%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP103^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n008.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 08:06:46 AM UTC 2026
% Result : Theorem 16.16s 4.68s
% Output : Refutation 16.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 186
% Syntax : Number of formulae : 374 ( 198 unt; 0 typ; 0 def)
% Number of atoms : 932 ( 458 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 2615 ( 170 ~; 38 |; 56 &;2005 @)
% ( 0 <=>; 346 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 824 ( 20 ^; 772 !; 32 ?; 824 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_P1891567085od_a_a_type,type,
list_P1891567085od_a_a: $tType ).
thf(list_P1458844246od_a_a_type,type,
list_P1458844246od_a_a: $tType ).
thf(list_P319927492_a_a_a_type,type,
list_P319927492_a_a_a: $tType ).
thf(list_P1467822637od_a_a_type,type,
list_P1467822637od_a_a: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(times_times_nat_decl,type,
times_times_nat: nat > nat > nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(produc1055075589od_a_a_decl,type,
produc1055075589od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1891567085od_a_a ).
thf(produc778776796_a_a_a_decl,type,
produc778776796_a_a_a: list_P1467822637od_a_a > list_a > list_P319927492_a_a_a ).
thf(produc16441326od_a_a_decl,type,
produc16441326od_a_a: list_a > list_P1467822637od_a_a > list_P1458844246od_a_a ).
thf(product_a_a_decl,type,
product_a_a: list_a > list_a > list_P1467822637od_a_a ).
thf(suc_decl,type,
suc: nat > nat ).
thf(size_s1052379225od_a_a_decl,type,
size_s1052379225od_a_a: list_P1891567085od_a_a > nat ).
thf(size_s736232240_a_a_a_decl,type,
size_s736232240_a_a_a: list_P319927492_a_a_a > nat ).
thf(size_s1875148994od_a_a_decl,type,
size_s1875148994od_a_a: list_P1458844246od_a_a > nat ).
thf(size_s642698393od_a_a_decl,type,
size_s642698393od_a_a: list_P1467822637od_a_a > 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_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(divide_divide_nat_decl,type,
divide_divide_nat: nat > nat > nat ).
thf(k_decl,type,
k: nat ).
thf(n_decl,type,
n: nat ).
thf(xs_decl,type,
xs: list_a ).
thf(12,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_list__decode_Ocases) ).
thf(234,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(106,axiom,
! [A: list_P1467822637od_a_a,B: list_a] :
( ( size_s736232240_a_a_a @ ( produc778776796_a_a_a @ A @ B ) )
= ( times_times_nat @ ( size_s642698393od_a_a @ A ) @ ( size_size_list_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_length__product) ).
thf(555,plain,
! [A: list_P1467822637od_a_a,B: list_a] :
( ( size_s736232240_a_a_a @ ( produc778776796_a_a_a @ A @ B ) )
= ( times_times_nat @ ( size_s642698393od_a_a @ A ) @ ( size_size_list_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(36,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_le0) ).
thf(333,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(127,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( divide_divide_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_div__mult__mult1) ).
thf(628,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( divide_divide_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Suc__lessD) ).
thf(741,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(379,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult__less__mono1) ).
thf(655,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(54,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_less__nat__zero__code) ).
thf(385,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_divisors__zero) ).
thf(747,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(39,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ ( suc @ zero_zero_nat ) ) )
= ( ( A = zero_zero_nat )
| ( A
= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_nat__lessSucSuc0__conv) ).
thf(340,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ ( suc @ zero_zero_nat ) ) )
= ( ( A = zero_zero_nat )
| ( A
= ( suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(58,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__mult__eq__cancel__disj) ).
thf(404,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_nat_Oinject) ).
thf(257,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_mult__nonneg__nonneg) ).
thf(357,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(114,axiom,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_mult_Ocommute) ).
thf(587,plain,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(124,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(619,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(3,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_old_Onat_Oinducts) ).
thf(189,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: nat] :
( ( divide_divide_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_div__0) ).
thf(228,plain,
! [A: nat] :
( ( divide_divide_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( divide_divide_nat @ B @ A )
= zero_zero_nat )
= ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_div__eq__0__conv_H) ).
