TSTP Solution File: DAT162^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT162^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 : Tue May 7 07:39:38 EDT 2024
% Result : Theorem 59.81s 22.55s
% Output : Refutation 60.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 326
% Syntax : Number of formulae : 608 ( 153 unt; 46 typ; 0 def)
% Number of atoms : 1695 ( 356 equ; 2 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 6408 ( 232 ~; 72 |; 101 &;5123 @)
% ( 0 <=>; 880 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 216 ( 216 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 11 con; 0-4 aty)
% Number of variables : 1653 ( 46 ^1491 !; 78 ?;1653 :)
% ( 38 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(dvd_type,type,
dvd:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(one_type,type,
one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_gcd_type,type,
semiring_gcd:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(no_bot_type,type,
no_bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(no_top_type,type,
no_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_mult_type,type,
semigroup_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(dense_order_type,type,
dense_order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(comm_monoid_mult_type,type,
comm_monoid_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(algebraic_semidom_type,type,
algebraic_semidom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(dense_linorder_type,type,
dense_linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(coindu351974385stinct_type,type,
coindu351974385stinct:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lfinite_type,type,
coinductive_lfinite:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_LNil_type,type,
coinductive_LNil:
!>[TA: $tType] : ( coinductive_llist @ TA ) ).
thf(coinductive_lnull_type,type,
coinductive_lnull:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lset_type,type,
coinductive_lset:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( set @ TA ) ) ).
thf(coinductive_lmember_type,type,
coinductive_lmember:
!>[TA: $tType] : ( TA > ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lsetp_type,type,
coinductive_lsetp:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > TA > $o ) ).
thf(coindu63249387sorted_type,type,
coindu63249387sorted:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(hammin2015774020amming_type,type,
hammin2015774020amming: coinductive_llist @ nat ).
thf(hammin1328233080lmerge_type,type,
hammin1328233080lmerge:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(hammin1138290136lmerge_type,type,
hammin1138290136lmerge:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(hammin1195055315smooth_type,type,
hammin1195055315smooth: nat > $o ).
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(prime_type,type,
prime: nat > $o ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(dvd_dvd_type,type,
dvd_dvd:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(n_type,type,
n: nat ).
thf(n2_type,type,
n2: nat ).
thf(na_type,type,
na: nat ).
thf(p_type,type,
p: nat ).
thf(124,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_lappend_Oexhaust) ).
thf(645,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(182,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_semiring__normalization__rules_I18_J) ).
thf(809,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(118,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_order_Ostrict__trans) ).
thf(629,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(211,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_nat__le__linear) ).
thf(893,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(173,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_minf_I1_J) ).
thf(777,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(280,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_infinite__descent__measure) ).
thf(1068,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)],[280]) ).
thf(269,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( dvd_dvd @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_gcd__nat_Oantisym) ).
thf(1041,plain,
! [A: nat,B: nat] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( dvd_dvd @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(43,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_lnull__imp__lfinite) ).
thf(408,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( coinductive_lfinite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(245,axiom,
dvd_dvd @ nat @ p @ na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__092_060open_062p_Advd_An_092_060close_062) ).
thf(977,plain,
dvd_dvd @ nat @ p @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(55,axiom,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( dvd_dvd @ TA @ B @ ( one_one @ TA ) )
=> ( dvd_dvd @ TA @ ( times_times @ TA @ A @ B ) @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_unit__prod) ).
thf(440,plain,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( dvd_dvd @ TA @ B @ ( one_one @ TA ) )
=> ( dvd_dvd @ TA @ ( times_times @ TA @ A @ B ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(77,axiom,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_unit__mult__left__cancel) ).
thf(511,plain,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( ( times_times @ TA @ A @ B )
= ( times_times @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(31,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_dual__order_Orefl) ).
thf(384,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_le__funI) ).
thf(550,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(66,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_LNil) ).
thf(472,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(184,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( coindu63249387sorted @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_lsorted__lmerge) ).
thf(814,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( coindu63249387sorted @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(145,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_dual__order_Oasym) ).
thf(698,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(235,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_nat__mult__eq__1__iff) ).
thf(945,plain,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( one_one @ nat ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ B @ C )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_pinf_I11_J) ).
thf(340,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(229,axiom,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_nat__mult__1) ).
thf(930,plain,
! [A: nat] :
( ( times_times @ nat @ ( one_one @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(133,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_semiring__normalization__rules_I11_J) ).
thf(670,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(163,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_minf_I4_J) ).
thf(747,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(220,axiom,
ab_semigroup_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(913,plain,
ab_semigroup_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(190,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ~ ( coinductive_lfinite @ TA @ C )
=> ( ? [D: TA] :
( ( member @ TA @ D @ ( coinductive_lset @ TA @ C ) )
& ( ord_less_eq @ TA @ A @ D ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1138290136lmerge @ TA @ C @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_in__lset__lmergeI2) ).
thf(829,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ~ ( coinductive_lfinite @ TA @ C )
=> ( ? [D: TA] :
( ( member @ TA @ D @ ( coinductive_lset @ TA @ C ) )
& ( ord_less_eq @ TA @ A @ D ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1138290136lmerge @ TA @ C @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(214,axiom,
comm_semiring_1 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(898,plain,
comm_semiring_1 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(253,axiom,
coindu63249387sorted @ nat @ hammin2015774020amming,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_lsorted__hamming) ).
thf(1001,plain,
coindu63249387sorted @ nat @ hammin2015774020amming,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_order__less__subst1) ).
thf(709,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(243,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( coindu351974385stinct @ TA @ A )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( ( ( coinductive_lset @ TA @ A )
= ( coinductive_lset @ TA @ B ) )
=> ( A = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_lsorted__ldistinct__lset__unique) ).
thf(973,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( coindu351974385stinct @ TA @ A )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( ( ( coinductive_lset @ TA @ A )
= ( coinductive_lset @ TA @ B ) )
=> ( A = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(5,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_le__cases) ).
thf(288,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ C @ ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_semiring__normalization__rules_I15_J) ).
thf(301,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ C @ ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_dense__ge__bounded) ).
thf(320,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(126,axiom,
prime @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__092_060open_062prime_Ap_092_060close_062) ).
thf(651,plain,
prime @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(34,axiom,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_ldistinct_OLNil) ).
thf(389,plain,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(179,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_dual__order_Ostrict__implies__order) ).
thf(802,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(63,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ B )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__1__mult) ).
thf(460,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ B )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( times_times @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(275,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_nat__neq__iff) ).
thf(1055,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(155,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_less__imp__neq) ).
thf(724,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(103,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_not__less__iff__gr__or__eq) ).
thf(587,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(194,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_less__mono__imp__le__mono) ).
thf(838,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(223,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_less__not__refl3) ).
thf(917,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(147,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_less__asym) ).
thf(702,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_le__funD) ).
thf(751,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(231,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ~ ( ( dvd_dvd @ nat @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_gcd__nat_Oasym) ).
