TSTP Solution File: ITP103^2 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP103^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:22:56 EDT 2024
% Result : Theorem 18.39s 4.72s
% Output : Refutation 18.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 321
% Syntax : Number of formulae : 604 ( 179 unt; 40 typ; 0 def)
% Number of atoms : 1793 ( 614 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 7131 ( 212 ~; 66 |; 130 &;5915 @)
% ( 0 <=>; 808 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 6 con; 0-4 aty)
% Number of variables : 1561 ( 20 ^1460 !; 46 ?;1561 :)
% ( 35 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(size_type,type,
size:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(field_type,type,
field:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(mult_zero_type,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(ordered_ring_type,type,
ordered_ring:
!>[TA: $tType] : $o ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : $o ).
thf(division_ring_type,type,
division_ring:
!>[TA: $tType] : $o ).
thf(semiring_bits_type,type,
semiring_bits:
!>[TA: $tType] : $o ).
thf(semidom_divide_type,type,
semidom_divide:
!>[TA: $tType] : $o ).
thf(semigroup_mult_type,type,
semigroup_mult:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_ring_type,type,
linordered_ring:
!>[TA: $tType] : $o ).
thf(ordered_semiring_type,type,
ordered_semiring:
!>[TA: $tType] : $o ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(ordered_semiring_0_type,type,
ordered_semiring_0:
!>[TA: $tType] : $o ).
thf(ordere1490568538miring_type,type,
ordere1490568538miring:
!>[TA: $tType] : $o ).
thf(linord581940658strict_type,type,
linord581940658strict:
!>[TA: $tType] : $o ).
thf(semiri1193490041visors_type,type,
semiri1193490041visors:
!>[TA: $tType] : $o ).
thf(linord20386208strict_type,type,
linord20386208strict:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_type,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(linord893533164strict_type,type,
linord893533164strict:
!>[TA: $tType] : $o ).
thf(semiri1923998003cancel_type,type,
semiri1923998003cancel:
!>[TA: $tType] : $o ).
thf(euclid191655569cancel_type,type,
euclid191655569cancel:
!>[TA: $tType] : $o ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(product_type,type,
product:
!>[TA: $tType,TB: $tType] : ( ( list @ TB ) > ( list @ TA ) > ( list @ ( product_prod @ TB @ TA ) ) ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(divide_divide_type,type,
divide_divide:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(k_type,type,
k: nat ).
thf(n_type,type,
n: nat ).
thf(xs_type,type,
xs: list @ a ).
thf(132,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_mult__neg__neg) ).
thf(645,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Suc__less__eq2) ).
thf(629,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)],[126]) ).
thf(69,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( divide_divide @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ A @ ( times_times @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_divide__divide__eq__left_H) ).
thf(479,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( divide_divide @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ A @ ( times_times @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(196,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_mult__less__cancel__left__pos) ).
thf(846,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(249,axiom,
! [TA: $tType] :
( ( ordere1490568538miring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_ordered__comm__semiring__class_Ocomm__mult__left__mono) ).
thf(1031,plain,
! [TA: $tType] :
( ( ordere1490568538miring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(207,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Suc__neq__Zero) ).
thf(893,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',fact_64_less__Suc__induct) ).
thf(1083,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)],[269]) ).
thf(277,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= C )
=> ( B
= ( divide_divide @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_eq__divide__imp) ).
thf(1110,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= C )
=> ( B
= ( divide_divide @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Suc__inject) ).
thf(352,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Suc__lessI) ).
thf(683,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)],[144]) ).
thf(264,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_nat__less__induct) ).
thf(1068,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)],[264]) ).
thf(236,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/sandbox2/benchmark/theBenchmark.p',fact_89_Ex__less__Suc2) ).
thf(994,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)],[236]) ).
thf(265,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/sandbox2/benchmark/theBenchmark.p',fact_184_div__less__imp__less__mult) ).
thf(1073,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)],[265]) ).
thf(36,axiom,
! [TA: $tType] :
( ( ordered_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_mult__right__mono) ).
thf(379,plain,
! [TA: $tType] :
( ( ordered_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(55,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_mult__pos__neg2) ).
thf(440,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(142,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_zero__less__iff__neq__zero) ).
thf(677,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(253,axiom,
semigroup_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult) ).
thf(1041,plain,
semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(38,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_times__divide__eq__left) ).
thf(384,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(96,axiom,
ab_semigroup_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(550,plain,
ab_semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',fact_9_one__eq__mult__iff) ).
thf(500,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)],[77]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Suc__lessE) ).
thf(472,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)],[67]) ).
thf(262,axiom,
! [TA: $tType] :
( ( ordered_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_mult__right__mono__neg) ).
thf(1063,plain,
! [TA: $tType] :
( ( ordered_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_gr__implies__not0) ).
thf(670,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(152,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_list__decode_Ocases) ).
thf(709,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(229,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ C ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_mult__less__cancel__right__disj) ).
thf(973,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ C ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(104,axiom,
ordere1490568538miring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__comm__semiring) ).
thf(565,plain,
ordere1490568538miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(53,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_lift__Suc__mono__less) ).
thf(436,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(259,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_zero__less__divide__iff) ).
thf(1055,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(113,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_mult__strict__right__mono) ).
thf(587,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',fact_171_div__eq__0__conv_H) ).
thf(702,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)],[150]) ).
thf(26,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_2) ).
thf(344,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(93,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_gr__implies__not__zero) ).
thf(542,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(100,axiom,
semidom_divide @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__divide) ).
thf(559,plain,
semidom_divide @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(46,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
& ( ord_less @ TA @ C @ A )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_field__lbound__gt__zero) ).
thf(416,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
& ( ord_less @ TA @ C @ A )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(5,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_divide__nonpos__nonneg) ).
thf(289,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',fact_93_mult__less__mono1) ).
