J) ).
thf(1412,plain,
( ( last_a @ xsa )
!= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(250,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_strict__sorted_Ocases) ).
thf(1289,plain,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(19,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_add__mono__thms__linordered__semiring_I1_J) ).
thf(368,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(134,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_a @ A @ C ) )
=> ( ord_less_eq_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_add__le__imp__le__left) ).
thf(813,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_a @ A @ C ) )
=> ( ord_less_eq_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(64,axiom,
! [A: list_nat] :
( ( append_nat @ A @ nil_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_append__Nil2) ).
thf(517,plain,
! [A: list_nat] :
( ( append_nat @ A @ nil_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(261,axiom,
! [A: list_a,B: list_a] :
( ( A = B )
=> ( A
= ( append_a @ nil_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_eq__Nil__appendI) ).
thf(1341,plain,
! [A: list_a,B: list_a] :
( ( A = B )
=> ( A
= ( append_a @ nil_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(295,axiom,
! [A: ( a > nat ) > list_a > list_nat > $o,B: a > nat,C: list_a,D: list_nat] :
( ! [E: a > nat,F: list_nat] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > nat,F: a,G: list_a,H: list_nat] :
( ( A @ E @ G @ ( cons_nat @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_map__tailrec__rev_Oinduct) ).
thf(1508,plain,
! [A: ( a > nat ) > list_a > list_nat > $o,B: a > nat,C: list_a,D: list_nat] :
( ! [E: a > nat,F: list_nat] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > nat,F: a,G: list_a,H: list_nat] :
( ( A @ E @ G @ ( cons_nat @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_less__add__same__cancel1) ).
thf(946,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_nat @ zero_zero_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(14,axiom,
! [A: list_nat,B: list_nat] :
( ( A = nil_nat )
=> ( ( last_nat @ ( append_nat @ B @ A ) )
= ( last_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_last__appendL) ).
thf(351,plain,
! [A: list_nat,B: list_nat] :
( ( A = nil_nat )
=> ( ( last_nat @ ( append_nat @ B @ A ) )
= ( last_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [A: nat,B: nat] :
( ( append_nat @ ( replicate_nat @ A @ B ) @ ( cons_nat @ B @ nil_nat ) )
= ( cons_nat @ B @ ( replicate_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_replicate__append__same) ).
thf(378,plain,
! [A: nat,B: nat] :
( ( append_nat @ ( replicate_nat @ A @ B ) @ ( cons_nat @ B @ nil_nat ) )
= ( cons_nat @ B @ ( replicate_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(253,axiom,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ A @ B ) )
= ( B = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_self__append__conv) ).
thf(1308,plain,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ A @ B ) )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_add__eq__0__iff__both__eq__0) ).
thf(478,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(231,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: a,E: list_a,F: list_a] :
( ( A @ F @ E )
=> ( A @ ( cons_a @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_splice_Oinduct) ).
thf(1212,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: a,E: list_a,F: list_a] :
( ( A @ F @ E )
=> ( A @ ( cons_a @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(122,axiom,
! [A: list_nat] :
( ( A != nil_nat )
=> ~ ! [B: list_nat,C: nat] :
( A
!= ( append_nat @ B @ ( cons_nat @ C @ nil_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_rev__exhaust) ).
thf(763,plain,
! [A: list_nat] :
( ( A != nil_nat )
=> ~ ! [B: list_nat,C: nat] :
( A
!= ( append_nat @ B @ ( cons_nat @ C @ nil_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(296,axiom,
! [A: nat,B: a] :
( ( A != zero_zero_nat )
=> ( ( last_a @ ( replicate_a @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_last__replicate) ).
thf(1513,plain,
! [A: nat,B: a] :
( ( A != zero_zero_nat )
=> ( ( last_a @ ( replicate_a @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(283,axiom,
! [A: a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( cons_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( cons_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Cons__eq__appendI) ).
thf(1442,plain,
! [A: a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( cons_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( cons_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_add__le__same__cancel2) ).
thf(800,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(214,axiom,
! [A: list_a,B: a] :
( ( last_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_last__snoc) ).
thf(1133,plain,
! [A: list_a,B: a] :
( ( last_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(181,axiom,
! [A: list_nat] :
( ( A != nil_nat )
=> ~ ! [B: nat,C: list_nat] :
( A
!= ( cons_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_list_Oexhaust) ).