thf(934,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ~ ( ( dvd_dvd @ nat @ B @ A )
& ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(25,axiom,
! [TA: $tType] :
( ( dvd @ TA @ ( type2 @ TA ) )
=> ( ( dvd_dvd @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( times_times @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_dvd__def) ).
thf(357,plain,
! [TA: $tType] :
( ( dvd @ TA @ ( type2 @ TA ) )
=> ( ( dvd_dvd @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( times_times @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(121,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ ( times_times @ TA @ A @ B ) @ C )
=> ( dvd_dvd @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_dvd__mult__right) ).
thf(638,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ ( times_times @ TA @ A @ B ) @ C )
=> ( dvd_dvd @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(48,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_semiring__normalization__rules_I12_J) ).
thf(421,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(242,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_eq__imp__le) ).
thf(969,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(46,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_dual__order_Otrans) ).
thf(416,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(225,axiom,
hammin1195055315smooth @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062smooth_An_H_092_060close_062) ).
thf(924,plain,
hammin1195055315smooth @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_le__fun__def) ).
thf(756,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(78,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_less__imp__not__less) ).
thf(514,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_ord__le__eq__trans) ).
thf(574,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(181,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_lmerge_Oexhaust) ).
thf(806,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(241,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_less__not__refl) ).
thf(966,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(70,axiom,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_lmember__code_I1_J) ).
thf(480,plain,
! [TA: $tType,A: TA] :
~ ( coinductive_lmember @ TA @ A @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(38,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) )
=> ( ( coinductive_lfinite @ TA @ A )
| ( coinductive_lfinite @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_lfinite__lmergeD) ).
thf(397,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) )
=> ( ( coinductive_lfinite @ TA @ A )
| ( coinductive_lfinite @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(7,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_ord__eq__le__trans) ).
thf(293,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(205,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_le__refl) ).
thf(866,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(60,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_order_Otrans) ).
thf(453,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(198,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ na )
=> ( ( hammin1195055315smooth @ A )
=> ( member @ nat @ A @ ( coinductive_lset @ nat @ hammin2015774020amming ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_less_OIH) ).
thf(849,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ na )
=> ( ( hammin1195055315smooth @ A )
=> ( member @ nat @ A @ ( coinductive_lset @ nat @ hammin2015774020amming ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(234,axiom,
! [A: nat,B: nat] :
( ( prime @ ( times_times @ nat @ A @ B ) )
=> ( ( A
= ( one_one @ nat ) )
| ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_prime__product) ).
thf(942,plain,
! [A: nat,B: nat] :
( ( prime @ ( times_times @ nat @ A @ B ) )
=> ( ( A
= ( one_one @ nat ) )
| ( B
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_lzip_Oexhaust) ).
thf(678,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(176,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_linorder__neqE__linordered__idom) ).
thf(793,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ 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)],[176]) ).
thf(226,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_nat__less__le) ).
thf(925,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(168,axiom,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_unit__mult__right__cancel) ).
thf(761,plain,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(84,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_order_Oasym) ).
thf(534,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(152,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_lnull__lmerge) ).
thf(714,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(187,axiom,
( prime
= ( ^ [A: nat] :
( ( ord_less @ nat @ ( one_one @ nat ) @ A )
& ! [B: nat] :
( ( dvd_dvd @ nat @ B @ A )
=> ( ( B
= ( one_one @ nat ) )
| ( B = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_prime__def) ).
thf(825,plain,
( prime
= ( ^ [A: nat] :
( ( ord_less @ nat @ ( one_one @ nat ) @ A )
& ! [B: nat] :
( ( dvd_dvd @ nat @ B @ A )
=> ( ( B
= ( one_one @ nat ) )
| ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_gcd__nat_Ostrict__implies__not__eq) ).
thf(1021,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(108,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LNil @ TA ) @ B )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_ord_Olmerge__LNil_I1_J) ).
thf(598,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( hammin1328233080lmerge @ TA @ A @ ( coinductive_LNil @ TA ) @ B )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(95,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) )
= ( ( coinductive_lnull @ TA @ B )
| ( coinductive_lnull @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_ord_Olnull__lmerge) ).
thf(561,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) )
= ( ( coinductive_lnull @ TA @ B )
| ( coinductive_lnull @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(36,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_minf_I8_J) ).
thf(392,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(8,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_less__imp__not__eq) ).
thf(297,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_less__asym_H) ).
thf(424,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(142,axiom,
hammin1195055315smooth @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_assms) ).
thf(693,plain,
hammin1195055315smooth @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(175,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( ( hammin1328233080lmerge @ TA @ C @ A @ B )
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_ord_Olmerge_Octr_I1_J) ).
thf(788,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( ( hammin1328233080lmerge @ TA @ C @ A @ B )
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(203,axiom,
ord @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_3) ).
thf(862,plain,
ord @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(22,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_lfinite__LNil) ).
thf(349,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(222,axiom,
order @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_2) ).
thf(916,plain,
order @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(72,axiom,
! [TA: $tType] :
( ( no_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_lt__ex) ).
thf(484,plain,
! [TA: $tType] :
( ( no_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(266,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_mult__le__mono2) ).
thf(1032,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ C @ A ) @ ( times_times @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(116,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_minf_I7_J) ).
thf(625,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(208,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( ( dvd_dvd @ nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd @ nat @ A @ C )
& ( A != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_gcd__nat_Ostrict__trans1) ).
thf(879,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( ( dvd_dvd @ nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd @ nat @ A @ C )
& ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(53,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_lsorted__code_I1_J) ).
thf(435,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( coindu63249387sorted @ TA @ ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(131,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_minf_I6_J) ).
thf(665,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(138,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_semiring__normalization__rules_I17_J) ).
thf(682,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ 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)],[138]) ).
thf(195,axiom,
! [A: nat,B: nat] :
( ( hammin1195055315smooth @ ( times_times @ nat @ A @ B ) )
= ( ( hammin1195055315smooth @ A )
& ( hammin1195055315smooth @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_smooth__times) ).
thf(842,plain,
! [A: nat,B: nat] :
( ( hammin1195055315smooth @ ( times_times @ nat @ A @ B ) )
= ( ( hammin1195055315smooth @ A )
& ( hammin1195055315smooth @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(15,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_less__not__sym) ).
thf(324,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(259,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( coinductive_lsetp @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Coinductive__List_Olset__into__lsetp) ).
thf(1012,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( coinductive_lsetp @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(4,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ ( times_times @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_semiring__normalization__rules_I14_J) ).
thf(285,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ ( times_times @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [TA: $tType] :
( ( dvd @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_dvdE) ).
thf(317,plain,
! [TA: $tType] :
( ( dvd @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(236,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_linorder__neqE__nat) ).
thf(948,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)],[236]) ).
thf(262,axiom,
monoid_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__mult) ).
thf(1017,plain,
monoid_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_ord__eq__le__subst) ).
thf(615,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(278,axiom,
comm_monoid_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(1064,plain,
comm_monoid_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(41,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_order_Onot__eq__order__implies__strict) ).