thf(448,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)],[58]) ).
thf(242,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_mult__strict__left__mono) ).
thf(1013,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(3,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_le__zero__eq) ).
thf(284,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_less__SucE) ).
thf(770,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)],[169]) ).
thf(176,axiom,
! [TA: $tType] :
( ( euclid191655569cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_div__mult__mult1__if) ).
thf(789,plain,
! [TA: $tType] :
( ( euclid191655569cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(17,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_divide__le__0__iff) ).
thf(321,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(35,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_zero__less__mult__iff) ).
thf(376,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',fact_79_nat__mult__eq__cancel__disj) ).
thf(514,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)],[83]) ).
thf(220,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_div__less) ).
thf(937,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)],[220]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_old_Onat_Oinject) ).
thf(348,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(182,axiom,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_mult__nonneg__nonpos2) ).
thf(806,plain,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ B @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(71,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Zero__neq__Suc) ).
thf(485,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',fact_65_less__trans__Suc) ).
thf(834,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)],[192]) ).
thf(128,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_nonzero__mult__div__cancel__left) ).
thf(634,plain,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(42,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__not__refl) ).
thf(396,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(137,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_less__not__refl3) ).
thf(660,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(80,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_mult__eq__0__iff) ).
thf(507,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(87,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( A != C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_le__greater__neq__conv) ).
thf(527,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( A != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(119,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_infinite__descent) ).
thf(602,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)],[119]) ).
thf(168,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/sandbox2/benchmark/theBenchmark.p',fact_188_mult__cancel2__gr0) ).
thf(766,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)],[168]) ).
thf(275,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_linorder__neqE__nat) ).
thf(1104,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)],[275]) ).
thf(197,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/sandbox2/benchmark/theBenchmark.p',fact_85_less__Suc__eq__0__disj) ).
thf(849,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)],[197]) ).
thf(12,axiom,
! [TA: $tType] :
( ( semiring_bits @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_bits__div__0) ).
thf(307,plain,
! [TA: $tType] :
( ( semiring_bits @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(222,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_divide__pos__neg) ).
thf(942,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(94,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_divide__strict__right__mono) ).
thf(546,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(184,axiom,
! [TA: $tType] :
( ( ordered_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_mult__left__mono__neg) ).
thf(810,plain,
! [TA: $tType] :
( ( ordered_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA] :
( ( size_size @ ( list @ ( product_prod @ TB @ TA ) ) @ ( product @ TB @ TA @ A @ B ) )
= ( times_times @ nat @ ( size_size @ ( list @ TB ) @ A ) @ ( size_size @ ( list @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_length__product) ).
thf(381,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA] :
( ( size_size @ ( list @ ( product_prod @ TB @ TA ) ) @ ( product @ TB @ TA @ A @ B ) )
= ( times_times @ nat @ ( size_size @ ( list @ TB ) @ A ) @ ( size_size @ ( list @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(90,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_mult__strict__right__mono__neg) ).
thf(534,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ B @ C ) @ ( times_times @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(178,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_1) ).
thf(798,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(22,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_divide__cancel__left) ).
thf(334,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(212,axiom,
! [TA: $tType] :
( ( ordered_semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_mult__mono) ).
thf(910,plain,
! [TA: $tType] :
( ( ordered_semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(161,axiom,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_lessI) ).
thf(746,plain,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(172,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_Ex__list__of__length) ).
thf(778,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',fact_98_n__less__m__mult__n) ).
thf(1042,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)],[254]) ).
thf(10,axiom,
! [TA: $tType] :
( ( semiring_bits @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_bits__div__by__0) ).
thf(302,plain,
! [TA: $tType] :
( ( semiring_bits @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(117,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_linorder__neqE__linordered__idom) ).
thf(598,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(188,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ C @ A ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_nonzero__mult__divide__mult__cancel__right) ).
thf(820,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ C @ A ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_nat_Oinject) ).
thf(297,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_divide__less__0__iff) ).
thf(424,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(147,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_mult__zero__right) ).
thf(693,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(186,axiom,
! [TA: $tType] :
( ( euclid191655569cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_div__mult__mult1) ).
thf(815,plain,
! [TA: $tType] :
( ( euclid191655569cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(105,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_bot__nat__0_Oextremum) ).
thf(566,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',fact_2_nat__mult__div__cancel__disj) ).
thf(361,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)],[33]) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',fact_212_le__less__div__conv) ).
thf(879,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)],[205]) ).
thf(198,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_divide__neg__neg) ).
thf(852,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',fact_90_nat__mult__less__cancel1) ).
thf(583,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)],[112]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Suc__mono) ).
thf(461,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)],[63]) ).
thf(74,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_divide__strict__right__mono__neg) ).
thf(493,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(166,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_mult__divide__mult__cancel__left__if) ).
thf(757,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(97,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_gr0__implies__Suc) ).
thf(551,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TB @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Nat_Osize_5) ).
thf(324,plain,
! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TB @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(267,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( times_times @ TA @ C @ A ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_mult__imp__div__pos__less) ).
thf(1079,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( times_times @ TA @ C @ A ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(247,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_less__numeral__extra_I3_J) ).
thf(1027,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(159,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( divide_divide @ TA @ C @ A ) )
= ( ord_less @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_neg__less__divide__eq) ).
thf(742,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( divide_divide @ TA @ C @ A ) )
= ( ord_less @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(134,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_nat__neq__iff) ).
thf(650,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)],[134]) ).
thf(272,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_divide__pos__pos) ).
thf(1096,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(31,axiom,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_mult__nonneg__nonpos) ).
thf(356,plain,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(174,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( divide_divide @ TA @ A @ ( divide_divide @ TA @ B @ C ) )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_divide__divide__eq__right) ).
thf(783,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( divide_divide @ TA @ A @ ( divide_divide @ TA @ B @ C ) )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',fact_217_one__le__mult__iff) ).