thf(999,plain,
! [A: list_nat] :
( ( A != nil_nat )
=> ~ ! [B: nat,C: list_nat] :
( A
!= ( cons_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_add__le__cancel__left) ).
thf(432,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(234,axiom,
! [A: nat,B: a,C: nat,D: a] :
( ( ( replicate_a @ A @ B )
= ( replicate_a @ C @ D ) )
= ( ( A = C )
& ( ( A != zero_zero_nat )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_replicate__eq__replicate) ).
thf(1229,plain,
! [A: nat,B: a,C: nat,D: a] :
( ( ( replicate_a @ A @ B )
= ( replicate_a @ C @ D ) )
= ( ( A = C )
& ( ( A != zero_zero_nat )
=> ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(305,axiom,
! [A: list_a,B: list_a,C: a,D: list_a] :
( ( ( append_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( ( A = nil_a )
& ( B
= ( cons_a @ C @ D ) ) )
| ? [E: list_a] :
( ( A
= ( cons_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_append__eq__Cons__conv) ).
thf(1546,plain,
! [A: list_a,B: list_a,C: a,D: list_a] :
( ( ( append_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( ( A = nil_a )
& ( B
= ( cons_a @ C @ D ) ) )
| ? [E: list_a] :
( ( A
= ( cons_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(275,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( ( C = D )
=> ( A @ ( cons_a @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_a @ D @ E ) ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_remdups__adj_Oinduct) ).
thf(1395,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( ( C = D )
=> ( A @ ( cons_a @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_a @ D @ E ) ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_less__imp__le__nat) ).
thf(854,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(219,axiom,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_add_Ogroup__left__neutral) ).
thf(1148,plain,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(240,axiom,
! [A: nat,B: a,C: list_a] :
( ( append_a @ ( replicate_a @ A @ B ) @ ( cons_a @ B @ C ) )
= ( cons_a @ B @ ( append_a @ ( replicate_a @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_replicate__app__Cons__same) ).
thf(1248,plain,
! [A: nat,B: a,C: list_a] :
( ( append_a @ ( replicate_a @ A @ B ) @ ( cons_a @ B @ C ) )
= ( cons_a @ B @ ( append_a @ ( replicate_a @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(290,axiom,
! [A: a,B: list_a,C: list_a] :
( ( append_a @ ( cons_a @ A @ B ) @ C )
= ( cons_a @ A @ ( append_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_append__Cons) ).
thf(1480,plain,
! [A: a,B: list_a,C: list_a] :
( ( append_a @ ( cons_a @ A @ B ) @ C )
= ( cons_a @ A @ ( append_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(21,axiom,
! [A: list_nat,B: nat,C: list_nat] :
( ( nth_nat @ ( append_nat @ A @ ( cons_nat @ B @ C ) ) @ ( size_size_list_nat @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_nth__append__length) ).
thf(373,plain,
! [A: list_nat,B: nat,C: list_nat] :
( ( nth_nat @ ( append_nat @ A @ ( cons_nat @ B @ C ) ) @ ( size_size_list_nat @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(138,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_less__nat__zero__code) ).
thf(833,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(172,axiom,
! [A: list_nat,B: nat,C: list_nat] :
( ( A
= ( cons_nat @ B @ C ) )
=> ( A != nil_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_list_OdiscI) ).
thf(967,plain,
! [A: list_nat,B: nat,C: list_nat] :
( ( A
= ( cons_nat @ B @ C ) )
=> ( A != nil_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(281,axiom,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_append_Oleft__neutral) ).
thf(1436,plain,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(259,axiom,
! [A: a] :
( ( ord_less_eq_a @ zero_zero_a @ ( plus_plus_a @ A @ A ) )
= ( ord_less_eq_a @ zero_zero_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_zero__le__double__add__iff__zero__le__single__add) ).
thf(1335,plain,
! [A: a] :
( ( ord_less_eq_a @ zero_zero_a @ ( plus_plus_a @ A @ A ) )
= ( ord_less_eq_a @ zero_zero_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(123,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( plus_plus_int @ D @ A )
= ( plus_plus_int @ B @ ( plus_plus_int @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_group__cancel_Oadd2) ).
thf(767,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( plus_plus_int @ D @ A )
= ( plus_plus_int @ B @ ( plus_plus_int @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(69,axiom,
! [A: list_nat,B: list_nat,C: list_nat] :
( ( append_nat @ ( append_nat @ A @ B ) @ C )
= ( append_nat @ A @ ( append_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_append__assoc) ).