thf(403,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(256,axiom,
! [A: nat] : ( dvd_dvd @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_gcd__nat_Orefl) ).
thf(1006,plain,
! [A: nat] : ( dvd_dvd @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(106,axiom,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( dvd_dvd @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_unit__imp__dvd) ).
thf(593,plain,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( dvd_dvd @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(250,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_less__imp__le__nat) ).
thf(989,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(201,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_le__square) ).
thf(857,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(80,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ ( times_times @ TA @ A @ B ) @ C )
=> ( dvd_dvd @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_dvd__mult__left) ).
thf(519,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ ( times_times @ TA @ A @ B ) @ C )
=> ( dvd_dvd @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(161,axiom,
! [TA: $tType] :
( ( dense_order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_dense) ).
thf(742,plain,
! [TA: $tType] :
( ( dense_order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(100,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( dvd_dvd @ TA @ A @ ( times_times @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dvd__mult) ).
thf(578,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( dvd_dvd @ TA @ A @ ( times_times @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(230,axiom,
dvd @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Odvd) ).
thf(933,plain,
dvd @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(68,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ~ ( coinductive_lfinite @ TA @ B )
=> ~ ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_linfinite__lmerge) ).
thf(476,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ~ ( coinductive_lfinite @ TA @ B )
=> ~ ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_order__subst1) ).
thf(642,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(89,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_mult_Oleft__neutral) ).
thf(547,plain,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(92,axiom,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_lfinite__code_I1_J) ).
thf(554,plain,
! [TA: $tType] : ( coinductive_lfinite @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_order__less__subst2) ).
thf(753,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(261,axiom,
no_top @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top) ).
thf(1016,plain,
no_top @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(104,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( dvd_dvd @ TA @ ( one_one @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_one__dvd) ).
thf(590,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( dvd_dvd @ TA @ ( one_one @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(115,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA] :
( ( hammin1138290136lmerge @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_lmerge__LNil_I1_J) ).
thf(622,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA] :
( ( hammin1138290136lmerge @ TA @ ( coinductive_LNil @ TA ) @ A )
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(252,axiom,
! [A: nat,B: nat,C: nat] :
( ( prime @ A )
=> ( ( dvd_dvd @ nat @ A @ ( times_times @ nat @ B @ C ) )
= ( ( dvd_dvd @ nat @ A @ B )
| ( dvd_dvd @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_prime__dvd__mult__eq__nat) ).
thf(997,plain,
! [A: nat,B: nat,C: nat] :
( ( prime @ A )
=> ( ( dvd_dvd @ nat @ A @ ( times_times @ nat @ B @ C ) )
= ( ( dvd_dvd @ nat @ A @ B )
| ( dvd_dvd @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(219,axiom,
! [A: nat] :
( ( prime @ A )
=> ( ord_less @ nat @ ( one_one @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_prime__gt__1__nat) ).
thf(911,plain,
! [A: nat] :
( ( prime @ A )
=> ( ord_less @ nat @ ( one_one @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(254,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lsetp @ TA @ A @ B )
=> ( member @ TA @ B @ ( coinductive_lset @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_lsetp__into__lset) ).
thf(1002,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: TA] :
( ( coinductive_lsetp @ TA @ A @ B )
=> ( member @ TA @ B @ ( coinductive_lset @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(28,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_neqE) ).
thf(371,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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)],[28]) ).
thf(232,axiom,
linorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(938,plain,
linorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(360,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(76,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_antisym) ).
thf(508,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(224,axiom,
( hammin2015774020amming
!= ( coinductive_LNil @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_hamming__eq__LNil__iff) ).
thf(921,plain,
( hammin2015774020amming
!= ( coinductive_LNil @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(87,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_order_Ostrict__implies__not__eq) ).
thf(541,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(128,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_ord_Olmerge_Odisc_I2_J) ).
thf(657,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(267,axiom,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( dvd_dvd @ nat @ B @ C )
=> ( dvd_dvd @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_gcd__nat_Otrans) ).
thf(1035,plain,
! [A: nat,B: nat,C: nat] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( dvd_dvd @ nat @ B @ C )
=> ( dvd_dvd @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(238,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_nat__less__induct) ).
thf(953,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)],[238]) ).
thf(172,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_dual__order_Ostrict__implies__not__eq) ).
thf(773,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(130,axiom,
! [TA: $tType] :
( ( semigroup_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_mult_Oassoc) ).
thf(662,plain,
! [TA: $tType] :
( ( semigroup_mult @ TA @ ( type2 @ 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)],[130]) ).
thf(94,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_linorder__cases) ).
thf(558,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(281,axiom,
( na
= ( times_times @ nat @ p @ n2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_n) ).
thf(1071,plain,
( na
= ( times_times @ nat @ p @ n2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(217,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_le__eq__less__or__eq) ).
thf(906,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(45,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_pinf_I3_J) ).
thf(412,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(51,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(430,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(200,axiom,
preorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_1) ).
thf(856,plain,
preorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_le__funE) ).
thf(745,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(140,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_6) ).
thf(689,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(158,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_pinf_I4_J) ).
thf(733,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(109,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(601,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ 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)],[109]) ).
thf(102,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_order__class_Oorder_Oantisym) ).
thf(584,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(143,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_minf_I5_J) ).
thf(694,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(207,axiom,
! [A: nat,B: nat] :
( ( prime @ A )
=> ( ( dvd_dvd @ nat @ B @ A )
=> ( ( B
= ( one_one @ nat ) )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_prime__nat__dvdD) ).
thf(875,plain,
! [A: nat,B: nat] :
( ( prime @ A )
=> ( ( dvd_dvd @ nat @ B @ A )
=> ( ( B
= ( one_one @ nat ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(239,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_le__antisym) ).
thf(958,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(88,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( ( dvd_dvd @ TA @ B @ C )
=> ( dvd_dvd @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_dvd__trans) ).
thf(545,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( ( dvd_dvd @ TA @ B @ C )
=> ( dvd_dvd @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(35,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_7) ).
thf(391,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(57,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) )
=> ( ( coinductive_lfinite @ TA @ B )
| ( coinductive_lfinite @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_ord_Olfinite__lmergeD) ).
thf(445,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) )
=> ( ( coinductive_lfinite @ TA @ B )
| ( coinductive_lfinite @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(11,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_dual__order_Oirrefl) ).
thf(313,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(112,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_order__trans) ).
thf(611,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(276,axiom,
! [A: nat,B: nat,C: nat] :
( ( prime @ A )
=> ( ( dvd_dvd @ nat @ A @ ( times_times @ nat @ B @ C ) )
=> ( ( dvd_dvd @ nat @ A @ B )
| ( dvd_dvd @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_prime__dvd__mult__nat) ).
thf(1058,plain,
! [A: nat,B: nat,C: nat] :
( ( prime @ A )
=> ( ( dvd_dvd @ nat @ A @ ( times_times @ nat @ B @ C ) )
=> ( ( dvd_dvd @ nat @ A @ B )
| ( dvd_dvd @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(17,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_lmerge_Odisc_I1_J) ).