thf(420,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)],[47]) ).
thf(20,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_n__not__Suc__n) ).
thf(328,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_le__numeral__extra_I3_J) ).
thf(339,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',fact_91_nat__mult__eq__cancel1) ).
thf(933,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)],[219]) ).
thf(98,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_mult__zero__left) ).
thf(554,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(131,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_zero__le__mult__iff) ).
thf(642,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',fact_87_All__less__Suc2) ).
thf(637,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)],[129]) ).
thf(72,axiom,
! [TA: $tType] :
( ( ordered_ring @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_mult__nonpos__nonpos) ).
thf(489,plain,
! [TA: $tType] :
( ( ordered_ring @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(244,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= C )
= ( ( ( B
!= ( zero_zero @ TA ) )
=> ( A
= ( times_times @ TA @ C @ B ) ) )
& ( ( B
= ( zero_zero @ TA ) )
=> ( C
= ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_divide__eq__eq) ).
thf(1016,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= C )
= ( ( ( B
!= ( zero_zero @ TA ) )
=> ( A
= ( times_times @ TA @ C @ B ) ) )
& ( ( B
= ( zero_zero @ TA ) )
=> ( C
= ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(151,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_gr__zeroI) ).
thf(706,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(145,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Zero__not__Suc) ).
thf(686,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(68,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( divide_divide @ TA @ B @ C ) )
= ( ( ( C
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ C )
= B ) )
& ( ( C
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_eq__divide__eq) ).
thf(476,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( divide_divide @ TA @ B @ C ) )
= ( ( ( C
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ C )
= B ) )
& ( ( C
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(193,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__antisym) ).
thf(837,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)],[193]) ).
thf(233,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_nat__leSuc0__conv) ).
thf(984,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)],[233]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_measure__induct) ).
thf(569,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(78,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( ( divide_divide @ TA @ C @ A )
= ( divide_divide @ TA @ D @ B ) )
= ( ( times_times @ TA @ C @ B )
= ( times_times @ TA @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_frac__eq__eq) ).
thf(503,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( ( divide_divide @ TA @ C @ A )
= ( divide_divide @ TA @ D @ B ) )
= ( ( times_times @ TA @ C @ B )
= ( times_times @ TA @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__Suc__eq) ).
thf(393,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)],[41]) ).
thf(278,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_bot__nat__0_Oextremum__strict) ).
thf(1114,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',fact_6_nat__0__less__mult__iff) ).
thf(647,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)],[133]) ).
thf(237,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( divide_divide @ TA @ B @ C ) )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_times__divide__eq__right) ).
thf(997,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( divide_divide @ TA @ B @ C ) )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',fact_69_All__less__Suc) ).
thf(1050,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)],[257]) ).
thf(61,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(457,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(216,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_infinite__descent0__measure) ).
thf(921,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(136,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_mult__left__cancel) ).
thf(657,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(251,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/sandbox2/benchmark/theBenchmark.p',fact_219_nat__mult__le__cancel__disj) ).
thf(1035,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)],[251]) ).
thf(141,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_less__nat__zero__code) ).
thf(674,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(88,axiom,
ordered_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__semiring) ).
thf(530,plain,
ordered_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(170,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Suc__less__eq) ).
thf(773,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)],[170]) ).
thf(163,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_mult__strict__left__mono__neg) ).
thf(750,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(200,axiom,
! [TA: $tType] : ( size @ ( list @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_4) ).
thf(856,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(160,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).
thf(745,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(156,axiom,
! [TA: $tType] :
( ( euclid191655569cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ C @ A ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_div__mult__mult2) ).
thf(733,plain,
! [TA: $tType] :
( ( euclid191655569cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ C @ A ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(118,axiom,
ordered_semiring_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oordered__semiring__0) ).
thf(601,plain,
ordered_semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(82,axiom,
linord893533164strict @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).
thf(513,plain,
linord893533164strict @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(51,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_nonzero__mult__divide__mult__cancel__right2) ).
thf(430,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(210,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( divide_divide @ TA @ B @ A )
= C )
= ( B
= ( times_times @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_nonzero__divide__eq__eq) ).
thf(904,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( divide_divide @ TA @ B @ A )
= C )
= ( B
= ( times_times @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(48,axiom,
size @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(423,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',fact_63_strict__inc__induct) ).
thf(402,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)],[44]) ).
thf(6,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_divide__cancel__right) ).
thf(291,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_mult_Oleft__commute) ).
thf(413,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(195,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_neq0__conv) ).
thf(843,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',fact_1_div__mult__self1__is__m) ).
thf(1125,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)],[282]) ).
thf(204,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/sandbox2/benchmark/theBenchmark.p',fact_183_div__less__conv) ).
thf(875,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)],[204]) ).
thf(190,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_nat_OdiscI) ).
thf(826,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_mult__is__0) ).
thf(577,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)],[110]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_not__less__less__Suc__eq) ).
thf(445,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)],[57]) ).
thf(108,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
= ( times_times @ TA @ C @ A ) )
=> ( ( divide_divide @ TA @ B @ A )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_divide__eq__imp) ).
thf(572,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
= ( times_times @ TA @ C @ A ) )
=> ( ( divide_divide @ TA @ B @ A )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(14,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_zero__le) ).
thf(313,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(122,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_linordered__field__no__lb) ).
thf(611,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(65,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_mult__right__cancel) ).
thf(466,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(270,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_infinite__descent__measure) ).
thf(1090,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(92,axiom,
! [TA: $tType] :
( ( linord893533164strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(540,plain,
! [TA: $tType] :
( ( linord893533164strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(153,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__induct) ).
thf(713,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)],[153]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_gr__implies__gr0) ).
thf(498,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)],[76]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',fact_8_mult__eq__1__iff) ).