thf(532,plain,
! [A: list_nat,B: list_nat,C: list_nat] :
( ( append_nat @ ( append_nat @ A @ B ) @ C )
= ( append_nat @ A @ ( append_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(106,axiom,
! [A: nat,B: list_nat] :
( ( cons_nat @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_not__Cons__self2) ).
thf(696,plain,
! [A: nat,B: list_nat] :
( ( cons_nat @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(167,axiom,
! [A: a] :
? [B: a] :
! [C: a] :
( ( ord_less_a @ C @ B )
=> ~ ( ord_less_eq_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_minf_I8_J) ).
thf(955,plain,
! [A: a] :
? [B: a] :
! [C: a] :
( ( ord_less_a @ C @ B )
=> ~ ( ord_less_eq_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(265,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_append__assoc) ).
thf(1363,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(255,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_rev__induct) ).
thf(1314,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(169,axiom,
( plus_plus_int
= ( ^ [A: int,B: int] : ( plus_plus_int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_add_Ocommute) ).
thf(960,plain,
( plus_plus_int
= ( ^ [A: int,B: int] : ( plus_plus_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(288,axiom,
! [A: nat,B: nat,C: list_a] :
( ( ord_less_nat @ A @ B )
=> ( ( nth_a @ ( take_a @ B @ C ) @ A )
= ( nth_a @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_nth__take) ).
thf(1473,plain,
! [A: nat,B: nat,C: list_a] :
( ( ord_less_nat @ A @ B )
=> ( ( nth_a @ ( take_a @ B @ C ) @ A )
= ( nth_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(152,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_a @ A @ C ) )
= ( ord_less_eq_a @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_add__le__cancel__left) ).
thf(886,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_a @ A @ C ) )
= ( ord_less_eq_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( last_nat @ ( replicate_nat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_last__replicate) ).
thf(415,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( last_nat @ ( replicate_nat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(177,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_add_Oassoc) ).
thf(987,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(77,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_add_Oright__cancel) ).
thf(575,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A )
= ( ord_less_nat @ B @ zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_add__less__same__cancel1) ).
thf(1019,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A )
= ( ord_less_nat @ B @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(104,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_bot__nat__0_Onot__eq__extremum) ).
thf(691,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(294,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ B )
= ( ord_less_eq_a @ A @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_add__le__same__cancel2) ).
thf(1505,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ ( plus_plus_a @ A @ B ) @ B )
= ( ord_less_eq_a @ A @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(202,axiom,
! [A: a] :
( ( ord_less_a @ ( plus_plus_a @ A @ A ) @ zero_zero_a )
= ( ord_less_a @ A @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_double__add__less__zero__iff__single__add__less__zero) ).
thf(1093,plain,
! [A: a] :
( ( ord_less_a @ ( plus_plus_a @ A @ A ) @ zero_zero_a )
= ( ord_less_a @ A @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(140,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_minf_I8_J) ).
thf(839,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(272,axiom,
! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( append_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( append_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_append__eq__appendI) ).
thf(1384,plain,
! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( append_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( append_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(303,axiom,
! [A: list_a > list_nat > $o,B: list_a,C: list_nat] :
( ( A @ nil_a @ nil_nat )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_nat )
=> ( ! [D: nat,E: list_nat] : ( A @ nil_a @ ( cons_nat @ D @ E ) )
=> ( ! [D: a,E: list_a,F: nat,G: list_nat] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_nat @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_list__induct2_H) ).
thf(1537,plain,
! [A: list_a > list_nat > $o,B: list_a,C: list_nat] :
( ( A @ nil_a @ nil_nat )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_nat )
=> ( ! [D: nat,E: list_nat] : ( A @ nil_a @ ( cons_nat @ D @ E ) )
=> ( ! [D: a,E: list_a,F: nat,G: list_nat] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_nat @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(84,axiom,
! [A: list_a] :
( ( ( size_size_list_a @ A )
= zero_zero_nat )
= ( A = nil_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_length__0__conv) ).
thf(596,plain,
! [A: list_a] :
( ( ( size_size_list_a @ A )
= zero_zero_nat )
= ( A = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(270,axiom,
xsa != nil_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_nonneg_Ohyps_I1_J) ).