thf(335,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(180,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_less__imp__triv) ).
thf(804,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(148,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_mult_Ocommute) ).
thf(704,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(86,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_9) ).
thf(540,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(42,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_le__numeral__extra_I4_J) ).
thf(406,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(191,axiom,
algebraic_semidom @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Oalgebraic__semidom) ).
thf(831,plain,
algebraic_semidom @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(137,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_8) ).
thf(681,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(272,axiom,
linordered_semidom @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom) ).
thf(1048,plain,
linordered_semidom @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_ord__le__eq__subst) ).
thf(377,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(159,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_mult_Oright__neutral) ).
thf(737,plain,
! [TA: $tType] :
( ( monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(204,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(863,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(169,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_less__imp__not__eq2) ).
thf(764,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(110,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_semiring__normalization__rules_I13_J) ).
thf(604,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ ( times_times @ TA @ C @ D ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(27,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_pinf_I2_J) ).
thf(362,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(97,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_minf_I3_J) ).
thf(567,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(33,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ( coindu351974385stinct @ TA @ A )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( coindu351974385stinct @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_ldistinct__lmerge) ).
thf(387,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coindu63249387sorted @ TA @ A )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ( coindu351974385stinct @ TA @ A )
=> ( ( coindu351974385stinct @ TA @ B )
=> ( coindu351974385stinct @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(75,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_le__cases3) ).
thf(494,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(119,axiom,
! [TA: $tType] :
( ( semiring_gcd @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( times_times @ TA @ B @ C ) )
=> ? [D: TA,E: TA] :
( ( A
= ( times_times @ TA @ D @ E ) )
& ( dvd_dvd @ TA @ D @ B )
& ( dvd_dvd @ TA @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_division__decomp) ).
thf(631,plain,
! [TA: $tType] :
( ( semiring_gcd @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( times_times @ TA @ B @ C ) )
=> ? [D: TA,E: TA] :
( ( A
= ( times_times @ TA @ D @ E ) )
& ( dvd_dvd @ TA @ D @ B )
& ( dvd_dvd @ TA @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(91,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( dvd_dvd @ TA @ A @ ( times_times @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_dvd__triv__left) ).
thf(552,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( dvd_dvd @ TA @ A @ ( times_times @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(185,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ( ( ( dvd_dvd @ nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd @ nat @ A @ C )
& ( A != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_gcd__nat_Ostrict__trans) ).
thf(816,plain,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ( ( ( dvd_dvd @ nat @ B @ C )
& ( B != C ) )
=> ( ( dvd_dvd @ nat @ A @ C )
& ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(178,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_semiring__normalization__rules_I7_J) ).
thf(799,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(212,axiom,
wellorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(895,plain,
wellorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(197,axiom,
semiring_gcd @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___GCD_Osemiring__gcd) ).
thf(848,plain,
semiring_gcd @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(146,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_less__irrefl) ).
thf(700,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_ord__eq__less__subst) ).
thf(462,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(277,axiom,
? [A: nat] :
( ( prime @ A )
& ( dvd_dvd @ nat @ A @ na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75__092_060open_062_092_060exists_062p_O_Aprime_Ap_A_092_060and_062_Ap_Advd_An_092_060close_062) ).
thf(1061,plain,
? [A: nat] :
( ( prime @ A )
& ( dvd_dvd @ nat @ A @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(247,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(983,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(39,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_10) ).
thf(399,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(206,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( one_one @ nat ) @ A )
=> ( ~ ( prime @ A )
=> ? [B: nat,C: nat] :
( ( A
= ( times_times @ nat @ B @ C ) )
& ( ord_less @ nat @ ( one_one @ nat ) @ B )
& ( ord_less @ nat @ B @ A )
& ( ord_less @ nat @ ( one_one @ nat ) @ C )
& ( ord_less @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_not__prime__eq__prod__nat) ).
thf(868,plain,
! [A: nat] :
( ( ord_less @ nat @ ( one_one @ nat ) @ A )
=> ( ~ ( prime @ A )
=> ? [B: nat,C: nat] :
( ( A
= ( times_times @ nat @ B @ C ) )
& ( ord_less @ nat @ ( one_one @ nat ) @ B )
& ( ord_less @ nat @ B @ A )
& ( ord_less @ nat @ ( one_one @ nat ) @ C )
& ( ord_less @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(61,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ( hammin1328233080lmerge @ TA @ A @ B @ C )
= ( coinductive_LNil @ TA ) )
= ( ( B
= ( coinductive_LNil @ TA ) )
| ( C
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_ord_Olmerge__eq__LNil__iff) ).
thf(455,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ( hammin1328233080lmerge @ TA @ A @ B @ C )
= ( coinductive_LNil @ TA ) )
= ( ( B
= ( coinductive_LNil @ TA ) )
| ( C
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(199,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_infinite__descent) ).
thf(851,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)],[199]) ).
thf(139,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_llist_OdiscI_I1_J) ).
thf(685,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_ord__less__eq__subst) ).
thf(521,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(170,axiom,
! [TA: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_less__induct) ).
thf(768,plain,
! [TA: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(188,axiom,
one @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(827,plain,
one @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(120,axiom,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( ( dvd_dvd @ TA @ B @ ( one_one @ TA ) )
=> ( dvd_dvd @ TA @ A @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_dvd__unit__imp__unit) ).
thf(636,plain,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( ( dvd_dvd @ TA @ B @ ( one_one @ TA ) )
=> ( dvd_dvd @ TA @ A @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(270,axiom,
coindu351974385stinct @ nat @ hammin2015774020amming,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_ldistinct__hamming) ).
thf(1044,plain,
coindu351974385stinct @ nat @ hammin2015774020amming,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(37,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_less__linear) ).
thf(394,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(248,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
= ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_gcd__nat_Ostrict__iff__order) ).
thf(986,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(135,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_antisym__conv3) ).
thf(675,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(50,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_dense__le__bounded) ).
thf(426,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(83,axiom,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( dvd_dvd @ TA @ B @ ( times_times @ TA @ C @ A ) )
= ( dvd_dvd @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_dvd__mult__unit__iff) ).
thf(531,plain,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( dvd_dvd @ TA @ B @ ( times_times @ TA @ C @ A ) )
= ( dvd_dvd @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(125,axiom,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( dvd_dvd @ TA @ ( times_times @ TA @ B @ A ) @ C )
= ( dvd_dvd @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_mult__unit__dvd__iff) ).
thf(648,plain,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
=> ( ( dvd_dvd @ TA @ ( times_times @ TA @ B @ A ) @ C )
= ( dvd_dvd @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(183,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_order_Ostrict__implies__order) ).
thf(812,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(79,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_llist_Ocollapse_I1_J) ).
thf(516,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(233,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_mult__le__mono) ).