thf(448,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( divide_divide_nat @ B @ A )
= zero_zero_nat )
= ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(130,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_mult__strict__left__mono) ).
thf(638,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(180,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_not__gr0) ).
thf(853,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(64,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_zero__less__iff__neq__zero) ).
thf(421,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Suc__mono) ).
thf(870,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_mult__eq__0__iff) ).
thf(756,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(13,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_old_Onat_Oinject) ).
thf(238,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ ( suc @ A ) @ B )
= ( times_times_nat @ ( suc @ A ) @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Suc__mult__cancel1) ).
thf(574,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ ( suc @ A ) @ B )
= ( times_times_nat @ ( suc @ A ) @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ B )
=> ( ord_less_nat @ A @ ( times_times_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_n__less__m__mult__n) ).
thf(821,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ B )
=> ( ord_less_nat @ A @ ( times_times_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( times_times_nat @ B @ C ) )
=> ( ord_less_nat @ ( divide_divide_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Util__Div_Oless__mult__imp__div__less) ).
thf(480,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( times_times_nat @ B @ C ) )
=> ( ord_less_nat @ ( divide_divide_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(119,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_nat__mult__le__cancel__disj) ).
thf(602,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(160,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Suc__less__SucD) ).
thf(774,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(26,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_bot__nat__0_Oextremum) ).
thf(292,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ( suc @ zero_zero_nat )
= ( times_times_nat @ A @ B ) )
= ( ( A
= ( suc @ zero_zero_nat ) )
& ( B
= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_one__eq__mult__iff) ).
thf(452,plain,
! [A: nat,B: nat] :
( ( ( suc @ zero_zero_nat )
= ( times_times_nat @ A @ B ) )
= ( ( A
= ( suc @ zero_zero_nat ) )
& ( B
= ( suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(136,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_gr0__implies__Suc) ).
thf(661,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(101,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_gr0I) ).
thf(534,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Nat_OlessE) ).
thf(714,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(166,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_gr0__conv__Suc) ).
thf(798,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(28,axiom,
! [A: nat] :
( ( divide_divide_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_div__by__0) ).
thf(297,plain,
! [A: nat] :
( ( divide_divide_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_mult__le__cancel2) ).
thf(424,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(59,axiom,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zero__less__Suc) ).
thf(407,plain,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(67,axiom,
! [A: nat] :
? [B: list_a] :
( ( size_size_list_a @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Ex__list__of__length) ).
thf(429,plain,
! [A: nat] :
? [B: list_a] :
( ( size_size_list_a @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(163,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_gr__zeroI) ).
thf(788,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_less__Suc__eq__0__disj) ).
thf(729,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(19,axiom,
! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a] :
( ( ( size_s642698393od_a_a @ A )
!= ( size_s642698393od_a_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_size__neq__size__imp__neq) ).
thf(260,plain,
! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a] :
( ( ( size_s642698393od_a_a @ A )
!= ( size_s642698393od_a_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(183,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_ge__less__neq__conv) ).
thf(862,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(42,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( times_times_nat @ B @ C ) )
=> ( ord_less_nat @ ( divide_divide_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Euclidean__Division_Oless__mult__imp__div__less) ).
thf(349,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( times_times_nat @ B @ C ) )
=> ( ord_less_nat @ ( divide_divide_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_mult__is__0) ).
thf(467,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__Suc__eq) ).
thf(484,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Suc__less__eq) ).
thf(625,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(35,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Suc__neq__Zero) ).
thf(329,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_less__SucE) ).
thf(461,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(88,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__SucI) ).
thf(493,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(113,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_nonzero__mult__div__cancel__left) ).
thf(583,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_mult__neg__pos) ).
thf(522,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ zero_zero_nat )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ A )
=> ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ B )
=> ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_one__less__mult) ).
thf(519,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ A )
=> ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ B )
=> ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(132,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( A != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_less__ge__neq__conv) ).
thf(650,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(146,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_lift__Suc__mono__less__iff) ).
thf(725,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1,conjecture,
ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(188,plain,
~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Suc__lessI) ).