thf(1378,plain,
xsa != nil_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(176,axiom,
! [A: list_nat,B: list_nat,C: nat] :
( ( ord_less_eq_nat @ ( size_size_list_nat @ A ) @ ( size_size_list_nat @ B ) )
=> ( A
!= ( cons_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_impossible__Cons) ).
thf(982,plain,
! [A: list_nat,B: list_nat,C: nat] :
( ( ord_less_eq_nat @ ( size_size_list_nat @ A ) @ ( size_size_list_nat @ B ) )
=> ( A
!= ( cons_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(279,axiom,
( xsa
= ( append_a @ xs1 @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_xs__decompose) ).
thf(1431,plain,
( xsa
= ( append_a @ xs1 @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_le__add__same__cancel1) ).
thf(803,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(162,axiom,
! [A: nat] :
? [B: list_a] :
( ( size_size_list_a @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_Ex__list__of__length) ).
thf(940,plain,
! [A: nat] :
? [B: list_a] :
( ( size_size_list_a @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(287,axiom,
! [A: ( nat > a ) > list_nat > list_a > $o,B: nat > a,C: list_nat,D: list_a] :
( ! [E: nat > a,F: list_a] : ( A @ E @ nil_nat @ F )
=> ( ! [E: nat > a,F: nat,G: list_nat,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_nat @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_map__tailrec__rev_Oinduct) ).
thf(1468,plain,
! [A: ( nat > a ) > list_nat > list_a > $o,B: nat > a,C: list_nat,D: list_a] :
( ! [E: nat > a,F: list_a] : ( A @ E @ nil_nat @ F )
=> ( ! [E: nat > a,F: nat,G: list_nat,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_nat @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(151,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( A = B )
& ( ord_less_eq_a @ C @ D ) )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_add__mono__thms__linordered__semiring_I2_J) ).
thf(882,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( A = B )
& ( ord_less_eq_a @ C @ D ) )
=> ( ord_less_eq_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(173,axiom,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_neq__if__length__neq) ).
thf(972,plain,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1,conjecture,
( ( descar1375166517sums_a @ xsa )
= ( append_a @ ( replicate_a @ p @ zero_zero_a ) @ ( descar1375166517sums_a @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( descar1375166517sums_a @ xsa )
!= ( append_a @ ( replicate_a @ p @ zero_zero_a ) @ ( descar1375166517sums_a @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(309,plain,
( ( descar1375166517sums_a @ xsa )
!= ( append_a @ ( replicate_a @ p @ zero_zero_a ) @ ( descar1375166517sums_a @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(286,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_minus__poly__rev__list_Oinduct) ).
thf(1463,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(293,axiom,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_rev__nonempty__induct) ).
thf(1490,plain,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(189,axiom,
( ( last_a @ xs )
!= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_assms_I2_J) ).
thf(1037,plain,
( ( last_a @ xs )
!= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1669,plain,
$false,
inference(e,[status(thm)],[892,365,760,777,666,1549,1110,481,1083,962,523,683,1522,1142,1533,741,1073,655,511,1078,384,550,715,472,1196,1127,709,841,1046,1366,1518,1254,785,504,949,460,702,751,902,1115,448,1232,1415,475,492,789,1450,443,376,1136,348,806,905,1040,321,1151,937,602,634,1447,866,453,660,1345,1433,1201,1104,1242,849,529,810,1338,381,1311,1067,957,746,952,862,1217,1487,429,815,1238,484,879,889,1159,1392,456,1555,435,583,830,1360,578,1089,1270,1328,1064,403,1096,356,593,1375,1121,339,669,686,1424,526,1207,547,1263,1099,1297,1266,1552,1525,1333,1086,508,311,541,1170,1286,1026,1185,586,718,412,965,513,1483,1273,856,573,733,1251,618,819,423,694,1389,772,875,1124,1226,641,445,1371,787,498,1107,335,391,1139,1209,1282,736,1349,1542,318,1043,616,900,406,1011,419,990,996,362,567,599,1439,387,631,345,535,1162,1325,895,1293,1381,330,1061,700,520,943,1022,1528,780,1015,394,1477,1102,438,922,636,1245,675,589,680,663,1277,487,749,342,1145,836,426,1166,580,1070,327,409,993,712,1003,705,1156,673,441,370,502,1235,463,359,1130,544,907,744,613,978,1008,314,1372,859,845,450,976,1517,495,1412,1289,368,813,517,1341,1508,946,351,378,1308,478,1212,763,1513,1442,800,1133,999,432,1229,1546,1395,854,1148,1248,1480,373,833,967,1436,1335,767,532,696,955,1363,1314,960,1473,886,415,987,575,1019,691,1505,1093,839,1384,1537,596,1378,982,1431,803,940,1468,882,972,309,1463,1490,1037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP043^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n004.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:40:37 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.03/1.18 % [INFO] Parsing done (400ms).