thf(939,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(263,axiom,
! [A: nat,B: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ( dvd_dvd @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_gcd__nat_Ostrict__implies__order) ).
thf(1018,plain,
! [A: nat,B: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ( dvd_dvd @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(273,axiom,
! [A: nat,B: nat] :
( ( ( one_one @ nat )
= ( times_times @ nat @ A @ B ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_nat__1__eq__mult__iff) ).
thf(1049,plain,
! [A: nat,B: nat] :
( ( ( one_one @ nat )
= ( times_times @ nat @ A @ B ) )
= ( ( A
= ( one_one @ nat ) )
& ( B
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(227,axiom,
! [A: nat] :
( ( prime @ A )
=> ( ord_less_eq @ nat @ ( one_one @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_prime__ge__1__nat) ).
thf(927,plain,
! [A: nat] :
( ( prime @ A )
=> ( ord_less_eq @ nat @ ( one_one @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(29,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_antisym__conv) ).
thf(374,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(62,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_pinf_I8_J) ).
thf(458,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(186,axiom,
~ ( coinductive_lfinite @ nat @ hammin2015774020amming ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_lfinite__hamming) ).
thf(823,plain,
~ ( coinductive_lfinite @ nat @ hammin2015774020amming ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(151,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_lmerge_Odisc_I2_J) ).
thf(712,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(101,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_ord__eq__less__trans) ).
thf(580,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(640,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(265,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ( ( dvd_dvd @ nat @ B @ C )
=> ( ( dvd_dvd @ nat @ A @ C )
& ( A != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_gcd__nat_Ostrict__trans2) ).
thf(1025,plain,
! [A: nat,B: nat,C: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
=> ( ( dvd_dvd @ nat @ B @ C )
=> ( ( dvd_dvd @ nat @ A @ C )
& ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1,conjecture,
member @ nat @ n2 @ ( coinductive_lset @ nat @ hammin2015774020amming ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ nat @ n2 @ ( coinductive_lset @ nat @ hammin2015774020amming ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(282,plain,
~ ( member @ nat @ n2 @ ( coinductive_lset @ nat @ hammin2015774020amming ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(149,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_5) ).
thf(707,plain,
! [TA: $tType] : ( order @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(134,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_order__refl) ).
thf(673,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(268,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_mult__le__mono1) ).
thf(1038,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(153,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ 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/sandbox/benchmark/theBenchmark.p',fact_111_semiring__normalization__rules_I19_J) ).
thf(717,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ 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)],[153]) ).
thf(18,axiom,
! [TA: $tType] :
( ( no_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_gt__ex) ).
thf(338,plain,
! [TA: $tType] :
( ( no_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(237,axiom,
~ ( prime @ ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_one__not__prime__nat) ).
thf(951,plain,
~ ( prime @ ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(113,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( dvd_dvd @ TA @ A @ ( times_times @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_dvd__triv__right) ).
thf(613,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] : ( dvd_dvd @ TA @ A @ ( times_times @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(274,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_measure__induct) ).
thf(1052,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(257,axiom,
ord_less @ nat @ ( one_one @ nat ) @ na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_True) ).
thf(1008,plain,
ord_less @ nat @ ( one_one @ nat ) @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(98,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_eq__iff) ).
thf(571,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(107,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
& ~ ( coinductive_lnull @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_lmerge_Odisc__iff_I2_J) ).
thf(595,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
& ~ ( coinductive_lnull @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(202,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_less__irrefl__nat) ).
thf(859,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(251,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( dvd_dvd @ nat @ A @ B )
=> ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_gcd__nat_Onot__eq__order__implies__strict) ).
thf(991,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( dvd_dvd @ nat @ A @ B )
=> ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(246,axiom,
! [A: nat] :
( ( A
!= ( one_one @ nat ) )
=> ? [B: nat] :
( ( prime @ B )
& ( dvd_dvd @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_prime__factor__nat) ).
thf(978,plain,
! [A: nat] :
( ( A
!= ( one_one @ nat ) )
=> ? [B: nat] :
( ( prime @ B )
& ( dvd_dvd @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(32,axiom,
hammin1195055315smooth @ na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_less_Oprems) ).
thf(386,plain,
hammin1195055315smooth @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(196,axiom,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
= ( coinductive_lmember @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_lset__lmember) ).
thf(845,plain,
! [TA: $tType,A: TA,B: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
= ( coinductive_lmember @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(117,axiom,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_ldistinct__LNil__code) ).
thf(627,plain,
! [TA: $tType] : ( coindu351974385stinct @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ 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/sandbox/benchmark/theBenchmark.p',fact_101_mult_Oleft__commute) ).
thf(450,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA @ ( type2 @ 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)],[59]) ).
thf(93,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_pinf_I7_J) ).
thf(556,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(71,axiom,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_llist_Odisc_I1_J) ).
thf(482,plain,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(167,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_lfinite__lmergeI) ).
thf(759,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(210,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1328233080lmerge @ TA @ B @ C @ D ) ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) )
| ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_ord_Oin__lset__lmergeD) ).
thf(891,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: coinductive_llist @ TA,D: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1328233080lmerge @ TA @ B @ C @ D ) ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) )
| ( member @ TA @ A @ ( coinductive_lset @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(171,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( dvd_dvd @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_dvd__mult2) ).
thf(771,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( dvd_dvd @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(244,axiom,
semigroup_mult @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult) ).
thf(976,plain,
semigroup_mult @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(216,axiom,
! [A: nat] :
? [B: nat] :
( ( prime @ B )
& ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_bigger__prime) ).
thf(903,plain,
! [A: nat] :
? [B: nat] :
( ( prime @ B )
& ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(240,axiom,
~ ! [A: nat] :
( na
!= ( times_times @ nat @ p @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_O_An_A_061_Ap_A_K_An_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(961,plain,
~ ! [A: nat] :
( na
!= ( times_times @ nat @ p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(213,axiom,
~ ( coinductive_lnull @ nat @ hammin2015774020amming ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_lnull__hamming) ).
thf(896,plain,
~ ( coinductive_lnull @ nat @ hammin2015774020amming ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(10,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_minf_I2_J) ).
thf(304,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(127,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( ( hammin1138290136lmerge @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_lmerge_Octr_I1_J) ).
thf(652,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( ( hammin1138290136lmerge @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(23,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_mult_Ocomm__neutral) ).
thf(351,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(157,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_4) ).
thf(731,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(47,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( hammin1328233080lmerge @ TA @ A @ B @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_ord_Olmerge__LNil_I2_J) ).
thf(418,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA] :
( ( hammin1328233080lmerge @ TA @ A @ B @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(174,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_dual__order_Ostrict__trans) ).
thf(786,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(433,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(132,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA] :
( ( hammin1138290136lmerge @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_lmerge__LNil_I2_J) ).
thf(667,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA] :
( ( hammin1138290136lmerge @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(228,axiom,
ord_less @ nat @ n2 @ na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062n_H_A_060_An_092_060close_062) ).
thf(929,plain,
ord_less @ nat @ n2 @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(69,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_pinf_I5_J) ).