thf(388,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(116,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( A != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_le__greater__neq__conv) ).
thf(593,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(90,axiom,
! [A: list_a,B: list_a] :
( ( size_s642698393od_a_a @ ( product_a_a @ A @ B ) )
= ( times_times_nat @ ( size_size_list_a @ A ) @ ( size_size_list_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_length__product) ).
thf(499,plain,
! [A: list_a,B: list_a] :
( ( size_s642698393od_a_a @ ( product_a_a @ A @ B ) )
= ( times_times_nat @ ( size_size_list_a @ A ) @ ( size_size_list_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(9,axiom,
! [A: nat] :
( ( divide_divide_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_bits__div__by__0) ).
thf(225,plain,
! [A: nat] :
( ( divide_divide_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(38,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_le__numeral__extra_I3_J) ).
thf(339,plain,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(155,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_not__less__eq) ).
thf(753,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(102,axiom,
! [A: list_a,B: list_P1467822637od_a_a] :
( ( size_s1875148994od_a_a @ ( produc16441326od_a_a @ A @ B ) )
= ( times_times_nat @ ( size_size_list_a @ A ) @ ( size_s642698393od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_length__product) ).
thf(537,plain,
! [A: list_a,B: list_P1467822637od_a_a] :
( ( size_s1875148994od_a_a @ ( produc16441326od_a_a @ A @ B ) )
= ( times_times_nat @ ( size_size_list_a @ A ) @ ( size_s642698393od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(105,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_less__Suc__induct) ).
thf(547,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less_nat @ D @ E )
=> ( ( ord_less_nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(125,axiom,
! [A: nat,B: nat,C: nat] :
( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
= ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_div__mult2__eq) ).
thf(622,plain,
! [A: nat,B: nat,C: nat] :
( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
= ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(139,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_mult__pos__neg2) ).
thf(701,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(150,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_mult__nonpos__nonneg) ).
thf(738,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',fact_144_length__induct) ).
thf(779,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)],[162]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_mult__left__cancel) ).
thf(605,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( A
= ( suc @ zero_zero_nat ) )
& ( B
= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_mult__eq__1__iff) ).
thf(343,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( A
= ( suc @ zero_zero_nat ) )
& ( B
= ( suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_div__mult__self1__is__m) ).
thf(360,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(30,axiom,
! [A: nat] :
( ( divide_divide_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_div__by__Suc__0) ).
thf(311,plain,
! [A: nat] :
( ( divide_divide_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(107,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_no__zero__divisors) ).
thf(558,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(165,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ C )
& ( ord_less_nat @ C @ ( times_times_nat @ ( suc @ B ) @ A ) ) )
= ( ( divide_divide_nat @ C @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_le__less__div__conv) ).
thf(794,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ C )
& ( ord_less_nat @ C @ ( times_times_nat @ ( suc @ B ) @ A ) ) )
= ( ( divide_divide_nat @ C @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(61,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_mult__cancel__left) ).
thf(412,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_linorder__neqE__nat) ).
thf(750,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(94,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_not__less0) ).
thf(513,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(173,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_nat__less__induct) ).
thf(824,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(20,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_le__zero__eq) ).
thf(264,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_mult__strict__right__mono) ).
thf(856,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_gr__implies__not0) ).
thf(444,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(171,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_gr__implies__gr0) ).
thf(819,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ zero_zero_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(108,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A = zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= zero_zero_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( divide_divide_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_nat__mult__div__cancel__disj) ).
thf(562,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A = zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= zero_zero_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( divide_divide_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(148,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_mult__nonneg__nonpos2) ).
thf(732,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(177,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_lessI) ).
thf(843,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(24,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_old_Onat_Oexhaust) ).
thf(286,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_div__mult__self__is__m) ).
thf(743,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(111,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_mult__0__right) ).
thf(577,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(142,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
& ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_mult__less__cancel2) ).
thf(711,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ B )
& ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(131,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A = zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= zero_zero_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( divide_divide_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_div__mult__mult1__if) ).