thf(1058,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)],[260]) ).
thf(276,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( divide_divide @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_divide__divide__eq__left) ).
thf(1107,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( divide_divide @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(231,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_mult__cancel__left) ).
thf(979,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(209,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_old_Onat_Oexhaust) ).
thf(900,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(191,axiom,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_mult__0) ).
thf(831,plain,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(279,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_mult__0__right) ).
thf(1117,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(59,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_less__irrefl__nat) ).
thf(451,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(16,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_zero__reorient) ).
thf(318,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',fact_82_div__mult2__eq) ).
thf(1122,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)],[281]) ).
thf(256,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ C )
=> ( ord_less @ TA @ B @ ( divide_divide @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_mult__imp__less__div__pos) ).
thf(1048,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ C )
=> ( ord_less @ TA @ B @ ( divide_divide @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',fact_218_mult__le__cancel2) ).
thf(736,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)],[157]) ).
thf(39,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less_eq @ TA @ B @ C )
=> ( A != C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_less__ge__neq__conv) ).
thf(387,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less_eq @ TA @ B @ C )
=> ( A != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(248,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_le0) ).
thf(1029,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(226,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( divide_divide @ TA @ B @ C ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ C ) @ B ) )
& ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ B @ ( times_times @ TA @ A @ C ) ) )
& ( ~ ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_less__divide__eq) ).
thf(964,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( divide_divide @ TA @ B @ C ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ C ) @ B ) )
& ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ B @ ( times_times @ TA @ A @ C ) ) )
& ( ~ ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(261,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_zero__less__mult__pos2) ).
thf(1061,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(27,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_divide__eq__0__iff) ).
thf(345,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(201,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_old_Onat_Oinducts) ).
thf(858,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)],[201]) ).
thf(179,axiom,
semiring_bits @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Parity_Osemiring__bits) ).
thf(799,plain,
semiring_bits @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(155,axiom,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_mult__not__zero) ).
thf(726,plain,
! [TA: $tType] :
( ( mult_zero @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(125,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ B @ A ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_nonzero__mult__div__cancel__right) ).
thf(626,plain,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ B @ A ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(214,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_mult__less__cancel__left__neg) ).
thf(915,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(43,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ ( suc @ A ) @ B )
= ( times_times @ nat @ ( suc @ A ) @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Suc__mult__cancel1) ).
thf(399,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)],[43]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',fact_100_nat__mult__div__cancel1) ).
thf(868,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)],[202]) ).
thf(206,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zero__induct) ).
thf(883,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)],[206]) ).
thf(243,axiom,
semiri1193490041visors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors) ).
thf(1015,plain,
semiri1193490041visors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(121,axiom,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_mult__cancel__right) ).
thf(608,plain,
! [TA: $tType] :
( ( semiri1923998003cancel @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(102,axiom,
semiri1923998003cancel @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel) ).
thf(563,plain,
semiri1923998003cancel @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(238,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( divide_divide @ TA @ C @ A ) )
= ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_pos__less__divide__eq) ).
thf(1000,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( divide_divide @ TA @ C @ A ) )
= ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_less__SucI) ).
thf(438,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(135,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_old_Onat_Odistinct_I1_J) ).
thf(653,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(213,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_gr0__conv__Suc) ).
thf(912,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(85,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ C )
= ( ord_less @ TA @ B @ ( times_times @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_pos__divide__less__eq) ).
thf(521,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ C )
= ( ord_less @ TA @ B @ ( times_times @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(266,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/sandbox2/benchmark/theBenchmark.p',fact_97_n__less__n__mult__m) ).
thf(1076,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)],[266]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',fact_72_Ex__less__Suc) ).
thf(589,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)],[114]) ).
thf(95,axiom,
( ( divide_divide @ nat @ ( size_size @ ( list @ a ) @ xs ) @ k )
= ( suc @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(548,plain,
( ( divide_divide @ nat @ ( size_size @ ( list @ a ) @ xs ) @ k )
= ( suc @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(185,axiom,
! [TA: $tType] :
( ( ordered_ring @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_split__mult__pos__le) ).
thf(812,plain,
! [TA: $tType] :
( ( ordered_ring @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(268,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_zero__less__mult__pos) ).
thf(1081,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(124,axiom,
! [A: nat > $o] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ~ ( A @ B )
& ( A @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_exists__least__lemma) ).
thf(617,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)],[124]) ).
thf(165,axiom,
( k
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(754,plain,
( k
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(89,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_not__less0) ).
thf(531,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',fact_56_infinite__descent0) ).
thf(944,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)],[223]) ).
thf(177,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ C )
= ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_neg__divide__less__eq) ).
thf(795,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ C )
= ( ord_less @ TA @ ( times_times @ TA @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(143,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ C @ A ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_divide__less__cancel) ).
thf(680,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ C @ A ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(62,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_not__gr0) ).
thf(458,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',fact_226_nat__geSucSuc0__conv) ).
thf(823,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)],[189]) ).
thf(171,axiom,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__less__Suc) ).
thf(776,plain,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(111,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_mult__less__0__iff) ).
thf(580,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(146,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_mult__le__0__iff) ).
thf(690,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(130,axiom,
! [TA: $tType] :
( ( linordered_ring @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( times_times @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_not__square__less__zero) ).
thf(640,plain,
! [TA: $tType] :
( ( linordered_ring @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( times_times @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(203,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ A ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_nonzero__mult__divide__mult__cancel__left2) ).
thf(872,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ A ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(228,axiom,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_mult__nonneg__nonneg) ).
thf(971,plain,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(158,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_gr0I) ).
thf(739,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(99,axiom,
! [TA: $tType] :
( ( linordered_ring @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_zero__le__square) ).
thf(557,plain,
! [TA: $tType] :
( ( linordered_ring @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',fact_78_Nat_OlessE) ).