thf(478,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(215,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_less__not__refl2) ).
thf(899,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(192,axiom,
! [A: nat] :
( ( dvd_dvd @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__dvd__1__iff__1) ).
thf(832,plain,
! [A: nat] :
( ( dvd_dvd @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(21,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_dual__order_Ostrict__iff__order) ).
thf(346,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(85,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_eq__refl) ).
thf(536,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(271,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_nat__mult__1__right) ).
thf(1045,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( one_one @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(6,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( hammin1138290136lmerge @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ( B
= ( coinductive_LNil @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_lmerge__eq__LNil__iff) ).
thf(290,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( hammin1138290136lmerge @ TA @ A @ B )
= ( coinductive_LNil @ TA ) )
= ( ( A
= ( coinductive_LNil @ TA ) )
| ( B
= ( coinductive_LNil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(221,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1138290136lmerge @ TA @ B @ C ) ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
| ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_in__lset__lmergeD) ).
thf(914,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1138290136lmerge @ TA @ B @ C ) ) )
=> ( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
| ( member @ TA @ A @ ( coinductive_lset @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(58,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_dual__order_Oorder__iff__strict) ).
thf(447,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(12,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( ( dvd_dvd @ TA @ C @ D )
=> ( dvd_dvd @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_mult__dvd__mono) ).
thf(315,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( dvd_dvd @ TA @ A @ B )
=> ( ( dvd_dvd @ TA @ C @ D )
=> ( dvd_dvd @ TA @ ( times_times @ TA @ A @ C ) @ ( times_times @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(44,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( dvd_dvd @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_dvd__refl) ).
thf(410,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( dvd_dvd @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(193,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_measure__induct__rule) ).
thf(835,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(96,axiom,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_one__reorient) ).
thf(564,plain,
! [TA: $tType] :
( ( one @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(16,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_pinf_I1_J) ).
thf(326,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_linorder__wlog) ).
thf(341,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(54,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_comm__monoid__mult__class_Omult__1) ).
thf(437,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(67,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_linear) ).
thf(474,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(40,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_neq__iff) ).
thf(400,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ 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)],[40]) ).
thf(189,axiom,
! [A: nat] :
~ ( ( dvd_dvd @ nat @ A @ A )
& ( A != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_gcd__nat_Oirrefl) ).
thf(828,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(279,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_le__neq__implies__less) ).
thf(1065,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(144,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_less__trans) ).
thf(696,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(154,axiom,
! [TA: $tType] :
( ( dvd @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( times_times @ TA @ B @ C ) )
=> ( dvd_dvd @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_dvdI) ).
thf(720,plain,
! [TA: $tType] :
( ( dvd @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( times_times @ TA @ B @ C ) )
=> ( dvd_dvd @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(209,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_less__or__eq__imp__le) ).
thf(886,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(177,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ord_Olmerge_Oexhaust) ).
thf(796,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(3,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_less__numeral__extra_I4_J) ).
thf(283,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(249,axiom,
( ( dvd_dvd @ nat )
= ( ^ [A: nat,B: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_gcd__nat_Oorder__iff__strict) ).
thf(987,plain,
( ( dvd_dvd @ nat )
= ( ^ [A: nat,B: nat] :
( ( ( dvd_dvd @ nat @ A @ B )
& ( A != B ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(82,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_ord_Olmerge_Odisc_I1_J) ).
thf(528,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(218,axiom,
! [A: nat,B: nat] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( dvd_dvd @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_dvd__antisym) ).
thf(908,plain,
! [A: nat,B: nat] :
( ( dvd_dvd @ nat @ A @ B )
=> ( ( dvd_dvd @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(255,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ ( times_times @ nat @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_le__cube) ).
thf(1004,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ ( times_times @ nat @ A @ ( times_times @ nat @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(141,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ord_Olfinite__lmergeI) ).
thf(691,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( coinductive_lfinite @ TA @ A )
=> ( ( coinductive_lfinite @ TA @ B )
=> ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(56,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_semiring__normalization__rules_I16_J) ).
thf(442,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ ( times_times @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(111,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_ord__less__eq__trans) ).
thf(607,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_order__subst2) ).
thf(728,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(160,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ~ ( coinductive_lfinite @ TA @ B )
=> ~ ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_ord_Olinfinite__lmerge) ).
thf(740,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ~ ( coinductive_lfinite @ TA @ A )
=> ( ~ ( coinductive_lfinite @ TA @ B )
=> ~ ( coinductive_lfinite @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(73,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_wlog__linorder__le) ).
thf(486,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ( ( A @ B @ C )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(65,axiom,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_lnull__def) ).
thf(469,plain,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(24,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_dual__order_Oantisym) ).
thf(354,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(258,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_le__trans) ).
thf(1009,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(129,axiom,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ ( times_times @ TA @ A @ B ) @ ( one_one @ TA ) )
= ( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
& ( dvd_dvd @ TA @ B @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_is__unit__mult__iff) ).
thf(659,plain,
! [TA: $tType] :
( ( algebraic_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( dvd_dvd @ TA @ ( times_times @ TA @ A @ B ) @ ( one_one @ TA ) )
= ( ( dvd_dvd @ TA @ A @ ( one_one @ TA ) )
& ( dvd_dvd @ TA @ B @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(74,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) ) )
= ( ~ ( coinductive_lnull @ TA @ B )
& ~ ( coinductive_lnull @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_ord_Olmerge_Odisc__iff_I2_J) ).
thf(491,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) ) )
= ( ~ ( coinductive_lnull @ TA @ B )
& ~ ( coinductive_lnull @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ C @ B )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_minf_I11_J) ).
thf(592,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(260,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ~ ( coinductive_lfinite @ TA @ C )
=> ( ? [D: TA] :
( ( member @ TA @ D @ ( coinductive_lset @ TA @ C ) )
& ( ord_less_eq @ TA @ A @ D ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1138290136lmerge @ TA @ B @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_in__lset__lmergeI1) ).