thf(641,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A = zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= zero_zero_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( divide_divide_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(56,axiom,
! [A: list_P1467822637od_a_a > $o,B: list_P1467822637od_a_a] :
( ! [C: list_P1467822637od_a_a] :
( ! [D: list_P1467822637od_a_a] :
( ( ord_less_nat @ ( size_s642698393od_a_a @ D ) @ ( size_s642698393od_a_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_length__induct) ).
thf(391,plain,
! [A: list_P1467822637od_a_a > $o,B: list_P1467822637od_a_a] :
( ! [C: list_P1467822637od_a_a] :
( ! [D: list_P1467822637od_a_a] :
( ( ord_less_nat @ ( size_s642698393od_a_a @ D ) @ ( size_s642698393od_a_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(53,axiom,
! [A: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ A )
= ( ( A != zero_zero_nat )
& ( A
!= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_nat__grSuc0__conv) ).
thf(382,plain,
! [A: nat] :
( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ A )
= ( ( A != zero_zero_nat )
& ( A
!= ( suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(37,axiom,
! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a] :
( ( ( size_s642698393od_a_a @ A )
!= ( size_s642698393od_a_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_neq__if__length__neq) ).
thf(335,plain,
! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a] :
( ( ( size_s642698393od_a_a @ A )
!= ( size_s642698393od_a_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(168,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_infinite__descent) ).
thf(804,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(140,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_mult_Oassoc) ).
thf(704,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(103,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_less__zeroE) ).
thf(540,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(138,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_strict__inc__induct) ).
thf(681,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_zero__less__mult__pos2) ).
thf(377,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_nat_OdiscI) ).
thf(245,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(123,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_mult__nonneg__nonpos) ).
thf(616,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(22,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_zero__induct) ).
thf(271,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(118,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Ex__less__Suc) ).
thf(599,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(93,axiom,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_neq__if__length__neq) ).
thf(509,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)],[93]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_nat__neq__iff) ).
thf(434,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_mult__right__mono) ).
thf(477,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(48,axiom,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_not__gr__zero) ).
thf(367,plain,
! [A: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ A ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(170,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_mult__zero__left) ).
thf(816,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mult__less__mono2) ).
thf(609,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Suc__le__mono) ).
thf(323,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(6,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_diff__induct) ).
thf(213,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ zero_zero_nat )
=> ( ! [D: nat] : ( A @ zero_zero_nat @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(179,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Suc__lessE) ).
thf(848,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(75,axiom,
! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a] :
( ( size_s1052379225od_a_a @ ( produc1055075589od_a_a @ A @ B ) )
= ( times_times_nat @ ( size_s642698393od_a_a @ A ) @ ( size_s642698393od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_length__product) ).
thf(455,plain,
! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a] :
( ( size_s1052379225od_a_a @ ( produc1055075589od_a_a @ A @ B ) )
= ( times_times_nat @ ( size_s642698393od_a_a @ A ) @ ( size_s642698393od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(21,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_old_Onat_Odistinct_I1_J) ).
thf(267,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_nat__mult__less__cancel1) ).
thf(505,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(14,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Zero__neq__Suc) ).
thf(241,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(135,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_mult__zero__right) ).
thf(658,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_less__not__refl3) ).
thf(473,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(87,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_less__irrefl__nat) ).
thf(490,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(115,axiom,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_size__neq__size__imp__neq) ).
thf(589,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)],[115]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( divide_divide_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_div__less) ).
thf(531,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( divide_divide_nat @ A @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_mult__left__mono) ).
thf(487,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not__less__less__Suc__eq) ).
thf(516,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_mult__cancel__right) ).
thf(458,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(175,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_mult_Oleft__commute) ).
thf(836,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(161,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Ex__less__Suc2) ).
thf(776,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
| ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ B )
=> ( ord_less_nat @ A @ ( times_times_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_n__less__n__mult__m) ).
thf(525,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ B )
=> ( ord_less_nat @ A @ ( times_times_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(112,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( divide_divide_nat @ B @ C ) )
= ( ( ( C = zero_zero_nat )
& ( A @ zero_zero_nat ) )
| ? [D: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ C @ D ) @ B )
& ( ord_less_nat @ B @ ( times_times_nat @ C @ ( suc @ D ) ) )
& ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_split__div_H) ).