thf(1003,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)],[239]) ).
thf(273,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/sandbox2/benchmark/theBenchmark.p',fact_7_nat__mult__less__cancel__disj) ).
thf(1098,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)],[273]) ).
thf(13,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_zero__le__divide__iff) ).
thf(310,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(258,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_not__less__zero) ).
thf(1053,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(252,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less_eq @ TA @ C @ A )
=> ( B != C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_greater__le__neq__conv) ).
thf(1038,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less_eq @ TA @ C @ A )
=> ( B != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',fact_20_mult__cancel2) ).
thf(840,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)],[194]) ).
thf(64,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ D ) )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_times__divide__times__eq) ).
thf(463,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ D ) )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(109,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Omult__zero) ).
thf(576,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(183,axiom,
! [TA: $tType] :
( ( ordered_semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_mult__mono_H) ).
thf(808,plain,
! [TA: $tType] :
( ( ordered_semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(211,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_not0__implies__Suc) ).
thf(907,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(246,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_old_Onat_Odistinct_I2_J) ).
thf(1023,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',fact_48_diff__induct) ).
thf(613,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)],[123]) ).
thf(240,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_mult__neg__pos) ).
thf(1008,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(116,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ A @ ( times_times @ TA @ C @ B ) ) )
& ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ B ) @ A ) )
& ( ~ ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_divide__less__eq) ).
thf(595,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ A @ ( times_times @ TA @ C @ B ) ) )
& ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ C @ B ) @ A ) )
& ( ~ ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(235,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ C ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_mult__less__cancel__left__disj) ).
thf(991,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ C ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(218,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Suc__lessD) ).
thf(931,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(70,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_lift__Suc__mono__less__iff) ).
thf(482,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(230,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ A )
= ( ( A
!= ( zero_zero @ nat ) )
& ( A
!= ( suc @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_nat__grSuc0__conv) ).
thf(976,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)],[230]) ).
thf(86,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__zeroE) ).
thf(524,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(75,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_divisors__zero) ).
thf(495,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( ( times_times @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(241,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_length__induct) ).
thf(1010,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',fact_170_div__eq__0__conv) ).
thf(699,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)],[149]) ).
thf(162,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_mult__pos__pos) ).
thf(748,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(274,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_not__less__eq) ).
thf(1101,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(29,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_3) ).
thf(351,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',fact_108_less__div__Suc__mult) ).
thf(390,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)],[40]) ).
thf(127,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_divide__neg__pos) ).
thf(632,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(175,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( divide_divide @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ D ) )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_divide__divide__times__eq) ).
thf(786,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( divide_divide @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ D ) )
= ( divide_divide @ TA @ ( times_times @ TA @ A @ D ) @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(173,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/sandbox2/benchmark/theBenchmark.p',fact_96_Euclidean__Division_Oless__mult__imp__div__less) ).
thf(781,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)],[173]) ).
thf(225,axiom,
wellorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(963,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__not__refl2) ).
thf(517,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(106,axiom,
euclid191655569cancel @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Euclidean__Division_Oeuclidean__semiring__cancel) ).
thf(568,plain,
euclid191655569cancel @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(139,axiom,
! [TA: $tType] :
( ( semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_mult_Oassoc) ).
thf(667,plain,
! [TA: $tType] :
( ( semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',fact_92_mult__less__mono2) ).
thf(763,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)],[167]) ).
thf(91,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_neq__if__length__neq) ).
thf(536,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(255,axiom,
! [A: nat] :
( ( divide_divide @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_div__by__Suc__0) ).
thf(1045,plain,
! [A: nat] :
( ( divide_divide @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',fact_211_split__div_H) ).
thf(433,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)],[52]) ).
thf(81,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_bot__nat__0_Onot__eq__extremum) ).
thf(510,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(180,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( suc @ ( zero_zero @ nat ) ) ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_nat__lessSucSuc0__conv) ).
thf(800,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)],[180]) ).
thf(4,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_divide__nonneg__nonpos) ).
thf(287,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_divide__right__mono) ).
thf(300,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(164,axiom,
! [TA: $tType] :
( ( ordered_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_mult__left__mono) ).
thf(752,plain,
! [TA: $tType] :
( ( ordered_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(15,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_division__ring__divide__zero) ).
thf(315,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(227,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_nat_Odistinct_I1_J) ).
thf(967,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(187,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ B @ A ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ C @ B ) @ ( divide_divide @ TA @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_divide__strict__left__mono) ).
thf(818,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ B @ A ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ C @ B ) @ ( divide_divide @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(199,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Suc__less__SucD) ).
thf(854,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)],[199]) ).
thf(103,axiom,
linord20386208strict @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semiring__strict) ).
thf(564,plain,
linord20386208strict @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(11,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_divide__nonpos__nonpos) ).
thf(305,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_divide__nonneg__nonneg) ).
thf(326,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(25,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_div__0) ).
thf(341,plain,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(79,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(506,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_measure__induct__rule) ).
thf(358,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(208,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ C @ A ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_mult__less__iff1) ).
thf(897,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( times_times @ TA @ B @ A ) @ ( times_times @ TA @ C @ A ) )
= ( ord_less @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',fact_94_Suc__mult__less__cancel1) ).
thf(664,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)],[138]) ).
thf(250,axiom,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_mult__pos__neg) ).
thf(1033,plain,
! [TA: $tType] :
( ( linord20386208strict @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',fact_21_mult__cancel1) ).
thf(960,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)],[224]) ).
thf(263,axiom,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_split__mult__neg__le) ).
thf(1065,plain,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(148,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_less__Suc0) ).
thf(696,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1,conjecture,
ord_less @ nat @ ( times_times @ nat @ n @ k ) @ ( size_size @ ( list @ a ) @ xs ),
file('/export/starexec/sandbox2/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(283,plain,
~ ( ord_less @ nat @ ( times_times @ nat @ n @ k ) @ ( size_size @ ( list @ a ) @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(217,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_mult_Ocommute) ).