thf(1014,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( member @ TA @ A @ ( coinductive_lset @ TA @ B ) )
=> ( ( coindu63249387sorted @ TA @ B )
=> ( ~ ( coinductive_lfinite @ TA @ C )
=> ( ? [D: TA] :
( ( member @ TA @ D @ ( coinductive_lset @ TA @ C ) )
& ( ord_less_eq @ TA @ A @ D ) )
=> ( member @ TA @ A @ ( coinductive_lset @ TA @ ( hammin1138290136lmerge @ TA @ B @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(25629,plain,
$false,
inference(cvc4,[status(thm)],[645,809,629,893,777,1068,1041,408,977,440,511,384,550,472,814,698,945,340,930,670,747,913,829,898,1001,709,973,288,301,320,651,389,802,460,1055,724,587,838,917,702,751,934,357,638,421,969,416,924,756,514,574,806,966,480,397,293,866,453,849,942,678,793,925,761,534,714,825,1021,598,561,392,297,424,693,788,862,349,916,484,1032,625,879,435,665,682,842,324,1012,285,317,948,1017,615,1064,403,1006,593,989,857,519,742,578,933,476,642,547,554,753,1016,590,622,997,911,1002,371,938,360,508,921,541,657,1035,953,773,662,558,1071,906,412,430,856,745,689,733,601,584,694,875,958,545,391,445,313,611,1058,335,804,704,540,406,831,681,1048,377,737,863,764,604,362,567,387,494,631,552,816,799,895,848,700,462,1061,983,399,868,455,851,685,521,768,827,636,1044,394,986,675,426,531,648,812,516,939,1018,1049,927,374,458,823,712,580,640,1025,282,707,673,1038,717,338,951,613,1052,1008,571,595,859,991,978,386,845,627,450,556,482,759,891,771,976,903,961,896,304,652,351,731,418,786,433,667,929,478,899,832,346,536,1045,290,914,447,315,410,835,564,326,341,437,474,400,828,1065,696,720,886,796,283,987,528,908,1004,691,442,607,728,740,486,469,354,1009,659,491,592,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : DAT162^1 : TPTP v8.1.2. Released v7.0.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n026.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 11:34:09 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.71/1.12 % [INFO] Parsing done (244ms).
% 1.71/1.13 % [INFO] Running in sequential loop mode.
% 2.62/1.35 % [INFO] eprover registered as external prover.
% 2.71/1.35 % [INFO] cvc4 registered as external prover.
% 2.71/1.36 % [INFO] Scanning for conjecture ...
% 2.92/1.45 % [INFO] Found a conjecture and 279 axioms. Running axiom selection ...
% 3.05/1.54 % [INFO] Axiom selection finished. Selected 279 axioms (removed 0 axioms).
% 3.72/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 3.72/1.72 % [INFO] Type checking passed.
% 3.72/1.72 % [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 ...
% 59.81/22.54 % External prover 'cvc4' found a proof!
% 59.81/22.54 % [INFO] Killing All external provers ...
% 59.81/22.54 % Time passed: 22005ms (effective reasoning time: 21409ms)
% 59.81/22.54 % 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)>
% 59.81/22.55 % Axioms used in derivation (279): fact_91_dvdE, fact_55_ord_Olmerge__eq__LNil__iff, fact_204_minf_I2_J, fact_233_less__not__sym, fact_53_ord_Olfinite__lmergeI, fact_103_mult_Oassoc, fact_163_gcd__nat_Otrans, tcon_HOL_Obool___Orderings_Opreorder_7, fact_31_ord_Olmerge_Octr_I1_J, fact_160_gcd__nat_Ostrict__trans, tcon_Nat_Onat___Orderings_Oorder_2, fact_97_mult__unit__dvd__iff, fact_165_gcd__nat_Oasym, fact_210_pinf_I3_J, fact_208_pinf_I5_J, fact_28_llist_OdiscI_I1_J, tcon_Nat_Onat___Orderings_Ono__top, fact_72_semiring__normalization__rules_I12_J, fact_140_less__imp__le__nat, fact_32_ord_Olmerge_Odisc_I2_J, fact_212_pinf_I1_J, fact_227_less__linear, fact_22_lmerge__LNil_I1_J, tcon_Nat_Onat___Orderings_Olinorder, fact_4_hamming__eq__LNil__iff, fact_74_comm__monoid__mult__class_Omult__1, fact_21_lmerge__LNil_I2_J, fact_173_le__antisym, fact_190_antisym__conv, fact_119_less__irrefl__nat, fact_64_lsetp__into__lset, fact_43_lnull__def, fact_87_dvd__mult2, fact_244_order_Ostrict__implies__not__eq, fact_58_lfinite__lmergeD, fact_84_mult__dvd__mono, fact_130_prime__dvd__mult__nat, fact_59_lfinite__lmergeI, fact_199_minf_I11_J, fact_242_dual__order_Ostrict__trans, fact_133_one__not__prime__nat, fact_0__092_060open_062smooth_An_H_092_060close_062, fact_114_infinite__descent__measure, tcon_Nat_Onat___Rings_Odvd, fact_170_le__refl, fact_156_gcd__nat_Ostrict__iff__order, fact_107_semiring__normalization__rules_I15_J, tcon_fun___Orderings_Oord, fact_104_semiring__normalization__rules_I7_J, fact_194_order__trans, fact_6_lsorted__hamming, tcon_Nat_Onat___Rings_Oalgebraic__semidom, fact_237_less__imp__triv, fact_195_dual__order_Orefl, fact_191_ord__eq__le__trans, fact_182_ord__le__eq__subst, fact_63_ldistinct__lmerge, fact_185_linear, fact_34_ord_Olmerge__LNil_I2_J, fact_85_dvd__triv__left, fact_94_one__dvd, fact_99_is__unit__mult__iff, tcon_Nat_Onat___Groups_Ocomm__monoid__mult, fact_138_in__lset__lmergeI2, fact_8_lnull__hamming, fact_224_less__asym, fact_92_dvd__unit__imp__unit, fact_186_eq__refl, fact_145_le__cube, fact_13_Coinductive__List_Olset__into__lsetp, fact_77_unit__prod, fact_48_lfinite__LNil, fact_226_less__trans, fact_193_order__class_Oorder_Oantisym, fact_3_n, fact_105_semiring__normalization__rules_I13_J, fact_162_gcd__nat_Oirrefl, fact_30_llist_Ocollapse_I1_J, fact_20_lnull__lmerge, tcon_HOL_Obool___Orderings_Oorder_9, fact_122_less__not__refl2, fact_14_assms, fact_134_prime__gt__1__nat, fact_116_linorder__neqE__nat, fact_220_neq__iff, fact_172_eq__imp__le, fact_149_mult__le__mono2, fact_164_gcd__nat_Orefl, fact_47_lnull__imp__lfinite, fact_111_semiring__normalization__rules_I19_J, fact_127_prime__def, fact_124_nat__neq__iff, fact_152_prime__ge__1__nat, fact_57_lsorted__ldistinct__lset__unique, fact_177_le__funI, fact_215_order__less__subst1, tcon_Nat_Onat___Groups_Oone, fact_95_unit__mult__right__cancel, fact_211_pinf_I2_J, fact_118_nat__less__induct, fact_243_not__less