thf(580,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( divide_divide_nat @ B @ C ) )
= ( ( ( C = zero_zero_nat )
& ( A @ zero_zero_nat ) )
| ? [D: nat] :
( ( ord_less_eq_nat @ ( times_times_nat @ C @ D ) @ B )
& ( ord_less_nat @ B @ ( times_times_nat @ C @ ( suc @ D ) ) )
& ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(187,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ ( suc @ A ) @ B ) @ ( times_times_nat @ ( suc @ A ) @ C ) )
= ( ord_less_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Suc__mult__less__cancel1) ).
thf(872,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ ( suc @ A ) @ B ) @ ( times_times_nat @ ( suc @ A ) @ C ) )
= ( ord_less_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(23,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_old_Onat_Odistinct_I2_J) ).
thf(282,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_less__not__refl2) ).
thf(707,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_mult__pos__neg) ).
thf(409,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ B @ zero_zero_nat )
=> ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(164,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_mult__cancel2) ).
thf(791,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( A = C )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(71,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ B @ ( times_times_nat @ ( suc @ ( divide_divide_nat @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_less__div__Suc__mult) ).
thf(441,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ B @ ( times_times_nat @ ( suc @ ( divide_divide_nat @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(49,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_lift__Suc__mono__less) ).
thf(370,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_nat @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(91,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_not__less__zero) ).
thf(502,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_ordered__comm__semiring__class_Ocomm__mult__left__mono) ).
thf(470,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(184,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( divide_divide_nat @ B @ A ) @ C )
=> ( ord_less_nat @ B @ ( times_times_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_div__less__imp__less__mult) ).
thf(864,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( divide_divide_nat @ B @ A ) @ C )
=> ( ord_less_nat @ B @ ( times_times_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Suc__inject) ).
thf(314,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_nat__0__less__mult__iff) ).
thf(571,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(117,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
= ( divide_divide_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_div__mult__mult2) ).
thf(595,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
= ( divide_divide_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_nat__mult__eq__cancel1) ).
thf(612,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(182,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_All__less__Suc2) ).
thf(859,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ zero_zero_nat )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(178,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_neq0__conv) ).
thf(845,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(84,axiom,
( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
= ( suc @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(482,plain,
( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
= ( suc @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(89,axiom,
! [A: nat,B: nat] :
( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
& ( ord_less_eq_nat @ B @ zero_zero_nat ) )
| ( ( ord_less_eq_nat @ A @ zero_zero_nat )
& ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_split__mult__neg__le) ).
thf(495,plain,
! [A: nat,B: nat] :
( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
& ( ord_less_eq_nat @ B @ zero_zero_nat ) )
| ( ( ord_less_eq_nat @ A @ zero_zero_nat )
& ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(157,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_mult__not__zero) ).
thf(759,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(7,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Zero__not__Suc) ).
thf(218,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(159,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__antisym) ).
thf(771,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(16,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_nat_Odistinct_I1_J) ).
thf(250,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ zero_zero_nat ) )
= ( ( A = zero_zero_nat )
| ( A
= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_nat__leSuc0__conv) ).
thf(231,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ zero_zero_nat ) )
= ( ( A = zero_zero_nat )
| ( A
= ( suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( ( divide_divide_nat @ A @ B )
= zero_zero_nat )
= ( ( B = zero_zero_nat )
| ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_div__eq__0__conv) ).
thf(813,plain,
! [A: nat,B: nat] :
( ( ( divide_divide_nat @ A @ B )
= zero_zero_nat )
= ( ( B = zero_zero_nat )
| ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(32,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_n__not__Suc__n) ).
thf(319,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(128,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_less__not__refl) ).
thf(632,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(63,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 @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_mult__mono_H) ).
thf(418,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 @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(133,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_less__Suc0) ).
thf(652,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(43,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 @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_mult__mono) ).
thf(351,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 @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(25,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_zero__le) ).
thf(290,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_mult__cancel1) ).
thf(346,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( B = C )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(29,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_nat__induct) ).
thf(300,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(68,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_zero__less__mult__pos) ).