thf(928,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(7,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_div__by__0) ).
thf(294,plain,
! [TA: $tType] :
( ( semidom_divide @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(215,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(918,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(271,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
= ( divide_divide @ TA @ C @ A ) )
= ( ( times_times @ TA @ B @ A )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_nonzero__eq__divide__eq) ).
thf(1093,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
= ( divide_divide @ TA @ C @ A ) )
= ( ( times_times @ TA @ B @ A )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(234,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/sandbox2/benchmark/theBenchmark.p',fact_0_div__mult__self__is__m) ).
thf(987,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)],[234]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(332,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_95_Euclidean__Division_Odiv__eq__0__iff) ).
thf(427,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)],[50]) ).
thf(245,axiom,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_size__neq__size__imp__neq) ).
thf(1019,plain,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(154,axiom,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_no__zero__divisors) ).
thf(723,plain,
! [TA: $tType] :
( ( semiri1193490041visors @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( ( times_times @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(232,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_linordered__field__no__ub) ).
thf(982,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(56,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_not__gr__zero) ).
thf(442,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(280,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ C @ A ) @ ( divide_divide @ TA @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_divide__strict__left__mono__neg) ).
thf(1120,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( times_times @ TA @ A @ B ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ C @ A ) @ ( divide_divide @ TA @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(34,axiom,
! [TA: $tType,A: nat > TA > $o,B: nat > TA > TA > $o] :
( ? [C: TA] : ( A @ ( zero_zero @ nat ) @ C )
=> ( ! [C: TA,D: nat] :
( ( A @ D @ C )
=> ? [E: TA] :
( ( A @ ( suc @ D ) @ E )
& ( B @ D @ C @ E ) ) )
=> ? [C: nat > TA] :
! [D: nat] :
( ( A @ D @ ( C @ D ) )
& ( B @ D @ ( C @ D ) @ ( C @ ( suc @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_dependent__nat__choice) ).
thf(369,plain,
! [TA: $tType,A: nat > TA > $o,B: nat > TA > TA > $o] :
( ? [C: TA] : ( A @ ( zero_zero @ nat ) @ C )
=> ( ! [C: TA,D: nat] :
( ( A @ D @ C )
=> ? [E: TA] :
( ( A @ ( suc @ D ) @ E )
& ( B @ D @ C @ E ) ) )
=> ? [C: nat > TA] :
! [D: nat] :
( ( A @ D @ ( C @ D ) )
& ( B @ D @ ( C @ D ) @ ( C @ ( suc @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(120,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(607,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Suc__le__mono) ).
thf(803,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)],[181]) ).
thf(23,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_divide__right__mono__neg) ).
thf(337,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',fact_5_mult__less__cancel2) ).
thf(560,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)],[101]) ).
thf(73,axiom,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_mult__nonpos__nonneg) ).
thf(491,plain,
! [TA: $tType] :
( ( ordered_semiring_0 @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( times_times @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',fact_99_one__less__mult) ).
thf(592,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)],[115]) ).
thf(60,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( B != C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_ge__less__neq__conv) ).
thf(454,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( B != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(66,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_nonzero__mult__divide__mult__cancel__left) ).
thf(469,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ A @ C ) )
= ( divide_divide @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(221,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/sandbox2/benchmark/theBenchmark.p',fact_172_Util__Div_Oless__mult__imp__div__less) ).
thf(940,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)],[221]) ).
thf(1211,plain,
$false,
inference(e,[status(thm)],[645,629,479,846,1031,893,1083,1110,352,683,1068,994,1073,379,440,677,1041,384,550,500,472,1063,670,709,973,565,436,1055,587,702,344,542,559,416,289,448,1013,284,770,789,321,376,514,937,348,806,485,834,634,396,660,507,527,602,766,1104,849,307,942,546,810,381,534,798,334,910,746,778,1042,302,598,820,297,424,693,815,566,361,879,852,583,461,493,757,551,324,1079,1027,742,650,1096,356,783,420,328,339,933,554,642,637,489,1016,706,686,476,837,984,569,503,393,1114,647,997,1050,457,921,657,1035,674,530,773,750,856,745,733,601,513,430,904,423,402,291,413,843,1125,875,826,577,445,572,313,611,466,1090,540,713,498,1058,1107,979,900,831,1117,451,318,1122,1048,736,387,1029,964,1061,345,858,799,726,626,915,399,868,883,1015,608,563,1000,438,653,912,521,1076,589,548,812,1081,617,754,531,944,795,680,458,823,776,580,690,640,872,971,739,557,1003,1098,310,1053,1038,840,463,576,808,907,1023,613,1008,595,991,931,482,976,524,495,1010,699,748,1101,351,390,632,786,781,963,517,568,667,763,536,1045,433,510,800,287,300,752,315,967,818,854,564,305,326,341,506,358,897,664,1033,960,1065,696,283,928,294,918,1093,987,332,427,1019,723,982,442,1120,369,607,803,337,560,491,592,454,469,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP103^2 : TPTP v8.2.0. Released v7.5.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 15:40:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.97/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.78/1.10 % [INFO] Parsing done (242ms).
% 1.78/1.11 % [INFO] Running in sequential loop mode.
% 2.60/1.32 % [INFO] eprover registered as external prover.
% 2.60/1.32 % [INFO] cvc4 registered as external prover.
% 2.60/1.33 % [INFO] Scanning for conjecture ...
% 2.75/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 280 axioms. Running axiom selection ...
% 3.19/1.51 % [INFO] Axiom selection finished. Selected 280 axioms (removed 0 axioms).
% 3.82/1.67 % [INFO] Problem is higher-order (TPTP THF).