% 2.03/1.20 % [INFO] Running in sequential loop mode.
% 2.96/1.48 % [INFO] eprover registered as external prover.
% 2.96/1.48 % [INFO] Scanning for conjecture ...
% 3.31/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 351 axioms. Running axiom selection ...
% 3.56/1.65 % [INFO] Axiom selection finished. Selected 306 axioms (removed 45 axioms).
% 4.43/1.84 % [INFO] Problem is higher-order (TPTP THF).
% 4.43/1.86 % [INFO] Type checking passed.
% 4.43/1.86 % [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 ...
% 20.86/5.43 % External prover 'e' found a proof!
% 20.86/5.43 % [INFO] Killing All external provers ...
% 20.86/5.43 % Time passed: 5086ms (effective reasoning time: 4229ms)
% 20.86/5.43 % 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)>
% 20.86/5.44 % Axioms used in derivation (306): fact_8_psums__replicate__0__append, fact_78_last__append, fact_267_add__mono__thms__linordered__semiring_I4_J, fact_117_induct__list012, fact_277_add_Oassoc, fact_4_psums__0__Cons, fact_289_less__imp__le__nat, fact_199_add__cancel__left__left, fact_287_less__or__eq__imp__le, fact_39_Nil__is__append__conv, fact_58_last__replicate, fact_204_add__cancel__right__left, fact_28_assms_I1_J, fact_316_add__mono, fact_71_take__0, fact_280_add_Ocommute, fact_35_append_Oright__neutral, fact_49_append__Nil2, fact_34_append_Oright__neutral, fact_186_bot__nat__0_Oextremum, fact_126_neq__Nil__conv, fact_312_add__left__mono, fact_248_double__add__less__zero__iff__single__add__less__zero, fact_0_nonneg_Ohyps_I1_J, fact_147_Cons__eq__append__conv, fact_118_induct__list012, fact_244_add__le__same__cancel1, fact_276_bot__nat__0_Oextremum__uniqueI, fact_286_le__neq__implies__less, fact_112_shuffles_Oinduct, fact_266_ab__semigroup__add__class_Oadd__ac_I1_J, fact_212_add__le__cancel__right, fact_64_last__appendL, fact_53_take__eq__Nil, fact_124_list__induct2_H, fact_138_append__Nil, fact_237_le__add__same__cancel1, fact_16_append__assoc, fact_130_list_Oexhaust, fact_156_replicate__append__same, fact_91_gr__zeroI, fact_293_comm__monoid__add__class_Oadd__0, fact_160_zero__reorient, fact_42_append__self__conv2, fact_305_add__le__imp__le__left, fact_63_last__appendL, fact_220_add__less__cancel__left, fact_288_le__eq__less__or__eq, fact_164_append__eq__append__conv2, fact_123_list__induct2_H, fact_14_append_Oassoc, fact_125_neq__Nil__conv, fact_96_strict__sorted_Ocases, fact_218_add__less__cancel__right, fact_278_add_Oleft__cancel, fact_284_size__neq__size__imp__neq, fact_99_map__tailrec__rev_Oinduct, fact_105_remdups__adj_Oinduct, fact_82_transpose_Ocases, fact_12_replicate__app__Cons__same, fact_318_add__mono__thms__linordered__semiring_I1_J, fact_61_append1__eq__conv, fact_56_replicate__empty, fact_265_less__eq__nat_Osimps_I1_J, fact_221_append__eq__append__conv, fact_232_double__add__le__zero__iff__single__add__le__zero, fact_10__092_060open_062take_Ap_Axs_A_061_Areplicate_Ap_A_I0_058_058_Ha_J_092_060close_062, fact_207_add__cancel__right__right, fact_240_add__le__same__cancel2, fact_79_last__append, fact_297_add_Ocomm__neutral, fact_76_last__ConsR, fact_51_nth__Cons__0, fact_100_map__tailrec__rev_Oinduct, fact_310_less__eqE, fact_169_v__decompose, fact_257_add__less__same__cancel2, fact_132_list_OdiscI, fact_48_append__Nil2, fact_306_le__iff__add, fact_45_self__append__conv, fact_201_add__cancel__left__right, fact_234_le__add__same__cancel2, fact_268_le__0__eq, fact_93_strict__