thf(432,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
=> ( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(174,axiom,
! [A: nat,B: nat] :
( ( ( divide_divide_nat @ A @ B )
= zero_zero_nat )
= ( ( ord_less_nat @ A @ B )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Euclidean__Division_Odiv__eq__0__iff) ).
thf(833,plain,
! [A: nat,B: nat] :
( ( ( divide_divide_nat @ A @ B )
= zero_zero_nat )
= ( ( ord_less_nat @ A @ B )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(185,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_bot__nat__0_Oextremum__strict) ).
thf(867,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(50,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_mult__cancel2__gr0) ).
thf(373,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(149,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_All__less__Suc) ).
thf(735,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(5,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_zero__reorient) ).
thf(210,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,axiom,
! [A: nat] :
? [B: list_P1467822637od_a_a] :
( ( size_s642698393od_a_a @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Ex__list__of__length) ).
thf(326,plain,
! [A: nat] :
? [B: list_P1467822637od_a_a] :
( ( size_s642698393od_a_a @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_mult__right__cancel) ).
thf(437,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(158,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_gr__implies__not__zero) ).
thf(767,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(137,axiom,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_infinite__descent0) ).
thf(664,plain,
! [A: nat > $o,B: nat] :
( ( A @ zero_zero_nat )
=> ( ! [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(57,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( divide_divide_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_nat__mult__div__cancel1) ).
thf(400,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( divide_divide_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(129,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ A @ B ) )
= ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ A )
& ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_one__le__mult__iff) ).
thf(635,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ A @ B ) )
= ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ A )
& ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(144,axiom,
k != zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(720,plain,
k != zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(62,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_bot__nat__0_Onot__eq__extremum) ).
thf(415,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(27,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_not0__implies__Suc) ).
thf(294,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_mult__pos__pos) ).
thf(801,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(176,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( divide_divide_nat @ B @ A ) @ C )
= ( ord_less_nat @ B @ ( times_times_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_div__less__conv) ).
thf(839,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ( ( ord_less_nat @ ( divide_divide_nat @ B @ A ) @ C )
= ( ord_less_nat @ B @ ( times_times_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(78,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_less__trans__Suc) ).
thf(464,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( suc @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(66,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_less__numeral__extra_I3_J) ).
thf(427,plain,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(99,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_nat__mult__less__cancel__disj) ).
thf(528,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
& ( ord_less_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(145,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_eq_nat @ C @ A )
=> ( B != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_greater__le__neq__conv) ).
thf(723,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_eq_nat @ C @ A )
=> ( B != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(4,axiom,
! [A: nat > $o] :
( ~ ( A @ zero_zero_nat )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_exists__least__lemma) ).
thf(200,plain,
! [A: nat > $o] :
( ~ ( A @ zero_zero_nat )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ A )
= ( ( A != zero_zero_nat )
& ( A
!= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_nat__geSucSuc0__conv) ).
thf(254,plain,
! [A: nat] :
( ( ord_less_eq_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ A )
= ( ( A != zero_zero_nat )
& ( A
!= ( suc @ zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Suc__less__eq2) ).
thf(354,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(104,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_nonzero__mult__div__cancel__right) ).
thf(543,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(8,axiom,
! [A: nat] :
( ( divide_divide_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_bits__div__0) ).
thf(222,plain,
! [A: nat] :
( ( divide_divide_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(47,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_mult__0) ).
thf(364,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1348,plain,
$false,
inference(e,[status(thm)],[234,555,333,628,741,379,655,385,747,340,404,257,357,587,619,189,228,448,638,853,421,870,756,238,574,821,480,602,774,292,452,661,534,714,798,297,424,407,429,788,729,260,862,349,467,484,625,329,461,493,583,522,519,650,725,188,388,593,499,225,339,753,537,547,622,701,738,779,605,343,360,311,558,794,412,750,513,824,264,856,444,819,562,732,843,286,743,577,711,641,391,382,335,804,704,540,681,377,245,616,271,599,509,434,477,367,816,609,323,213,848,455,267,505,241,658,473,490,589,531,487,516,458,836,776,525,580,872,282,707,409,791,441,370,502,470,864,314,571,595,612,859,845,482,495,759,218,771,250,231,813,319,632,418,652,351,290,346,300,432,833,867,373,735,210,326,437,767,664,400,635,720,415,294,801,839,464,427,528,723,200,254,354,543,222,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP103^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:54:39 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.91/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.85/1.11 % [INFO] Parsing done (351ms).