% 3.82/1.69 % [INFO] Type checking passed.
% 3.82/1.69 % [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 ...
% 18.39/4.70 % External prover 'e' found a proof!
% 18.39/4.71 % [INFO] Killing All external provers ...
% 18.39/4.71 % Time passed: 4191ms (effective reasoning time: 3598ms)
% 18.39/4.71 % 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)>
% 18.39/4.72 % Axioms used in derivation (280): fact_26_div__mult__mult1, fact_166_divide__eq__imp, fact_113_mult__zero__right, fact_214_bot__nat__0_Oextremum, fact_20_mult__cancel2, fact_6_nat__0__less__mult__iff, fact_165_eq__divide__eq, fact_108_less__div__Suc__mult, fact_41_not0__implies__Suc, fact_19_lessI, fact_69_All__less__Suc, fact_67_less__antisym, fact_85_less__Suc__eq__0__disj, fact_188_mult__cancel2__gr0, tcon_Product__Type_Oprod___Nat_Osize_5, fact_181_divide__strict__left__mono, fact_134_divide__divide__eq__left_H, fact_160_zero__less__divide__iff, fact_136_not__square__less__zero, fact_98_n__less__m__mult__n, fact_138_mult__neg__pos, fact_40_size__neq__size__imp__neq, fact_14_bot__nat__0_Onot__eq__extremum, tcon_Nat_Onat___Orderings_Olinorder, fact_236_mult__right__mono, fact_70_not__less__eq, tcon_Nat_Onat___Nat_Osize, fact_217_one__le__mult__iff, fact_140_mult__pos__pos, fact_77_Suc__lessD, fact_215_le0, fact_43_old_Onat_Oexhaust, fact_129_no__zero__divisors, fact_95_Euclidean__Division_Odiv__eq__0__iff, fact_51_old_Onat_Odistinct_I1_J, fact_63_strict__inc__induct, fact_240_mult__left__mono__neg, fact_114_mult__eq__0__iff, fact_153_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_163_frac__eq__eq, fact_110_divide__divide__eq__right, fact_60_not__gr0, fact_94_Suc__mult__less__cancel1, fact_159_divide__less__cancel, fact_84_lift__Suc__mono__less, fact_82_div__mult2__eq, fact_224_greater__le__neq__conv, fact_167_eq__divide__imp, fact_1_div__mult__self1__is__m, fact_101_nonzero__mult__divide__mult__cancel__right2, fact_190_mult_Oleft__commute, fact_142_zero__less__mult__iff, fact_28_measure__induct, fact_189_zero__reorient, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors, fact_178_pos__less__divide__eq, fact_97_n__less__n__mult__m, fact_23_mult__is__0, fact_52_old_Onat_Odistinct_I2_J, fact_88_gr0__conv__Suc, fact_99_one__less__mult, fact_135_mult__neg__neg, fact_122_division__ring__divide__zero, fact_115_mult__cancel__left, fact_73_less__SucI, fact_17_Suc__less__eq, fact_231_mult__nonpos__nonneg, fact_172_Util__Div_Oless__mult__imp__div__less, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, fact_176_neg__less__divide__eq, fact_10_less__Suc0, tcon_Nat_Onat___Rings_Oordered__semiring, fact_216_Suc__le__mono, fact_76_Suc__lessE, fact_21_mult__cancel1, fact_184_div__less__imp__less__mult, fact_208_field__lbound__gt__zero, fact_9_one__eq__mult__iff, fact_198_gr__implies__gr0, fact_221_zero__le, fact_105_nonzero__mult__div__cancel__left, fact_248_divide__nonneg__nonpos, fact_55_bot__nat__0_Oextremum__strict, tcon_List_Olist___Nat_Osize_4, fact_36_less__not__refl3, fact_132_times__divide__times__eq, fact_124_linordered__field__no__lb, fact_187_not__gr__zero, fact_205_list__decode_Ocases, tcon_Nat_Onat___Groups_Oab__semigroup__mult, fact_202_length__induct, fact_168_nonzero__divide__eq__eq, fact_120_divide__cancel__left, fact_92_mult__less__mono2, fact_173_divide__less__eq, fact_141_mult__pos__neg2, fact_90_nat__mult__less__cancel1, fact_243_mult__mono_H, fact_74_less__SucE, fact_107_mult__divide__mult__cancel__left__if, fact_200_nat__grSuc0__conv, fact_118_divide__eq__0__iff, fact_180_mult__imp__less__div__pos, fact_53_nat_Odistinct_I1_J, fact_8_mult__eq__1__iff, fact_89_Ex__less__Suc2, fact_46_Suc__neq__Zero, fact_123_times__divide__eq__left, fact_25_div__mult__mult2, fact_148_mult__strict__left__mono, fact_239_mult__nonpos__nonpos, fact_218_mult__le__cancel2, fact_242_zero__le__square, fact_226_nat__geSucSuc0__conv, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel, fact_30_Suc__inject, fact_93_mult__less__mono1, fact_195_gr__implies__not__zero, fact_183_div__less__conv, fact_126_linorder__neqE__linordered__idom, fact_83_lift__Suc__mono__less__iff, fact_27_measure__induct__rule, fact_152_mult__less__cancel__right__disj, fact_62_not__less__less__Suc__eq, fact_86_gr0__implies__Suc, fact_220_le__numeral__extra_I3_J, fact_116_mult__cancel__right, fact_186_bits__div__by__0, tcon_Nat_Onat___Orderings_Owellorder, fact_229_zero__le__mult__iff, fact_162_divide__strict__right__mono__neg, tcon_Nat_Onat___Groups_Ozero, fact_197_gr__zeroI, fact_35_less__irrefl__nat, fact_75_Suc__lessI, fact_119_div__by__0, fact_16_neq0__conv, fact_223_less__ge__neq__conv, fact_102_nonzero__mult__div__cancel__right, fact