sorted_Oinduct, fact_180_minf_I8_J, fact_109_remdups__adj_Ocases, fact_235_le__add__same__cancel2, fact_335_add__strict__mono, fact_209_add__eq__0__iff__both__eq__0, fact_95_strict__sorted_Ocases, fact_223_take__all__iff, fact_254_less__add__same__cancel1, fact_104_successively_Oinduct, fact_37_append__is__Nil__conv, fact_69_last__snoc, fact_110_remdups__adj_Ocases, fact_116_min__list_Ocases, fact_90_not__less__zero, fact_225_length__replicate, fact_315_add__mono, fact_269_impossible__Cons, fact_331_add__strict__right__mono, fact_57_replicate__empty, fact_80_take__Nil, fact_246_zero__less__double__add__iff__zero__less__single__add, fact_161_not__Cons__self2, fact_27_Cons__eq__appendI, fact_271_Ex__list__of__length, fact_283_add__right__imp__eq, fact_177_plus__coeffs_Oinduct, fact_88_zero__less__iff__neq__zero, fact_122_list__induct2_H, fact_157_psums_Osimps_I2_J, fact_134_list_Odistinct_I1_J, fact_179_minf_I8_J, fact_282_add__left__imp__eq, fact_185_le0, fact_342_list_Osize_I3_J, fact_250_less__add__same__cancel2, fact_148_Cons__eq__append__conv, fact_18_append__same__eq, fact_31_replicate__eq__replicate, fact_301_add__le__imp__le__right, fact_145_append__eq__Cons__conv, fact_259_add__less__same__cancel1, fact_33_not__gr__zero, fact_133_list_Odistinct_I1_J, fact_191_add_Oright__neutral, fact_143_rev__nonempty__induct, fact_166_append__eq__appendI, fact_230_zero__le__double__add__iff__zero__le__single__add, fact_144_rev__nonempty__induct, fact_7_psums__replicate__0__append, fact_120_splice_Oinduct, fact_222_append__eq__append__conv, fact_68_nth__replicate, fact_52_take0, fact_23_list_Oinject, fact_111_shuffles_Oinduct, fact_158_psums_Osimps_I2_J, fact_319_add__mono__thms__linordered__semiring_I1_J, fact_281_add_Oleft__commute, fact_213_add__le__cancel__right, fact_77_last__ConsR, fact_74_last__ConsL, fact_273_group__cancel_Oadd1, fact_296_add_Ocomm__neutral, fact_291_nat__less__le, fact_106_remdups__adj_Oinduct, fact_343_length__induct, fact_146_append__eq__Cons__conv, fact_1_p__nz, fact_102_list__nonempty__induct, fact_119_splice_Oinduct, fact_337_add__mono__thms__linordered__field_I1_J, fact_26_Cons__eq__appendI, fact_40_self__append__conv2, fact_98_map__tailrec__rev_Oinduct, fact_142_psums_Ocases, fact_302_add__le__imp__le__right, fact_47_append__self__conv, fact_215_add__le__cancel__left, fact_176_minus__poly__rev__list_Oinduct, fact_272_neq__if__length__neq, fact_127_list_Oinducts, fact_192_add_Oright__neutral, fact_67_nth__replicate, fact_170_p__less__length, fact_304_add__le__imp__le__left, fact_216_add__le__cancel__left, fact_3_psums__0__Cons, fact_36_append__is__Nil__conv, fact_270_impossible__Cons, fact_60_append1__eq__conv, fact_84_longest__common__suffix, fact_349_add__nonneg__eq__0__iff, fact_97_map__tailrec__rev_Oinduct, fact_171_neq0__conv, fact_346_add__nonpos__eq__0__iff, fact_325_add__mono__thms__linordered__semiring_I3_J, fact_228_length__psums, fact_165_append__eq__appendI, fact_128_list_Oinducts, fact_241_add__le__same__cancel2, fact_21_nonneg_Ohyps_I4_J, fact_114_min__list_Oinduct, fact_154_psums_Osimps_I1_J, fact_262_length__greater__0__conv, fact_70_last__snoc, fact_149_rev__exhaust, fact_238_le__add__same__cancel1, fact_159_zero__reorient, fact_173_bot__nat__0_Onot__eq__extremum, fact_121_list__induct2_H, fact_81_take__equalityI, fact_153_psums_Osimps_I1_J, fact_189_add_Oleft__neutral, fact_83_transpose_Ocases, fact_137_append__Nil, fact_194_double__zero, fact_115_min__list_Ocases, fact_129_list_Oexhaust, fact_279_add_Oright__cancel, fact_22_list_Oinject, fact_54_empty__replicate, fact_227_length__psums, fact_308_add__right__mono, fact_85_longest__common__suffix, fact_73_last_Osimps, fact_6_xs__decompose, fact_155_replicate__append__same, fact_163_append__eq__append__conv2, fact_175_order__refl, fact_43_append__self__conv2, fact_94_strict__sorted_Oinduct, fact_196_double__zero__sym, fact_210_zero__eq__add__iff__both__eq__0, fact_309_add__right__mono, fact_182_minf_I6_J, fact_243_add__le__same__cancel1, fact_113_min__list_Oinduct, fact_274_group__cancel_Oadd2, fact_339_add__mono__thms__linordered__field_I2_J, fact_59_last__replicate, fact_92_zero__le, fact_183_add__left__cancel, fact_313_add__left__mono, fact_184_add__right__cancel, fact_20_same__append__eq, fact_135_append_Oleft__neutral, fact_344_nth__take__lemma, fact_261_length__0__conv, fact_101_list__nonempty__induct, fact_151_rev__induct, fact_30_replicate__eq__replicate, fact_294_comm__monoid__add__class_Oadd__0, fact_290_ex__least__nat__le, fact_29_assms_I2_J, fact_15_append__assoc, fact_75_last__ConsL, fact_251_less__add__same__cancel2, fact_253_less__add__same__cancel1, fact_322_add__mono__thms__linordered__semiring_I2_J, fact_72_last_Osimps, fact_11_replicate__app__Cons__same, fact_19_same__append__eq, fact_41_self__append__conv2, fact_55_empty__replicate, fact_347_add__nonpos__eq__0__iff, fact_205_add__cancel__right__left, fact_202_add__cancel__left__right, fact_44_self__append__conv, fact_87_replicate__0, fact_333_add__strict__left__mono, fact_86_replicate__0, fact_139_eq__Nil__appendI, fact_66_last__appendR, fact_198_add__cancel__left__left, fact_136_append_Oleft__neutral, fact_38_Nil__is__append__conv, fact_260_add__less__same__cancel1, fact_226_length__replicate, fact_299_add_Ogroup__left__neutral, fact_263_nth__append__length, fact_178_plus__coeffs_Oinduct, fact_5_xs1__def, fact_181_minf_I6_J, fact_168_append__Cons, fact_162_not__Cons__self2, fact_167_append__Cons, fact_327_add__less__imp__less__right, fact_103_successively_Oinduct, fact_50_nth__Cons__0, fact_89_gr__implies__not__zero, fact_329_add__less__imp__less__left, fact_13_append_Oassoc, fact_65_last__appendR, fact_341_add__mono__thms__linordered__field_I5_J, fact_208_add__cancel__right__right, fact_321_add__mono__thms__linordered__semiring_I2_J, fact_174_order__refl, fact_350_add__nonneg__eq__0__iff, fact_107_sorted__wrt_Oinduct, fact_324_add__mono__thms__linordered__semiring_I3_J, fact_188_add_Oleft__neutral, fact_275_bot__nat__0_Oextremum__unique, fact_25_append__replicate__commute, fact_256_add__less__same__cancel2, fact_264_nth__append__length, fact_140_eq__Nil__appendI, fact_17_append__same__eq, fact_150_rev__exhaust, fact_32_le__zero__eq, fact_9_less__p__zero, fact_285_less__mono__imp__le__mono, fact_152_rev__induct, fact_2_nonneg_Ohyps_I2_J, fact_224_take__all, fact_46_append__self__conv, fact_172_less__nat__zero__code, fact_108_sorted__wrt_Oinduct, fact_24_append__replicate__commute, fact_62_nth__take, fact_131_list_OdiscI, fact_141_psums_Ocases
% 20.86/5.44 % No. of inferences in proof: 616
% 20.86/5.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5086 ms resp. 4229 ms w/o parsing
% 21.85/5.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.85/5.65 % [INFO] Killing All external provers ...
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