% 1.85/1.13 % [INFO] Running in sequential loop mode.
% 3.18/1.52 % [INFO] eprover registered as external prover.
% 3.18/1.53 % [INFO] Scanning for conjecture ...
% 3.38/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 3.57/1.76 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 4.16/1.96 % [INFO] Problem is higher-order (TPTP THF).
% 4.16/1.99 % [INFO] Type checking passed.
% 4.16/1.99 % [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 ...
% 16.16/4.68 % External prover 'e' found a proof!
% 16.16/4.68 % [INFO] Killing All external provers ...
% 16.16/4.68 % Time passed: 4349ms (effective reasoning time: 3543ms)
% 16.16/4.68 % 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)>
% 16.16/4.68 % Axioms used in derivation (185): fact_144_length__induct, fact_26_div__mult__mult1, fact_104_mult__cancel__left, fact_31_nat__less__induct, fact_82_less__Suc__eq__0__disj, fact_20_mult__cancel2, fact_107_div__by__0, fact_6_nat__0__less__mult__iff, fact_156_split__div_H, fact_19_lessI, fact_95_n__less__m__mult__n, fact_157_le__less__div__conv, fact_111_mult__left__cancel, fact_155_length__product, fact_166_zero__le, fact_145_Ex__list__of__length, fact_130_mult__cancel2__gr0, fact_93_Euclidean__Division_Oless__mult__imp__div__less, fact_14_bot__nat__0_Onot__eq__extremum, fact_172_nat__leSuc0__conv, fact_59_not__less__less__Suc__eq, fact_135_ab__semigroup__mult__class_Omult__ac_I1_J, fact_87_nat__mult__less__cancel1, fact_92_Euclidean__Division_Odiv__eq__0__iff, fact_65_Suc__less__eq2, fact_139_gr__zeroI, fact_160_le0, fact_41_old_Onat_Oexhaust, fact_47_nat__induct, fact_103_mult__eq__0__iff, fact_113_mult__neg__pos, fact_149_list__decode_Ocases, fact_88_nat__mult__eq__cancel1, fact_1_div__mult__self1__is__m, fact_167_ge__less__neq__conv, fact_36_nat__neq__iff, fact_147_neq__if__length__neq, fact_53_infinite__descent0, fact_23_mult__is__0, fact_119_mult__strict__left__mono, fact_78_Suc__mult__cancel1, fact_17_Suc__less__eq, fact_29_linorder__neqE__nat, fact_50_old_Onat_Odistinct_I2_J, fact_143_length__induct, fact_32_less__irrefl__nat, fact_40_old_Onat_Oinducts, fact_10_less__Suc0, fact_55_less__zeroE, fact_131_zero__reorient, fact_133_mult_Ocommute, fact_71_less__SucE, fact_125_div__less__conv, fact_21_mult__cancel1, fact_106_div__0, fact_181_mult__mono_H, fact_164_nat__mult__le__cancel__disj, fact_90_mult__less__mono1, fact_9_one__eq__mult__iff, fact_128_bits__div__by__0, fact_39_not0__implies__Suc, fact_153_length__product, fact_146_Ex__list__of__length, fact_57_not__gr0, fact_68_less__Suc__eq, fact_77_mult__0, fact_140_gr__implies__gr0, fact_180_mult__left__mono, fact_8_mult__eq__1__iff, fact_25_div__mult__mult2, fact_74_Suc__lessD, fact_109_divisors__zero, fact_79_div__mult2__eq, fact_137_gr__implies__not__zero, fact_67_not__less__eq, fact_129_not__gr__zero, fact_27_n__not__Suc__n, fact_44_Suc__neq__Zero, fact_120_mult__strict__right__mono, fact_98_nonzero__mult__div__cancel__right, fact_179_mult__right__mono, fact_60_strict__inc__induct, fact_110_no__zero__divisors, fact_49_old_Onat_Odistinct_I1_J, fact_151_less__numeral__