__iff__gr__or__eq, tcon_Nat_Onat___Groups_Oab__semigroup__mult, fact_126_prime__dvd__mult__eq__nat, fact_157_gcd__nat_Oorder__iff__strict, fact_217_lt__ex, tcon_Nat_Onat___Rings_Olinordered__semidom, fact_137_in__lset__lmergeI1, fact_5_ldistinct__hamming, fact_100_linorder__neqE__linordered__idom, fact_222_dense, fact_27_llist_Odisc_I1_J, fact_23_lsorted__code_I1_J, fact_154_gcd__nat_Ostrict__implies__not__eq, fact_61_lmerge__eq__LNil__iff, fact_252_dense__ge__bounded, fact_33_ord_Olmerge_Odisc_I1_J, fact_251_dense__le__bounded, fact_79_dvd__refl, fact_112_ab__semigroup__mult__class_Omult__ac_I1_J, fact_115_measure__induct__rule, fact_216_order__less__subst2, fact_54_ord_Olinfinite__lmerge, fact_234_less__induct, fact_161_gcd__nat_Oantisym, fact_35_ord_Olmerge__LNil_I1_J, fact_150_wlog__linorder__le, fact_248_dual__order_Ostrict__iff__order, tcon_Set_Oset___Orderings_Oord_6, fact_98_dvd__mult__unit__iff, fact_128_not__prime__eq__prod__nat, fact_189_le__cases3, fact_7_True, fact_241_less__imp__not__less, fact_232_less__imp__not__eq, fact_68_mult_Oright__neutral, fact_142_less__or__eq__imp__le, fact_51_ord_Olmerge_Oexhaust, fact_37_lmerge_Octr_I1_J, fact_123_less__not__refl, fact_60_linfinite__lmerge, fact_66_nat__mult__eq__1__iff, fact_89_dvd__def, fact_18_lfinite__code_I1_J, tcon_Nat_Onat___Orderings_Owellorder, fact_39_lmerge_Odisc_I1_J, fact_144_less__mono__imp__le__mono, fact_139_nat__less__le, fact_201_minf_I5_J, fact_12_ord_Oin__lset__lmergeD, fact_56_lmerge_Oexhaust, fact_82_dvd__triv__right, fact_11_in__lset__lmergeD, fact_132_bigger__prime, fact_207_pinf_I7_J, fact_235_antisym__conv3, fact_70_nat__mult__1, fact_2_less_OIH, tcon_HOL_Obool___Orderings_Oord_10, tcon_Nat_Onat___Groups_Omonoid__mult, fact_19_lmerge_Odisc__iff_I2_J, fact_169_pinf_I8_J, fact_206_pinf_I11_J, fact_230_ord__less__eq__trans, fact_225_less__asym_H, fact_229_ord__eq__less__trans, fact_249_dual__order_Oorder__iff__strict, fact_171_le__trans, fact_96_unit__mult__left__cancel, fact_117_infinite__descent, fact_239_dual__order_Oirrefl, fact_213_ord__eq__less__subst, fact_155_gcd__nat_Ostrict__implies__order, tcon_Nat_Onat___Orderings_Oord_3, fact_245_dual__order_Ostrict__implies__not__eq, fact_143_le__neq__implies__less, fact_41_ldistinct_OLNil, fact_16__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_O_An_A_061_Ap_A_K_An_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_168_minf_I6_J, fact_86_dvd__mult__left, fact_9_lset__lmember, fact_209_pinf_I4_J, fact_202_minf_I4_J, fact_187_le__cases, fact_24_ldistinct__LNil__code, fact_121_less__not__refl3, tcon_Set_Oset___Orderings_Opreorder_4, fact_151_le__numeral__extra_I4_J, fact_183_eq__iff, fact_246_order_Onot__eq__order__implies__strict, fact_231_dual__order_Oasym, fact_167_minf_I8_J, tcon_Nat_Onat___GCD_Osemiring__gcd, fact_17__092_060open_062prime_Ap_092_060close_062, fact_93_unit__imp__dvd, fact_75__092_060open_062_092_060exists_062p_O_Aprime_Ap_A_092_060and_062_Ap_Advd_An_092_060close_062, fact_67_mult_Oleft__neutral, fact_15_less_Oprems, fact_106_semiring__normalization__rules_I14_J, fact_113_one__reorient, fact_73_semiring__normalization__rules_I11_J, fact_240_order_Ostrict__trans, fact_197_dual__order_Otrans, tcon_Nat_Onat___Rings_Ocomm__semiring__1, fact_214_ord__less__eq__subst, fact_200_minf_I7_J, tcon_fun___Orderings_Opreorder, tcon_Set_Oset___Orderings_Oorder_5, fact_101_mult_Oleft__commute, fact_45_Collect__mem__eq, fact_228_less__irrefl, fact_175_le__funD, tcon_Nat_Onat___Orderings_Opreorder_1, fact_71_nat__mult__1__right, fact_65_nat__1__eq__mult__iff, fact_29_lmember__code_I1_J, fact_40_lzip_Oexhaust, fact_196_linorder__wlog, fact_69_less__1__mult, fact_108_semiring__normalization__rules_I16_J, fact_120_measure__induct, fact_198_dual__order_Oantisym, fact_102_mult_Ocommute, fact_136_less__numeral__extra_I4_J, fact_76_nat__dvd__1__iff__1, fact_78_dvd__trans, fact_148_mult__le__mono1, tcon_HOL_Obool___Orderings_Olinorder_8, fact_218_gt__ex, fact_26__092_060open_062p_Advd_An_092_060close_062, fact_153_gcd__nat_Onot__eq__order__implies__strict, fact_38_lmerge_Odisc_I2_J, tcon_fun___Orderings_Oorder, fact_125_mult_Ocomm__neutral, fact_223_less__imp__neq, fact_131_prime__product, fact_83_dvd__mult__right, fact_36_ord_Olmerge_Odisc__iff_I2_J, fact_1__092_060open_062n_H_A_060_An_092_060close_062, fact_147_mult__le__mono, fact_90_dvdI, fact_250_order_Ostrict__implies__order, fact_62_lsorted__lmerge, fact_166_order__refl, fact_203_minf_I3_J, fact_110_semiring__normalization__rules_I18_J, tcon_Nat_Onat___Groups_Osemigroup__mult, fact_52_ord_Olfinite__lmergeD, fact_10_lfinite__hamming, fact_247_dual__order_Ostrict__implies__order, fact_88_dvd__mult, fact_219_neqE, fact_192_ord__le__eq__trans, fact_184_antisym, fact_221_order_Oasym, fact_174_nat__le__linear, fact_80_dvd__antisym, fact_205_minf_I1_J, fact_181_ord__eq__le__subst, fact_49_LNil, fact_158_gcd__nat_Ostrict__trans2, fact_81_prime__nat__dvdD, fact_25_smooth__times, fact_236_less__imp__not__eq2, fact_50_ord_Olnull__lmerge, fact_178_le__fun__def, fact_42_lappend_Oexhaust, fact_188_order_Otrans, fact_146_le__square, fact_180_order__subst2, fact_129_prime__factor__nat, fact_176_le__funE, fact_46_Collect__cong, fact_179_order__subst1, fact_44_mem__Collect__eq, fact_141_le__eq__less__or__eq, fact_135_division__decomp, fact_109_semiring__normalization__rules_I17_J, fact_159_gcd__nat_Ostrict__trans1, fact_238_linorder__cases
% 59.81/22.55 % No. of inferences in proof: 562
% 59.81/22.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 22005 ms resp. 21409 ms w/o parsing
% 60.22/22.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 60.22/22.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------