_4_div__by__Suc__0, fact_64_less__Suc__induct, fact_39_nat__neq__iff, fact_175_neg__divide__less__eq, fact_161_divide__strict__right__mono, fact_112_mult__zero__left, fact_185_bits__div__0, tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict, fact_203_Ex__list__of__length, fact_244_mult__mono, fact_147_mult__strict__left__mono__neg, fact_228_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_170_div__eq__0__conv, fact_171_div__eq__0__conv_H, fact_174_less__divide__eq, fact_49_nat__induct, fact_192_mult_Oassoc, fact_206_dependent__nat__choice, fact_37_less__not__refl2, fact_232_mult__nonneg__nonpos, fact_79_nat__mult__eq__cancel__disj, fact_131_mult__right__cancel, fact_32_linorder__neqE__nat, fact_80_mult__0, tcon_Nat_Onat___Euclidean__Division_Oeuclidean__semiring__cancel, fact_149_mult__less__cancel__left__disj, fact_104_nonzero__mult__divide__mult__cancel__left2, fact_117_div__0, fact_96_Euclidean__Division_Oless__mult__imp__div__less, tcon_Nat_Onat___Parity_Osemiring__bits, fact_29_n__not__Suc__n, tcon_Nat_Onat___Rings_Omult__zero, tcon_Nat_Onat___Rings_Oordered__semiring__0, fact_158_divide__less__0__iff, fact_251_divide__right__mono, fact_103_nonzero__mult__divide__mult__cancel__right, fact_209_less__numeral__extra_I3_J, fact_72_Ex__less__Suc, fact_201_mult__less__iff1, fact_234_split__mult__neg__le, fact_204_neq__if__length__neq, fact_100_nat__mult__div__cancel1, fact_194_zero__less__iff__neq__zero, fact_109_times__divide__eq__right, fact_42_old_Onat_Oinducts, fact_18_Suc__mono, fact_213_le__zero__eq, fact_13_nat_Oinject, fact_5_mult__less__cancel2, fact_196_not__less__zero, fact_34_nat__less__induct, fact_250_zero__le__divide__iff, fact_143_zero__less__mult__pos, fact_252_divide__le__0__iff, fact_139_mult__pos__neg, fact_210_length__product, tcon_HOL_Obool___Orderings_Oorder_3, fact_155_divide__neg__pos, fact_44_Zero__not__Suc, fact_179_mult__imp__div__pos__less, fact_235_mult__le__0__iff, fact_121_divide__cancel__right, fact_81_Suc__mult__cancel1, conj_1, fact_61_gr0I, fact_199_nat__lessSucSuc0__conv, fact_207_exists__least__lemma, fact_219_nat__mult__le__cancel__disj, fact_3_div__less, tcon_HOL_Obool___Orderings_Olinorder_2, fact_50_nat_OdiscI, fact_225_le__greater__neq__conv, fact_233_mult__nonneg__nonneg, fact_45_Zero__neq__Suc, fact_144_zero__less__mult__pos2, fact_65_less__trans__Suc, fact_87_All__less__Suc2, fact_157_divide__pos__pos, fact_7_nat__mult__less__cancel__disj, fact_133_divide__divide__times__eq, fact_130_mult__left__cancel, fact_177_pos__divide__less__eq, fact_212_le__less__div__conv, fact_48_diff__induct, fact_56_infinite__descent0, fact_24_div__mult__mult1__if, fact_227_nat__leSuc0__conv, fact_78_Nat_OlessE, fact_156_divide__pos__neg, fact_59_not__less0, fact_241_split__mult__pos__le, fact_151_mult__strict__right__mono, fact_247_divide__nonpos__nonneg, fact_191_mult_Ocommute, fact_145_mult__less__cancel__left__neg, fact_111_divide__divide__eq__left, tcon_Nat_Onat___Rings_Oordered__comm__semiring, tcon_fun___Orderings_Oorder, fact_0_div__mult__self__is__m, fact_57_gr__implies__not0, tcon_Nat_Onat___Orderings_Oorder_1, fact_66_Suc__less__SucD, fact_54_infinite__descent0__measure, fact_91_nat__mult__eq__cancel1, fact_58_less__zeroE, tcon_Nat_Onat___Groups_Osemigroup__mult, fact_12_old_Onat_Oinject, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_238_mult__left__mono, fact_2_nat__mult__div__cancel__disj, fact_164_divide__eq__eq, tcon_Nat_Onat___Rings_Osemidom__divide, fact_249_divide__nonneg__nonneg, fact_237_mult__right__mono__neg, fact_38_less__not__refl, tcon_Nat_Onat___Rings_Olinordered__semiring__strict, fact_128_divisors__zero, fact_154_divide__neg__neg, fact_22_mult__0__right, fact_71_less__Suc__eq, fact_31_infinite__descent__measure, conj_0, fact_33_infinite__descent, fact_150_mult__strict__right__mono__neg, fact_169_nonzero__eq__divide__eq, fact_246_divide__nonpos__nonpos, fact_68_Suc__less__eq2, fact_15_less__nat__zero__code, fact_222_ge__less__neq__conv, fact_146_mult__less__cancel__left__pos, fact_182_divide__strict__left__mono__neg, fact_127_mult__not__zero, fact_211_split__div_H, fact_47_zero__induct, fact_245_divide__right__mono__neg, fact_125_linordered__field__no__ub, fact_106_nonzero__mult__divide__mult__cancel__left, fact_193_ab__semigroup__mult__class_Omult__ac_I1_J, fact_11_zero__less__Suc, fact_230_mult__nonneg__nonpos2, fact_137_mult__less__0__iff
% 18.39/4.72 % No. of inferences in proof: 564
% 18.39/4.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4191 ms resp. 3598 ms w/o parsing
% 18.84/4.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.84/4.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------