extra_I3_J, fact_16_neq0__conv, fact_54_gr__implies__not0, fact_138_not__less__zero, fact_70_less__SucI, fact_34_less__not__refl2, fact_33_less__not__refl3, fact_169_greater__le__neq__conv, fact_132_mult_Oleft__commute, fact_69_Ex__less__Suc, fact_118_zero__less__mult__pos2, fact_48_nat_OdiscI, fact_51_nat_Odistinct_I1_J, fact_73_Suc__lessE, fact_170_le__greater__neq__conv, fact_121_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_102_mult__zero__right, fact_76_nat__mult__eq__cancel__disj, fact_52_bot__nat__0_Oextremum__strict, fact_4_div__by__Suc__0, fact_116_mult__pos__neg2, fact_85_gr0__conv__Suc, fact_42_Zero__not__Suc, fact_80_lift__Suc__mono__less__iff, fact_178_split__mult__neg__le, fact_114_mult__pos__neg, fact_84_All__less__Suc2, fact_86_Ex__less__Suc2, fact_115_mult__pos__pos, fact_168_less__ge__neq__conv, fact_63_Suc__less__SucD, fact_91_Suc__mult__less__cancel1, fact_56_not__less0, fact_72_Suc__lessI, fact_134_mult_Oassoc, fact_163_mult__le__cancel2, fact_148_neq__if__length__neq, fact_124_Util__Div_Oless__mult__imp__div__less, fact_89_mult__less__mono2, fact_75_Nat_OlessE, fact_81_lift__Suc__mono__less, fact_171_nat__geSucSuc0__conv, fact_165_le__numeral__extra_I3_J, fact_62_less__trans__Suc, fact_35_less__not__refl, fact_154_length__product, fact_142_nat__grSuc0__conv, fact_100_less__div__Suc__mult, fact_150_exists__least__lemma, fact_18_Suc__mono, fact_161_Suc__le__mono, fact_13_nat_Oinject, fact_176_mult__nonneg__nonpos, fact_64_less__antisym, fact_38_size__neq__size__imp__neq, fact_61_less__Suc__induct, fact_182_mult__mono, fact_5_mult__less__cancel2, conj_1, fact_175_mult__nonpos__nonneg, fact_127_bits__div__0, fact_174_mult__nonneg__nonpos2, fact_3_div__less, fact_94_n__less__n__mult__m, fact_105_mult__cancel__right, fact_117_zero__less__mult__pos, fact_83_gr0__implies__Suc, fact_7_nat__mult__less__cancel__disj, fact_158_le__zero__eq, fact_28_Suc__inject, fact_101_mult__zero__left, fact_45_zero__induct, fact_24_div__mult__mult1__if, fact_152_length__product, fact_122_div__eq__0__conv, fact_177_mult__nonneg__nonneg, fact_112_mult__right__cancel, fact_0_div__mult__self__is__m, fact_58_gr0I, fact_46_diff__induct, fact_173_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_12_old_Onat_Oinject, fact_159_bot__nat__0_Oextremum, fact_162_one__le__mult__iff, fact_136_zero__less__iff__neq__zero, fact_37_size__neq__size__imp__neq, fact_96_one__less__mult, fact_30_infinite__descent, fact_2_nat__mult__div__cancel__disj, fact_66_All__less__Suc, fact_22_mult__0__right, fact_99_nonzero__mult__div__cancel__left, fact_123_div__eq__0__conv_H, conj_0, fact_126_div__less__imp__less__mult, fact_97_nat__mult__div__cancel1, fact_43_Zero__neq__Suc, fact_15_less__nat__zero__code, fact_108_mult__not__zero, fact_141_nat__lessSucSuc0__conv, fact_11_zero__less__Suc
% 16.16/4.68 % No. of inferences in proof: 374
% 16.16/4.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4349 ms resp. 3543 ms w/o parsing
% 16.73/4.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.73/4.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------